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[ "## Matrix models for beta ensembles.(English)Zbl 1060.82020\n\nSummary: This paper constructs tridiagonal random matrix models for general $$(\\beta > 0) \\;\\beta$$-Hermite (Gaussian) and $$\\beta$$-Laguerre (Wishart) ensembles. These generalize the well-known Gaussian and Wishart models for $$\\beta = 1,2,4$$. Furthermore, in the cases of the $$\\beta$$-Laguerre ensembles, we eliminate the exponent quantization present in the previously known models. We further discuss applications for the new matrix models, and present some open problems.\n\n### MSC:\n\n 82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) 82B10 Quantum equilibrium statistical mechanics (general)\nFull Text:\n\n### References:\n\n Aomoto K., SIAM (Soc. Ind. Appl. Math.) J. Math. Anal. 18 pp 545– (1987) Baker T., Commun. Math. Phys. 188 pp 175– (1997) · Zbl 0903.33010 Barsky D., Electronic J. Combinatorics 3 (2) pp R1– (1996) Chikuse Y., Linear Algebr. Appl. 176 pp 237– (1992) Delannay R., Phys. Rev. E 62 pp 1526– (2000) Dyson F., J. Math. Phys. 3 pp 1199– (1963) · Zbl 0134.45703 Edelman A., J. Multivariate Anal. 60 pp 203– (1997) · Zbl 0886.15024 Ivanov, D. A. ”Random-matrix ensembles in p-wave vortices,” e-print cond-mat/0103089. DOI: 10.1214/aoms/1177703550 · Zbl 0121.36605 Johnstone I. M., Ann. Stat. 29 pp 295– (2001) · Zbl 1016.62078 Kadell K., Adv. Math. 130 pp 33– (1997) · Zbl 0885.33009 Kaneko J., SIAM (Soc. Ind. Appl. Math.) J. Math. Anal. 24 pp 1086– (1993) Lal Mehta M., J. Phys. A 31 pp 5377– (1998) · Zbl 1054.62553 Okounkov A., Mathematical Research Letters 4 pp 69– (1997) Silverstein J. W., Ann. Prob. 13 pp 1364– (1985) · Zbl 0591.60025 DOI: 10.1016/0001-8708(89)90015-7 · Zbl 0743.05072 Tracy C. A., J. Stat. Phys. 92 pp 809– (1996) · Zbl 0942.60099 Trotter H. F., Adv. Math. 54 pp 67– (1984) · Zbl 0562.15005 DOI: 10.1063/1.531675 · Zbl 0871.58005\nThis reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching." ]

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[ "# #bec1f9 Color Information\n\nIn a RGB color space, hex #bec1f9 is composed of 74.5% red, 75.7% green and 97.6% blue. Whereas in a CMYK color space, it is composed of 23.7% cyan, 22.5% magenta, 0% yellow and 2.4% black. It has a hue angle of 236.9 degrees, a saturation of 83.1% and a lightness of 86.1%. #bec1f9 color hex could be obtained by blending #ffffff with #7d83f3. Closest websafe color is: #ccccff.\n\n• R 75\n• G 76\n• B 98\nRGB color chart\n• C 24\n• M 22\n• Y 0\n• K 2\nCMYK color chart\n\n#bec1f9 color description : Very soft blue.\n\n# #bec1f9 Color Conversion\n\nThe hexadecimal color #bec1f9 has RGB values of R:190, G:193, B:249 and CMYK values of C:0.24, M:0.22, Y:0, K:0.02. Its decimal value is 12501497.\n\nHex triplet RGB Decimal bec1f9 `#bec1f9` 190, 193, 249 `rgb(190,193,249)` 74.5, 75.7, 97.6 `rgb(74.5%,75.7%,97.6%)` 24, 22, 0, 2 236.9°, 83.1, 86.1 `hsl(236.9,83.1%,86.1%)` 236.9°, 23.7, 97.6 ccccff `#ccccff`\nCIE-LAB 79.572, 10.686, -27.92 57.401, 55.926, 97.388 0.272, 0.265, 55.926 79.572, 29.895, 290.944 79.572, -4.805, -46.36 74.784, 6.138, -24.863 10111110, 11000001, 11111001\n\n# Color Schemes with #bec1f9\n\n• #bec1f9\n``#bec1f9` `rgb(190,193,249)``\n• #f9f6be\n``#f9f6be` `rgb(249,246,190)``\nComplementary Color\n• #bedff9\n``#bedff9` `rgb(190,223,249)``\n• #bec1f9\n``#bec1f9` `rgb(190,193,249)``\n• #d9bef9\n``#d9bef9` `rgb(217,190,249)``\nAnalogous Color\n• #dff9be\n``#dff9be` `rgb(223,249,190)``\n• #bec1f9\n``#bec1f9` `rgb(190,193,249)``\n• #f9d9be\n``#f9d9be` `rgb(249,217,190)``\nSplit Complementary Color\n• #c1f9be\n``#c1f9be` `rgb(193,249,190)``\n• #bec1f9\n``#bec1f9` `rgb(190,193,249)``\n• #f9bec1\n``#f9bec1` `rgb(249,190,193)``\n• #bef9f6\n``#bef9f6` `rgb(190,249,246)``\n• #bec1f9\n``#bec1f9` `rgb(190,193,249)``\n• #f9bec1\n``#f9bec1` `rgb(249,190,193)``\n• #f9f6be\n``#f9f6be` `rgb(249,246,190)``\n• #787ef3\n``#787ef3` `rgb(120,126,243)``\n• #8f94f5\n``#8f94f5` `rgb(143,148,245)``\n• #a7abf7\n``#a7abf7` `rgb(167,171,247)``\n• #bec1f9\n``#bec1f9` `rgb(190,193,249)``\n• #d5d7fb\n``#d5d7fb` `rgb(213,215,251)``\n• #edeefd\n``#edeefd` `rgb(237,238,253)``\n• #ffffff\n``#ffffff` `rgb(255,255,255)``\nMonochromatic Color\n\n# Alternatives to #bec1f9\n\nBelow, you can see some colors close to #bec1f9. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #bed0f9\n``#bed0f9` `rgb(190,208,249)``\n• #becbf9\n``#becbf9` `rgb(190,203,249)``\n• #bec6f9\n``#bec6f9` `rgb(190,198,249)``\n• #bec1f9\n``#bec1f9` `rgb(190,193,249)``\n• #c0bef9\n``#c0bef9` `rgb(192,190,249)``\n• #c5bef9\n``#c5bef9` `rgb(197,190,249)``\n• #cabef9\n``#cabef9` `rgb(202,190,249)``\nSimilar Colors\n\n# #bec1f9 Preview\n\nThis text has a font color of #bec1f9.\n\n``<span style=\"color:#bec1f9;\">Text here</span>``\n#bec1f9 background color\n\nThis paragraph has a background color of #bec1f9.\n\n``<p style=\"background-color:#bec1f9;\">Content here</p>``\n#bec1f9 border color\n\nThis element has a border color of #bec1f9.\n\n``<div style=\"border:1px solid #bec1f9;\">Content here</div>``\nCSS codes\n``.text {color:#bec1f9;}``\n``.background {background-color:#bec1f9;}``\n``.border {border:1px solid #bec1f9;}``\n\n# Shades and Tints of #bec1f9\n\nA shade is achieved by adding black to any pure hue, while a tint is created by mixing white to any pure color. In this example, #010107 is the darkest color, while #f4f4fe is the lightest one.\n\n• #010107\n``#010107` `rgb(1,1,7)``\n• #020319\n``#020319` `rgb(2,3,25)``\n• #04062b\n``#04062b` `rgb(4,6,43)``\n• #06083d\n``#06083d` `rgb(6,8,61)``\n• #070b4f\n``#070b4f` `rgb(7,11,79)``\n• #090d61\n``#090d61` `rgb(9,13,97)``\n• #0b1073\n``#0b1073` `rgb(11,16,115)``\n• #0c1285\n``#0c1285` `rgb(12,18,133)``\n• #0e1596\n``#0e1596` `rgb(14,21,150)``\n• #1017a8\n``#1017a8` `rgb(16,23,168)``\n• #111aba\n``#111aba` `rgb(17,26,186)``\n• #131ccc\n``#131ccc` `rgb(19,28,204)``\n• #151fde\n``#151fde` `rgb(21,31,222)``\n• #1c27ea\n``#1c27ea` `rgb(28,39,234)``\n• #2e38ec\n``#2e38ec` `rgb(46,56,236)``\n• #4049ed\n``#4049ed` `rgb(64,73,237)``\n• #525aef\n``#525aef` `rgb(82,90,239)``\n• #646bf1\n``#646bf1` `rgb(100,107,241)``\n• #767cf2\n``#767cf2` `rgb(118,124,242)``\n• #888ef4\n``#888ef4` `rgb(136,142,244)``\n• #9a9ff6\n``#9a9ff6` `rgb(154,159,246)``\n• #acb0f7\n``#acb0f7` `rgb(172,176,247)``\n• #bec1f9\n``#bec1f9` `rgb(190,193,249)``\n• #d0d2fb\n``#d0d2fb` `rgb(208,210,251)``\n• #e2e3fc\n``#e2e3fc` `rgb(226,227,252)``\n• #f4f4fe\n``#f4f4fe` `rgb(244,244,254)``\nTint Color Variation\n\n# Tones of #bec1f9\n\nA tone is produced by adding gray to any pure hue. In this case, #d9dade is the less saturated color, while #b9bcfe is the most saturated one.\n\n``#d9dade` `rgb(217,218,222)``\n• #d7d7e0\n``#d7d7e0` `rgb(215,215,224)``\n• #d4d5e3\n``#d4d5e3` `rgb(212,213,227)``\n• #d1d2e6\n``#d1d2e6` `rgb(209,210,230)``\n• #ced0e9\n``#ced0e9` `rgb(206,208,233)``\n• #cccdeb\n``#cccdeb` `rgb(204,205,235)``\n• #c9cbee\n``#c9cbee` `rgb(201,203,238)``\n• #c6c8f1\n``#c6c8f1` `rgb(198,200,241)``\n• #c3c6f4\n``#c3c6f4` `rgb(195,198,244)``\n• #c1c3f6\n``#c1c3f6` `rgb(193,195,246)``\n• #bec1f9\n``#bec1f9` `rgb(190,193,249)``\n• #bbbffc\n``#bbbffc` `rgb(187,191,252)``\n• #b9bcfe\n``#b9bcfe` `rgb(185,188,254)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #bec1f9 is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population" ]

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[ "Date: Tue, 25 Jan 2022 10:32:12 +0000 (UTC) Message-ID: <1429623190.9520.1643106732362@wiki-2.tor.rgcloud.net> Subject: Exported From Confluence MIME-Version: 1.0 Content-Type: multipart/related; boundary=\"----=_Part_9519_361382533.1643106732361\" ------=_Part_9519_361382533.1643106732361 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Content-Location: file:///C:/exported.html Help Center\n\nHelp Center\n\n=20\n= =20\n=20\n\n=20\n=20\n=20\n=20\n=20 =20 Search= =20\n=20 =20 =20 =20 =20\n=20\n=20\n=20\n\n=20\n=20\n=20\n=20\n=20\n=20\n=20\n=20\n=20\n=20\n=20\n=20\n=20\n\n=20\n=20\n=20\n=20\n=20\n=20\n=20\n\n=20\n=20\n=20\n=20\n=20\n\n=20\n=20\n=20\n=20\n=20\n\n=09ThemePress.toFinalize(function (\\$) { =09=09// Initialization can happen more than once when used in tabs or layo= uts, so mark after initialization =09=09\\$(\"#whole-section-link-8970876\").closest(\".brikit-content-block:not(.= block-link-initialized)\") =09=09=09.addClass(\"block-link\") =09=09=09.hover(function (event) { if (\"/display/support/RG+Score\") window.= status =3D location.protocol + \"//\" + location.host + \"/display/support/RG+= Score\"; }, =09=09=09=09 function (event) { window.status =3D \"\"; } =09=09=09) =09=09=09.on(\"click\", \".inline-comment-marker.valid\" , function (event) { e= vent.inlineCommentMarker =3D true; }) =09=09=09.click(function (event) { =09=09=09=09if (event.inlineCommentMarker) { =09=09=09=09=09event.inlineCommentMarker =3D false; =09=09=09=09=09return; =09=09=09=09} =09=09=09=09=09=09=09=09=09if (event.metaKey || event.ctrlKey ) window.open= (\"/display/support/RG+Score\"); =09=09=09=09=09else window.location.href =3D \"/display/support/RG+Score\"; =09=09=09=09=09return false; =09=09=09=09=09=09=09}) =09=09=09.addClass(\"block-link-initialized\"); =09});\n\n=20\n=20\n=20\n\n------=_Part_9519_361382533.1643106732361--" ]

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[ "# What Is the Unit of Flow Rate\n\nIn physics and engineering, especially in fluid dynamics, the volume flow rate (also known as volume flow rate, fluid flow rate, or volume velocity) is the volume of fluid that passes per unit time; It is usually denoted by the symbol Q (sometimes V̇). The SI unit is cubic meter per second (m3 / S) .\n\nAlso, are the flow rate and velocity the same?\n\nFlow, velocity and pressure defined\n\nFlow is a measure of air output in terms of volume per unit of time. … Velocity refers to how fast the air is moving per unit time. Common units are feet per second, meters per second, etc. Pressure is a measure of the force applied to an area.\n\nNext, what is lpm in flow rate?\n\nLPM is an abbreviation for liters per minute (L/minute). When used in reference to the flow rate of a particle counter, it is a measure of the velocity at which air flows across the sample probe. For example, a flow rate of 2.83 lpm means that the particle counter will sample 2.83 liters of air per minute.\n\nAlso to know what are the 2 types of flows? type of fluid flow. Fluid flow is generally broken down into two different types of flow, laminar flow and turbulent flow .\n\nWhat is the unit of flow rate for gases?\n\nThe gas mass flow rate is the actual mass of a gas that moves through a measurement device per unit of time. Its units are usually in standard liters per minute (slpm) or standard cubic centimeters per minute (sccm) in SI units. The most common English units include the standard cubic feet per minute (scfm).\n\n## What is the relationship between flow rate and pressure?\n\nThis relationship can be expressed by the equation F = Q / T . Fluid flow requires a pressure gradient (ΔP) between two points, so that the flow is directly proportional to the pressure difference. Higher pressure difference will drive greater flow rate. The pressure gradient determines the direction of flow.\n\n## Is the flow rate constant in a pipe?\n\nThe equation of continuity states that for an incompressible fluid flowing in a tube of different cross-sections, the mass flow rate is the same everywhere in the tube. … Normally, the density remains constant and then it is only the flow rate (Av) that is constant.\n\n#### Does the flow rate increase with pressure?\n\nFlow rate effect. Due to the high pressure, the flow rate increases . If the flow rate increases, it is because of the increased pressure.\n\n#### What is normal LPM?\n\nIn men, readings lower than expected to 100 l/min are within the normal range. For women, the equivalent figure is 85 litres/min .\n\n#### 2 What does LPM mean?\n\nAn oxygen flow rate of 2 lpm means 1 liter of oxygen will flow into the patient’s nostrils over a period of 2 minutes . Oxygen prescriptions typically range from 1 liter per minute to 10 liters per minute, with 70% of patients being prescribed 2 liters or less.\n\n#### What is GPM and LPM?\n\nLiters per minute converts to the unit number 4.55 L/min 1 imp gpm , UK one gallon per minute. This is the UK single flow rate value of 1 gallon per minute but the liter per minute flow rate is in the unit option.\n\n#### What is flow and types of flow\n\nBasically, flow types can be sub-divided into laminar flow and turbulent flow : flow type. physical event. flow rate. the flow.\n\n#### What are the 2 characteristics of laminar flow?\n\ncharacteristic of laminar flow\n\n• Laminar is characterized by smooth streamlines and high order speed. ,\n• Steady laminar flow of an incompressible fluid with constant properties over the full developed area of ​​a straight circular pipe.\n\n## What are the types of flows?\n\ntype of fluid flow\n\n• Uniform and non-uniform flow.\n• One, two and three dimensional flow.\n• rotational or motionless flow.\n• laminar or turbulent flow.\n• Compressed or uncompressed flow.\n\n## What is the SCCM unit for Flow Rate?\n\nVolumetric flow rate is sometimes measured in ” standard cubic centimeters per minute ” (abbreviation sccm), a unit that is acceptable for use with the SI, except with additional information attached to the unit symbol. SI standard m3 /s (with any appropriate prefix, with temperature and pressure specified).\n\n## Why is flow rate important?\n\nFlow rate is the amount of fluid that passes through a given cross-sectional area per unit time. Accurate flow rate measurement using an appropriate flowmeter is of paramount importance ensuring fluid control processes run smoothly , safely and cost-effectively.\n\n## How do you measure gas flow rate?\n\nDifferential pressure flow meters use laminar plates, an orifice, nozzle, or venturi tube to create an artificial constriction, then measure the pressure loss of the fluid as they pass that constriction. The higher the pressure, the higher the flow rate.\n\n## Does the pressure drop reduce the flow rate?\n\nThe pressure drop is the volumetric flow rate under comparative laminar flow conditions. … the pressure drop increases as the square of the volumetric flow rate under turbulent flow conditions. When the flow rate is doubled, the pressure is four times lower. The pressure drops as the viscosity of the gas increases.\n\n## Does reducing pipe size increase pressure?\n\nYou ‘ve just traded low flow for increased pressure . … The same thing will happen in your sprinkler system if you use a smaller pipe to increase the pressure. The short pipe will restrict the flow of water. Low flow will reduce the pressure loss in the pipes, resulting in more pressure.\n\n## What is the flow rate proportional to?\n\nFor current, the flow rate is directly proportional to the potential difference and inversely proportional to the resistance. There are other flows such as surface diffusion, permeability and diffusion of one gas into another.\n\n## Does the flow rate change with altitude?\n\nThis shows that the flow rate of a fluid is proportional to the square root of its height . …the relative mass flow rate (kg/s) is calculated by multiplying the volumetric flow rate by the density, ( ), of the liquid.\n\n## What does the flow rate depend on?\n\nIn short, the flow rate depends on the area of ​​the nozzle , on the delta pressure, on the viscosity of the fluid (and also on the type of nozzle). For a constant delta pressure, the increased area increases the flow. For a continuous nozzle area, increasing the delta pressure increases the flow.\n\n## What happens when the flow rate increases?\n\nAs the flow rate increases, the maximum solid temperature decreases which means better micro-channel cooling performance. However, an increase in the fluid flow rate also results in an increase in pumping power (see Equations (17), (18), and (24)).\n\n## Is 400 a good peak flow?\n\nPeak expiratory flow (PEF) is measured in liters per minute. The normal adult peak flow score is between about 400 and 700 liters per minute, although the score may be lower in older women and still be normal. The most important thing is whether your score is normal for you or not.\n\n##### What is FiO2 normal range?\n\nNatural air is comprised of 21% oxygen, which is less than F. is equal to IO 2 of 0.21 . F of oxygenated air. is greater IO 2 by 0.21 ; Up to 1.00 i.e. 100% oxygen. F I O 2 is generally maintained below 0.5 even with mechanical ventilation to avoid oxygen toxicity, but there are applications when used regularly up to 100%.\n\n## How many liters of oxygen is normal?\n\nThe average adult, while resting, breathes in and out about 7 or 8 liters of air per minute. It totals about 11,000 liters of air per day. The exhaled air contains about 20 percent oxygen. The exhaled air contains about 15 percent oxygen." ]

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[ "# Wired2Code\n\n## N-dimension array initialization\n\nIn the previous article Container assignment list I show how to assign items to STL containers using a list of items separated by a comma.\n\nThis example will show how to do the same with a N-dimensional array, with debug build bounds checking. First an example which shows how to declare and initialize a N-dimensional array of type int or type double with a comma separated list of items.\n\n1. // define a 3 dimensional array of int's\n2. // and initialize.\n3. MyArray<int, 3> intArray3D;\n4. intArray3D = 1, 2, 3;\n5.\n6. // define a 2 diemsional array of double's\n7. // and initialize.\n8. MyArray<double, 2> doubleArray2D;\n9. doubleArray2D = 10.0, 20.0;\n10.\n11. // define a 3 x 3 matrix of double and initialize\n12. MyArray<double, 9> doubleMatrix3x3;\n13. doubleMatrix3x3 = 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0;\n\n### The N-Dimensional array class implementation\n\nThe array class code below only shows enough code to get the assignment and comma operator overloaded. Other useful code and overloads that this class would have is not shown, in order to keep the discussion simple and on topic.\n\nMyArray Class\n1. template<class T, int ArraySize>\n2. class MyArray\n3. {\n4. public:\n5.     MyArray()\n6.     {\n7.         assert(ArraySize != 0);\n8.         // Set items in array to 0\n9.         for(size_t i = 0; i < ArraySize; ++i)\n10.             m_array[i] = 0;\n11.     }\n12.\n13.     Initializer<T, ArraySize> operator=(T val)\n14.     {\n15.         // store RHS of = to first array item location\n16.         m_array = val;\n17.\n18.         // Call Initializer construct with address of m_array,\n19.         // return Initializer object.\n20.         // Allows the overloaded comma operator for Initializer\n21.         // to be called repeatedly.\n22.         return Initializer<T, ArraySize>(&m_array);\n23.     }\n24. private:\n25.     T m_array[ArraySize];\n26. };\n\nMyArray is a template class that needs 2 template parameters, the first is the type of array to create, and the second is the number of elements the array can store.\n\nThe default constructor assigns 0 to each element in the array, if this does not make sense for the type object being stored in the array then modify as needed.\n\nThe overloaded assignment operator takes the first item in the list, right of the = sign (RHS), and assigns it to first position in the array. It then calls Initializer’s constructor with the address of the second element in the array, and returns the Initializer object.\n\nThis sets up Initializer, which overloads the comma operator, to handle the rest of the assignment list. Overloading the assignment and comma operators is discussed in the article Container assignment list.\n\nThe Initializer class is simple and documented below.\n\nInitializer Class for MyArray\n1. // Initializer class. Helper class for MyArray,\n2. // keeping track of the current element being\n3. // assigned, with the overloaded comma operator,\n4. template<class T, int ArraySize>\n5. class Initializer\n6. {\n7. public:\n8.     Initializer() : m_ptr(0)\n9.     {\n10.         #ifndef NDEBUG\n11.             m_nCount = 0;\n12.         #endif\n13.     }\n14.\n15.     // Constructor called by MyArray operator=\n16.     // ptr will equal MyArray::m_array. Since\n17.     // For debug builds set m_nCount to 1 since\n18.     // MyArray already assigned element .\n19.     Initializer(T * ptr) : m_ptr(ptr)\n20.     {\n21.         #ifndef NDEBUG\n22.             m_nCount = 1;\n23.         #endif\n24.     }\n25.\n26.     // Overloaded comma operator\n27.     Initializer & operator,(T val)\n28.     {\n29.         #ifndef NDEBUG\n30.             // Debug assert for array overrun\n31.             assert(m_nCount < ArraySize);\n32.             ++m_nCount;\n33.         #endif\n34.\n35.         // store value in pointer to array, then\n36.         // increment pointer to array to next location\n37.         *m_ptr++ = val;\n38.         return *this;\n39.     }\n40. private:\n41.     // Pointer to array location\n42.     T * m_ptr;\n43.     #ifndef NDEBUG\n44.         int m_nCount;\n45.     #endif\n46. };\n\nJuly 12, 2010\n\n## Container assignment lists\n\nA few weeks ago while reading the Blitz++ Documentation I noticed Blitz++ was initializing Matrices and other containers using commas.\n\n1. Container<int> bucket;\n2. bucket = 1, 2, 3, 4, 5;\n\nFinding this both useful and cool, had to figure out how it was done.\n\n### But first…\n\nIf the container has a std::vector member then a constructor taking both the start and end of the array can be used to initialize vector. First an array is initialized, and the beginning and end of the array is passed to the container’s constructor.\n\n1. const int elements = 5;\n2. int a[elements] = {1, 2, 3, 4, 5, };\n3. Container<int> vec(a, &a[elements]);\n\nAlthough this is doable it isn’t flexible and you might be incline to code a bunch of push_back calls\n\n1. Container<int> vec;\n2. vec.push_back(1);\n3. vec.push_back(2);\n4. vec.push_back(3);\n5. vec.push_back(4);\n6. vec.push_back(5);\n\nIf we have to go that route it would be much nicer to write code as shown at the beginning of the article.\n\nThe goal again, is to be able to write code such as\n\n1. Container<int> bucket;\n2. bucket = 1, 2, 3, 4, 5;\n\nwhich assigns values to a container using a list.\n\nBelow is code for a template container class that has std::vector as a member. Only the two operators to be overloaded are shown in the example.\n\nContainer class\n1. template<class T>\n2. class Container\n3. {\n4. public:\n5. std::vector<T> & operator=(const T & nVal) {\n6. m_vector.clear();\n7. m_vector.push_back(nVal);\n8. return m_vector;\n9. }\n10. friend std::vector<T> & operator,(std::vector<T> & lst, T val)\n11. {\n12. lst.push_back(val);\n13. return lst;\n14. }\n15. std::vector<T> m_vector;\n16. };\n\nAssignment operator\n\nThe assignment operator is overloaded to take a const reference T as the first parameter and returns a reference to m_vector. In the previous examples T is an int.  When the compiler sees\n\n1. bucket = 1\n\nit grabs the value to the right of = and if the correct type, produces code for the assignment operator. The overloaded operator= first clears the contents of m_vector, then pushes the value onto m_vector.\n\nThe assignment operator returns a reference of m_vector which allows the overloaded comma operator to be called from the assignment list.\n\nComma operator\n\nThe second operator overloaded for the container class is the comma operator, which evaluates the object type to the left, evaluates the object type to the right and operates on it.\n\nFor the purposes of the example, the assignment operator returned a reference to std::vector<int> (m_vector) from the first item in the list.\n\n1. bucket = 1, 2, 3, 4, 5;\n\nThe compiler uses the returned type on the first seen comma (LHS), looks to the right of the comma and sees it is an int type (RHS). This matches the overloaded comma operator’s definition of\n\n1. friend std::vector<int> & operator,(std::vector<int> & lst, int val)\n\nSince the comma operator is a binary operator, it needs have global scope and declaring the function as a friend provides that.\n\nFor the container class the overloaded comma operator simply pushes the RHS hand value onto the LHS object, and returns a reference to the std::vector<T> (m_vector), and repeats until no items in the list are left.\n\nConclusion\n\nThis type of operator overloading can eliminate ugly lists of repeated push_back calls and can easily be used with the other STL containers.\n\nIt is important that your container class has a member of the STL container you want to use. Do not inherit from one of the STL containers. They do not have a virtual destructor, which is needed for a derived class.\n\nJuly 9, 2010" ]

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[ "Ĺéęüíĺň óĺëßäáň PDF Çëĺęôń. Ýęäďóç\n .flow { margin: 0; font-size: 1em; } .flow .pagebreak { page-break-before: always; } .flow p { text-align: left; text-indent: 0; margin-top: 0; margin-bottom: 0.5em; } .flow .gstxt_sup { font-size: 75%; position: relative; bottom: 0.5em; } .flow .gstxt_sub { font-size: 75%; position: relative; top: 0.3em; } .flow .gstxt_hlt { background-color: yellow; } .flow div.gtxt_inset_box { padding: 0.5em 0.5em 0.5em 0.5em; margin: 1em 1em 1em 1em; border: 1px black solid; } .flow div.gtxt_footnote { padding: 0 0.5em 0 0.5em; border: 1px black dotted; } .flow .gstxt_underline { text-decoration: underline; } .flow .gtxt_heading { text-align: center; margin-bottom: 1em; font-size: 150%; font-weight: bold; font-variant: small-caps; } .flow .gtxt_h1_heading { text-align: center; font-size: 120%; font-weight: bold; } .flow .gtxt_h2_heading { font-size: 110%; font-weight: bold; } .flow .gtxt_h3_heading { font-weight: bold; } .flow .gtxt_lineated { margin-left: 2em; margin-top: 1em; margin-bottom: 1em; white-space: pre-wrap; } .flow .gtxt_lineated_code { margin-left: 2em; margin-top: 1em; margin-bottom: 1em; white-space: pre-wrap; font-family: monospace; } .flow .gtxt_quote { margin-left: 2em; margin-right: 2em; margin-top: 1em; margin-bottom: 1em; } .flow .gtxt_list_entry { margin-left: 2ex; text-indent: -2ex; } .flow .gimg_graphic { margin-top: 1em; margin-bottom: 1em; } .flow .gimg_table { margin-top: 1em; margin-bottom: 1em; } .flow { font-family: serif; } .flow span,p { font-family: inherit; } .flow-top-div {font-size:83%;} the product of the extremes. Therefore the missing extreme may be found by dividing the product of the means (4 x 5) by the given extreme (10). The missing term then is 2, and the proportion is 2:5=4: 10. 645. From the preceding illustration may be derived the following principles : 1. When four general numbers form a proportion, the product of the means is equal to the product of the extremes. 2. A missing extreme may be found by dividing the product of the means by the given extreme. 3. A missing mean may be found by dividing the product of the extremes by the given mean. 646. Oral Exercises. Supply the missing terms represented by x in the following proportions : a. 3:4= 9: x. d. X : 7 = 8: 9. b. 8:6 e. 27 : 3 = x : 1. c. 12 : x = 15 : 3. f. x: 4 days = \\$5: \\$15. NOTE. To find x in Example f, disregard the denominations, and proceed as if the terms were general numbers. 4 = 1}. Then x equals 1} days. =X : 3. 647. Examples for the Slate. Supply the missing terms in the following: (10.) 2 : 100 -- 17 : x. (13.) 750 A. : 3 A. = x : 13 tons. (11.) 9: 150 = 105 : 2. (14.) x : 200 hats = \\$ 87.50: \\$ 500. (12.) 65: x = \\$75: \\$850. (15.) \\$800 : \\$ 56 = \\$390 : x. ANALYSIS AND PROPORTION. 648. ILLUSTRATIVE EXAMPLE. If 14 slates cost 98 cents, what will 10 slates cost? By Analysis. WRITTEN WORK. Explanation. — If 14 slates cost 98 cents, 7 1 slate will cost i fourteenth of 98 cents, and 98 x 10 10 slates will cost 10 times 1 fourteenth of 98 14 cents, which is 70 cents. Ans. 70 cents. Ans. 70 cents. = 70. By Proportion. WRITTEN WORK. Explanation. — The ratio of 14 slates to 10 14:10 = 98 : X. slates must be the same as the ratio of 98 cents, 7 the cost of 14 slates, to the cost of 10 slates. 98 x 10 We may arrange the terms in any order which 70. 14 will express the equality of these ratios. For convenience, we make 98 cents the third term, Ans. 70 cents. and x, the unknown cost of 10 slates, the fourth term. As the cost of 10 slates will be less than 98 cents, we make 10 the second term and 14 the first. Multiplying 98 by 10 and dividing the product by 14, we have for the fourth or missing term, 70. Ans. 70 cents. 649. Rule. To solve examples by simple proportion: 1. Make the number that is of the same denomination as the required answer the third term. 2. Determine from the statement of the example whether the answer is to be greater or less than the third term. 3. Make the other two numbers in the example the first and second terms of the proportion, taking the greater number for the second term if the answer is to be greater than the third term, and the less number for the second term if the answer is to be less than the third term. 4. Multiply the third term by the second term, and divide the product by the first term. 650. Examples for the Slate. The following examples may be solved by analysis or by proportion, or by both methods, at the option of the teacher. 16. If 4 yards of velvet cost \\$20, what will 14 yards cost? 17. If 12 bushels of wheat cost \\$ 8, what will 30 bushels cost? 18. What will 250 sheep cost if 24 sheep cost \\$ 72 ? 19. What will 75 pounds rf cheese cost if 64 pounds cost \\$ 6.0 ? 20. How many feet of plank will be required for a bridge 528 feet long, if 17280 feet of plank are required for 288 feet? 21. If 500 bushels of plaster were sufficient for the dressing of 3} acres of land, what would be required for 17} acres of the same kind of soil ? 22. If a building 13 ft. high casts a shadow of 4 ft., what length of shadow will a church spire 3462 ft. high cast at the same time? 23. If crackers can be sold at 10 cents a pound when flour is worth \\$ 6.50 a barrel, for what can they be sold when flour is worth \\$ 9.75 a barrel, the cost of making not being considered? 24. If a hind wheel, which is 83 feet in circumference, turns 800 times in a journey, how many times will the fore wheel, which is 6} feet in circumference, turn in the same journey ? 25. If 400 bushels of potatoes were bought for \\$350.90, and sold for \\$425.50, what was gained on 25 bushels ? 26. If a 10-cent loaf weighs 1 lb. 2 oz. when flour is worth \\$7} per bbl., what should it weigh when flour is \\$6 per bbl. ? 27. If my friend lends me \\$ 7000 for 15 days, for what time should I lend him \\$ 4500 to requite the favor ? 28. If my friend lends me money for 4 months when interest is 10 per cent, for what time should I lend him the same sum to requite the favor when interest is 7 per cent ? 29. If 2 lbs. 5 oz. of wool make 1 yd. of cloth 32 inches wide, how much will make a yard of the same quality 14 yards wide ? 30. How many yards of cambric 34 inches wide will be required to line 14} yards of silk which is 22 inches wide ? 31. If 400 lbs. of coal are required to run an engine 12 hours, what number of tons will be required to run three similar engines for 30 days, day and night? 32. A deer, 150 rods before a hound, runs 30 rods a minute; the hound follows at the rate of 42 rods a minute. In what time will the deer be overtaken ? COMPOUND PROPORTION. 651. A compound proporti n is a proportion in which one of the ratios is compound. 652. ILLUSTRATIVE EXAMPLE If it takes a man 5 days of 9 hours each to earn \\$ 15, how many days of 8 hours each will it take him to earn \\$ 20 ? WRITTEN WORK. 5 3 74 By Analysis. Explanation. - If it takes a man 5 days to earn \\$15, it will take him 1 fifteenth of 5 days 3 x 20 x to earn \\$1, and 20 times that to earn \\$ 20. If 15 ~ 8 it takes him this number of days when the days 3 2 are 9 hours long, it will take him 9 times as Ans. 7} days. many days when they are 1 hour long, and 1 eighth of that number when they are 8 hours long, which is 7 days. Ans. 7 days. By Compound Proportion. WRITTEN WORK. Explanation. The number of days it 1 1 will take depends, first, on the amount 3 4 of money to be earned, and, secondly, on 15 : 20 5 days : x. the number of hours a day the man works. We might get the answer by 3 using two simple proportions. In the 5 x 3 first we could find the number of days, 2 so far as it depends on the amount of Ans. 71 days. money to be earned ; and then, taking this result as the third term of another proportion, we could find the number of days so far as it depends on the number of hours in a day's work. It will be more convenient, however, to combine the two proportions, thus forming a compound proportion. To do this we make 5 days, which is a number of the same denomi. nation as the required answer, the third term, and then consider the statements of the example in order (1) As \\$ 20 is a larger sum than \\$15, it will take a larger number of days to earn it ; that is, the answer, so far as it depends on the", null, "amount of money to be earned, will be larger than the third term ; so we make 20 the second term and 15 the first term of the first ratio. (2.) As it will take more days 8 hours long to earn this money than days 9 hours long, the answer, so far as it depends on the length of the days, will be larger than the third term ; so we make 9 the second term and 8 the first term of the second ratio. We now have the compound proportion, 15 : 20 = 5 days : a days. 8 Multiplying 5 days by 20 x 9, and dividing the product by 15 R8, gives 7 days. Ans. 7} days. The work may be shortened, as shown in the written work, by cancelling. 653. Rule. To solve examples by compound proportion: 1. Make the number that is of the same denomination as the answer the third term. 2. Take the two numbers in each separate statement in the example, and consider whether the answer, so far as it depends on them alone, will be greater or less than the third term. Arrange these two numbers accordingly as terms of a ratio. 3. Multiply the third term by the product of the second terms and divide this product by the product of the first terms. 654. Examples for the Slate. 33. If \\$90 is paid for the work of 20 men 6 days, what should be paid for the work of 5 men 8 days ? 34. If in 84 days 75 men can earn \\$68.75, in how many days can 90 men earn \\$ 41.25 ? 35. If it costs \\$ 30 to paint the front of a building 140 ft. long and 25 ft. high, what will it cost to paint the front of a building 180 ft. long and 20 ft. high? 36. If 450 pounds of merchandise can be carried 26 miles for 304, how many miles can 3 tons be carried for \\$4 ? « ĐńďçăďýěĺíçÓőíÝ÷ĺéá »" ]

[ null, "https://books.google.gr/books/content", null ]

[ "# Bass model example\n\nBass Model Functions in Excel Visual Basic. To use these functions, download the spreadsheet described at Which Bass Model Equations Should I Use? The Excel file also contains additional documentation, examples of function use and comparison of the three sets of Bass Model functions.\n\n## Identify linear quadratic and exponential functions from tables calculator\n\nDelta sweet beginnings bassinet instructions" ]

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[ "x", null, "Showing 20 of 125 courses\nProbability and statistics: Joint and conditional probabilities and densities. Moments, cumulants, generating functions, characteristic function. Binomial, Poisson, Gaussian d\n• FREE\n• Self Paced\nIntroduction:Course mechanics - Goals and VR definitions - Historical perspective - Birds-eye view (general) - Birds-eye view (hardware) - Birds-eye view (software) - Birds-ey\n• FREE\n• Self Paced\nTheorems of Picard, Casorati-Weierstrass and Riemann on Removable Singularities:Properties of the Image of an Analytic Function:Introduction to the Picard Theorems,Recalling S\n• FREE\n• Self Paced\nStructure of present day electronic products - Analog signal conditioning and processing functions in instrumentation and control and communication - One-port networks for ana\n• FREE\n• Self Paced\nVectors and Elementary linear algebra - Linear vector space and matrices - Determinants, trace and special matrices - Linear first order differential equations - First and sec\n• FREE\n• Self Paced\nTheorems of Rouche and Hurwitz:Fundamental Theorems Connected with Zeros of Analytic Functions - The Argument (Counting) Principle, Rouche's Theorem and The Fundamental Theore\n• FREE\n• Self Paced\nSymmetry and Physical Properties of Crystals Point groups, Bravais lattices, Space groups, Neumann�s Principle and tensor properties of crystalline solids, elements of group\n• FREE\n• Self Paced\nIntroduction to digital system - Number Systems - Complement Numbers - Complement Subtraction and codes - Review of First Four Lectures and Introduction to logic Gates - Basic\n• FREE\n• Self Paced\nIntroduction to Indian Philosophy:Brief Discussion on Veda and Upanishads - Origin of Indian Philosophy;Charvaka Philosophy:Epistemology - Metaphysics;Samkhya Philosophy:Metap\n• FREE\n• Self Paced\nAnalytic functions of a complex variable:Complex numbers. Equations to curves in the plane in terms of z and z* - The Riemann sphere and stereographic projection. Analytic fu\n• FREE\n• Self Paced\nIntroduction - Compressibility of Fluids; Compressible and Incompressible Flows; Perfect Gas Equation of State; Calorically Perfect Gas - One Dimensional Flows � Basics Gove\n• FREE\n• Self Paced\nMechanics of a system of particles in vector form. Conservation of linear momentum, energy and angular momentum - Degrees of freedom, generalized coordinates and velocities. L\n• FREE\n• Self Paced\nGoverning Equations: Continuity, Momentum and Energy Equations and their derivations in different coordinate systems, Boundary layer Approximations to momentum and energy - La\n• FREE\n• Self Paced\nIntroduction and mathematical preliminaries:What is Pattern recognition; Applications and Examples - Clustering vs. Classification; Supervised vs. unsupervised - Relevant basi\n• FREE\n• Self Paced\nBasics of magnetic circuits - Analysis of magnetic circuits with airgap and permanent magnets - Analysis of singly excited electromechanical system with linear magnetics - Non\n• FREE\n• Self Paced\nIntroduction to the course; Current and Voltage; Kirchhoff's Current and Voltage laws - Electrical circuit elements: Voltage and current sources; R, C, L, M - Elements in se\n• FREE\n• Self Paced\nIntroduction to chemical bonding and development of band gap - Introduction and types of semiconductors. Explanation of density of states, Fermi energy, and band occupancy - P\n• FREE\n• Self Paced\nThermodynamics and the Chemical Industry - James Prescot Joule and the first law - Sadi Carnot and the second law - Equilibrium and Extrema in work - Illustrative Calculation\n• FREE\n• Self Paced\nBasics:Prologue � Introduction to the course - Science, Engineering and Technology of Materials;Microstructure:Atomic Bonding - Structure of Solids - Movement of Atoms - Dev\n• FREE\n• Self Paced" ]

[ null, "https://freevideolectures.com/assets2/images/Seperateicons/Logo.png", null ]

[ "", null, "# Molar Volume Calculator\n\nMolar Volume(Vm) = Atomic Weight × Molar MassDensity(ρ)\n\nEnter the unknown value as ‘x.’\n\nAtomic Weight =\n\nMolar Mass = kg/mol\n\nDensity(ρ) = kg/m3\n\nMolar Volume(Vm) = m3/mol\n\nx =\n\nMolar Volume Calculator is a free online tool that displays the molar volume of the substance. BYJU’S online molar volume calculator tool performs the calculation faster, and it displays the molar volume in a fraction of seconds.\n\n## How to Use the Molar Volume Calculator?\n\nThe procedure to use the molar volume calculator is as follows:\n\nStep 1: Enter the atomic weight, molar mass, density of the substance and x for the unknown in the input field\n\nStep 2: Now click the button “Calculate x” to get the result\n\nStep 3: Finally, the molar volume of the substance will be displayed in the output field\n\n### What is Meant by Molar Volume?\n\nThe molar volume is defined as the volume of one mole of substance at the specified temperature and pressure. The molar volume is represented by the notation Vm. The SI unit of molar volume is cubic meters per mole (m3/mole). For solids and liquids, cubic centimetre per mole is used (cm3/mole). And for gases, cubic decimeters per mole (dm3/mole) is used. The formula to calculate the molar volume is the ratio of molar mass to the density. The molar volume formula is\n\nMolar volume = Molar Mass / Density" ]

[ null, "https://www.facebook.com/tr", null ]

[ "# How to quickly find a set of solutions that meet the requirements\n\nNote: The following questions are from the 21th question of the 2010 Chinese Graduate Mathematical Entrance Examination (first set):\n\nIt is known that the canonical form of the quadratic form $$f\\left(x_{1}, x_{2}, x_{3}\\right)=x^{T} A x$$ under the orthogonal transformation $$x=Qy$$ is $$y_{1}^{2}+y_{2}^{2}$$, and the third column of Q is $$\\left(\\frac{\\sqrt{2}}{2}, 0, \\frac{\\sqrt{2}}{2}\\right)^{T}$$.Now I need to find the matrices A and Q.\n\nI use the following code to calculate this problem, hoping to find a set of solutions that meet the requirements. But the following code runs all the time:\n\nQ = {{x1, x2, Sqrt/2}, {x3, x4, 0}, {x5, x6, Sqrt/2}};\nA = Array[x, {3, 3}];\nFindInstance[\nThread[Transpose[Q] . A . Q == {{1, 0, 0}, {0, 1, 0}, {0, 0, 0}}],\nJoin[{x1, x2, x3, x4, x5, x6}, Flatten[A]], Reals]\n\n\nHow can I improve this code to quickly find a set of solutions that meet the requirements?\n\nThe reference answer is $$Q=\\left(\\begin{array}{ccc} \\frac{\\sqrt{2}}{2} & 0 & \\frac{\\sqrt{2}}{2} \\\\ 0 & 1 & 0 \\\\ -\\frac{\\sqrt{2}}{2} & 0 & \\frac{\\sqrt{2}}{2} \\end{array}\\right)$$, $$A=Q\\left(\\begin{array}{lll} 1 & & \\\\ & 1 & \\\\ & & 0 \\end{array}\\right) Q^{T}=\\frac{1}{2}\\left(\\begin{array}{ccc} 1 & 0 & -1 \\\\ 0 & 2 & 0 \\\\ -1 & 0 & 1 \\end{array}\\right)$$.\n\n• Your reference answer doesn't satisfy Transpose[Q] . A . Q == {{1, 0, 0}, {0, 1, 0}, {0, 0, 0}} ! Aug 12, 2020 at 8:32\n• @UlrichNeumann Note that the reference answer is $Q.A.Q^{T}$. if $Q=\\left(\\begin{array}{ccc} \\frac{\\sqrt{2}}{2} & 0 & \\frac{\\sqrt{2}}{2} \\\\ 0 & 1 & 0 \\\\ -\\frac{\\sqrt{2}}{2} & 0 & \\frac{\\sqrt{2}}{2} \\end{array}\\right)^{T}$, the answer is still correct Aug 12, 2020 at 8:55\n• I agree, my fault. But right Q as given in your question without transposition! Aug 12, 2020 at 9:06\n\nNMinimize evaluates quite fast:\n\nmini = NMinimize[{#.# &[Flatten[Transpose[Q].A.Q - {{1, 0, 0}, {0, 1, 0}, {0, 0, 0}} ]] + 10^10 #.# &[ Flatten[IdentityMatrix - Transpose[Q].Q] ]},\nJoin[{x1, x2, x3, x4, x5, x6}, Flatten[A]], WorkingPrecision -> 15]\n\nTranspose[Q].A.Q - {{1, 0, 0}, {0, 1, 0}, {0, 0, 0}} /. mini[]\n(*{{0.*10^-15, 0.*10^-15, 0.*10^-15}, {0.*10^-15, 0.*10^-15,0.*10^-15}, {0.*10^-16, 0.*10^-16, 0.*10^-15}}*)\n\n\nThe result for matrix A matches the reference answer\n\n A /. mini[] // Chop // Rationalize\n(* {{1/2, 0, -(1/2)}, {0, 1, 0}, {-(1/2), 0, 1/2}} *)\n\n\nbut Q doesn't match the reference.\n\n• Thank you very much. I hope to find a set of exact solutions rather than numerical solutions quickly. Aug 12, 2020 at 7:43\n• @Montevideo Ok you could try Minimize? Thereby you should add a constraint Q^T.Q==Identity Aug 12, 2020 at 9:09\n• After I added the constraint Q^T.Q==IdentityMatrix, it still runs without returning results. Aug 12, 2020 at 9:52\n• @Montevidoe I modified my answer. Minimize version doesn't evaluate... Aug 12, 2020 at 10:14\n• @Montevideo What a simple trick. Solve instead of FindInstance fgives 8 solutions quite fast. Aug 13, 2020 at 7:21\n\nI will leave the rigorous proof of the following to the interested reader:\n\nv = {Sqrt[1/2], 0, Sqrt[1/2]};\nqq = Transpose[Simplify[TrigExpand[Append[RotationMatrix[2 ArcTan[u]].\n(Normalize /@ NullSpace[{#}]), #] &[v]]]]\n{{(-1 + u^2)/(Sqrt (1 + u^2)), -((Sqrt u)/(1 + u^2)), 1/Sqrt},\n{-((2 u)/(1 + u^2)), (1 - u^2)/(1 + u^2), 0},\n{-((-1 + u^2)/(Sqrt (1 + u^2))), (Sqrt u)/(1 + u^2), 1/Sqrt}}\n\naa = FullSimplify[qq.{{1, 0, 0}, {0, 1, 0}, {0, 0, 0}}.Transpose[qq]]\n{{1/2, 0, -1/2}, {0, 1, 0}, {-1/2, 0, 1/2}}\n\n• This answer is great, but I don’t yet know its mathematical principles. Aug 15, 2020 at 5:43" ]

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[ "Title Probability and Statistics Probability Theory Randomness Dice Meteorology Odds 1.5 MB 241\n``` Cover\nFront Matter\nAcknowledgments\nIntroduction\nPart One: What is Probability?\n1. The Idea of Randomness\nRandomness before the Theory of Probability\nEarly Difficulties in Developing a Theory of Randomness\nRandomness and Religion Today in Burkina Faso\n2. The Nature of Chance\nCardano's Mistake\nCardano on Luck and Math\nGalileo Galilei\nPeirre de Fermat and Blaise Pascal\nThe Division of Stakes, an Alternative Interpretation\nChristian Huygens\nJacob Bernoulli\nAbraham de Moivre\nDe Moivre on Math and Luck\nThe Bell Curve\n3. Surprising Insights into Probability and Its Uses\nThomas Bayes and Inverse Probability\nBuffon and the Needle Problem\nDaniel Bernoulli and Smallpox\nJean le Rond d'Alembert and the Evaluation of Risk\nLeonhard Euler and Lotteries\n4. Randomness in a Deterministic Universe\nSimeon-Denis Poisson\nThe Poisson Distribution\n5. Random Processes\nJames Clerk Maxwell\nBrownian Motion Revisited\nMarkov Processes\nA Markov Chain\n6. Probability as a Mathematical Discipline\nTheory and Practice\n7. Three Applications of the Theory of Probability\nNuclear Reactor Safety\nMarkov Chains and Information Theory\nSmallpox in Modern Historical Times\nPart Two: Statistics\nIntroduction: The Age of Information\n8. The Beginnings of Statistics\nThe Beginnings of Statistics\nEdmund Halley\nBreslau Table for Number and Infinity\nInsurance\n9. Data Analysis and the Problem of Precision\nThe Misuse of Statistics\n10. The Birth of Modern Statistics\nKarl Pearson\nR.A. Fisher\n11. The Theory of Sampling\nThe Problem\nWalter Shewhart and Statistical Quality Control\nWilliam Edwards Deming\n12. Three Applications of Statistics\nThe Birth of Epidemiology\nThe U.S. Census\nPolitical Polling\nChronology\nGlossary" ]

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[ "# Small ditetrahedronary prismatocubihexacosihecatonicosachoron\n\nSmall ditetrahedronary prismatocubihexacosihecatonicosachoron", null, "Rank4\nTypeUniform\nSpaceSpherical\nNotation\nElements\nCells120 compounds of five cubes, 600 tetrahedra, 120 icosidodecahedra, 720 pentagonal prisms\nFaces2400 triangles, 3600 squares, 1440 pentagons\nEdges3600\nVertices600\nMeasures (edge length 1)\nCircumradius$\\frac{\\sqrt2+\\sqrt{10}}{2} \\approx 2.28825$", null, "Number of external pieces106920\nLevel of complexity211\nRelated polytopes\nArmyHi\nRegimentSidtaxhi\nAbstract & topological properties\nFlag count115200\nEuler characteristic2400\nOrientableYes\nProperties\nSymmetryH4, order 14400\nConvexNo\nNatureWild\n\nThe small ditetrahedronary prismatocubihexacosihecatonicosachoron, or sadtip caxhi, is a nonconvex uniform polychoron that consists of 600 cubes (lying in the same hyperplanes, forming 120 compounds of five cubes), 600 tetrahedra, 120 icosidodecahedra, and 720 pentagonal prisms. Eight cubes (or four compounds), four tetrahedra, six icosidodecahedra, and twelve pentagonal prisms join at each vertex.\n\n## Vertex coordinates\n\nIts vertices are the same as those of its regiment colonel, the small ditetrahedronary hexacosihecatonicosachoron." ]

[ null, "https://static.miraheze.org/polytopewiki/thumb/4/45/Sadtip_caxhi_card_Bowers.jpeg/200px-Sadtip_caxhi_card_Bowers.jpeg", null, "https://polytope.miraheze.org/w/index.php", null ]

[ "", null, "", null, "", null, "Chapter 17.2, Problem 17.3CYU\n\nChapter\nSection\nTextbook Problem\n\nUse the Henderson-Hasselbalch equation to calculate the pH of 1.00 L of a buffer solution containing 15.0 g of NaHCO3 and 18.0 g of Na2CO3. (Consider this buffer as a solution of the weak acid HCO3− and its conjugate base, CO32−.)\n\nInterpretation Introduction\n\nInterpretation:\n\nThe value of pH for the solution containing 15.0g of sodium bicarbonate and 18.0g of sodium carbonate were dissolved in 1litre of water is to be calculated by using Henderson-Hasselbalch equation.\n\nConcept introduction:\n\nThe Henderson-Hasselbalch equation relates pH of a buffer with pKa of acid, concentration of conjugate base and concentration of acid. The expression is written as,\n\npH=pKa+log[conjugatebase][acid] (1)\n\nThis equation shows that pH of buffer solution is controlled by two major factors. First, is strength of the acid which can be expressed on terms of pKa and second, the relative concentration of acid and its conjugate base at equilibrium.\n\nExplanation\n\nThe equilibrium between HCO3 and its conjugate base CO32 is written as follows;\n\nHCO3(aq)+H2O(l)H3O+(aq)+CO32(aq)(acid)(conjugatebase)\n\nThe calculation of pH is done by using Henderson-Hasselbalch equation is given below.\n\nGiven:\n\nRefer to table no. 16.2 in the textbook for the value of Ka.\n\nThe value of Ka for hydrogen carbonate ion is 4.8×1011.\n\nNegative logarithm of the Ka value gives the pKa value of the acid.\n\npKa=log(Ka)=log(4.8×1011)=10.31\n\nTherefore, pKa value for the hydrogen carbonate ion is 10.31.\n\nThe 15.0g of sodium bicarbonate (NaHCO3) is dissolved in 1litre of H2O.\n\nMolar mass of sodium bicarbonate (NaHCO3) is 84.0gmol1.\n\nThe 18.0g of sodium carbonate (Na2CO3) is dissolved in 1litre of H2O.\n\nMolar mass of sodium carbonate is 105.98gmol1.\n\nThe concentration of sodium bicarbonate is calculated as follows;\n\nMolarity=Numberofmoles1L of solvent (2)\n\nNumberofmoles are calculated by using expression.\n\nNumberofmoles=weightmolarmass\n\nSubstitute 15.0g for weight and 84.0gmol1 for molarmass for sodium bicarbonate (NaHCO3)\n\nStill sussing out bartleby?\n\nCheck out a sample textbook solution.\n\nSee a sample solution\n\nThe Solution to Your Study Problems\n\nBartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!\n\nGet Started\n\nFind more solutions based on key concepts", null, "" ]

[ null, "https://www.bartleby.com/static/search-icon-white.svg", null, "https://www.bartleby.com/static/close-grey.svg", null, "https://www.bartleby.com/static/solution-list.svg", null, "https://www.bartleby.com/static/logo.svg", null ]

[ "Date: Tue, 1 Dec 2020 11:39:35 +0000 (WET) Message-ID: <1427791698.33673.1606822775412@confluence> Subject: Exported From Confluence MIME-Version: 1.0 Content-Type: multipart/related; boundary=\"----=_Part_33672_855199671.1606822775411\" ------=_Part_33672_855199671.1606822775411 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Content-Location: file:///C:/exported.html Conditional Blocks\n\n# Conditional Blocks\n\n=20\n\nConditional blocks allow you to show or hide sections of the document ac= cording to conditional expressions.\n\nIt has the following notation:\n\n=20\n=20 Expand to see the sample code=20 Expand source=20 =20\n=20\n=20\n```#{if (%{<Javascript>})}\n=09CONTENT\n#{end}\n```\n=20\n=20\n\n<Javascript> is a Java= Script expression that should evaluate to true or false.\n\nBelow is a working example:\n\n=20\n=20 Expand to see the sample code=20 Expand source=20 =20\n=20\n=20\n```This is the header of the document.=20\n\n#{if (%{'\\${IssueTypeName}'.equals('Bug')})}\nThis section will only be visible if the issue type of the issue is Bug\nThis issue is a bug created by \\${AssigneeUserName} with priority \\${Priority=\n}.\n#{end}\n\n#{if (%{'\\${Priority}'.equals('Major')})}\nThis section will only be visible if the priority of the issue is major.\nThis issue has top priority, needs to be resolved until \\${DueDate}.\n#{end}\n\n#{if (%{'\\${escape:Description}'.equals('')})}\nThis issue has no description\n#{end}\n\n#{if (%{'\\${escape:Description}'.length > 0})}\nIssue description: \\${Description}\n#{end}\n\nThis is the footer of the document.  ```\n=20\n=20\n\nFor more examples, check the Sample Conditions= .docx template in the Template Store.\n\nThe image below demonstrates a Word template w= ith a conditional block:", null, "The image below demonstrates an Excel template= with a conditional block:", null, "" ]

[ null, "https://confluence.xpand-it.com/3D\"9a694c568b16f53ecf6f5ddd83e0cf26\"", null, "https://confluence.xpand-it.com/3D\"dda629a40e740f79ace13e528c54373b\"", null ]

[ "Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.\n\nThis is a guest post by Prasad Patil that answers the question: how to put a shape in the margin of an R plot?\n\nThe help page for R‘s par() function is a somewhat impenetrable list of abbreviations that allow you to manipulate anything and everything in the plotting device. You may have used this function in the past to create an array of plots (using mfrow or mfcol) or to set margins (mar or mai).\n\nWay down toward the end of the list is the often-overlooked xpd parameter. This value specifies where in the plotting device an object can actually be plotted. The default is xpd = FALSE, which means that plotting is clipped, or restricted, to the plotting region. In other words, if your plot has xlim = c(0, 10) and ylim = c(0, 10) and you try to plot the point (-1, -1), it will not appear anywhere in the device.\n\nxpd takes two other values, TRUE and NA, which limit plotting to the figure and device region, respectively. If you’re fuzzy on plotting terms, this tutorial presents those topics well.\n\n## Plotting outside the plot\n\nIf you want to plot outside of the plotting region, I find that setting xpd = NA easiest since it opens up all external space. We also need to make sure that we keep space outside of the plot so that we have room to place our objects. Let’s say we want to put an ugly border above and below our plot:\n\n# Set xpd=NA and expand the top and bottom margins\npar(xpd = NA, mar = par()$mar + c(2.5, 0, 1, 0)) plot(1:10) # Note that the rectangle we make here has corner coordinates outside of # our plotting device rect(-5, 11, 12, 14, col=\"red\") # Random dots in our rectangluar region points(runif(100, -4.2, 12.8), runif(100, 11.2, 13.6), col = \"green\", pch = 19, cex = 1.2) # And another rectangle for below rect(-5, -1.7, 12, -3.5, col=\"red\") points(runif(100, -4.2, 12.8), runif(100, -3.3, -1.8), col = \"green\", pch = 19, cex = 1.2)", null, "Here we mentally extend the axes of our plot to determine where to put our margin elements. One can imagine a diagonal for the top rectangle running from (-5,11) to (12,14). Neither of these points appear in the plot itself, but we used the established axes to estimate them and plot outside the plotting region. ## Images outside the plot Now let’s say we want to add a logo or other external image in the margin of our plot. We will use R‘s png library to load a PNG image and rasterImage() to plot it: ## If needed: install.packages(\"png\") library(png) img <- readPNG(\"logo.png\") par(xpd = NA, mar=par()$mar + c(3, 0, 0, 0))\nplot(1:10)\nrasterImage(img, 0.5, -2.5, 10.5, -1)", null, "Here we used the png library and the rasterImage() command to read in and plot the \"logo.png\" file. Based on the previously-known dimensions of the logo, we can choose which points to use as endpoints for the image. Note that this image may appear stretched or contorted depending on the size of your R plot device, and it will not stay consistent if you resize.", null, "" ]

[ null, "https://i2.wp.com/lcolladotor.github.io/figs/2014-11-21-add-logo-in-R/plot-1.png", null, "https://i1.wp.com/lcolladotor.github.io/figs/2014-11-21-add-logo-in-R/imgplot-1.png", null, "https://feeds.feedburner.com/~r/FellgernonBit-rstats/~4/fH97-LBa7Mw", null ]

[ "#### Abstract\n\nIn order to improve the performance of robot dexterous hand, a controller based on GA-fuzzy-immune PID was designed. The control system of a robot dexterous hand and mathematical model of an index finger were presented. Moreover, immune mechanism was applied to the controller design and an improved approach through integration of GA and fuzzy inference was proposed to realize parameters’ optimization. Finally, a simulation example was provided and the designed controller was proved ideal.\n\n#### 1. Introduction\n\nIn the past few years, massive research is committed to study the anthropomorphic robot hands with dexterous manipulation abilities. As an important tool to improve the intelligence and manipulation levels of robots, multi-DOF and multisensory robot dexterous hand has become one of the most promising researches in robot field [1, 2]. The robot dexterous hand could distinguish objects with different materials and shapes and snatch them successfully through the control system. Therefore, the robustness and control accuracy of a control system would play an important role in evaluating the performance of a robot dexterous hand .\n\nNowadays, robot dexterous hands have been used in many fields such as industry field, agriculture field, service field, and medical rehabilitation field. However, most of them have some common disadvantages such as slow response, poor flexibility, weak anti-interference ability, and poor controllability [4, 5]. To the best of our knowledge, the problem of robust and intelligent control for a robot dexterous hand has almost not been dealt with. Based on our past researches on robot dexterous hands and control methods, this paper tries to tackle this problem.\n\nBearing the above observation in mind, a GA-fuzzy-immune PID (genetic algorithm-fuzzy- immune proportion-integration-differentiation) controller with incomplete derivation for robot dexterous hand is developed and the rest of this paper is organized as follows. In Section 2, some related works are outlined based on the literatures. The control system of a robot dexterous hand and mathematical model of an index finger are presented in Section 3. In Section 4, the GA-fuzzy-immune PID controller is designed and some improvements are proposed. Section 5 provides a simulation example to verify the feasibility and efficiency of proposed controller. Our conclusions and future works are summarized in Section 6.\n\n#### 2. Literature Review\n\nRecent publications relevant to this paper are mainly concerned with three research streams: robot dexterous hand control methods, PID control methods, and fuzzy-immunity feedback control methods. In this section, we try to summarize the relevant literatures.\n\n##### 2.1. Robot Dexterous Hand Control Methods\n\nFor the robot dexterous hand control methods, many researchers had worked on the problem and proposed different solutions since the last decades. As early as in 1962, a robot dexterous hand named after Belgrade was designed by Tomovic and Boni based on the most advanced control theory, which was considered to be the real significance dexterous hand . Nowadays, with the development of computer technology, microelectronics technology, and advanced control theory, robot dexterous hand has entered a new period. Jafarov et al. took both sliding and stability issues into account to present an augmented sliding surface design for robot hand. In , a new variable structure PID controller design approach was considered for the tracking stabilization of robot motion. Atia designed a new nonlinear PID sliding mode controller for set-point control of robot hand, which ensured that the error tended to zero asymptotically if there was no disturbance applied to the robot dynamics. Chen et al. presented two types of adaptive control program combining conventional computed-torque control and different fuzzy compensators for the robust tracking control of robotic manipulators with structured and unstructured uncertainties. In , a model-free recurrent fuzzy neural network (RFNN) control system for robot hand was proposed to approximate the ideal backstepping control law, which was further proved stable by the Lyapunov stability analysis. By combining feedback linearization with Lyapunov’s second method and genetic algorithm, Hassanzadeh et al. designed a robust controller with performance tuning for robot hand, and the stability and robust performance of proposed controller were verified through a four-bar linkage robot simulation. In , two fault-tolerant control strategies for robot hand were implemented based on output-feedback controller and experimental results illustrated that the improvements were feasible and efficient.\n\n##### 2.2. PID Control Methods\n\nAs one of the earliest control strategies, PID control has been developed to deal with more complex control problems due to the advantages of simple description, high dependability, strong robustness, and so forth. Han proposed a nonlinear PID controller with the capability of auto-disturbance-rejection control and combination of differentiator and extended state observer, and transition process overcame the disturbance effectively and improved the control performance. Besides, Su et al. applied the method of Han proposed for controlling of manipulator successfully. Gundes and Ozguler investigated the problem of closed-loop stabilization using PID controller for MIMO plants to show the existence of stabilizing PID controllers for MIMO plants. Alvarez-Ramirez et al. addressed the position regulation problem of robot manipulators under control input constraints and experiment results showed that the saturated linear PID control was semiglobally asymptotically stable. Oliveira et al. used Hermite-Biehler theorem to establish results on the design of PID controllers for a class of time delay systems. Ziegler and Nichols proposed the most well-known Ziegler and Nichols tuning formula for PID parameter tuning. Chen and Huang presented a method for regulating PID parameters on line automatically with neural net algorithm. Neurofuzzy controller and genetic-fuzzy controller for second-order control systems were presented to improve the performance of conventional PID and fuzzy controller . Genetic-fuzzy controller was applied in the drum boiler simulated dynamics to improve the control speed and precision . Moreover, further improvements for neurofuzzy controller and genetic-fuzzy controller were carried out by genetic-neurofuzzy arithmetic . Kim et al. achieved automatic tuning of PID parameters through integration of taking as performance index and particle swarm optimization algorithm. Juang and Lu proposed power-system load-frequency control by fuzzy-PI controller and simulations on a multiarea interconnected power system with different kinds of perturbations were performed to verify the performance of the proposed approach. Lu et al. proposed an evolutionary fuzzy lead-lag control approach for coordinated control of flexible AC transmission system devices in a multimachine power system. Tang et al. put forward a new method integrated with genetic algorithm and fuzzy distance to tune parameters. Zheng et al. applied linear matrix inequalities (LMIs) in PID controller and a numerical example validated the stability of the closed-loop systems, or performance specifications, or maximum output control requirement, respectively.\n\n##### 2.3. Fuzzy Immunity Feedback Control Methods\n\nBack to 1986, Farmer et al. suggested a dynamic model of an immune system based on immune network theory firstly and discussed the links between an immune system and other artificial intelligence methods. Xin et al. designed a fuzzy-immune-PD-type control algorithm for trajectory tracking based on dynamics nonlinearities of robot manipulator, and experimental results showed that the control scheme had better tracking precision, stronger robustness, and superior control performance to conventional PD controller. Lei and Ren-hou proposed a fuzzy immune algorithm to design a classification system, and the results of comparison with other classification schemes demonstrated the effectiveness of the proposed immune algorithm. Wang et al. designed a fuzzy-immune-PID control system based on a mutative scale chaos optimization method to avoid a mass of tuning parameters work in the progress of design. An immune-fuzzy sliding mode controller (FISMC) was presented not only eliminating the synchronous reluctance motor system uncertainty but also overcoming the drawback of sign function and sat function . Chang et al. presented an effective procedure based on fuzzy logic and immune algorithm for the placement and sizing of shunt capacitor banks in a distorted power network. Kuo et al. proposed an artificial immune system (AIS) based on fuzzy neural network (FNN) to avoid falling into the local optimum and improve the learning capability.\n\n##### 2.4. Discussion\n\nHowever, although many approaches for robot dexterous hand have been proposed in above literatures, they have some common disadvantages summarized as follows. Firstly, some proposed controllers for self-adaption robot dexterous hand need to calculate the inverse of Jacobian matrix, but it is difficult to obtain and would consume much time. Secondly, due to the frictional disturbances at joints and external disturbance of payload, it is difficult to design a faster response, less overshoot, and satisfactory robust stability control system. Thirdly, the performance of some methods is actually related to specific weights, which is difficult to obtain. Finally, because of inherent deficiencies of some methods, it is easy to produce premature convergence.\n\nIn order to solve the above problems, a PID position controller based on immunity feedback control theory, fuzzy inference, and improved genetic algorithm is designed. A simulation example is provided and experiment results show that the proposed controller can achieve shorter adjust time, better rapidity, and higher steady-state precision than traditional PID position controller.\n\n#### 3. Robot Dexterous Hand\n\n##### 3.1. Robot Dexterous Hand Control System\n\nA dexterous hand (named after ABS-I) has been developed in our laboratory, which is made by the reinforced acrylonitrile butadiene styrene copolymers (ABS) in a 3D printer. It is composed of DC servo motors, cup-type planetary gear reducers, sensors, IE2-400 encoders, complicated programmable logic device (CPLD), and digital signal processor (DSP) unit. Figure 1 shows the control circuit board of robot dexterous hand and the index finger.\n\nThe hierarchical control strategy adopted by the dexterous hand control system takes perfect purpose in practice. Feedback data glove or personal computer as the upper microcomputer communicates with bottom-level block through serial communication interface (SCI). The top-level block is responsible for the signal processing of upper microcomputer and the communicating with bottom-level block. The bottom-level block consists of DSP-CPLD servo controller, SCI circuit, motor driver, and so forth, and it is responsible for the signal processing of torque sensors, position sensors, and magnetoelectric encoders. Moreover, it is responsible for controlling the pulses and directing signals to drive servo motors. The dexterous hand control system can be shown as in Figure 2.\n\n##### 3.2. Mathematical Model for the Index Finger\n\nTaking the single multijoint finger as an example, the equation of DC servo drive motor on armature loop can be introduced as follows: where is the armature control voltage, is the armature resistance, is the instantaneous current in coil, is the armature inductance, is the back electromotive force produced by coil, , is the motor angle, and is the voltage feedback coefficient.\n\nBased on torque equations of DC servo motor, the torque equation of single multijoint finger can be expressed as follows: where is drive torque of motor, is the motor moment coefficient, is the equivalent moment of inertia of motor, is the viscosity damp coefficient of motor, is the load torque, , is the equivalent moment of inertia of the finger, is the viscosity damp coefficient of the finger, and is the distal phalanx. Among them, the relationship between and is expressed as , where is the general transmission ratio.\n\nIn the synthesis, ignoring reducer clearance and transmission error of mechanism, the position transfer function of control voltage and distal phalanx angle can be expressed as follows: where , , and .\n\nIn the single multijoint finger system, the Faulhaber 1319006SR DC servo motor has some important parameters; that is,  mNm/rpm,  mNm/A,  Ω, H, and  gcm2. The speed control system consists of a gearbox and one-grade bevel gear, and the gearbox ratio is 415 : 1 and the bevel gears ratio is 2 : 1. Moreover, by using coupling four-bar linkage mechanism, the three phalanxes’ transmission ratio is kept exactly 1 : 1 : 1 over the whole movement range. The hand material is ABS; is set to  gcm2 and is set to  mNm/rpm. According to the parameters, we can obtain the transfer function as follows:\n\n#### 4. GA-Fuzzy-Immune PID Controller\n\n##### 4.1. Immune-Based PID Controller Design\n\nAs a general rule in the discrete-time domain, traditional increment PID controller can be expressed as follows: where , is the proportional gain, is the integral time constant, is the derivative time constant, , , is the systematic deviation between reference input and system output, is the sampling period, and is the control signal.\n\nIn general, differential signal can be used to improve the system dynamic characteristics, which is likely to cause the problem of high frequency interference to the control system. Using low pass filter in control algorithm can bring significant improvements in system performance and its transfer function is , where is a filter coefficient. The transfer function of PID controller with incomplete derivation can be expressed as follows:\n\nIn the discrete-time domain, differential equation of PID controller with incomplete derivation can be written as follows:\n\nThen, differentiation element can be expressed as follows:\n\nThus, we can obtain the differential equation of differentiation element as follows: where and is the initial value of differentiation element. is set equal to a constant. is the th power of and is the ()th power of .\n\nSubstituting formula (10) into (8), the PID controller with incomplete derivation can be obtained:\n\nAs a kind of control system, biological immune system has very strong robustness and self-adapted ability even when encountering strong disturbances and uncertain conditions. For invasion by a foreign antigen, it can produce corresponding antibodies to resist the antigen. A series of biological reactions could be carried out after combining antigens with antibodies and it eliminates antigen under the function of phagocyte or special enzymes. The immune system consists of lymphocyte and antibody. The lymphocyte consists of B cell produced from marrow and T cell produced from thymus. T cell includes assistant T cell and restrained T cell . When cell obtains signal from the antigen, it would transmit the information to and , and then B cell produces corresponding antibodies to resist the antigen with the stimulation by and . The immunity feedback control mechanism is shown in Figure 3.\n\nAccording to immunity feedback control mechanism, all of the received simulations of B cell can be obtained: where is the th generation output of cell which receives antigen presenting cell activation, is the th generation restrain action on B cell by cell, is the th generation antigen amount, is enhancing factor of cell, is inhibitory factor of cell, and . is a nonlinear function, which describes the immunity result that B-cell antibody and antigen act on each other and relate with the amount of B cell.\n\nIn this paper, we try to apply body’s immune mechanism to the ABS-I position controller to overcome the weakness of traditional PID controller. For a PID controller, we assume that position error on the th sampling period represents ; the position controller output on the th sampling period represents . Therefore, .\n\nIn the synthesis, the immune PID controller with incomplete derivation can be obtained: where () is used to improve the response time and () can enhance the stability of control system. Therefore, the method for setting the parameters reasonably plays an important role in the improved PID controller with higher precision, faster response, and better robustness.\n\n##### 4.2. Parameters Optimization through Fuzzy Theory and Genetic Algorithm\n\nThe performance of improved PID controller largely depends on (), (), and . As can be seen from the above formulas, namely, (15), (16), (17), and (18), because of the nonlinear characteristics of function , a fuzzy inference algorithm is used to optimize the function . Because of the difficulty to obtain () and () based on analysis method, an improved genetic algorithm is proposed to solve this problem. The framework of GA-fuzzy-immune PID position controller with incomplete derivation can be built up as shown in Figure 4.\n\nAccording to the immune feedback mechanism of biological systems , four stages in the autoimmune reaction can be summarized as follows.\n\nIn the initial stage, the antigen amount is higher and the antibody amount is expected to increase quickly, so the cell should be suppressed to produce. After a period of immunization, the restrained action on cell would decrease; in other words, the antibody should not increase continually. When most of antigens have been eliminated, should increase quickly to restrain B cell and the production of antibody. Finally, when all of the antigens have been eliminated, both of antigen and antibody amount should keep stable till the immunization end.\n\nIn the controller, two inputs of and fuzzy subsets are all selected as , and the output of fuzzy subset is all selected as , where stands for negative big, stands for negative middle, stands for negative small, stands for zero, stands for positive small, stands for positive middle, and stands for positive big. According to the above immunologic processes, 16 fuzzy rules are proposed to compute the nonlinear function , as shown in Table 1. The fuzzy discourse domain of is defined as , the fuzzy discourse domain of is defined as , and the fuzzy discourse domain of is defined as .\n\nAs a frequently used membership function, Gaussian membership function has the feature of good smoothness and can express the concept of fuzzy language more exactly; thus, it is applied for the proposed controller. Figure 5 shows the membership functions for , Figure 6 shows the membership functions for , and Figure 7 shows the membership functions for .\n\nThe immune PID parameters () and () are tuned and optimized by an improved genetic algorithm. Traditional genetic algorithm in solving the problem, especially the complex problems, is easily trapped in the local optimum and appeared premature convergence. To settle this question, some improvements of traditional genetic algorithm are presented. The overall process can be described as follows.\n\nStep 1 (coding). As a general coding method for GA, binary coding is used widely due to the simple processes of coding and decoding and easy operation of crossover and mutation. However, for a multivariable optimization problem, the string of binary gene is too long to result in lower search efficiency. In order to solve this problem, float-point genes are used in the optimization model. With this strategy, the number of variables is not limited; coding and decoding are not needed. Furthermore, the precision and efficiency can be increased and the calculation speed is high. A mixed coding program is presented in the improved GA. During the initial stage, binary coding is adopted to quickly search for the area with excellent properties. In the later stage, float-point coding is used to improve the precision.\n\nStep 2 (generating initial population). According to experience, six empirical coefficients (,  ,  ,  ,   and ) are determined and initial population can be generated around the coefficients. By this generating method, the searching space is reduced and the operating rate is increased.\n\nStep 3 (selecting fitness function). In an evolution search process, an appropriate fitness function plays an important role in parameter optimization. In order to obtain satisfactory dynamic characteristics of the transition process, the integral of time multiplied absolute value of error (ITAE) is also provided as a comprehensive performance index, and the square of control input is introduced to prevent the control energy from growing too big. The comprehensive performance index function can be calculated as follows: where , , , and are weights and , is the system error, is the output of controller, and is the rising time. To avoid overshoot, the introduction of punitive function is essential in the function.\nThen, the fitness function can be defined as follows: where is a constant and can be set equal to 1 in this paper, is a small positive number to prevent from becoming equal to zero, and .\n\nStep 4 (selection). Selection is a very important step in the criteria of “survival of the fittest” that means selecting the superior individual and eliminating the inferior one from a population. For genetic algorithm, an individual is selected as a parent according to its fitness. In rank-based selection algorithm, all individuals of every generation are ranked in order of increasing fitness value. The survival probability of the th individual is , where is evolutionary pressure.\n\nStep 5 (crossover and mutation). Because of its strong global search capability, crossover operator of GA can be regarded as the main operator, and due to its local search capability, mutation operator can be regarded as an auxiliary operator. Self-adaptive crossover and mutation operators are proposed in this paper; in other words, crossover probabilities and mutation probabilities are automatically adjusted with the addition of evolutionary generations. In the initial stage, a larger and a smaller can effectively accelerate convergence velocity of iteration; however, in the later stage, a smaller and a larger would avoid local optimal solution. The formulas of and are given as follows: where is the generation number of heredity, , is the maximum generation number, is the crossover probability of first generation, and is the mutation probability of first generation.\nAccording to these operators, the and of best individuals are not equal to zero, where and , so the performance of excellent individual would not be in a circle due to the and being too small or equal to zero. To protect excellent individuals of each generation, the elitist strategy was applied in GA to improve the convergence and optimization results; thus, the best individual would be copied directly into next generation.\n\n#### 5. A Simulation Example\n\nIn order to verify the performance of proposed GA-fuzzy-immune PID controller, a simulation example is provided in this section and the parameters are illustrated as follows.\n\n, , , and . The population size is set to 50, is set to 100, is set to 0.9, is set to 0.01, is set to 9, and sampling time is set to 1 ms.\n\nIn order to indicate the comparison with other controllers, fuzzy PID, immune PID, fuzzy-immune PID, and real-coded GA PID simulations are carried out. The configurations of simulation environment for these controllers were uniform. In immune PID and fuzzy-immune PID, , , , , , and , and in immune PID. In fuzzy PID and real-coded GA PID, , , and . Other parameters are the same as GA-fuzzy-immune PID.\n\nThe input of robot dexterous hand system is a unit step signal and the simulation time is 1 s. The unit step responses of this system are shown in Figure 8. The first curve is response obtained with fuzzy inference, the second curve is response obtained with immune algorithm, the third curve is response obtained with fuzzy-immune inference (F-I), the fourth curve is response obtained with real-coded GA, and the fifth curve is response obtained through integration of improved genetic algorithm and fuzzy-immune inference (GA-F-I).\n\nThe PID parameters and performance indexes of the five control methods are shown in Table 2. The proposed controller parameters can be calculated by improved GA and fuzzy inference:\n\nCompared with other four methods, the overshoot   based on GA-F-I PID controller with incomplete derivation is decreased from 36.30% to 0. The settling time is reduced from 0.592 s to 0.362 s. The rising time is reduced from 0.393 s to 0.226 s. Although the rising time is not the best, the nonovershoot and shortest settling time can be achieved by the proposed PID controller.\n\n#### 6. Conclusions and Future Works\n\nIn this paper, a GA-fuzzy-immune PID controller was designed to improve the performance of robot dexterous hand. The control system of a robot dexterous hand and mathematical model of an index finger were presented. In order to improve the characteristics of proposed controller, immune mechanism, genetic algorithm, and fuzzy inference were applied. Finally, a simulation experiment was carried out and the results showed that the designed controller was ideal.\n\nIn future studies, the authors plan to investigate multifinger coordination control system. Furthermore, more intelligent control algorithms for multifinger coordination control system are worth further study for the authors.\n\n#### Conflict of Interests\n\nThe authors declare that there is no conflict of interests regarding the publication of this paper.\n\n#### Acknowledgments\n\nThe support of Fundamental Research Funds for the Central Universities (no. 2014QNA38) and the Priority Academic Program Development of Jiangsu Higher Education Institutions in carrying out this research are gratefully acknowledged." ]

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[ "", null, "# Greater Than Less Than Worksheets\n\nIn math, we compare two numbers and use a symbol between two determine which of the numbers is greater or lesser than the other. The best way to help kids understand the concept is through math worksheets for kids like greater than less than worksheets for practice.\n\nThe greater than symbol is >. Greater than and less than symbols are used to compare expressions and numbers. For example, 8 > 6 and is read as ‘8 is greater than 6’. And, the less than symbol is denoted as, <. Two other comparison symbols are represented as (greater than or equal to) and (less than or equal to). Help your child practice comparing numbers using free printable greater than less than worksheets.\n\n## Printable Greater Than Less Than Worksheets For Kids\n\nSolving greater than and less than worksheets also improve the child’s fine and gross motor skills, decision making, problem solving, comparing and logical reasoning abilities. Solving worksheets for kids also helps children grasp the concept and remember it too. Here is a list of kindergarten greater than less than worksheets for the little ones to practice. Here are a few kindergarten greater than less than worksheets for kids.\n\n### Count and Choose Greater than or Less than Symbol Worksheet\n\nHelp your children learn and practice worksheet on greater than or less than problems. Ask kids to compare the images and circle the symbols of greater than or less than on the worksheet given below. These visually appealing worksheets attracts children’s attention to learn symbols in a creative way.\n\n### Draw to Show Which Number is Greater than or Less than Worksheet\n\nApart from identification, kids must learn to draw symbols of greater than or less than using the worksheet given below. In this worksheet, kids need to compare the numbers and draw the symbols in the space provided. These worksheet help children learn to compare numbers effectively.\n\n## List of Greater Than Less Than Worksheets\n\nParents and teachers can give kids greater than and less than worksheets to kids and help them solve each problem. Worksheets are a great way to teach the greater than and less than concepts to little minds. Also, introducing these concepts must be done in a step by step method rather than teaching them everything at once.\n\nKids understand quickly when they don’t feel the stress of learning. Hence, tutors can engage them in Problem Solving For Kids, available at Osmo. Comprehending math concepts might be pretty challenging for the children during the initial stages of learning. But, with a regular practice of worksheets, they learn and remember the concepts. Here are the greater than and less than worksheets for kids.\n\n### Greater than Less than Worksheets for Kindergarten\n\nAs kindergarten is the first stage in a child’s education, it is essential to teach them the basics. Once they have a solid understanding of math concepts like addition, subtraction, multiplication, division and greater than or lesser than, they can be provided with free printable greater than less than worksheets. Greater than less than worksheets encourage kids to learn and understand independently. In addition, worksheets help kids to revise and remember the lessons learned during class hours. Here are the greater than less than worksheets for kindergarten. Also, refer to Kindergarten Math Games.\n\n### Greater than Less than Equal to Worksheets\n\nOnce the kids have finished learning the difference between greater and less than, it is time to teach them greater than less than equal to concept. Including coloring activities, place value games for kids and other fun educational games allow the little minds to relax and learn efficiently. Children focus when they don’t have the pressure of learning. Hence, it is essential to engage children in practicing worksheets and games. Here is the greater than less than equal to worksheet for the little ones to practice.\n\n## Activities that Help in Learning Greater Than and Less Than Worksheets\n\nComparing numbers is not boring when fun activities are a part of learning sessions. Allowing little ones to regularly practice the greater than or less than worksheets can be helpful for them to learn this concept. By including math games for kids that can engage them in learning alongside having fun is a great idea. Hence, engage little learners in the activities that help in learning greater than less than concept. Here are some activities mentioned below\n\n• Hands-on Symbolic activities: Kids can associate with the letter ‘V’ as a greater than symbol in this activity. Parents and teachers can give the little ones alphabet stickers or stencils for math group or individual activities. Also, children can use straws to make greater than or less than symbols. As the straws are pretty flexible, it makes it easy for kids to bend them and create the < or > shapes. Once symbols are made, make symbols used on the greater than less than worksheet for practice. Then, compare two numbers using the greater than or less than symbol created with the straw.\n• Scavenger Hunt: Now, this is one of the most interesting and exciting activities for kids. Search the magazines and newspapers for numbers. And, another great place to get numbers is in the sales ads that are printed in the newspapers. Finally, cut them and use those numbers in a scavenger hunt activity. Ask kids to mark the greater than less than numbers for their understanding of the concept on the worksheet.\n• Random numbers: Make a greater than less than worksheet of different numbers printed or written in bold. Like, 21 17, 7 3, etc., Now give the little ones this worksheet of random numbers and ask them to analyze the numbers and mark the greater than or less than symbols. The first child who finishes this can be declared as a winner.\n• Alligator Teeth: This is a fun and exciting game for little learners. Tutors can draw alligator teeth on every symbol. Then, let them know that the alligator always ‘eats’ the biggest number. Next, draw an instance of a number comparison on the paper or board, such as 3 < 7. Using the interactive boards, play Greater Than or Less Than 1 to 20 with the little minds.\n• Spin: Create one, two, or three digit numbers by flipping over number flashcards or playing cards. Make a note of the number. Now, spin to learn which symbol to use: > , <  or =. Then, write down the symbol. Later, think of a number that completes the comparison and make a note of it.\n• Spot the number: Make opportunities for kids to practice greater than less than worksheets by spotting the numbers in the house. For instance, you can ask kids to explore the house and check if there are any comparing numbers written anywhere in the house. If yes, ask them to write the numbers on the worksheet and compare using the greater than or less than symbols. It is the best way to introduce the concept of symbols to children. It help them write the symbols accurately while solving mathematical problems.\n• Count the number of images: This is a visually appealing activity for children where they can count the number of images and mark the greater than or less than symbols. You can include different themes for the activity such as food, animals, toys, etc. Ask them to count the number of items and mark the symbols on the greater than less than worksheet provided. This hands-on activity help them stay focused and active throughout their learning process.\n\nAlso, explore One Minute Games for Kids.\n\n## Benefits of Greater Than Less Than Worksheet With Answer\n\nSome of the benefits of kindergarten greater than less than worksheet are mentioned below:\n\n• Develops mathematical skills in children.\n• Improves understanding of numbers and their order effectively.\n• Increases academic performance of children and help them score good marks in related concepts.\n• Enables quick and accurate mathematical calculations in children\n• Develops fine motor skills in children.\n• Enables children to compare integers, fractions and decimals using the worksheets.\n• Enables children to understand the concept of difference between numbers clearly.\n• Develops problem-solving skills and logical reasoning skills.\n• Boosts children’s confidence to learn and practice greater than or less than worksheets effectively.\n\nOsmo has a great collection of STEM Activities for Kids and Activities For Kids At Home. These activities are a great way to teach kids numbers. Make sure to visit Osmo’s website to learn more.\n\n## Frequently Asked Questions on Greater Than Less Than Worksheets\n\n### What are the types of Greater Than Less Than Worksheets?\n\nThe types of Greater Than Less Than Worksheets are Greater than Less than Worksheets for Kindergarten, Greater than Less than Equal to Worksheets, Greater than Less than Equal to Worksheets for preschoolers, etc.\n\n### What are the activities that help kids to learn Greater Than Less Than Worksheets?\n\nThe activities that help kids to learn Greater Than Less Than Worksheets are, number hunt games, scavenger hunts, spotting the missing numbers, counting the images or objects on worksheets, etc." ]

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[ "## Manipulate altitudes (height)\n\nThe height filter allows the correction of altitude values. At least one popular gps logger does store the ellipsoidal height (sum of the height above mean see level and the height of the geoid above the WGS84 ellipsoid) instead of the height above sea level, as it can be found on maps. The height filter allows for the correction of these altitude values. This filter supports two options: `wgs84tomsl` and `add`. At least one of these options is required, both can be combined.\n\nExample 4.6.  This option subtracts the WGS84 geoid height from every altitude. For GPS receivers like the iBlue747 the result is the height above mean see level.\n\n` gpsbabel -i gpx -f in.gpx -x height,wgs84tomsl -o gpx -F out.gpx`\n\nThe coordinates and altitude vales must be based an the WGS84 ellipsoid for this option to produce sensible results\n\nExample 4.7.  This options adds a constant value to every altitude.\n\n` gpsbabel -i gpx -f in.gpx -x height,add=10.2f -o gpx -F out.gpx`\n\nYou can specify negative numbers to subtract the value. If no unit is specified meters are assumed. For feet you can attach an \"f\" to the value.\n\nAdds a constant value to every altitude (meter, append \"f\" (x.xxf) for feet).\n\nAdds a constant value to every altitude. You can specify negative numbers to subtract the value.\n\nIf no unit is specified, (m)eters are assumed. You can override this by attaching a \"f\" for feet to the number.\n\n### wgs84tomsl option\n\nConverts WGS84 ellipsoidal height to orthometric height (MSL).\n\nSubtracts the WGS84 geoid height from every altitude.\n\nFor GPS receivers like the iBlue747 this corrects the logged altitudes to height above mean sea level." ]

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[ "# Number 14207536242\n\n### Properties of number 14207536242\n\nCross Sum:\nFactorization:\n2 * 3 * 3 * 3 * 3 * 17 * 37 * 139429\nDivisors:\nCount of divisors:\nSum of divisors:\nPrime number?\nNo\nFibonacci number?\nNo\nBell Number?\nNo\nCatalan Number?\nNo\nBase 3 (Ternary):\nBase 4 (Quaternary):\nBase 5 (Quintal):\nBase 8 (Octal):\n34ed5cc72\nBase 32:\nd7dbj3i\nsin(14207536242)\n0.43457395362468\ncos(14207536242)\n0.9006361523007\ntan(14207536242)\n0.48251888680523\nln(14207536242)\n23.377038382039\nlg(14207536242)\n10.15251877256\nsqrt(14207536242)\n119195.3700527\nSquare(14207536242)\n2.0185408606774E+20\n\n### Number Look Up\n\nLook Up\n\n14207536242 (fourteen billion two hundred seven million five hundred thirty-six thousand two hundred forty-two) is a very special figure. The cross sum of 14207536242 is 36. If you factorisate 14207536242 you will get these result 2 * 3 * 3 * 3 * 3 * 17 * 37 * 139429. 14207536242 has 80 divisors ( 1, 2, 3, 6, 9, 17, 18, 27, 34, 37, 51, 54, 74, 81, 102, 111, 153, 162, 222, 306, 333, 459, 629, 666, 918, 999, 1258, 1377, 1887, 1998, 2754, 2997, 3774, 5661, 5994, 11322, 16983, 33966, 50949, 101898, 139429, 278858, 418287, 836574, 1254861, 2370293, 2509722, 3764583, 4740586, 5158873, 7110879, 7529166, 10317746, 11293749, 14221758, 15476619, 21332637, 22587498, 30953238, 42665274, 46429857, 63997911, 87700841, 92859714, 127995822, 139289571, 175401682, 191993733, 263102523, 278579142, 383987466, 417868713, 526205046, 789307569, 835737426, 1578615138, 2367922707, 4735845414, 7103768121, 14207536242 ) whith a sum of 34619353560. The number 14207536242 is not a prime number. The figure 14207536242 is not a fibonacci number. 14207536242 is not a Bell Number. The figure 14207536242 is not a Catalan Number. The convertion of 14207536242 to base 2 (Binary) is 1101001110110101011100110001110010. The convertion of 14207536242 to base 3 (Ternary) is 1100200010222121210000. The convertion of 14207536242 to base 4 (Quaternary) is 31032311130301302. The convertion of 14207536242 to base 5 (Quintal) is 213044112124432. The convertion of 14207536242 to base 8 (Octal) is 151665346162. The convertion of 14207536242 to base 16 (Hexadecimal) is 34ed5cc72. The convertion of 14207536242 to base 32 is d7dbj3i. The sine of the number 14207536242 is 0.43457395362468. The cosine of the number 14207536242 is 0.9006361523007. The tangent of 14207536242 is 0.48251888680523. The root of 14207536242 is 119195.3700527.\nIf you square 14207536242 you will get the following result 2.0185408606774E+20. The natural logarithm of 14207536242 is 23.377038382039 and the decimal logarithm is 10.15251877256. You should now know that 14207536242 is very special figure!" ]

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[ "", null, "## Thursday, May 16, 2019\n\n### Lecture Notes on Control System Engineering-II (3-1-0)\n\nSyllabus:-\nMODULE-I (10 HOURS)\nState Variable Analysis and Design: Introduction, Concepts of State, Sate Variables and State Model, State Models for Linear Continuous-Time Systems, State Variables and Linear Discrete-Time Systems, Diagonalization, Solution of State Equations, Concepts of Controllability and Observability, Pole Placement by State Feedback, Observer based state feedback control.\n\nMODULE-II (10 HOURS)\nIntroduction of Design: The Design Problem, Preliminary Considerations of Classical Design, Realization of Basic Compensators, Cascade Compensation in Time Domain(Reshaping the Root Locus), Cascade Compensation in Frequency Domain(Reshaping the Bode Plot), Introduction to Feedback Compensation and Robust Control System Design. Digital Control Systems: Advantages and disadvantages of Digital Control, Representation of Sampled process, The z-transform, The z-transfer Function. Transfer function Models and dynamic response of Sampled-data closed loop Control Systems, The Z and S domain Relationship, Stability Analysis.\n\nMODULE-III (10 HOURS)\nNonlinear Systems: Introduction, Common Physical Non-linearities, The Phase-plane Method: Basic Concepts, Singular Points, Stability of Nonlinear System, Construction of Phase-trajectories, The Describing Function Method: Basic Concepts, Derivation of Describing Functions, Stability analysis by Describing Function Method, Jump Resonance, Signal Stabilization. Liapunov‟s Stability Analysis: Introduction, Liapunov‟s Stability Criterion, The Direct Method of Liapunov and the Linear System, Methods of Constructing Liapunov Functions for Nonlinear Systems, Popov‟s Criterion.\n\nMODULE-IV (10 HOURS)\nOptimal Control Systems: Introduction, Parameter Optimization: Servomechanisms, Optimal Control Problems: State Variable Approach, The State Regulator Problem, The Infinite-time Regulator Problem, The Output regulator and the Tracking Problems, Parameter Optimization: Regulators, Introduction to Adaptive Control." ]

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[ "# Examples¶\n\nTNG files can be read using the `TNGFileIterator` class as a file handle, which supports use as a context manager.\n\nThe TNGFileIterator has attributes related to the trajectory metadata, such as the number of integrator steps, the number of steps with data, the block_ids available at each step, and the stride at which each block is written.\n\nThe TNGFileIterator returns one frame at a time, which is accessed from the `TNGFileIterator.current_integrator_step` attribute or as part of any slicing or indexing operation. A NumPy array of the right size and datatype must then be provided to a getter method for the data to be read into. The required datatype is dictated by what type of block is being read. Supported datatypes are:\n\n• TNG_INT_DATA : np.int64\n\n• TNG_FLOAT_DATA : np.float32\n\n• TNG_DOUBLE_DATA : np.float64\n\nHelper methods are provided to create `np.ndarray` instances of the right shape and datatype for a particular block in `TNGFileIterator.make_ndarray_for_block_from_name` and `TNGFileIterator.make_ndarray_for_block_from_name`.\n\nAn example of how to read positions and box vectors from a TNG file is shown below:\n\n```import pytng\nimport numpy as np\n\nwith pytng.TNGFileIterator(\"traj.tng\", 'r') as tng:\n\n# make a numpy array to hold the data using helper function\n# this array will then be updated in-place\n\npositions = tng.make_ndarray_for_block_from_name(\"TNG_TRAJ_POSITIONS\")\nbox_vec = tng.make_ndarray_for_block_from_name(\"TNG_TRAJ_BOX_SHAPE\")\n\n# the TNG API uses regular strides for data deposition, here we check\n# that the strides for positions and box_vectors are the same\n# and then iterate over all timesteps with this data\n# len(tng) is the total number of steps in the file\n\nassert (tng.block_strides[\"TNG_TRAJ_POSITIONS\"] == tng.block_strides[\"TNG_TRAJ_BOX_SHAPE\"])\n\nfor ts in tng[0:len(tng):tng.block_strides[\"TNG_TRAJ_POSITIONS\"]]:\n# read the integrator timestep, modifying the current_integrator_step\n# which is returned as ts\n\n# get the data from the requested block by supplying NumPy array which\n# is updated in-place or returned\n\n# update in place or return by value\nts.get_positions(positions)\n# positions = ts.get_positions(positions) is equivalent\n\n# you can check if the last read was successful (contained data) easily\nraise IOError(\"No position data at this timestep\")\n\nts.get_box(box_vec)\n# box_vec = ts.get_box(box_vec) is equivalent\n\n# you can check if the last read was successful (contained data) easily\nraise IOError(\"No box data at this timestep\")\n```\n\nIt is also possible to slice and index the file object to select particular frames individually:\n\n```import pytng\nimport numpy as np\n\nwith pytng.TNGFileIterator('traj.tng', 'r') as tng:\npositions = tng.make_ndarray_for_block_from_name(\"TNG_TRAJ_POSITIONS\")\nbox_vec = tng.make_ndarray_for_block_from_name(\"TNG_TRAJ_BOX_SHAPE\")\npositions = tng.get_positions(positions)\nbox_vec = tng.get_box(box_vec)\n```\n\nIf the step to read is not on the stride of the requested datatype, the NumPy array will be returned filled with np.nan. A contrived example of this is given below:\n\n```import pytng\nimport numpy as np\n\nwith pytng.TNGFileIterator(\"traj.tng\", 'r') as tng:\n# make array for positions\npositions = tng.make_ndarray_for_block_from_name(\"TNG_TRAJ_POSITIONS\")\n\n# choose a step\nstep = 42\n\n# check that we are off stride (stride%step != 0)\nassert(tng.block_strides[\"TNG_TRAJ_POSITIONS\"]%step != 0 )\n\n# slice a single timestep\nts = tng[step]\n\n# get the data, which will be returned full of np.nan\nts.get_positions(positions)\n\n# the read_success property will indicate that there was no data found\n# when the getter was called\n\n# but we can also double check that the read was blank\nis_blank_read = np.all(np.isnan(positions)) # this will be true\n```\n\nAvailable data blocks are listed at the end of this documentation. Common blocks for which there are getter methods include:\n\n• positions : `TNGFileIterator.get_positions`\n\n• box vectors : `TNGFileIterator.get_box`\n\n• forces : `TNGFileIterator.get_forces`\n\n• velocities : `TNGFileIterator.get_velocities`\n\nOther blocks can be accessed using the `TNGCurrentIntegratorStep.get_blockid` method, where the block id needs to be supplied and can be accessed from the `TNGFileIterator.block_ids` attribute. An example of this is shown below:\n\n```import pytng\nimport numpy as np\n\nwith pytng.TNGFileIterator(\"traj.tng\", 'r') as tng:\n\n# make array for the GMX potential energy block\nEpot = tng.make_ndarray_for_block_from_name(\"TNG_GMX_ENERGY_POTENTIAL\")\n\n# get the block id for the GMX potential energy block\nEpot_block_id = tng.block_ids[\"TNG_GMX_ENERGY_POTENTIAL\"]\n\n# get the block data for frame 0 with get_blockid\ntng.get_blockid[Epot_block_id]\n```" ]

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[ "index 0006fa8..525e9a7 100644 (file)\n@@ -1,11 +1,8 @@\n/*  This file is part of libDAI - http://www.libdai.org/\n*\n- *  libDAI is licensed under the terms of the GNU General Public License version\n- *  2, or (at your option) any later version. libDAI is distributed without any\n- *  warranty. See the file COPYING for more details.\n+ *  Copyright (c) 2006-2011, The libDAI authors. All rights reserved.\n*\n- *  Copyright (C) 2006-2009  Joris Mooij  [joris dot mooij at libdai dot org]\n- *  Copyright (C) 2006-2007  Radboud University Nijmegen, The Netherlands\n+ *  Use of this source code is governed by a BSD-style license that can be found in the LICENSE file.\n*/\n\n@@ -30,20 +27,20 @@ namespace dai {\nclass Region : public VarSet {\nprivate:\n/// Counting number\n-        Real          _c;\n+        Real _c;\n\npublic:\n/// Default constructor\nRegion() : VarSet(), _c(1.0) {}\n\n/// Construct from a set of variables and a counting number\n-        Region( const VarSet &x, Real c ) : VarSet(x), _c(c) {}\n+        Region( const VarSetx, Real c ) : VarSet(x), _c(c) {}\n\n/// Returns constant reference to counting number\n-        const Real & c() const { return _c; }\n+        const Real& c() const { return _c; }\n\n/// Returns reference to counting number\n-        Real & c() { return _c; }\n+        Real& c() { return _c; }\n};\n\n@@ -58,13 +55,13 @@ class FRegion : public Factor {\nFRegion() : Factor(), _c(1.0) {}\n\n/// Constructs from a factor and a counting number\n-        FRegion( const Factor & x, Real c ) : Factor(x), _c(c) {}\n+        FRegion( const Factor& x, Real c ) : Factor(x), _c(c) {}\n\n/// Returns constant reference to counting number\n-        const Real & c() const { return _c; }\n+        const Real& c() const { return _c; }\n\n/// Returns reference to counting number\n-        Real & c() { return _c; }\n+        Real& c() { return _c; }\n};\n\n@@ -83,6 +80,13 @@ class FRegion : public Factor {\n*\n*  Each factor in the factor graph belongs to an outer region; normally, the factor contents\n*  of an outer region would be the product of all the factors that belong to that region.\n+ *  \\idea Generalize the definition of region graphs to the one given in [\\ref YFW05], i.e., replace\n+ *  the current implementation which uses a BipartiteGraph with one that uses a DAG.\n+ *  \\idea The outer regions are products of factors; right now, this product is constantly cached:\n+ *  changing one factor results in an update of all relevant outer regions. This may not be the most\n+ *  efficient approach; an alternative would be to only precompute the factor products at the start\n+ *  of an inference algorithm - e.g., in init(). This has the additional advantage that FactorGraph\n+ e  can offer write access to its factors.\n*/\nclass RegionGraph : public FactorGraph {\nprotected:\n@@ -142,7 +146,7 @@ class RegionGraph : public FactorGraph {\nvirtual RegionGraph* clone() const { return new RegionGraph(*this); }\n//@}\n\n-    /// \\name Queries\n+    /// \\name Accessors and mutators\n//@{\n/// Returns number of outer regions\nsize_t nrORs() const { return _ORs.size(); }\n@@ -180,9 +184,20 @@ class RegionGraph : public FactorGraph {\n\n/// Returns constant reference to the neighbors of outer region \\a alpha\nconst Neighbors& nbOR( size_t alpha ) const { return _G.nb1(alpha); }\n+\n/// Returns constant reference to the neighbors of inner region \\a beta\nconst Neighbors& nbIR( size_t beta ) const { return _G.nb2(beta); }\n\n+        /// Returns DAG structure of the region graph\n+        /** \\note Currently, the DAG is implemented as a BipartiteGraph; the nodes of\n+         *  type 1 are the outer regions, the nodes of type 2 the inner regions, and\n+         *  edges correspond with arrows from nodes of type 1 to type 2.\n+         */\n+        const BipartiteGraph& DAG() const { return _G; }\n+    //@}\n+\n+    /// \\name Queries\n+    //@{\n/// Check whether the counting numbers are valid\n/** Counting numbers are said to be (variable) valid if for each variable \\f$x\\f$,\n*    \\f[\\sum_{\\alpha \\ni x} c_\\alpha + \\sum_{\\beta \\ni x} c_\\beta = 1\\f]\n@@ -197,7 +212,7 @@ class RegionGraph : public FactorGraph {\n/// Set the content of the \\a I 'th factor and make a backup of its old content if \\a backup == \\c true\nvirtual void setFactor( size_t I, const Factor& newFactor, bool backup = false ) {\nFactorGraph::setFactor( I, newFactor, backup );\n-            RecomputeOR( I );\n+            recomputeOR( I );\n}\n\n/// Set the contents of all factors as specified by \\a facs and make a backup of the old contents if \\a backup == \\c true\n@@ -206,23 +221,58 @@ class RegionGraph : public FactorGraph {\nVarSet ns;\nfor( std::map<size_t, Factor>::const_iterator fac = facs.begin(); fac != facs.end(); fac++ )\nns |= fac->second.vars();\n-            RecomputeORs( ns );\n+            recomputeORs( ns );\n+        }\n+    //@}\n+\n+    /// \\name Input/output\n+    //@{\n+        /// Reads a region graph from a file\n+        /** \\note Not implemented yet\n+         */\n+        virtual void ReadFromFile( const char* /*filename*/ ) {\n+            DAI_THROW(NOT_IMPLEMENTED);\n+        }\n+\n+        /// Writes a factor graph to a file\n+        /** \\note Not implemented yet\n+         */\n+        virtual void WriteToFile( const char* /*filename*/, size_t /*precision*/=15 ) const {\n+            DAI_THROW(NOT_IMPLEMENTED);\n+        }\n+\n+        /// Writes a RegionGraph to an output stream\n+        friend std::ostream& operator<< ( std::ostream& os, const RegionGraph& rg );\n+\n+        /// Writes a region graph to a GraphViz .dot file\n+        /** \\note Not implemented yet\n+         */\n+        virtual void printDot( std::ostream& /*os*/ ) const {\n+            DAI_THROW(NOT_IMPLEMENTED);\n}\n+    //@}\n+\n+    protected:\n+        /// Helper function for constructors\n+        void construct( const FactorGraph& fg, const std::vector<VarSet>& ors, const std::vector<Region>& irs, const std::vector<std::pair<size_t,size_t> >& edges );\n+\n+        /// Helper function for constructors (CVM style)\n+        void constructCVM( const FactorGraph& fg, const std::vector<VarSet>& cl, size_t verbose=0 );\n\n/// Recompute all outer regions\n/** The factor contents of each outer region is set to the product of the factors belonging to that region.\n*/\n-        void RecomputeORs();\n+        void recomputeORs();\n\n/// Recompute all outer regions involving the variables in \\a vs\n/** The factor contents of each outer region involving at least one of the variables in \\a vs is set to the product of the factors belonging to that region.\n*/\n-        void RecomputeORs( const VarSet& vs );\n+        void recomputeORs( const VarSet& vs );\n\n/// Recompute all outer regions involving factor \\a I\n/** The factor contents of each outer region involving the \\a I 'th factor is set to the product of the factors belonging to that region.\n*/\n-        void RecomputeOR( size_t I );\n+        void recomputeOR( size_t I );\n\n/// Calculates counting numbers of inner regions based upon counting numbers of outer regions\n/** The counting numbers of the inner regions are set using the Moebius inversion formula:\n@@ -231,21 +281,8 @@ class RegionGraph : public FactorGraph {\n*  the partial ordering induced by the subset relation (i.e., a region is a child of another\n*  region if its variables are a subset of the variables of its parent region).\n*/\n-        void calcCountingNumbers();\n-    //@}\n+        void calcCVMCountingNumbers();\n\n-    /// \\name Input/output\n-    //@{\n-        /// Writes a RegionGraph to an output stream\n-        friend std::ostream& operator << ( std::ostream& os, const RegionGraph& rg );\n-    //@}\n-\n-    protected:\n-        /// Helper function for constructors\n-        void construct( const FactorGraph& fg, const std::vector<VarSet>& ors, const std::vector<Region>& irs, const std::vector<std::pair<size_t,size_t> >& edges );\n-\n-        /// Helper function for constructors (CVM style)\n-        void constructCVM( const FactorGraph& fg, const std::vector<VarSet>& cl );\n};" ]

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[ "PHP 7.4.0 alpha 3 Released\n\n# get_object_vars\n\n(PHP 4, PHP 5, PHP 7)\n\nget_object_vars指定したオブジェクトのプロパティを取得する\n\n### 説明\n\nget_object_vars ( object `\\$object` ) : array\n\n`object`\n\nオブジェクトのインスタンス。\n\n### 変更履歴\n\nバージョン 説明\n5.3.0 `object` がオブジェクトではない場合に `NULL` を返すようになりました。 これより前のバージョンでは、`FALSE` を返していました。\n\n### 例\n\n``` <?phpclass foo {    private \\$a;    public \\$b = 1;    public \\$c;    private \\$d;    static \\$e;       public function test() {        var_dump(get_object_vars(\\$this));    }}\\$test = new foo;var_dump(get_object_vars(\\$test));\\$test->test();?> ```\n\n```array(2) {\n[\"b\"]=>\nint(1)\n[\"c\"]=>\nNULL\n}\narray(4) {\n[\"a\"]=>\nNULL\n[\"b\"]=>\nint(1)\n[\"c\"]=>\nNULL\n[\"d\"]=>\nNULL\n}\n```\n\n### 参考", null, "add a note\n\n### User Contributed Notes 38 notes\n\n38\nfmmarzoa at librexpresion dot org\n14 years ago\n``` You can still cast the object to an array to get all its members and see its visibility. Example:<?phpclass Potatoe {    public \\$skin;    protected \\$meat;    private \\$roots;    function __construct ( \\$s, \\$m, \\$r ) {        \\$this->skin = \\$s;        \\$this->meat = \\$m;        \\$this->roots = \\$r;    }}\\$Obj = new Potatoe ( 1, 2, 3 );echo \"<pre>\\n\";echo \"Using get_object_vars:\\n\";\\$vars = get_object_vars ( \\$Obj );print_r ( \\$vars );echo \"\\n\\nUsing array cast:\\n\";\\$Arr = (array)\\$Obj;print_r ( \\$Arr );?>This will returns:Using get_object_vars:Array(    [skin] => 1)Using array cast:Array(    [skin] => 1    [ * meat] => 2    [ Potatoe roots] => 3)As you can see, you can obtain the visibility for each member from this cast. That which seems to be spaces into array keys are '\\0' characters, so the general rule to parse keys seems to be:Public members: member_nameProtected memebers: \\0*\\0member_namePrivate members: \\0Class_name\\0member_nameI've wroten a obj2array function that creates entries without visibility for each key, so you can handle them into the array as it were within the object:<?phpfunction obj2array ( &\\$Instance ) {    \\$clone = (array) \\$Instance;    \\$rtn = array ();    \\$rtn['___SOURCE_KEYS_'] = \\$clone;    while ( list (\\$key, \\$value) = each (\\$clone) ) {        \\$aux = explode (\"\\0\", \\$key);        \\$newkey = \\$aux[count(\\$aux)-1];        \\$rtn[\\$newkey] = &\\$rtn['___SOURCE_KEYS_'][\\$key];    }    return \\$rtn;}?>I've created also a <i>bless</i> function that works similar to Perl's bless, so you can further recast the array converting it in an object of an specific class:<?phpfunction bless ( &\\$Instance, \\$Class ) {    if ( ! (is_array (\\$Instance) ) ) {        return NULL;    }    // First get source keys if available    if ( isset (\\$Instance['___SOURCE_KEYS_'])) {        \\$Instance = \\$Instance['___SOURCE_KEYS_'];    }    // Get serialization data from array    \\$serdata = serialize ( \\$Instance );    list (\\$array_params, \\$array_elems) = explode ('{', \\$serdata, 2);    list (\\$array_tag, \\$array_count) = explode (':', \\$array_params, 3 );    \\$serdata = \"O:\".strlen (\\$Class).\":\\\"\\$Class\\\":\\$array_count:{\".\\$array_elems;    \\$Instance = unserialize ( \\$serdata );    return \\$Instance;}?>With these ones you can do things like:<?phpdefine(\"SFCMS_DIR\", dirname(__FILE__).\"/..\");require_once (SFCMS_DIR.\"/Misc/bless.php\");class Potatoe {    public \\$skin;    protected \\$meat;    private \\$roots;    function __construct ( \\$s, \\$m, \\$r ) {        \\$this->skin = \\$s;        \\$this->meat = \\$m;        \\$this->roots = \\$r;    }    function PrintAll () {        echo \"skin = \".\\$this->skin.\"\\n\";        echo \"meat = \".\\$this->meat.\"\\n\";        echo \"roots = \".\\$this->roots.\"\\n\";    }}\\$Obj = new Potatoe ( 1, 2, 3 );echo \"<pre>\\n\";echo \"Using get_object_vars:\\n\";\\$vars = get_object_vars ( \\$Obj );print_r ( \\$vars );echo \"\\n\\nUsing obj2array func:\\n\";\\$Arr = obj2array(\\$Obj);print_r ( \\$Arr );echo \"\\n\\nSetting all members to 0.\\n\";\\$Arr['skin']=0;\\$Arr['meat']=0;\\$Arr['roots']=0;echo \"Converting the array into an instance of the original class.\\n\";bless ( \\$Arr, Potatoe );if ( is_object (\\$Arr) ) {    echo \"\\\\$Arr is now an object.\\n\";    if ( \\$Arr instanceof Potatoe ) {        echo \"\\\\$Arr is an instance of Potatoe class.\\n\";    }}\\$Arr->PrintAll();?> ```\n16\nananda dot putra at gmail dot com\n13 years ago\n``` Hi all, I just wrote a function which dumps all the object propreties and its associations recursively into an array. Here it is..<?phpfunction object_to_array(\\$obj) {        \\$_arr = is_object(\\$obj) ? get_object_vars(\\$obj) : \\$obj;        foreach (\\$_arr as \\$key => \\$val) {                \\$val = (is_array(\\$val) || is_object(\\$val)) ? object_to_array(\\$val) : \\$val;                \\$arr[\\$key] = \\$val;        }        return \\$arr;}?>Example:You have an object like this:fruitsbasket Object(    [Fruits] => Array        (            => fruits Object                (                    [_name] => Mango                    [_color] => Green                    [_weight] => 10                )            => fruits Object                (                    [_name] => Apple                    [_color] => Red                    [_weight] => 15                )            => fruits Object                (                    [_name] => Grape                    [_color] => Purple                    [_weight] => 5                )        )    [total_weight] => 30)just do:<?php\\$the_array = object_to_array(\\$the_object);print_r(\\$the_array);?>it will produce an array:Array(    [Fruits] => Array        (            => Array                (                    [_name] => Mango                    [_color] => Green                    [_weight] => 10                )            => Array                (                    [_name] => Apple                    [_color] => Red                    [_weight] => 15                )            => Array                (                    [_name] => Grape                    [_color] => Purple                    [_weight] => 5                )        )    [total_weight] => 30)I wish function like this could be usefull for you all. :) ```\n16\noom at oscarotero dot com\n5 years ago\n``` You can use call_user_func() to return public variables from inside the class:class Test {    protected \\$protected;    public \\$public;    private \\$private;    public function getPublicVars () {        return call_user_func('get_object_vars', \\$this);    }}\\$test = new Test();var_dump(\\$test->getPublicVars()); // array(\"public\" => NULL) ```\n7 years ago\n``` It seems like there's no function that determines all the *static* variables of a class. I've come out with this one as I needed it in a project: <?php function get_class_static_vars(\\$object) {      return array_diff(get_class_vars(get_class(\\$object)), get_object_vars(\\$object)); } ?> It relies on an interesting property: the fact that get_object_vars only returns the non-static variables of an object. ```\npardini at gmail dot com\n11 years ago\n``` get_object_vars() has confusing behaviour when called as get_object_vars(\\$this) or similar: since a method inside a class definition can access private vars, apparently so can get_object_vars(), so it returns private vars as well. A simple workaround is to define a method that in itself calls get_object_vars, like:<?phpfunction getPublicObjectVars(\\$obj) {  return get_object_vars(\\$obj);}class Smth {  private \\$notShown = 1;  public \\$shown = 2;  function test() {    \\$vars = get_object_vars(\\$this); // includes 'notShown'    \\$vars = getPublicObjectVars(\\$this); // only 'shown'  }}?> ```\nAnonymous\n14 years ago\n``` actually, it's not entirely true that php5 will only return public members....php5 will return any variable IT HAS ACCESS TOIn other words, if you do a get_class_variables(\\$this) inside a class, you'll get everything - public, private, the whole shebang...really annoying since you can't check to see what's private/public without using reflection ```\nrabatto1 at web dot de\n5 years ago\n``` function to convert object (with children) to an (associative) array ... recusive <?php // --------------------------------------------------------- // ----- object_to_array_recusive --- function (PHP) ------ // -------------------------------------------------------- // -- arg1:  \\$object  =  (PHP Object with Children) // -- arg2:  \\$assoc   =  (TRUE / FALSE) - optional // -- arg3:  \\$empty   =  ('' or NULL) - optional // -------------------------------------------------------- // ----- return: Array from Object --- (associative) ------ // -------------------------------------------------------- function object_to_array_recusive ( \\$object, \\$assoc=1, \\$empty='' ) {     \\$out_arr = array();     \\$assoc = (!empty(\\$assoc)) ? TRUE : FALSE;         if (!empty(\\$object)) {                 \\$arrObj = is_object(\\$object) ? get_object_vars(\\$object) : \\$object;            \\$i=0;         foreach (\\$arrObj as \\$key => \\$val) {             \\$akey = (\\$assoc !== FALSE) ? \\$key : \\$i;               if (is_array(\\$val) || is_object(\\$val)) {                 \\$out_arr[\\$key] = (empty(\\$val)) ? \\$empty : object_to_array_recusive(\\$val);               }               else {                 \\$out_arr[\\$key] = (empty(\\$val)) ? \\$empty : (string)\\$val;               }         \\$i++;         }    }     return \\$out_arr;}// -------------------------------------------------------- // -------------------------------------------------------- ?>Example / Usage: a) return an associative (recusive) array from object \\$new_arr1 = object_to_array_recusive(\\$my_object); // --- or --- object_to_array_recusive(\\$my_object,TRUE); // --- or --- object_to_array_recusive(\\$my_object,1); b) return a numeric  (recusive) array from object (set 2nd argument = FALSE) \\$new_arr2 = object_to_array_recusive(\\$my_object,FALSE); you can pre-set the Array-Value of Empty (Sub-) Objects in 3rd argument (\\$empty) // --- eg: NULL --- object_to_array_recusive(\\$my_object,1,NULL); ```\n@chozilla\n6 years ago\n``` A simple way to call this function within an Object and to only export the *public* params would be to artificially change the scope - for example with a closure in php 5.3: <?php class Example {     public \\$publicSetting = 'public';     protected \\$protectedSetting = 'protected';     private \\$privateSetting = 'private';         public function showEverything()     {         return get_object_vars(\\$this);     }         public function showMyPublicsOnly()     {         \\$me = \\$this;         \\$publics = function() use (\\$me) {             return get_object_vars(\\$me);         };         return \\$publics();     } } ?> ```\nbeat\n4 years ago\n``` If your object contains a reference, beware that you might get references for all object properties in the array values, thus when changing values in the array, they may change the object too (confirmed and not yet fixed PHP bug https://bugs.php.net/bug.php?id=66961 affecting all PHP versions up to at least 5.6.2 and 5.5.18 and 5.4.34).This 10-years old comment tried reporting this: http://php.net/manual/en/function.get-object-vars.php#40515 but its exemple was incomplete. See bug report for example. ```\njozef at mostka dot com\n5 years ago\n``` class A{    private \\$priA;    protected \\$proA;    public \\$pubA;}class B extends A{    private \\$priB;    protected \\$proB;    public \\$pubB;    public function getVars(){        return array_diff_key(get_object_vars(\\$this), get_class_vars(get_parent_class(\\$this)));    }}\\$b = new B();var_dump(\\$b->getVars());array(3) {  [\"priB\"]=>  NULL  [\"proB\"]=>  NULL  [\"pubB\"]=>  NULL} ```\nkuko at webperfection dot net\n6 years ago\n``` get_object_vars(\\$this)php5.3 + it returns only public and protected; NOT private vars ```\nDionisiy\n7 years ago\n``` Note that before PHP 5.3.9 numeric object variables of unserialized object are not public, and get_object_vars() won't return them:https://bugs.php.net/bug.php?id=61774 ```\nmarkus at emedia-solutions-wolf dot de\n16 years ago\n``` Hi,I figured out that in prior version to 4.2 the returned array only contains attributes directly in this class, excluding the derived ones from parentclasses. ```\nbenny at nospam dot com\n9 years ago\n``` Be aware of the fact that this is scope-sensitive. If you're calling this from an objects own method, then private and protected vars will be outputted as well. Call it from outside the object and the result will most likely be what you want to archive. ```\nMarc\n13 years ago\n``` If you want to access all properties (private, protected, public) of a class and his base class(es) from outside the object you can take a look in the code below.You can even reffrence them.Example:<?php// Dummy class to act as parent class.class Dummy{    private        \\$d1 = 1;    protected    \\$d2 = 2;    public        \\$d3 = 3;}// The class to test on.class Test extends Dummy{    private        \\$t1 = 11;    protected    \\$t2 = 12;    public        \\$t3 = 13;}// Instance of the test class.\\$test =& new Test();// The propertynames of the test class and his parent.\\$nameD1 = \"\\0Dummy\\0d1\";    // class Dummy, private      \\$d1\\$nameD2 = \"\\0*\\0d2\";        // class Dummy, protected \\$d2\\$nameD3 = \"d3\";            // class Dummy, public    \\$d3\\$nameT1 = \"\\0Test\\0t1\";        // class Test,  private      \\$t1\\$nameT2 = \"\\0*\\0t2\";        // class Test,  protected \\$t2\\$nameT3 = \"t3\";            // class Test,  public    \\$t3// Printing all members (private, protected, public) of test class and parent.// These are the values at construction.print(\"Original object:\\n\");print(\"\\t\\\\$d1 = \".\\$test->\\$nameD1.\"\\n\");print(\"\\t\\\\$d2 = \".\\$test->\\$nameD2.\"\\n\");print(\"\\t\\\\$d3 = \".\\$test->\\$nameD3.\"\\n\");print(\"\\t\\\\$t1 = \".\\$test->\\$nameT1.\"\\n\");print(\"\\t\\\\$t2 = \".\\$test->\\$nameT2.\"\\n\");print(\"\\t\\\\$t3 = \".\\$test->\\$nameT3.\"\\n\");print(\"\\n\");// Create new values to use as reffrence.\\$varD1 = 31;\\$varD2 = 32;\\$varD3 = 33;\\$varT1 = 41;\\$varT2 = 42;\\$varT3 = 43;// Reffrence these to the class properties.\\$test->\\$nameD1 =& \\$varD1;\\$test->\\$nameD2 =& \\$varD2;\\$test->\\$nameD3 =& \\$varD3;\\$test->\\$nameT1 =& \\$varT1;\\$test->\\$nameT2 =& \\$varT2;\\$test->\\$nameT3 =& \\$varT3;// Printing all members (private, protected, public) of test class and parent.// The values have changed by assigning reffrence to them.print(\"Object Changed by reffrence (1):\\n\");print(\"\\t\\\\$d1 = \".\\$test->\\$nameD1.\"\\n\");print(\"\\t\\\\$d2 = \".\\$test->\\$nameD2.\"\\n\");print(\"\\t\\\\$d3 = \".\\$test->\\$nameD3.\"\\n\");print(\"\\t\\\\$t1 = \".\\$test->\\$nameT1.\"\\n\");print(\"\\t\\\\$t2 = \".\\$test->\\$nameT2.\"\\n\");print(\"\\t\\\\$t3 = \".\\$test->\\$nameT3.\"\\n\");print(\"\\n\");// Change the original values.// This will change the class properties.\\$varD1 = 61;\\$varD1 = 62;\\$varD1 = 63;\\$varT1 = 71;\\$varT1 = 72;\\$varT1 = 73;// Printing all members (private, protected, public) of test class and parent.// The values have changed because the variables \\$varXX have been changed.print(\"Object Changed by reffrence (2):\\n\");print(\"\\t\\\\$d1 = \".\\$test->\\$nameD1.\"\\n\");print(\"\\t\\\\$d2 = \".\\$test->\\$nameD2.\"\\n\");print(\"\\t\\\\$d3 = \".\\$test->\\$nameD3.\"\\n\");print(\"\\t\\\\$t1 = \".\\$test->\\$nameT1.\"\\n\");print(\"\\t\\\\$t2 = \".\\$test->\\$nameT2.\"\\n\");print(\"\\t\\\\$t3 = \".\\$test->\\$nameT3.\"\\n\");print(\"\\n\");// Printing the object using print_r() shows the changes// have been done on the object.print(\"Object Changed (print_r):\\n\");print_r(\\$test);print(\"\\n\");// If you dont now the class propertynames you can get these by casting the// object to an array. The array keys are the names\\$prop = array_keys((array) \\$test);print(\"Getting all class propertynames (print_r)\\n\");print_r(\\$prop);//Result/*Original object:    \\$d1 = 1    \\$d2 = 2    \\$d3 = 3    \\$t1 = 11    \\$t2 = 12    \\$t3 = 13Object Changed by reffrence (1):    \\$d1 = 31    \\$d2 = 32    \\$d3 = 33    \\$t1 = 41    \\$t2 = 42    \\$t3 = 43Object Changed by reffrence (2):    \\$d1 = 63    \\$d2 = 32    \\$d3 = 33    \\$t1 = 73    \\$t2 = 42    \\$t3 = 43Object Changed (print_r):Test Object(    [t1:private] => 73    [t2:protected] => 42    [t3] => 43    [d1:private] => 63    [d2:protected] => 32    [d3] => 33)Getting all class propertynames (print_r)Array(    => Test*/?> ```\njon at websandbox dot net\n11 years ago\n``` If you're using the SPL ArrayObject class (or similar, or the ArrayAccess interface), you may have noticed that it's difficult to loop through an object's properties.  get_object_vars does not return the properties of an ArrayObject.  The only workaround I can see is to use get_class_vars.<?php\\$obj = new ArrayObject();\\$obj->foo = \"bar\";\\$obj[] = \"1\";\\$obj[] = \"2\";foreach(\\$obj as \\$key => \\$value) { // will iterate over the array, iterating over \"1\" and \"2\", but ignoring \\$obj->foo}var_dump(\\$obj); // dumps the array values, ignores \\$obj->foo\\$a = get_object_vars(\\$obj); // returns an empty arrayclass Fart extends ArrayObject {    public \\$foo = \"bar\";}\\$obj = new Fart();\\$a = get_object_vars(\\$obj); // return an empty array\\$a = get_class_vars(get_class(\\$obj)); // returns array(\"foo\"=>\"bar\"), Yay!/* The above works with subclasses as well */class Toot extends Fart {    public \\$weeble = \"wobble\";}\\$a = get_class_vars(get_class(\\$obj)); // returns array(\"weeble\" => \"wobble\", \"foo\"=>\"bar\"), Yay again!?>So, to iterate over the properties of an ArrayObject, and not the array values:<?php\\$obj = new Toot(); // which is a subclass of ArrayObject\\$props = get_class_vars(get_class(\\$obj));foreach(\\$props as \\$prop => \\$defaultValue) {  \\$value = \\$obj->\\$prop; // now you have the property name and  its value}?> ```\nchristopher AT NOSPAM AT idealab DOT com\n15 years ago\n``` Please note that you cannot affect the object via the array values...in other words, the returned array does not contain references to the values within the object, but copies.If you are making an object inspector or editor, this is not good enough.  So I made the following methods:METHODS:function &getVar(\\$obj, \\$name){        \\$expr=\"\\\\$prop=&\\\\$obj->\\$name;\";        eval(\\$expr);        return \\$prop;}function &getObjectVars(\\$obj){        \\$result=array();        \\$vars=get_object_vars(\\$obj);        foreach (\\$vars as \\$var => \\$value)        {                \\$result[\\$var]=&getVar(&\\$obj, \\$var);        }        return \\$result;}[NOTE:  You must pass in a reference to an object, not an object.  Sorry if this  offends PHP'ers, but the distinction of pass-by-value and copy-on-assignment drives me batty (compared to Python, Java, Smalltalk), so I make all my functions pass by value, and force myself to pass in a reference to keep track of what is happening under the hood.]EXAMPLE:class Bob{        function Bob()        {                \\$this->thing=13;                \\$this->other=\"whatever\";        }        var \\$thing;        var \\$other;}\\$obj=&new Bob();# NOTE:  Passing in a reference!\\$props=getObjectVars(&\\$obj);\\$props[\"thing\"]=-11;var_dump(\\$obj);RESULTS:object(bob)(2) {  [\"thing\"]=>  &int(-11)  [\"other\"]=>  &string(8) \"whatever\"} ```\nbiga888 AT gmail\n11 years ago\n``` Just thought I would pass this on.Working with PHP 5.2.4In Windows this works by reading the vars from the passed in object and copying them to the vars of the current object.    public function copyMe(User \\$user) {        \\$varArray = get_object_vars(\\$this);        \\$copyVarArray = get_object_vars(\\$user);        foreach (\\$varArray as \\$key=>\\$value) {            \\$this->\\$key = \\$copyVarArray[\\$key];        }    }This did not work in Linux, I had to add another function to return the array of vars. Calling get_array_vars on the passed in object would return an empty array.        public function copyMe(User \\$user) {        \\$varArray = \\$this->getArray();        \\$copyVarArray = \\$user->getArray();        foreach (\\$varArray as \\$key=>\\$value) {            \\$this->\\$key = \\$copyVarArray[\\$key];        }    }    public function getArray() {        return get_object_vars(\\$this);    } ```\nC.H.\n11 years ago\n``` function conv_obj(\\$Data){     if(is_object(\\$Data)){         foreach(get_object_vars(\\$Data) as \\$key=>\\$val){             if(is_object(\\$val)){                 \\$ret[\\$key]=conv_obj(\\$val);             }else{                 \\$ret[\\$key]=\\$val;             }         }         return \\$ret;     }elseif(is_array(\\$Data)){         foreach(\\$Data as \\$key=>\\$val){             if(is_object(\\$val)){                 \\$ret[\\$key]=conv_obj(\\$val);             }else{                 \\$ret[\\$key]=\\$val;             }         }         return \\$ret;     }else{         return \\$Data;     } }Very simple function to convert any Subobject to an array.Created it while working with Soap.For me as an beginner with PHP, very useful :o) ```\nMaikel\n12 years ago\n``` To follow the code of d11wtq (enquiries AT chriscorbyn.co.uk). I did this function to inspect all properties(public, private, protected) of object. <?phpheader(\"content-type: text/plain\");// Classes to test!class OtherClass{    private \\$privateVarOtherClass = 11;}class MyClass extends OtherClass{    protected \\$protectedVar = \"some\";    public \\$publicVar = \"nk\";    private \\$privateVar = \"algo\";    var \\$oldStyle;}// Dangerous functionfunction get_properties(\\$obj, \\$values=false){    \\$obj_dump  = print_r(\\$obj, 1);    \\$matches =  array();    preg_match_all('/^\\s+\\[(\\w+).*\\] => (\\w*)/m', \\$obj_dump, \\$matches);    if (\\$values)    {        \\$output = array();        foreach (\\$matches as \\$key => \\$property)        {            \\$output[\\$property] = \\$matches[\\$key];        }        return \\$output;    }    else    {        return \\$matches;    }}\\$instance = new MyClass();echo \"Properties\\n\";print_r(get_properties(\\$instance));echo \"Properties and values\\n\";print_r(get_properties(\\$instance, true));?>Note: remember that static properties are not visible to the object. By that not supported to them ```\nflorian at XCLUDETHISgsf dot de\n17 years ago\n``` There is a strange behaviour, not sure whether it is a bug:if I call<?\\$single_object = \\$data_array_of_objects;\\$array_of_objectvars = get_object_vars(\\$single_object);     foreach(\\$array_of_objectvars as \\$key => \\$val) {     echo(\" \\$key => \\$val<br>\");     }?>I get only _ONE_ line with the \\$key = first variable name of the object and \\$val = the values of _ALL_ variables of the object including the first separated by a space.NOW:if I call<?\\$single_object = \\$data_array_of_objects;\\$array_of_objectvars = get_object_vars(\\$single_object);     foreach(\\$array_of_objectvars as \\$key => \\$val) {     echo(\" \\$key => \\$val<br>\");     }     echo(\\$data_array_of_objects->objectvar1.\"<br>\");     echo(\\$data_array_of_objects->objectvar2.\"<br>\");?>I get a list of \\$key = \\$ val as expected, before the other echos' are printed.It seems to me that get_object_vars works differently when you access a variable in those objects explicitly (as in the echos) ```\n-2\nlee dot howarth dot 90 at gmail dot com\n5 years ago\n``` I find this function very helpful, What i wanted to do was to get the object properties of an exception so i could sanitize them for output.           try   {       throw new Exception( 'Test Exception.', 100 );   }   catch( Exception \\$e )   {       var_dump( ( object ) get_object_vars( ( object ) ( new ArrayObject( \\$e ) ) -> getarrayCopy() ) );   }Example return:object(stdClass)#10 (4) { [\"message\"]=> string(15) \"Test Exception.\" [\"code\"]=> int(100) [\"file\"]=> string(29) \"C:\\xampp\\htdocs\\dev\\index.php\" [\"line\"]=> int(19) } ```\nmanicdepressive AT mindless DOT com\n15 years ago\n``` more strange, strange behaviour: if you are trying to deep-copy an object with get_object_vars(), strange behaviour can accidentally clobber your original object properties.  please read very, very carefully: get_object_vars() may either return references to *or* deep copies of the object's properties *depending on whether that property has been set with the -> operator*.   (this behaviour probably varies per php platform and os so please confirm for yourself.) furthermore, consider   \\$properties = get_object_vars(\\$obj);normally, unset()ting a reference does not affect the original, i.e. \\$ref = NULL; is not the same as unset(\\$ref); per the references documentation.  However, if you have this strange references version and you unset() an array element of \\$properties, it will *SET THE OBJECT PROPERTY TO NULL*, which is not how references normally work.  even stranger behaviour comes into effect that i can only express with an example.  please test this with your version and OS and proceed very carefully:--><?phpecho \"<pre>\\n\";class Lump{   var \\$size = 'average';   function & copy()   {  // return a deep copy      \\$copy = new Lump();         \\$properties = get_object_vars(\\$this);      foreach( array_keys( \\$properties ) as \\$property ){         \\$copy->\\$property = \\$properties[\\$property];  // deep, right?      }      return \\$copy;   } }\\$lump = new Lump();\\$lump->size = 'huge';  // <--- this line changes everything// comment above line out, and see the difference// also, try substituting another property for 'size'\\$properties = get_object_vars(\\$lump);\\$properties['size'] = 'small'; // this behavior variesecho \"after changing the properties array:\\n\";var_dump( \\$lump );  // it's either big or small (never huge) depending on // whether you commented-out the indicated line//------------- let's try using our copy() method\\$original_lump = new Lump();\\$original_lump->size = 'huge'; // this line changes the behaviour\\$other_lump =& \\$original_lump->copy();unset( \\$other_lump->size );echo \"after unsetting in copy:\\n\";var_dump( \\$original_lump ); // i'm afraid so -- original value clobbered !echo \"</pre>\\n\";?>code till dawn,    mark meves ```\nchristopher AT NOSPAM AT idealab DOT com\n15 years ago\n``` Hmmm.  A bit embarassing...It turns out the best way to get references to all of your objects member variables is NOT with the functions I provided before, or with get_object_vars.Just cast the object to array.\\$a=(array)\\$obj;# The two following statements are now equivalent and identical\\$a[\"member\"]=3;\\$obj->member=3;A very powerful tool, for inspectors and what not. ```\n-1\nfiremouth at gmail dot com\n11 years ago\n``` This is a slight modification of the previous poster's function.  We ran into a problem using this function when we had a JS array nested inside a JS hash.Something like this...myHash = new Hash();myHash[address] = new Array();When we threw that at this function, it found the first hash as an object, and then using the previous poster's function, it did not consider the array as an \"object.\"  Instead it gave us a std_object type and we were unable to make any use of it.The modification we made was adding a check for is_array inside both the is_object and is_array checks when you call the function.  This checks for an array inside either an object or a nested array.function conv_obj(\\$Data){    if(is_object(\\$Data)){            foreach(get_object_vars(\\$Data) as \\$key=>\\$val){            if(is_object(\\$val) || is_array(\\$val)){                \\$ret[\\$key]=conv_obj(\\$val);            }else{                \\$ret[\\$key]=\\$val;            }        }        return \\$ret;    }elseif(is_array(\\$Data)){        foreach(\\$Data as \\$key=>\\$val){            if(is_object(\\$val) || is_array(\\$val)){                \\$ret[\\$key]=conv_obj(\\$val);            }else{                \\$ret[\\$key]=\\$val;            }        }        return \\$ret;    }else{        return \\$Data;    }} ```\n-1\nthinice at gmail dot com\n11 years ago\n``` To add to my previous comment - the error message should have meant same structure.As my implementation called for cross-class comparison. ```\ninfo at phpken dot de\n16 years ago\n``` hello,this example will look like all values of vars was set in your class. write a method like the name: dumpClass and then fill in follow code:\\$vars = get_object_vars(\\$this);echo \"<b>class vars</b>\";foreach( \\$vars as \\$name => \\$value ) {    echo \"<li>\".\\$name.\" : \".\\$value;}look at: get_object_vars(\\$this);andreas v.l ```\nmark at dreamzpace dot com\n16 years ago\n``` In case your object contains again objects (and so on), this function might be useful:function makeAssoc(\\$res) {  \\$res = get_object_vars(\\$res);  while (list(\\$key, \\$value) = each(\\$res)) {    if (is_object(\\$value)) {      \\$res[\\$key] = makeAssoc(\\$value);    }  }  return \\$res;} ```\nnick_eby at bonzidev dot com\n17 years ago\n``` Furthermore, variables not declared in the class but set on a given object, will be returned by get_object_vars().Example, ver. 4.2.1:<?class MyTest {        var \\$classVar1 = 'Class Var 1';        var \\$classVar2;        var \\$classVar3;        function MyTest()        {                \\$this->classVar2 = 'class var 2';        }}\\$test = new MyTest();// This var isn't declared in the class\\$test->newObjVar = 'foobar';echo \"<pre>\";print_r(get_object_vars(\\$test));echo \"</pre>\";?>The output is:Array(    [classVar1] => Class Var 1    [classVar2] => class var 2    [classVar3] =>     [newObjVar] => foobar)Prior to version 4.2, classVar3 would not be output as it was never assigned a value. ```\nmichael at tapinternet dot com\n17 years ago\n``` It seems that get_object_vars will now return properties of an object even if they have no value  - meaning only defined by var \\$foo in the class declaration.  This is noted behaviour in 4.2.1 which is different from previous versions and hitherto undocumented on this page. ```\n-2\nelminster2031 at hotmail dot com\n9 years ago\n``` Also note that this is recursive. For example:<?phpclass Sarah{    private \\$Father;    private \\$Mother;    public function __construct(){        \\$this->Father    =    NULL; //I don't know Sarah's Father        \\$this->Mother    =    NULL; //I don't know Sarah's Mother    }}class John_Connor{    private \\$Father;    private \\$Mother;    public function __construct(){        \\$this->Father    =    \\$this; //John went back in time and fathered himself        \\$this->Mother    =    new Sarah(); //Sarah was his mom and his mate ewww    }    public function showParents(){        return get_object_vars(\\$this);    }}\\$John    =    new John_Connor();var_dump(\\$John->showParents());?>You will see this outputs:array(2) {  [\"Father\"]=>  object(John_Connor)#1 (2) {    [\"Father\":\"John_Connor\":private]=>    object(John_Connor)#1 (2) {      [\"Father\":\"John_Connor\":private]=>      *RECURSION*      [\"Mother\":\"John_Connor\":private]=>      object(Sarah)#2 (2) {        [\"Father\":\"Sarah\":private]=>        NULL        [\"Mother\":\"Sarah\":private]=>        NULL      }    }    [\"Mother\":\"John_Connor\":private]=>    object(Sarah)#2 (2) {      [\"Father\":\"Sarah\":private]=>      NULL      [\"Mother\":\"Sarah\":private]=>      NULL    }  }  [\"Mother\"]=>  object(Sarah)#2 (2) {    [\"Father\":\"Sarah\":private]=>    NULL    [\"Mother\":\"Sarah\":private]=>    NULL  }} ```\n-1\nsupport at sascha minus diebel dot de\n13 years ago\n``` Note that get_object_vars() returns the variables of the object not the class. You need to know if your class is extended from a parent class. ```\n-1\nd11wtq (enquiries AT chriscorbyn.co.uk)\n13 years ago\n``` Since there's no apparent means of obtaining all the *private* properties in an object I wrote a little function to do it.  Built in support would be much more efficient since mine uses a preg_  search to do this....<?phpfunction get_private_properties(\\$obj, \\$inside=false){    \\$obj_dump  = print_r(\\$obj, 1);    preg_match_all('/^\\s+\\[(\\w+):private\\]/m', \\$obj_dump, \\$matches);    if (\\$inside)    {        \\$output = array();        foreach (\\$matches as \\$property)        {            \\$output[\\$property] = \\$obj->\\$property;            return \\$output;        }    }    else return \\$matches;} ?>So if you run it with the optional second paramter missing you'll just get an array of the variable names that are private inside the class.  This is the only option if you are not inside the actual object and the object has no private properties inherited.If you run it with the second parameter set to true you will get an associative array with the properties and their corresponding values.  I'd only advise to do that for singletons since you may get errors if there are any private properites in parents/children. ```\n-1\npascal dot poncet at netconsult dot com\n13 years ago\n``` Subject: using \"sql_calc_found_rows\" in a MySQL query while exploiting result in a PHP db class object.Hello,There is a nice function in MySQL that allows to know how many records would have been returned if no \"where\" clause were set : SQL_CALC_FOUND_ROWS.If you have create a db object to collect the returned lines, you will be a little perplex when trying to call the result of this function.Why ?Simply because the returned field's name is \"found_rows()\" and obviously it's not possible to call something like :<?php \\$result->found_rows() ?>...as it will try to acces a method, not a property !Then, the only way to get the right result seems to be the use of a class function, like :<?php  \\$db->query(\"select found_rows()\");  \\$count=current(get_object_vars(current(\\$db->result)));?>Of course, if somebody found an other way to solve it, like a special syntax (see the one used with curled arrays in a string), I'm really open to discuss.Good luck,Pascal ```\n-1\nstachnik at gmail dot com\n13 years ago\n``` In PHP5 to get an array with all properties (even the private ones) all you have to do is write a public method that returns an array for your class:public function getArray(){  return get_object_vars(\\$this);}and then\\$myBeautifulArray = \\$myBeautifulObject->getArray ();Have BEAUTIFUL day :) ```\n-1\njordi at laigu dot net\n15 years ago\n``` In case your object contains again OBJECTS or ARRAYS:function makeAssoc(\\$res) {  if (is_object(\\$res)) \\$res = get_object_vars(\\$res);  while (list(\\$key, \\$value) = each(\\$res)) {    if (is_object(\\$value) || is_array(\\$value)) {      \\$res[\\$key] = makeAssoc(\\$value);    }  }  return \\$res;}Thanks to mark at dreamzpace dot com ```\n-1\nthiago dot henrique dot mata at gmail dot com\n12 years ago\n``` <?php# How to make a function change the private attributes# from some object without use serialize functions or# lose the control of the changes./** * Parent Class to allow the change of privates attributes * Look the abstract function __setAttribute. * * @author Renan de Lima ( renandelima@gmail.com ) * @author Thiago Mata ( thiago.henrique.mata@gmail.com ) * @date 2007-02-21 */abstract class father{    /**     * Receive the Aray and try to change the attribute value     *     * @param array \\$arrNewValues     */    public function __fromDatabase( \\$arrNewValues )    {        \\$arrToSet = array_intersect_key( \\$arrNewValues, get_object_vars( \\$this ) );        foreach( \\$arrToSet as \\$strAttribute => \\$mixValue )        {            \\$this->__setAttribute( \\$strAttribute , \\$mixValue );        }    }        /**     * Required method to control the attributes of class      * @param string \\$strAttribute     * @param unknown \\$mixValue     */    abstract protected function __setAttribute( \\$strAttribute, \\$mixValue );    }/** * Just a example of a child class using the functionality * * Note: if you don't wanna to allow the change of some attribute * by this method you can just make more complex the __setAttribute function. * * @author Renan de Lima ( renandelima@gmail.com ) * @author Thiago Mata ( thiago.henrique.mata@gmail.com ) * @date 2007-02-21 */class son extends father{        private \\$atr = 9;        /**     * This is the most simple implementation of the method.     * This way it's allowed to the parent class change any attribute     * @param string \\$strAttribute     * @param unknown \\$mixValue     */    protected function __setAttribute( \\$strAttribute, \\$mixValue )    {        \\$this->{ \\$strAttribute } = \\$mixValue;    }    }\\$objSon = new son();\\$objSon->__fromDatabase( array( 'atr' => 55 ) );var_dump( \\$objSon );?> ```\n-3\nhuzursuz at mailinator dot com\n10 years ago\n``` better version of conv_obj, based on XML... this converts XML to an array... use it by<?php\\$result = xmlobj2arr(simplexml_load_string(\\$xmlContent));function xmlobj2arr(\\$Data) {       if (is_object(\\$Data)) {               foreach (get_object_vars(\\$Data) as \\$key => \\$val) {                       \\$ret[\\$key] = xmlobj2arr(\\$val);               }               return \\$ret;       } elseif (is_array(\\$Data)) {               foreach (\\$Data as \\$key => \\$val) {                       \\$ret[\\$key] = xmlobj2arr(\\$val);               }               return \\$ret;       } else {               return \\$Data;       }}?> ```", null, "" ]

[ null, "https://www.php.net/images/notes-add@2x.png", null, "https://www.php.net/images/to-top@2x.png", null ]

[ "## Substitute Scalars with Matrices\n\nCreate the following expression representing the sine function.\n\n```syms w t f = sin(w*t);```\n\nSuppose, your task involves creating a matrix whose elements are sine functions with angular velocities represented by a Toeplitz matrix. First, create a 4-by-4 Toeplitz matrix.\n\n`W = toeplitz(sym([3 2 1 0]))`\n```W = [ 3, 2, 1, 0] [ 2, 3, 2, 1] [ 1, 2, 3, 2] [ 0, 1, 2, 3]```\n\nNext, replace the variable `w` in the expression `f` with the Toeplitz matrix `W`. When you replace a scalar in a symbolic expression with a matrix, `subs` expands the expression into a matrix. In this example, `subs` expands ```f = sin(w*t)``` into a 4-by-4 matrix whose elements are `sin(w*t)`. Then it replaces `w` in that matrix with the corresponding elements of the Toeplitz matrix `W`.\n\n`F = subs(f, w, W)`\n```F = [ sin(3*t), sin(2*t), sin(t), 0] [ sin(2*t), sin(3*t), sin(2*t), sin(t)] [ sin(t), sin(2*t), sin(3*t), sin(2*t)] [ 0, sin(t), sin(2*t), sin(3*t)]```\n\nFind the sum of these sine waves at `t = π`, ```t = π/2```, `t = π/3`, ```t = π/4```, `t = π/5`, and ```t = π/6```. First, find the sum of all elements of matrix `F`. Here, the first call to `sum` returns a row vector containing sums of elements in each column. The second call to `sum` returns the sum of elements of that row vector.\n\n`S = sum(sum(F))`\n```S = 6*sin(2*t) + 4*sin(3*t) + 4*sin(t)```\n\nNow, use `subs` to evaluate `S` for particular values of the variable `t`.\n\n`subs(S, t, sym(pi)./[1:6])`\n```[ 0,... 0,... 5*3^(1/2), 4*2^(1/2) + 6,... 2^(1/2)*(5 - 5^(1/2))^(1/2) + (5*2^(1/2)*(5^(1/2) + 5)^(1/2))/2,... 3*3^(1/2) + 6]```\n\nYou also can use `subs` to replace a scalar element of a matrix with another matrix. In this case, `subs` expands the matrix to accommodate new elements. For example, replace zero elements of the matrix `F` with a column vector `[1;2]`. The original 4-by-4 matrix `F` expands to an 8-by-4 matrix. The `subs` function duplicates each row of the original matrix, not only the rows containing zero elements.\n\n`F = subs(F, 0, [1;2])`\n```F = [ sin(3*t), sin(2*t), sin(t), 1] [ sin(3*t), sin(2*t), sin(t), 2] [ sin(2*t), sin(3*t), sin(2*t), sin(t)] [ sin(2*t), sin(3*t), sin(2*t), sin(t)] [ sin(t), sin(2*t), sin(3*t), sin(2*t)] [ sin(t), sin(2*t), sin(3*t), sin(2*t)] [ 1, sin(t), sin(2*t), sin(3*t)] [ 2, sin(t), sin(2*t), sin(3*t)]```\n\n#### Mathematical Modeling with Symbolic Math Toolbox\n\nGet examples and videos" ]

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[ "Cody\n\nProblem 1570. Is the input divisible by 3?\n\nSolution 279857\n\nSubmitted on 12 Jul 2013 by JeremyR\nThis solution is locked. To view this solution, you need to provide a solution of the same size or smaller.\n\nTest Suite\n\nTest Status Code Input and Output\n1   Pass\n%% x = 1; y_correct = false; assert(isequal(your_fcn_name(x),y_correct))\n\ny = 0\n\n2   Pass\n%% x = 3; y_correct = true; assert(isequal(your_fcn_name(x),y_correct))\n\ny = 0 y = 1" ]

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[ "# Convert slope from ppm (‰) to cm per m length  (ppm to cm/m) online\n\nTo convert the slope from ppm to cm in height per meter of length, just indicate the slope in ppm in the cells below:\n\nEnter the slope in ppm (‰):\n\nConversion result to centimeters per meter length (cm per m, cm/m)\n\n0.00cm per m\n\n## How to translate the slope from ppm to cm per meter of length?\n\nTo find out how much the slope is in ppm, you need to familiarize yourself with the definition:\n\nA ppm (‰) is one tenth of a percent or 1/1000.\n\nA slope of 1 ‰ is equal to a slope of 0.1 cm in height for 1 m in length\n\n1 ‰ = 0.1 cm / m (cm per meter length)." ]

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[ "Article | Open | Published:\n\n# Wetting theory for small droplets on textured solid surfaces\n\nScientific Reports volume 6, Article number: 37813 (2016) | Download Citation\n\n## Abstract\n\nConventional wetting theories on rough surfaces with Wenzel, Cassie-Baxter, and Penetrate modes suggest the possibility of tuning the contact angle by adjusting the surface texture. Despite decades of intensive study, there are still many experimental results that are not well understood because conventional wetting theory, which assumes an infinite droplet size, has been used to explain measurements of finite-sized droplets. Here, we suggest a wetting theory applicable to a wide range of droplet size for the three wetting modes by analyzing the free energy landscape with many local minima originated from the finite size. We find that the conventional theory predicts the contact angle at the global minimum if the droplet size is about 40 times or larger than the characteristic scale of the surface roughness, regardless of wetting modes. Furthermore, we obtain the energy barrier of pinning which can induce the contact angle hysteresis as a function of geometric factors. We validate our theory against experimental results on an anisotropic rough surface. In addition, we discuss the wetting on non-uniformly rough surfaces. Our findings clarify the extent to which the conventional wetting theory is valid and expand the physical understanding of wetting phenomena of small liquid drops on rough surfaces.\n\n## Introduction\n\nThe contact angle is a material property determined by the surface tensions between substrate, liquid, and vapor1. Because the materials with extremely small or large contact angles, i.e., with super hydrophilicity or super hydrophobicity, are applicable in many ways, there have been a myriad of studies that have investigated tuning the contact angle via the surface roughness of the substrate based on the conventional wetting theory of rough surface with Wenzel (W), Cassie-Baxter (CB), and Penetrate (P, which is also referred to as hemi-wicking2) modes3,4,5,6,7,8,9.\n\nHowever, the conventional wetting theory1,10,11,12 assumes that the liquid droplet is much larger than the characteristic scale of the surface roughness, which frequently is not justifiable in many experiments. Therefore, the contact angle predictions using the conventional theory differ from experimental results when the droplet size is small13,14,15,16,17,18,19. The conventional theory considers a straight boundary between the liquid and the vapor regardless of the three-phase contact line location or the droplet size1,10,11,12,20. However, because the realistic contour of a liquid droplet forms part of a sphere21, the assumption does not hold when the droplet size to surface texture scale ratio is small. There have been several studies to overcome the limitations of the conventional wetting theories for the small droplet, based on wetting free energy calculations. As a pioneer of the subject, Marmur et al.12,13 modelled the 2D circular droplet on the heterogeneous in CB mode or the saw-tooth-like rough surface in W mode, and clarified that the wetting on the rough surface can involve multiple local free energy minima with different contact angles and that the contact angle of the global free energy minimum approaches to that of the conventional theory only when the scale of the liquid droplet is much bigger than the scale of the periodicity of the rough surface. Shahraz et al.22 computed the wetting free energies of every possible pinning points on the surface with periodic rectangular protrusions in W or CB mode, to predict the contact angles of the liquid droplet with finite volume at multiple pinning points. However, since the free energy landscape between the pinning points were not investigated, it cannot be guaranteed that all the pinning points investigated in the study are at local free energy minima.\n\nIn this work, we present a more generalized wetting theory by considering the entire free energy landscape including the transition configuration between the pinning points in three wetting modes, P, W, and CB, on a surface with rectangular protrusions as well as non-uniformly rough surfaces. First, we confirm that the pinning phenomena can be understood by the existence of multiple local minima of the free energy landscape separated by energy barriers. For all wetting modes (P, W, and CB), we show that the contact angle at the global minimum recovers the prediction of conventional wetting theory within 2° when the droplet size (diameter of the initial droplet) becomes at least 40 times larger than the characteristic scale of the surface roughness (periodicity of the texture). Second, we compute the free energy barriers between available pinning points in all wetting modes. For P and CB modes, the energy barrier between local minima tends to decrease as the contact angle becomes further apart from the contact angle at the global minimum energy and eventually becomes zero, which enables us to predict the ultimate bound of advancing and receding angles. Our theory is then applied to explain the measured contact angle on the surface with anisotropic roughness19. Finally, we calculate the free energy of the wetting on the non-uniformly rough surface and reaffirm in terms of free energy that the contact angle is determined by the roughness of the substrate near the three-phase contact line20,23, not by the overall roughness within the droplet-substrate contact area. When the effect of gravity is ignored22, the proposed theory is universally valid for any scale of droplets unless the droplet diameter is a few nanometers or smaller because we assume that the interfacial energy of rough surface can be written as the flat surface interfacial energy multiplied the ratio of true area to the apparent area. The length scale of the molecular interaction is known to be about one to two nanometers24. Our theory reproduces the conventional wetting theory in the limit of an infinite ratio between the droplet size and characteristic scale of surface roughness.\n\nFor the mathematical simplicity, we consider a two-dimensional (2D) finite-sized liquid droplet. As illustrated in Fig. 1a, we model the rough surface as periodic rectangular textures and model the boundary of the liquid droplet as an arc of a circle while ignoring the effect of gravity. In other words, our 2D droplet is a simplification of an infinitely long cylindrical droplet. Even though our theory cannot provide the exact quantitative prediction of contact angle of realistic spherical-cap-like 3D droplets, it can still offer qualitative physical understanding about the wetting of small droplet on rough surface, such as the origin of pinning, the wetting on non-uniformly rough surface, and contact angle change upon droplet volume change. The transition between the pinning points in CB and P modes is modelled by assuming that the three-phase contact line horizontally slides between the top of grooves. In W mode, we assume that the liquid tip forms a vertical straight line when inside a groove. While such an assumption may cause a small numerical difference, the resulting free energy landscape would correctly capture the multiple local minima and the energy barriers between them qualitatively well (See Supplementary Information).", null, "Figure 1: Assumptions and methods to achieve r − θ relation.\n\nWe find that the free energy has local minima when one end of the droplet is fixed at either the left or right corner of the step. Two cases are illustrated in the inset of Fig. 1b. Because a hydrophobic surface prefers to reduce the contact area between the droplet and the substrate at a given contact angle, Case I has the lower free energy for the hydrophobic surfaces (θe > 90°), and Case II has the lower free energy for the hydrophilic surfaces (θe < 90°) (see Supplementary Information for more details). θe refers to the equilibrium contact angle on a flat surface determined by Young’s equation1, σLV cos θe = σSV − σSL, where σLV, σSV and σSL denote the liquid-vapor, solid-vapor and solid-liquid interfacial energies, respectively. For the two cases, the number of grooves below the liquid droplet n can be expressed with length of the baseline L, width of the step W, and width of the groove G, as described below.", null, "n1 is the number of groove-step pairs which fully covered with liquid, hence a natural number, and n is defined to account for partially filled grooves (real number). The overbar indicates the dimensionless variables. In what follows, all length and energy variables are normalized against the radius of the circular droplet R0 (i.e. the volume of droplet is", null, ") and σLVR0, respectively. The values of n are visualized in Fig. 1b. for the case when", null, "and", null, ". As illustrated in the figure, n continuously increases when the three-phase contact line is on the groove and is conserved when the contact line is on the step, as", null, "increases. Thereafter, the radius of the curvature and the free energy of each wetting modes can be derived in terms of n, geometrical factors, and θ, which are presented in Table 1. Details on the numerical calculations are described in the Supporting Information. Because the current study considers only 2D droplet cases, the effect of the line tension25 can be ignored. However, one needs to incorporate the line tension effect when dealing with 3D droplets on textured surfaces26,27.\n\nBased on the free energy expression as a function of θ, we can find the allowable contact angles with free energy minima at a given roughness factor28", null, ", i.e., the ratio of the true surface area to the projected area. For example, Fig. 1c–e show the relationship between the free energy and the contact angle for the W mode when r = 1.2, 1.5 and 1.8, respectively when", null, "(i.e., a droplet size of 2R0 is 20 times that of the characteristic scale of the surface roughness, G + W). The vertical dotted line is the contact angle determined by the conventional wetting theory on the Wenzel mode, cos θ = r cos θe. The contact angles at the global free energy minima under different surface roughnesses, which are highlighted by the blue circle, green triangle, and red square, do not match perfectly with the prediction from the conventional wetting theory. Thereafter, one can predict the contact angle as a function of the surface roughness factor r by connecting the contact angles at the global free energy minima, as illustrated in Fig. 1f. The conventional wetting theory prediction (red dotted curve), cos θ = r cos θe, is also presented in comparison. The contact angles for the CB and P modes can be obtained in a similar way as functions of", null, ", which is the fraction of the step area from the projected area.\n\nWe then consider how the contact angle changes with the droplet size by varying the dimensionless variable", null, ", which is the ratio of the groove width to the initial droplet radius. For a given", null, ", the roughness factor28 r and the step fraction f can be tuned by changing the height or width of the steps,", null, "or", null, ". The predicted contact angles for W, CB, and P modes are presented in Fig. 2a–d with varying values of r and f. When", null, ", i.e., the droplet size is 2 times the characteristic scale of the surface roughness, our theory and the conventional theory10,11,12 predict different contact angles because the wetting free energy landscape of a small droplet is extremely different from that of a large droplet. Hence, the conventional theory should not be used. However, in case of", null, ", the contact angle from our theory converges to that from the conventional theory within the range of ±10°. When", null, "reaches 0.005, the contact angle from our theory recovers the prediction of conventional theory10,11,12 almost perfectly, which is expected. Considering the typical resolution of the contact angle measurements (1~2°)15, we suggest the conventional theory10,11,12 should be applied in the case when", null, "(see Supplementary Information for details), i.e., when the droplet size is at least about 40 times bigger than the characteristic scale of the surface roughness.", null, "Figure 2: Results of contact angle and wetting mode prediction from the proposed theory.\n\nWe can predict the most stable wetting mode for the substrates with different Young’s angle θe by comparing the free energies of the three modes29. As depicted in Fig. 3d, we find that in accordance with the conventional theory, on a hydrophilic surface (θe < 90°), the contact angle is given by the higher contact angle between the predictions based on the P mode and W mode and on the hydrophobic surface (θe < 90°) by the lower contact angle between the predictions based on the CB mode and W mode. The choice between the W mode and the CB mode is made by comparing the free energy values in Table 1. To select between the W mode and the P mode, we use the critical contact angle theory2 instead of the direct free energy comparison because the initial free energy of the P mode differs from the other modes. The critical contact angle, θC is determined when the free energy variation to fill an additional groove is 0. If the contact angle of the flat surface θe is smaller than θC, the free energy variation to fill another groove becomes negative, spreading occurs, and the Penetrate mode is selected. In our work, the critical contact angle can be expressed with geometric factors as", null, ". As illustrated in Fig. 2d, for the case of", null, ", r = 1.5, and f = 0.5, one can find that the most stable wetting mode curve follows a similar path as that of the conventional theory.", null, "Figure 3: Relation between θ and with respect to wetting modes.\n\nWe then confirm the origin of the pinning effect is the occurrence of multiple local minima and calculate the free energy barriers in terms of geometric factors for the three wetting modes. In the W mode, a drastic free energy change occurs when the three-phase contact line is located near the corner of the step because the additional boundary may form or disappear. The A’ and B’ points at the end of the step in Fig. 3a include an additional boundary line while A and B do not. As depicted in Fig. 3a, the free energy differences between A’ and A(", null, ") or B’ and B(", null, ") act as the primary free energy barrier and form a local free energy minimum. The amount of the energy barrier can be expressed with", null, "and θ, as shown in Table 2. When the substrate is hydrophobic, the local minimum point is located on B, and one can notice that this corresponds to the experimentally observed three-phase contact line location19 when pinning occurs. A similar discussion can be repeated for the Cassie-Baxter or the Penetrate mode. By calculating the free energy of each point of Fig. 3b and c, the energy barriers can be formulated, as summarized in Table 2. The superscripts A and B refer to the points A and B in the figures, respectively, and the subscripts C and P refer to the wetting modes. Interestingly, while the Wenzel mode always has local free energy minima because of the additional liquid-vapor boundary line, the Cassie-Baxter or the Penetrate mode do not possess local minimum points when θ < θe or θ > θe, respectively. The disappearance of the energy barrier indicates the ultimate bound of advancing and receding angles which are determined by available local free energy minima. The maximum advancing (receding) angle can be obtained from experiments will be the highest (lowest) contact angle at the pinning points with nonzero energy barrier. We speculate that the conventional Wenzel state has very large contact angle hysteresis because of the non-vanishing energy barrier between local minima30.\n\nNow, we apply the proposed theory to understand the wetting experiments on the surface with anisotropic roughness19. An experiment performed by Chen et al.19 used morphologically patterned surface to measure the contact angle of the surface with anisotropic roughness made of PDMS (θe = 114°) along both perpendicular and parallel directions. The width of step and groove were 23 μm and 25.6 μm each. The height of the step was 30 μm. The measurement of the contact angle were conducted with water droplet of volume from 0.59 mm3 to 5.679 mm3. They confirmed that droplets are in the CB mode, and measure the number of pillars filled by or the base line length of the droplet. It was reported that the contact angle at the direction perpendicular to the grooves is likely to be similar to the advancing contact angle31,32, and that the advancing contact angle is chosen as the maximum contact angle among the local free energy minima33. However, since there exists an external energy perturbation such as ambient vibration and the inertia associated with the droplet spreading, we expect that the measured advancing contact angle must be smaller than the maximum contact angle among local minima. We compute the energy barrier at each local minima for different droplet volumes, and compared the energy barrier at the measured contact angle for corresponding droplet volume. We could see that the free energy barrier between B state and C state in Fig. 3b plays a main role in determining the advancing contact angle in CB mode. The energy barrier can be calculated by the formula in Table 2. Since the energy barrier formula is non-dimensional, we multiply R0σLV and the baseline length parallel to the groove direction to dimensionalize the formula to compare the energy barriers for different droplet volume. The energy barrier between B state and C state, at each local minimum is plotted in Fig. 4a. Each dot in the curves refers to the energy barrier at each pinning point and all open symbols refer to the experimental result for different droplet volume. In the figure, one can notice that the energy barriers for different droplet volumes are similar. The average energy barrier is represented with the black dotted horizontal line which is located close to all open symbols. One may consider the black dotted line as the typical external energy perturbation in the series of experiments reported in the study. The contact angle for specific liquid volume can be predicted by capturing the pinning point which has the smallest distance from the average energy barrier (black dotted in Fig. 4b). The predicted contact angle agrees well with experimental results and show the same trend with experiments. One may perform a similar analysis to predict the receding contact angle or the contact angle hysteresis of other experiments.", null, "Figure 4: Energy barrier and experimental results on surface with anisotropic roughness.\n\nWe then apply our theory to analyse a surface with non-uniform roughness that has a rough center and flat periphery. In other words, we compute the free energy landscape when there exists an upper bound nMAX in the number of filled grooves, n. For example, we compute the free energies of the wetting states when", null, "and θe = 120° as functions of contact angle θ with nMAX = 14 and 19, as depicted in Fig. 5a and b, respectively. Figure 5a illustrates the situation where the area of the rough central region is small enough that the three-phase contact line is located on the flat region. We find that the global free energy minimum is located at the Young’s angle θe. It is the case for any nMAX ≤ 14 because the free energy curve with a fixed n has a minimum at θe, as depicted by the red dotted curves in Fig. 5a. On the contrary, Fig. 5b shows a case where the area of the rough region is large enough and the contact line is located within the rough center. In this case, the local minimum associated with n = nMAX = 19 has a higher free energy than the global minimum. Hence, the contact angle prediction becomes identical to the surface with uniform roughness. Our results agree with the previously proposed wetting theory for a non-uniform rough surface20,23, which proposed that the contact angle is determined by the roughness condition near the three-phase contact line. Our work offers an extended theory that enables us to predict whether the contact line will be located on the rough center or on the flat region. We note that our theory can be generalized to study the wetting on surfaces with a more complex non-uniform roughness or be used to build a surface to fix the droplet to the specific location34, complementing the pioneering works by Johnson and Dettre35,36.", null, "Figure 5: Relation between θ and of the Wenzel mode when the surface has non-uniform roughness.\n\nIn conclusion, we have developed a wetting theory that can predict the wetting angle and wetting mode when the liquid droplet is not much larger than the surface texture scale. Because the conventional theory assumes a much larger size of the droplet compared to the texture scale, there have been limitations in how to analyse experiments that investigate the wetting of small liquid drops. Our theory suggests that conventional theory should be used when the droplet size is about 40 times larger than the characteristic scale of the surface roughness and provides a deeper physical understanding regarding the wetting of smaller liquid droplets on non-uniform rough surfaces.\n\nHow to cite this article: Kim, D. et al. Wetting theory for small droplets on textured solid surfaces. Sci. Rep. 6, 37813; doi: 10.1038/srep37813 (2016).\n\nPublisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.\n\n1. 1.\n\nAn Essay on the Cohesion of Fluids. Philosophical Transactions of the Royal Society of London 95, 65–87 (1805).\n\n2. 2.\n\n, & Wetting of textured surfaces. Colloid Surface A 206, 41–46 (2002).\n\n3. 3.\n\n, , & Super-hydrophobic/super-hydrophilic patterning of gold surfaces by photocatalytic lithography. J Mater Chem 15, 1523–1527 (2005).\n\n4. 4.\n\net al. Sol–gel-derived super-hydrophilic nickel doped TiO2 film as active photo-catalyst. Applied Catalysis A: General 314, 40–46 (2006).\n\n5. 5.\n\n, & Enhanced effect and mechanism of SiO2 addition in super-hydrophilic property of TiO2 films. Surf Coat Tech 173, 219–223 (2003).\n\n6. 6.\n\n, , & Preparation and characterization of super-hydrophilic porous TiO2 coating films. Mater Chem Phys 68, 253–259 (2001).\n\n7. 7.\n\n, , , & Mechanisms of Oxygen Plasma Nanotexturing of Organic Polymer Surfaces: From Stable Super Hydrophilic to Super Hydrophobic Surfaces. Langmuir: the ACS journal of surfaces and colloids 25, 11748–11759 (2009).\n\n8. 8.\n\n, , & Preparation and super-hydrophilic properties of TiO2/SnO2 composite thin films. Mater Res Bull 37, 2255–2262 (2002).\n\n9. 9.\n\n& Super-hydrophilic and transparent thin films of TiO2 nanotube arrays by a hydrothermal reaction. J Mater Chem 17, 2095–2100 (2007).\n\n10. 10.\n\nResistance of Solid Surfaces To Wetting By Water. Industrial & Engineering Chemistry 28, 988–994 (1936).\n\n11. 11.\n\n& Wettability of porous surfaces. Transactions of the Faraday Society 40, 546–551 (1944).\n\n12. 12.\n\n, & Rough wetting. EPL (Europhysics Letters) 55, 214 (2001).\n\n13. 13.\n\n& When Wenzel and Cassie Are Right: Reconciling Local and Global Considerations. Langmuir: the ACS journal of surfaces and colloids 25, 1277–1281 (2009).\n\n14. 14.\n\n& Apparent contact angles on rough surfaces: the Wenzel equation revisited. Colloid Surface A 156, 381–388 (1999).\n\n15. 15.\n\n, & Contact angle measurement on rough surfaces. J Colloid Interf Sci 274, 637–644 (2004).\n\n16. 16.\n\n, , & Effect of Roughness Geometry on Wetting and Dewetting of Rough PDMS Surfaces. Langmuir: the ACS journal of surfaces and colloids 30, 7358–7368 (2014).\n\n17. 17.\n\n, , , & Tunable lotus-leaf and rose-petal effects via graphene paper origami. Extreme Mechanics Letters 4, 18–25 (2015).\n\n18. 18.\n\n, , , & Comparing Contact Angle Measurements and Surface Tension Assessments of Solid Surfaces. Langmuir: the ACS journal of surfaces and colloids 26, 15289–15294 (2010).\n\n19. 19.\n\n, , & Anisotropy in the wetting of rough surfaces. J Colloid Interf Sci 281, 458–464 (2005).\n\n20. 20.\n\nCassie and Wenzel: Were they really so wrong? Langmuir: the ACS journal of surfaces and colloids 23, 8200–8205 (2007).\n\n21. 21.\n\nVariational Methods with Applications in Science and Engineering 28–89 (Cambridge University Press, 2013).\n\n22. 22.\n\n, & A Theory for the Morphological Dependence of Wetting on a Physically Patterned Solid Surface. Langmuir: the ACS journal of surfaces and colloids 28, 14227–14237 (2012).\n\n23. 23.\n\n& How Wenzel and Cassie were wrong. Langmuir: the ACS journal of surfaces and colloids 23 (2007).\n\n24. 24.\n\n, , & Solving the Controversy on the Wetting Transparency of Graphene. Sci Rep-Uk 5 (2015).\n\n25. 25.\n\nLine Tension and the Shape of a Sessile Drop. The Journal of Physical Chemistry 99, 2803–2806 (1995).\n\n26. 26.\n\n& Dependence of macroscopic wetting on nanoscopic surface textures. Langmuir: the ACS journal of surfaces and colloids 25, 12851–12854 (2009).\n\n27. 27.\n\nGeneral equation describing wetting of rough surfaces. J Colloid Interf Sci 360, 317–319 (2011).\n\n28. 28.\n\net al. Beyond the lotus effect: Roughness, influences on wetting over a wide surface-energy range. Langmuir 24, 5411–5417 (2008).\n\n29. 29.\n\n, & Wetting transitions on rough surfaces. Europhys Lett 68, 419–425 (2004).\n\n30. 30.\n\n, , & Slippery Wenzel State. Acs Nano 9, 9260–9267 (2015).\n\n31. 31.\n\n, , & Macroscopic-wetting anisotropy on the line-patterned surface of fluoroalkylsilane monolayers. Langmuir: the ACS journal of surfaces and colloids 21, 911–918 (2005).\n\n32. 32.\n\n, & Anisotropic wetting on tunable micro-wrinkled surfaces. Soft Matter 3, 1163–1169 (2007).\n\n33. 33.\n\nThermodynamic Aspects of Contact-Angle Hysteresis. Adv Colloid Interfac 50, 121–141 (1994).\n\n34. 34.\n\net al. Spheroform: therapeutic spheroid-forming nanotextured surfaces inspired by desert beetle Physosterna cribripes. Advanced healthcare materials 4, 511–515 (2015).\n\n35. 35.\n\n& The Journal of Physical Chemistry 68, 1744–1750 (1964).\n\n36. 36.\n\n& The Journal of Physical Chemistry 69, 1507–1515 (1965).\n\n## Acknowledgements\n\nThis work is supported by the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (2016M3D1A1900038). N.M.P. is supported by the European Research Council (ERC StG Ideas 2011 BIHSNAM n. 279985, ERC PoC 2015 SILKENE nr. 693670), by the European Commission under the Graphene Flagship (WP14 Polymer Composites, no. 696656). N.M.P. thanks Profs. Della Volpe and Siboni for useful comments on the paper.\n\n## Affiliations\n\n1. ### Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea\n\n• Donggyu Kim\n•  & Seunghwa Ryu\n2. ### Laboratory of Bio-Inspired and Graphene Nanomechanics, Department of Civil, Environmental, and Mechanical Engineering, University of Trento, Trento, Italy\n\n• Nicola M. Pugno\n3. ### Center for Materials and Microsystems, Fondazione Bruno Kessler, Trento, Italy\n\n• Nicola M. Pugno\n4. ### School of Engineering and Materials Science, Queen Mary University of London, Mile End Road, London, United Kingdom\n\n• Nicola M. Pugno\n\n## Authors\n\n### Contributions\n\nD.K. and S.R. designed the research, developed the theoretical models, and analyzed the results. D.K. carried out numerical calculations. N.M.P. contributed to the theoretical analysis. D.K. and S.R. wrote the manuscript. All authors discussed the results and commented on the manuscript.\n\n### Competing interests\n\nThe authors declare no competing financial interests.\n\n## Corresponding author\n\nCorrespondence to Seunghwa Ryu.\n\n## PDF files\n\n1. 1.\n\n### DOI\n\nhttps://doi.org/10.1038/srep37813", null, "" ]

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[ "# MST Kruskal's algorithm in Python\n\nI have this code for finding MST for undirected weighted graph, currently works for graphs with maximum 10 vertices. How can I update the code to scale for larger graphs?\n\n# Python program for Kruskal's algorithm to find Minimum Spanning Tree\n# of a given connected, undirected and weighted graph\n\nfrom collections import defaultdict\n\n#Class to represent a graph\nclass Graph:\n\ndef __init__(self,vertices):\nself.V= vertices #No. of vertices\nself.graph = [] # default dictionary to store graph\n\n# function to add an edge to graph\nself.graph.append([u,v,w])\n\n# A utility function to find set of an element i\n# (uses path compression technique)\ndef find(self, parent, i):\nif parent[i] == i:\nreturn i\nreturn self.find(parent, parent[i])\n\n# A function that does union of two sets of x and y\n# (uses union by rank)\ndef union(self, parent, rank, x, y):\nxroot = self.find(parent, x)\nyroot = self.find(parent, y)\n\n# Attach smaller rank tree under root of high rank tree\n# (Union by Rank)\nif rank[xroot] < rank[yroot]:\nparent[xroot] = yroot\nelif rank[xroot] > rank[yroot]:\nparent[yroot] = xroot\n#If ranks are same, then make one as root and increment\n# its rank by one\nelse :\nparent[yroot] = xroot\nrank[xroot] += 1\n\n# The main function to construct MST using Kruskal's algorithm\ndef KruskalMST(self):\n\nresult =[] #This will store the resultant MST\n\ni = 0 # An index variable, used for sorted edges\ne = 0 # An index variable, used for result[]\n\n#Step 1: Sort all the edges in non-decreasing order of their\n# weight. If we are not allowed to change the given graph, we\n# can create a copy of graph\nself.graph = sorted(self.graph,key=lambda item: item)\n#print self.graph\n\nparent = [] ; rank = []\n\n# Create V subsets with single elements\nfor node in range(self.V):\nparent.append(node)\nrank.append(0)\n\n# Number of edges to be taken is equal to V-1\nwhile e < self.V -1 :\n\n# Step 2: Pick the smallest edge and increment the index\n# for next iteration\nu,v,w = self.graph[i]\ni = i + 1\nx = self.find(parent, u)\ny = self.find(parent ,v)\n\n# If including this edge does't cause cycle, include it\n# in result and increment the index of result for next edge\nif x != y:\ne = e + 1\nresult.append([u,v,w])\nself.union(parent, rank, x, y)\n\n# print the contents of result[] to display the built MST\nprint \"Following are the edges in the constructed MST\"\nfor u,v,weight in result:\n#print str(u) + \" -- \" + str(v) + \" == \" + str(weight)\nprint (\"%d -- %d == %d\" % (u,v,weight))\ng = Graph(14)\n\ng.KruskalMST()\n\n\nWhy do you assume this code is limited to 10 vertices? This code comes from: http://www.geeksforgeeks.org/greedy-algorithms-set-2-kruskals-minimum-spanning-tree-mst/\n\nBut you have an error in use:\n\n g = Graph(14)\n\n\nDefines a graph with 14 vertices but then you used 0-14 which is 15 vertices. Either use:\n\n g = Graph(15)\n\n\nOr remove all the edges with vertex 14." ]

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[ "# Arrays\n\nJavaScript can hold an array of variables in an Array object. In JavaScript, an array also functions as a list, a stack or a queue.\n\nTo define an array, either use the brackets notation or the Array object notation:\n\n``````var myArray = [1, 2, 3];\nvar theSameArray = new Array(1, 2, 3);\n``````\n\nWe can use the brackets `[]` operator to address a specific cell in our array. Addressing uses zero-based indices, so for example, in `myArray` the 2nd member can be addressed with index 1. One of the benefits of using an array datastructure is that you have constant time look-up, if you already know the index of the element you are trying to access.\n\n``````console.log(myArray); // prints out 2\n``````\n\nArrays in JavaScript are sparse, meaning that we can also assign variables to random locations even though previous cells were undefined. For example:\n\n``````var myArray = []\nmyArray = \"hello\"\nconsole.log(myArray);\n``````\n\nWill print out:\n\n``````[undefined, undefined, undefined, \"hello\"]\n``````\n\n### Array Elements\n\nBecause JavaScript Arrays are just special kinds of objects, you can have elements of different types stored together in the same array. The example below is an array with a string, a number, and an empty object.\n\n``````var myArray = [\"string\", 10, {}]\n``````\n\n## Exercise\n\nYou must define an array with the following three variables:\n\n1. A string which has the value of \"What is the meaning of life?\"\n2. A number which has a value of `42`\n3. A boolean which has a value of `true`" ]

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[ "# 2008-9 Integer-valued function\n\nLet $$\\mathbb{R}$$ be the set of real numbers and let $$\\mathbb{N}$$ be the set of positive integers. Does there exist a function $$f:\\mathbb{R}^3\\to \\mathbb{N}$$ such that f(x,y,z)=f(y,z,w) implies x=y=z=w?\n\nGD Star Rating" ]

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[ "# Graphing Given Point(s) & Slope Practice (Linear Equations/Functions) Worksheet", null, "", null, "", null, "", null, "", null, "", null, "", null, "", null, "Subject\nGrade Levels\nResource Type\nProduct Rating\nFile Type\n\nPDF (Acrobat) Document File\n\nBe sure that you have an application to open this file type before downloading and/or purchasing.\n\n1 MB|8 pages\nShare\nProduct Description\n\nThis worksheet is designed to give students practice graphing points and linear equations given a point and the slope of the line. It also practices finding the slope of a line and the x and y intercepts given two points on the line.\n\nOne of the difficulties I have found that students have with linear equations is that they don't see a line as infinite points. They graph two points, connect them, and then call it good. They don't understand that a linear equation is a continuation of points. This worksheet forces students to continue a linear equation across the graph and write down different points on the line. Having students write down and continue points across a graph really helps them to see what is going on with linear equations.\n\nThis worksheet is 4 pages long (blank graphs take up a lot of room). I have included an answer key with this worksheet. Please note that some answers may be different depending on what points the students choose to list.\n\nThis worksheet is the final slope/graphing practice I do with students before getting to slope-intercept form of linear equations (y = mx + b).\n\nTotal Pages\n8 pages\nAnswer Key\nIncluded\nTeaching Duration\n50 minutes\nReport this Resource", null, "Sign Up" ]

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[ "## matlab中霍夫线检测函数,matlab 霍夫检测_星瀚Air的博客-程序员秘密\n\n%霍夫检测\n\nBW=rgb2gray(BW);\n\nthresh=[0.01,0.17];\n\nsigma=2;%定义高斯参数\n\nf = edge(double(BW),'canny',thresh,sigma);\n\nfigure(1),imshow(f,[]);\n\ntitle('canny 边缘检测');\n\n[H, theta, rho]= hough(f,'RhoResolution', 0.5);\n\n%imshow(theta,rho,H,[],'notruesize'),axis on,axis normal\n\n%xlabel('\\theta'),ylabel('rho');\n\npeak=houghpeaks(H,5);\n\nhold on\n\nlines=houghlines(f,theta,rho,peak);\n\nfigure,imshow(f,[]),title('Hough Transform Detect Result'),hold on\n\nfor k=1:length(lines)\n\nxy=[lines(k).point1;lines(k).point2];\n\nplot(xy(:,1),xy(:,2),'LineWidth',4,'Color',[.6 .6 .6]);\n\nend\n\n%%\n\nIhsv=rgb2hsv(I);\n\nIv=Ihsv(:,:,3);                    %提取v空间\n\nIvl=Iv(500:end,:);              %截取下半部\n\nIedge=edge(Ivl,'sobel');    %边沿检测\n\nIedge = imdilate(Iedge,ones(3));%图像膨胀\n\n%新建窗口，绘图用\n\nfigure (2)\n\nimshow(Iedge);\n\nhold on\n\n%左方直线检测与绘制\n\n%得到霍夫空间\n\n[H1,T1,R1] = hough(Iedge,'Theta',20:0.1:75);\n\n%求极值点\n\nPeaks=houghpeaks(H1,5);\n\n%得到线段信息\n\nlines=houghlines(Iedge,T1,R1,Peaks);\n\n%绘制线段\n\nfor k=1:length(lines)\n\nxy=[lines(k).point1;lines(k).point2];\n\nplot(xy(:,1),xy(:,2),'LineWidth',4);\n\nend\n\n%右方直线检测与绘制\n\n[H2,T2,R2] = hough(Iedge,'Theta',-75:0.1:-20);\n\nPeaks1=houghpeaks(H2,5);\n\nlines1=houghlines(Iedge,T2,R2,Peaks1);\n\nfor k=1:length(lines1)\n\nxy1=[lines1(k).point1;lines1(k).point2];\n\nplot(xy1(:,1),xy1(:,2),'LineWidth',4);\n\nend\n\nhold off\n\n%%\n\n%以下只是做一个带直线的图像而已\n\nr=300;\n\njiaodu=30;      %更改这个值测试，90度270度时不管用\n\njiaodu1=mod(jiaodu,360);\n\nflag=0;\n\nif jiaodu1>=0 && jiaodu1<90\n\njiaodu1=jiaodu1;\n\nflag=1;\n\nend\n\nif jiaodu1>=90 && jiaodu1<180\n\njiaodu1=180-jiaodu1;\n\nflag=2;\n\nend\n\nif jiaodu1>=180 && jiaodu1<270\n\njiaodu1=jiaodu1-180;\n\nflag=3;\n\nend\n\nif jiaodu1>=270 && jiaodu1<360\n\njiaodu1=360-jiaodu1;\n\nflag=4;\n\nend\n\nH=floor(r*sin(jiaodu1*pi/180));\n\nW=floor(r*cos(jiaodu1*pi/180));\n\nif mod(H,2)==0\n\nH=H+1;\n\nend\n\nif mod(W,2)==0\n\nW=W+1;\n\nend\n\nw=zeros(H,W);\n\nif jiaodu1 ~= 90 && jiaodu1 ~= 270\n\nfor i=1:H\n\nfor j=1:W\n\ntmp=floor(j*tan(jiaodu1*pi/180));\n\nif tmp+1==i\n\nw(i,j)=r;\n\nend\n\nend\n\nend\n\nelse\n\nfor i=1:H\n\nw(i,1)=r;\n\nend\n\nend\n\nif flag==1 || flag==3      %如果角度在1,3象限，卷积矩阵上下翻转\n\nw=flipud(w);\n\nend\n\n%下面是真正的霍夫变换\n\nimg=mat2gray(w);      %处理这个图像\n\n[m n]=size(img);\n\nimshow(img);\n\ndata=zeros(314,2*(m+n));\n\nfor i=1:m                      %将图像二维空间的一个点映射到p=x*cos(theta)+y*sin(theta)方程对应的参数空间的一条曲线\n\nfor j=1:n\n\nif img(i,j)==1\n\nfor theta=0.01:0.01:3.14\n\ndata(round(theta*100),round(i*sin(theta)+j*cos(theta)+m+n))= ...\n\ndata(round(theta*100),round(i*sin(theta)+j*cos(theta)+m+n))+1;\n\nend\n\nend\n\nend\n\nend\n\ntheta=0;\n\nma=0;\n\nfor i=1:314                %寻找曲线相交最多的那个点，即找最大值\n\nfor j=1:2*(m+n)\n\nif data(i,j)>ma\n\nma=data(i,j);\n\ntheta=i/100;\n\nrou=j-m-n;\n\nend\n\nend\n\nend\n\nfigure;imshow(data)    %形象的显示参数空间曲线\n\nsr_k=tan(jiaodu*pi/180)    %设置的斜率\n\nre_k=cos(theta)/sin(theta)  %求得的斜率\n\n### pytorch中BatchNorm1d、BatchNorm2d、BatchNorm3d的区别_Flowiiiing的博客-程序员秘密\n\n1.nn.BatchNorm1d(num_features)1.对小批量(mini-batch)的2d或3d输入进行批标准化(Batch Normalization)操作2.num_features：来自期望输入的特征数，该期望输入的大小为’batch_size x num_features [x width]’意思即输入大小的形状可以是’batch_size x num_features’ 和 ‘batch_size x num_features x width’ 都可以。（输入输出相同）输入\n\n### DSL语句_weixin_33736649的博客-程序员秘密\n\n2019独角兽企业重金招聘Python工程师标准&gt;&gt;&gt; ...\n\n### 百分之九十九的JAVA工作者都不知道的知识_weixin_34409357的博客-程序员秘密\n\n1.Core Java部分 这是最基础的,对于一个java高级开发/设计人员,你需要对这一部分达到精通的水平,重点内容如下: a.面向对象编程思想(封装继承多态接口) b.字符串处理 c.java.lang包,java.util包等常用包 4.java异常处理 2.Java高级部分 a.Java I/O流 b.Java多线程技术 c.Java网络编程 d.Java Swing...\n\n### 阿里云分布式事务seata：springcloud-eureka-feign-mybatis_邪神大叔的博客-程序员秘密\n\nspringcloud-eureka-feign-mybatis-seata-client/server注：来源阿里云开源seata，本人只做修改概览：seata由服务端及客户端组成，服务端是阿里的项目需要在后台一直运行，客户端只是集成了客户端部分配置文件而已。需要两端同时运行才可以完成分布式事务；服务端：https://github.com/xieshenace/springclou...\n\n### 大数据产品推荐：神策分析——可私有化部署的用户行为分析平台_大数据应用产品_乐投网的博客-程序员秘密\n\n1、产品名称神策分析（Sensors Analytics）2、所属分类金融科技·风控、征信、反欺诈、大数据安全、智能获客3、产品介绍神策分析（Sensors Analytics）是一个深度用户行为分析平台，支持私有化部署、基础数据采集与建模，并作为PaaS平台支持二次开发。此外，还提供大数据相关咨询和数据驱动完整解决方案。4、应用场景／人群在\n\n### send，recv，sendto，recvfrom_Jody1989的博客-程序员秘密\n\nsend函数int send( SOCKET s,    const char FAR *buf,    int len,    int flags ); 不论是客户还是服务器应用程序都用send函数来向TCP连接的另一端发送数据。客户程序一般用send函数向服务器发送请求，而服务器则通常用send函数来向客户程序发送应答。该函数的第一个参数指定发送端套接字描述符；" ]

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[ "# Integral evalutation\n\nI am trying to integrate the following expression over $L$.\n\nE^(-2 L n) (1 - L/(2 s))^(-1 + 4 n µ) (L/s)^(-1 + 4 n v)\n\n\nI did...\n\nIntegrate[E^(-2 L n) (1 - L/(2 s))^(-1 + 4 n µ) (L/s)^(-1 + 4 n v), L]\n\n\nbut Mathematica fails to solve this integral. I tried with actual values but this issue remains.\n\nIntegrate[ E^(-2 L 100) (1 - L/(2 0.08))^(-1 + 4 100 3*^-7) (L/0.08)^(-1 + 4 100 3*^-7), L]\n\n\nHow can I calculate or approximate this integral?\n\nNote the following assumptions\n\n0 <= s <= 1\n0 <= µ <= 1\n0 <= v <= 1\n1 <= n <= Infinity\n\n\n, where the sign <= means \"smaller or equal\". Note also that µ and v are typically very small (on the order of $10^{-7}$)\n\nSetting\n\nintegrand= E^(-2 L 100) (1 - L/(2 0.08))^(-1 + 4 100 3*^-7) (L/0.08)^(-1 + 4 100 3*^-7)\n\n\nwith the example given in your question, you can use\n\nni[x_]:=NIntegrate[integrand,{L,0.1,x}]\n\n\nand\n\nPlot[Re@ni[x],{x,0.1,0.5}]\n\n\nto plot the numerical integrand. Your example does not seem to lend itself well to approximation, though. Or perhabs I chose the L in the wrong interval? Also, there may not exist a \"nice\" solution to your integral.\n\n• Thanks for your answer @Berg. The range of values for L is slightly high but correspond to what I am interested in. Can you point me to some source of information so that I can understand the expression Re@ that might explain why the plot looks like a cardiogram rather than like a continuously increasing function of $x$! – Remi.b Oct 27 '14 at 23:48\n• Not sure about a reference, but numerical approximations can fail, if, for example, the numerical values involved are very small. In that case the floating point reals in the computer cannot properly store those values. One could try to rescale the problem. Another problem can appear if one has highly oscillating integrals. Think of a, say, a sinus function with very high frequency. One then has lots of parts that cancel, but the numerical approximation only evaluates some of those. Depending on what points exactly are used for the approximation the resulting integral can be large or small. – Berg Oct 28 '14 at 8:43\n• Oh, and Re@x=Re[x] is just the real part of x. – Berg Oct 28 '14 at 8:53" ]

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[ "", null, "or", null, "or", null, "taken", null, "why\n\nMake sure to remember your password. If you forget it there is no way for StudyStack to send you a reset link. You would need to create a new account.\n\nDon't know\nKnow\nremaining cards\nSave\n0:01\nEmbed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.\n\nNormal Size     Small Size show me how\n\n# WGU\n\n### WGU Study Final Material\n\nMode Most frequent number in a set of numbers.\nA triangle with no congruent sides Scalene\nA triangle with 2 congruent sides Isosceles\nA triangle with 3 congruent sides Equilateral\nOrder of Operations 1. Parentheses 2. Exponents 3. Multiplication/Division (left to right) 4. Addition/Subtraction (left to right)\nSkip Counting Skip counting is counting by 2 or 5 or 10 and so forth.\nA triangle less than 90 Acute\nTriangle 3 sides\nPentagon 5 sides\nHexagon 6 sides\nHeptagon 7 sides\nOctogon 8 sides\nNonogon 9 sides\nDecagon 10 sides\nMean Average, add up all the numbers in a set of values, then divide that number by the number of numbers in the set\nComplementary Angles Two angles that together equal 90\nSupplementary Angles Two angles that together equal 180\nRange The largest number minus the smallest number in a set of values\nStraight Angles Measures 180\nInterior Angle of a Triangle 60\nInterior Angle of a Square 90\nInterior Angle of a Pentagon 108\nInterior Angle of a Hexagon 120\nParallel Lines Equals 180 (also known as straight angles)\nSurface Area Surface area is the sum of the lateral surface area and the area of bases.\nPerimeter The sum of the length of it's sides.\nVolume Number of unit cubes it will hold.\nWeight Force exerted by a gravitational pull.\nMass The quantity of matter, as opposed to the weight of the object.\nEven + Even numbers Always equal an even\nEven + Odd numbers Always equal an odd\nOdd + Odd numbers Always equal an even\nSquare A rectangle with two adjacent sides congruent. Equivently a square is a quadrilateral with four right angles and four congruent sides.\nRhombus A parallelogram with two adjacent sides congruent.\nRectangle A parallelogram with a right angle. Equivalently a rectangle is a quadrilateral with four right angles.\nParallelogram A quadrilateral on which each pair of opposite sides is parallel.\nIsosceles Trapezoid A trapezoid with exactly one pair of congruent sides. Equivalently an isosceles trapezoid is a trapezoid with two congruent base angles.\nKite A quadrilateral with two sides adjacent and congruent. The other two sides are also congruent.\nGreatest Possible Error The GPE is a measurement one-half the unit used. For example, if the width of a peice of board was measured to the nearest centimeter as 5cm, the actual width must be between 4.5cm and 5.5cm.\nRote Counting -The child is able to recite the number name sequence correctly.\nGraphs Graphs should have 1. Title 2.Lables on both axes 3. Source of data 4. Key to pictograph 5. Uniform size of symbols in pictograph 6. Scale: is the break shown 7. Scale: are the numbers equally spaced.\nArea The surface included within a set of lines; specifically: the number of unit squares equal in measure to the surface.\nCircumference the external boundary or surface of a figure or object\nFormula to find missing leg of hypotenuse of a triangle Use this formula for both problems A(to the second power) + B(to the second power)= C squared\nDefinition of Rote Counting Child has no number concept\nEven divided by Even Answer can be even or odd\nGraphing Calculators have enriched learning in which ways? 1. Tools for expediency 2. Amplifiers for conceptual understanding. 3. Catalysts for critical thinking. 4. Vehicles for integration.\nWhen to use four operation calculators Adding, Subtraction, Multiplication, Division\nCubit A cubit is equal to one forearm\nVertical Angles These are two angles whose sides form two pairs of opposite rays. We can think of these as opposite angles formed by an X.\nEven-Odd Equals Odd\nEven-Even Equals Even\nOdd-Odd Equals Even\nOdd-Even Equals Even\nOdd*Even Equals Even\nOdd*Odd Equals Odd\nEven+Even Equals Even\nOdd+Odd Equals Even\nEven+Odd Equals Odd\nPrime Numbers Prime numbers are natural numbers that have themselves and 1 as factors.\nComposite Numbers Composite numbers are any number that is not prime.\n1 Gallon Equals 4 Quarts\n1 Quart Equals 2 Pints\nPints in a Gallon There are 8 Pints in 1 Gallon\n1 Yard Equals 3 Feet\n1 Foot Equals 12 Inches\n1 Pint Equals 2 Cups\n1 Cup Equals 8fl. oz's\nRational Counting A child uses one-to-one correspondence between objects and numbers.\n4 Types of Statistical Bias 1. Relying on voluntary response 2. Undercoverage of population 3. Non-Response Bias 4. Response Bias\nExample of One-to-One Correspondence Suppose a child knows how to count only to 3. The child might still tell that there are as many fingers on the left hand as on the right hand by matching the fingers up.\nKilo (Metric System) Symbol=k Factor=1000\nHecto (Metric System) Symbol=h Factor=100\nDeka (Metric System) Symbol=da Factor=10\nDeci (Metric System) Symbol=d Factor=.1\nCenti (Metric System) Symbol=c Factor=.01\nMilli (Metric System) Symbol=m Factor=.001\nOutlier A number in a set of numbers that is much greater or less than the rest in a set of values.\nThe sum of the exterior angle of a tirangle 360 Degree's\nCreated by: swallace80" ]

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[ "Categories\n\nLesson 6.5 Dividing Polynomials\n\nSkill B Dividing polynomials Recall To divide a polynomial by you can divide synthetically by 24. P x 4 2x 8x 3 2x 8.\n\nLesson 65 Dividing Polynomials Day 1 WS 65A.", null, "Lesson 6.5 dividing polynomials. 56 Multiplying and Dividing a Polynomials by a Monomial P94 C Students will learn how to multiply and divide polynomials by a monomial by connecting it to prior learning in section 55. The other three expressions are polynomials. Checking Your Long Division.\n\n2 36P 11. This third degree polynomial has 2 terms. Example 2 Given show that when is divided by the remainder is equal to P5.\n\n65 Dividing Polynomials Essential Question. Then multiply and add for. Since the denominator of contains a variable it is not a polynomial.\n\n6-1 Polynomials LESSON Degree Polynomial in Standard Form 08 1 2x 3 2 x 2 4x 5 3 4 x 3 x 4 6 x 4 x 3 5x 2 3x 1 5 9 x 5 x 3 1 6 is the leading coefficient of this polynomial. Common Core State Standards. 69 519 3 x x 5 92 1 x x 8.\n\nThe divisor is x 3. Warm Up 3-4 Quiz. 2 14 3 3 x x 5.\n\nModule 6 65 Dividing Polynomials. In a game of bingo the contestants have a 1 in 12 chance of winning. If it is find the remaining factors of p x.\n\nPages 255 257 7 9 14 16 17 a 19 21. What are some ways to divide polynomials and how do you know when. Find a 372 Bring down the first coefficient.\n\nEXAMPLES – Dividing Polynomials using LONG or SYNTHETIC DIVISION Name_____ ID. Then write the coefficients of the dividend. Then write the coefficients and a in the synthetic division format.\n\n2 Divide polynomial expressions using Synthetic Division. Step 2 Write a in the upper left corner. SmartBoard Notes and Examples.\n\nExplain 1 Dividing Polynomials Using Long Division Recall that arithmetic long division proceeds as follows. 339 647 7 x x 9. It is the greatest monomial that can divide every term in a polynomial.\n\n3 11P 10. 65 – Dividing Polynomials. How the long division algorithm used in arithmetic can be adapted to divide polynomials.\n\nDividing Polynomials Practice and Problem Solving. Module 6 Review. A b Dividing Polynomials Example 1.\n\nI can divide one polynomial by another polynomial to determine the quotient and the remainder Warm Up. Multiply the previous answer by 2. Find out how to divide polynomials with missing terms and divide polynomials with remainders.\n\n23 Quotient Divisor 12 277 Dividend 24 37 36 1 Remainder Notice that the long division leads to the result _____dividend divisor quotient _____remainder divisor. 165 does not belong with the other three. 2 x 2 x 10 x 3.\n\nWe divide with monomial divisors and also do long division involving polynomial divisors. 1 Y Q2M0H1R6t KrutKah wSKoyfEtgwVaFrseT cLlLZCB Z pA_lilF irxiDglhMtesQ froeVsNefrvreodr-1-Divide using LONG DIVISION. Determine whether the given binomial is a factor of the polynomial p x.\n\nAccording to the polynomial Vt t3 – 4t – 25t 100 where Vis in volts and t is in seconds. Add 3 and 8. How does knowing one linear factor of a polynomial help find the other.\n\nLESSON 6-5 Practice and Problem Solving. 9×4 I Ix2 4 16 D 4×4 3x27x2. Constants have degree 0.\n\nYeah even many books are offered this book can steal the reader heart thus much. Lesson 65 Dividing Polynomials Day 2 Binomial Theorem Group Quiz. Elementary Algebra Skill Dividing Polynomials Divide.\n\n120 32 248232 1 228 0 quotient. 32 21 10 Step 3. Highlight the quotient and remainder.\n\nP x 3 3x-2x 5. 9×4 I Ix2 4 16 D 4×4 3x27x2. Read Book 6 5 Dividing Polynomials Cusd80 6 5 Dividing Polynomials Cusd80 Dear endorser bearing in mind you are hunting the 6 5 dividing polynomials cusd80 collection to way in this day this can be your referred book.\n\nStep 1 Find a. Module 6 Quiz. X 4 9.\n\nThen write the coefficients and a in the synthetic division format. Divide the following numbers using long division. Lets extend our knowledge of long.\n\n5k3 4k2 4k 6 5 -8×3 40×2 – 37x 30. 0 hrs 35 mins Scoring. 1 Divide polynomial expressions using Long Division.\n\nCompare long division and synthetic division of polynomials. Module 6 Review. Practice Problems Check your understanding of the lesson.\n\n1 18r5 36r4 27r3 9r 2 9×5 9×4 45×3 9×2 3 2n3 20n2 n 10n2 4 3v3 v2 2v 9v3 5 45v4 18v3 4v2 9v3 6 9n3 n2 3n 9n2 7 30r3 2r2 30r 10r2 8 9k3m2n 3k2mn2 54km3n 6kmn 9 6p3 150p2 5p 15p 10 12m3y4 12m2y3 3my2 6m2y2 11 m2 14m 31 m 10 12 x2 2x 36 x 5. Lesson 71 Finding Rational Solutions of. This fifth degree polynomial.\n\nDividing Polynomials Learn how to do long division with polynomials. Continue this sequence Of Steps until you reach. Solution 5 4 213 232 20 35 47 3.\n\nThe students will be able to. LESSON Reteach 6-3 Dividing Polynomials continued When the divisor is in the form x a use synthetic division to divide. Example 1 Divide by using along division.\n\nHere is a set of practice problems to accompany the Dividing Polynomials section of the Polynomial Functions chapter of the notes for Paul Dawkins Algebra course at Lamar University. 65 Dividing Polynomialsnotebook 20 February 04 2016. WRITING IN MATH Use the information at the beginning of the lesson to write assembly instruction using the division of polynomials to make a paper cover for your textbook.\n\nThat a polynomial dividend can be built back up from a divisor quotient and remainder using the formula dividend divisor x quotient remainder.", null, "Dividing Polynomials Worksheet Polynomials Division Worksheets Math Word Problems", null, "Screenshot 21 Png Name Date Unit 5 Polynomial Functions Bell Homework 6 Dividing Polynomials Directions Use Factoring To Find The Following Quotients Course Hero", null, "Warm Up2 26 09 Skill Review Simplify Each Expression Use Only Positive Exponents 1 3a 2 4a 6 2 8a 5 2a 2 3 6m 2 N 2 3mn 4 X 4 X 2 X Ppt Download", null, "Factoring Polynomials Remainder Amp Factor Theorems", null, "Dividing Polynomials Long Division Module 6 5 Part 1 Youtube", null, "", null, "", null, "Math 3 6 5 Dividing Polynomials Youtube", null, "Ch7 3 Pdf Area Division Mathematics", null, "Pdf The Proficiency Level In Dividing Polynomials Using Synthetic Division", null, "", null, "", null, "", null, "", null, "", null, "" ]

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[ "Equidistribution of cusp forms on ${\\mathrm{PSL}}_{2}\\left(𝐙\\right)\\setminus {\\mathrm{PSL}}_{2}\\left(𝐑\\right)$\nAnnales de l'Institut Fourier, Tome 47 (1997) no. 3, pp. 967-984.\n\nNous donnons la preuve d’une version microlocale d’un résultat de W. Luo et P. Sarnak concernant la répartition asymptotique des fonctions de Wigner associées aux formes paraboliques sur ${\\mathrm{PSL}}_{2}\\left(\\mathbf{Z}\\right)\\setminus {\\mathrm{PSL}}_{2}\\left(\\mathbf{R}\\right)$.\n\nWe prove a microlocal version of the equidistribution theorem for Wigner distributions associated to cusp forms on ${\\mathrm{PSL}}_{2}\\left(\\mathbf{Z}\\right)\\setminus {\\mathrm{PSL}}_{2}\\left(\\mathbf{R}\\right)$. This generalizes a recent result of W. Luo and P. Sarnak who prove equidistribution on ${\\mathrm{PSL}}_{2}\\left(\\mathbf{Z}\\right)\\setminus \\mathbf{H}$.\n\n@article{AIF_1997__47_3_967_0,\nauthor = {Jakobson, Dmitri},\ntitle = {Equidistribution of cusp forms on ${\\rm PSL}_2({\\bf Z})\\backslash {\\rm PSL}_2({\\bf R})$},\njournal = {Annales de l'Institut Fourier},\npages = {967--984},\npublisher = {Association des Annales de l{\\textquoteright}institut Fourier},\nvolume = {47},\nnumber = {3},\nyear = {1997},\ndoi = {10.5802/aif.1588},\nzbl = {0868.43011},\nmrnumber = {99c:11063},\nlanguage = {en},\nurl = {http://www.numdam.org/articles/10.5802/aif.1588/}\n}\nJakobson, Dmitri. Equidistribution of cusp forms on ${\\rm PSL}_2({\\bf Z})\\backslash {\\rm PSL}_2({\\bf R})$. Annales de l'Institut Fourier, Tome 47 (1997) no. 3, pp. 967-984. doi : 10.5802/aif.1588. http://www.numdam.org/articles/10.5802/aif.1588/\n\n[CdV] Y. Colin De Verdière, Ergodicité et fonctions propres du laplacien, Comm. Math. Phys, 102 (1985), 497-502. | MR 87d:58145 | Zbl 0592.58050\n\n[GR] I.S. Gradshteyn and I.M. Ryzhik, Tables of Integrals, Series and Products, Academic Press, 4th edition, 1980.\n\n[Ja94] D. Jakobson, Quantum Unique Ergodicity for Eisenstein Series on PSL2(ℤ) PSL2(ℝ), Annales de l'Institut Fourier, 44-5 (1994), 1477-1504. | Numdam | MR 96b:11068 | Zbl 0820.11040\n\n[Ja95] D. Jakobson, Thesis, Princeton University, 1995.\n\n[Kuz] N. Kuznetsov, Peterson's conjecture for cusp forms of weight zero and Linnik's conjecture; sums of Kloosterman sums, Mat. Sb., 111 (1980), 334-383. | MR 81m:10053 | Zbl 0427.10016\n\n[LS] M. Luo and P. Sarnak. Quantum Ergodicity of Eigenfunctions on PSL2(ℤ)\\ℍ, IHES Publ., 81 (1995), 207-237. | Numdam | Zbl 0852.11024\n\n[MOS] W. Magnus, F. Oberhettinger and R.P. Soni, Formulas and theorems for the special functions of mathematical physics, Springer, 1966. | MR 38 #1291 | Zbl 0143.08502\n\n[Sn74] A.I. Shnirelman, Ergodic Properties of Eigenfunctions, Uspekhi Mat. Nauk, 29-6 (1974), 181-182.\n\n[Sn93] A.I. Shnirelman, On the Asymptotic Properties of Eigenfunctions in the Regions of Chaotic Motions, Addendum to V. F. Lazutkin's book KAM Theory and Semiclassical Approximations, Springer, 1993.\n\n[S1] J. Slater, Generalized hypergeometric functions, Cambridge Univ. Press, 1966. | Zbl 0135.28101\n\n[Ze87] S. Zelditch, Uniform distribution of Eigenfunctions on compact hyperbolic surfaces, Duke Math. Journal, 55 (1987), 919-941. | MR 89d:58129 | Zbl 0643.58029\n\n[Ze91] S. Zelditch, Mean Lindelöf hypothesis and equidistribution of cusp forms and Eisenstein series, Jour. of Funct. Analysis, 97 (1991), 1-49. | MR 92h:11046 | Zbl 0743.58034\n\n[Ze92] S. Zelditch, Selberg Trace Formulas and Equidistribution Theorems for Closed Geodesics and Laplace Eigenfunctions: Finite Area Surfaces, Mem. AMS, 90 (No. 465), 1992. | Zbl 0753.11023" ]

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[ "", null, "Dataplot Vol 2 Vol 1\n\n# LV\n\nName:\nLV (LET)\nType:\nLibrary Function\nPurpose:\nCompute the modified Struve function.\nDescription:\nThe modified Struve function can be expressed as:", null, "where v is the order of the modified Struve function and", null, "is the gamma function.\n\nDataplot computes this function using the STVL0, STVL1, and STVLV routines from \"Computation of Special Functions\" (see the Reference section below).\n\nSyntax 1:\nLET <y> = LV(<x>,<v>)             <SUBSET/EXCEPT/FOR qualification>\nwhere <x> is a number, variable or parameter;\n<v> is a number, parameter, or variable;\n<y> is a variable or a parameter (depending on what <x> and <v> are) where the computed modified Struve function values are stored;\nand where the <SUBSET/EXCEPT/FOR qualification> is optional.\n\nDataplot supports the modified Struve function for non-negative real x and for orders between -8.5 and 12.5. This syntax is used for arbitrary order.\n\nSyntax 2:\nLET <y> = L0(<x>)             <SUBSET/EXCEPT/FOR qualification>\nwhere <x> is a number, variable or parameter;\n<y> is a variable or a parameter (depending on what <x> is) where the computed modified Struve function values are stored;\nand where the <SUBSET/EXCEPT/FOR qualification> is optional.\n\nDataplot supports the modified Struve function for non-negative real x. This syntax is used for the modified Struve function of order 0.\n\nSyntax 3:\nLET <y> = L1(<x>)             <SUBSET/EXCEPT/FOR qualification>\nwhere <x> is a number, variable or parameter;\n<y> is a variable or a parameter (depending on what <x> is) where the computed modified Struve function values are stored;\nand where the <SUBSET/EXCEPT/FOR qualification> is optional.\n\nDataplot supports the modified Struve function for non-negative real x. This syntax is used for the modified Struve function of order 1.\n\nExamples:\nLET A = LV(2.3,1)\nLET A = LV(X,A1)\nLET X2 = LV(X1,4) FOR X1 = 0.1 0.1 3.0\nDefault:\nNone\nSynonyms:\nNone\nRelated Commands:\n HV = Compute the Struve function. BESSJN = Compute the Bessel function of the first kind. BESSYN = Compute the Bessel function of the second kind. BESSIN = Compute the modified Bessel function. BESSKN = Compute the modified Bessel function of the third kind.\nReference:\n\"Computation of Special Functions\", Shanjie Zhang and Jianming Jin, John Wiley and Sons, 1996, chapter 11.\n\n\"AMS 55: Handbook of Mathematical Functions\", Abramowitz and Stegun, Eds., Washington, DC, National Bureau of Standards, 1964.\n\nApplications:\nSpecial Functions\nImplementation Date:\n1997/12\nProgram:\nMULTIPLOT 2 2\nMULTIPLOT CORNER COORDINATES 5 5 95 95\nTITLE ORDER 0\nPLOT LV(X,0) FOR X = 0 0.01 10\nTITLE ORDER 1\nPLOT LV(X,1) FOR X = 0 0.01 10\nTITLE ORDER 2\nPLOT LV(X,2) FOR X = 0 0.01 10\nTITLE ORDER 3\nPLOT LV(X,3) FOR X = 0 0.01 10\nEND OF MULTIPLOT\nMOVE 50 97\nJUSTIFICATION CENTER\nTEXT MODIFIED STRUVE FUNCTIONS\n\nDate created: 6/5/2001\nLast updated: 4/4/2003" ]

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[ "justification for method to factorize n knowing RSA private exponent d\n\nI know that knowing the private exponent $d$ corresponding to the private key $k_{pub}\\langle n,e\\rangle$ it is possible to efficiently factorize n.\n\nThe procedure starts stating that:\n\n$ed -1 = s(p-1)(q-1)$\n\nand then saying that:\n\nRandomly picking $x\\in\\mathbb{Z}_n^*$ we know that $x^{ed-1}\\equiv 1\\pmod n$ and computing $y=\\sqrt{x^{ed-1}}=x^{\\frac{ed-1}2}$\n\nWe have the identity:\n\n$y^2-1$\n\nAnd so:\n\n• If $y\\neq\\pm1\\pmod n$, a factor of $n$ is obtained as: $gcd(y-1,n)$\n• If $y=-1\\pmod n$, we repeat this procedure from the beginning and pick another value for $x$\n• If $y=+1\\pmod n$, we iterate the whole procedure starting from the square root of $y^2$\n\nCould someone give me a justification for this? Especially for:\n\n\"If $y\\neq\\pm1\\pmod n$, a factor of $n$ is obtained as: $gcd(y-1,n)$\"\n\n• Hint: you know that $y^2\\equiv 1 \\pmod n$ and you know that $y\\not\\equiv 1 \\pmod n\\Leftrightarrow (y-1)(y+1)\\equiv 0 \\pmod n\\Leftrightarrow (y-1)(y+1)=k\\cdot n$ – SEJPM Jun 30 '16 at 11:19\n\nWe have $y^2-1 \\equiv 0 \\pmod n$, meaning that $y^2-1 = (y+1)(y-1)$ is a multiple of $n$. $y \\not \\equiv \\pm 1 \\pmod n$ means that neither of $y+1$ and $y-1$ is a multiple of $n$. Now, clearly $\\gcd(y-1,n)$ is a divisor of $n$; we want to show that it is not $1$ or $n$.\n• It cannot be $1$, because that would imply that $n$ divides $y+1$, which we assume is not the case.\n• Likewise it cannot be $n$, because that would imply that $n$ divides $y-1$.\nThe reason we take $y$ such that $y^2 - 1 \\equiv 0 \\pmod n$, by the way, is so that we have a good chance of finding a non-trivial factor. Indeed, if we just pick any random $y$, it is overwhelmingly likely that $\\gcd(y-1,n) = 1$, which does not help us.\n• \"$y \\not \\equiv \\pm 1 \\pmod n$ means that neither $y+1$ and $y-1$ is a multiple of n\" is because: $\\\\$ for $y=+1$ we'd have $y-1= 0\\pmod n \\Rightarrow \\ y-1$ multiple of $n$ and for $y=-1$ we'd have $y+1= 0\\pmod n \\Rightarrow \\ y+1$ multiple of $n$ , right? – Alessio Martorana Jun 30 '16 at 11:57\n• Could you please explain me the reasoning why if $gcd(y-1,n) = 1 \\Rightarrow$ $n$ divides $(y+1)$ ? – Alessio Martorana Jun 30 '16 at 12:17" ]

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[ "Model.GB {BinaryEPPM} R Documentation\n\n## Probabilities for binomial and generalized binomial distributions given p's and b.\n\n### Description\n\nCalculates the probabilities for binomial and generalized binomial given values for p's and b.\n\n### Usage\n\n```Model.GB(parameter, model.name, link, ntrials, covariates.matrix.p,\noffset.p = c(rep(0, length(ntrials))))\n```\n\n### Arguments\n\n `parameter` A vector of the parameters of the model which is set to initial estimates on function call. `model.name` The model being fitted is one of the two 'binomial' or 'generalized binomial'. `link` Takes one of nine values i.e., 'logit', 'probit', 'cloglog', 'cauchit', 'log', 'loglog', 'double exponential', 'double reciprocal', 'power logit'. The default is 'cloglog'. The 'power logit' has an attribute of 'power' for which the default is 1 i.e., a logit link. `ntrials` This is a scalar representing the denominator i.e., the length of the probability mass function returned is this scalar + 1. `covariates.matrix.p` A matrix of covariates for p where rows are the number of values in listbinary and columns the covariates. This matrix is extracted from the formulae in function BinaryEPPM. However, in the accompanying example it is shown how it can be constructed independently of function BinaryEPPM. `offset.p` An offset vector for p. The default is a vector of ones.\n\n### Value\n\nList of arguments input together with a list of probabilities vectors and a data frame of values of a and b of Equation (5) of Faddy and Smith (2012).\n\n `model` The model is either 'binomial' or 'generalized binomial'. `link` The link is either 'logit' or 'cloglog'. `parameter` A vector of the parameters of the model which is set to initial estimates on function call. `probabilities` A list of the vectors of probabilities of the model. `Dparameters` A data frame of values of a and b of Equation (5) of Faddy and Smith (2012).\n\n### Author(s)\n\nDavid M. Smith <smithdm1@us.ibm.com>\n\n### References\n\nFaddy M, Smith D. (2012). Extended Poisson Process Modeling and Analysis of Grouped Binary Data. Biometrical Journal, 54, 426-435. doi: 10.1002/bimj.201100214.\n\n### Examples\n\n```link <- 'cloglog'" ]

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[ "# Definition:Binomial Coefficient/Complex Numbers\n\n## Definition\n\nLet $z, w \\in \\C$.\n\nThen $\\dbinom z w$ is defined as:\n\n$\\dbinom z w := \\ds \\lim_{\\zeta \\mathop \\to z} \\lim_{\\omega \\mathop \\to w} \\dfrac {\\map \\Gamma {\\zeta + 1} } {\\map \\Gamma {\\omega + 1} \\map \\Gamma {\\zeta - \\omega + 1} }$\n\nwhere $\\Gamma$ denotes the Gamma function.\n\nWhen $z$ is a negative integer and $w$ is not an integer, $\\dbinom z w$ is infinite.\n\n## Also rendered as\n\nSome sources give this as:\n\n$\\dbinom z w := \\ds \\lim_{\\zeta \\mathop \\to z} \\lim_{\\omega \\mathop \\to w} \\dfrac {\\zeta!} {\\omega! \\, \\paren {\\zeta - \\omega}!}$\n\nwhere $\\zeta! := \\map \\Gamma {\\zeta + 1}$.\n\nThis is unusual, however, as the factorial is usually defined only for positive integers." ]

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[ "Solutions by everydaycalculation.com\n\n## Multiply 56/50 with 5/63\n\n1st number: 1 6/50, 2nd number: 5/63\n\nThis multiplication involving fractions can also be rephrased as \"What is 56/50 of 5/63?\"\n\n56/50 × 5/63 is 4/45.\n\n#### Steps for multiplying fractions\n\n1. Simply multiply the numerators and denominators separately:\n2. 56/50 × 5/63 = 56 × 5/50 × 63 = 280/3150\n3. After reducing the fraction, the answer is 4/45\n\nMathStep (Works offline)", null, "Download our mobile app and learn to work with fractions in your own time:" ]

[ null, "https://answers.everydaycalculation.com/mathstep-app-icon.png", null ]

[ "## Algebra 1: Common Core (15th Edition)\n\n$(4x+11)(4x-11)$\n$16x^{2}-121=$ ...write each term as a square. $=(4x)^{2}-11^{2}$ ...factor using the rule for a difference of two squares. ($a^{2}-b^{2}=(a+b)(a-b),\\ a=4x,\\ b=11$) $=(4x+11)(4x-11)$" ]

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[ "NumWords.com\n\nHow to write Four thousand three hundred eighty-six in numbers in English?\n\nWe can write Four thousand three hundred eighty-six equal to 4386 in numbers in English\n\n< Four thousand three hundred eighty-five :||: Four thousand three hundred eighty-seven >\n\nEight thousand seven hundred seventy-two = 8772 = 4386 × 2\nThirteen thousand one hundred fifty-eight = 13158 = 4386 × 3\nSeventeen thousand five hundred forty-four = 17544 = 4386 × 4\nTwenty-one thousand nine hundred thirty = 21930 = 4386 × 5\nTwenty-six thousand three hundred sixteen = 26316 = 4386 × 6\nThirty thousand seven hundred two = 30702 = 4386 × 7\nThirty-five thousand eighty-eight = 35088 = 4386 × 8\nThirty-nine thousand four hundred seventy-four = 39474 = 4386 × 9\nForty-three thousand eight hundred sixty = 43860 = 4386 × 10\nForty-eight thousand two hundred forty-six = 48246 = 4386 × 11\nFifty-two thousand six hundred thirty-two = 52632 = 4386 × 12\nFifty-seven thousand eighteen = 57018 = 4386 × 13\nSixty-one thousand four hundred four = 61404 = 4386 × 14\nSixty-five thousand seven hundred ninety = 65790 = 4386 × 15\nSeventy thousand one hundred seventy-six = 70176 = 4386 × 16\nSeventy-four thousand five hundred sixty-two = 74562 = 4386 × 17\nSeventy-eight thousand nine hundred forty-eight = 78948 = 4386 × 18\nEighty-three thousand three hundred thirty-four = 83334 = 4386 × 19\nEighty-seven thousand seven hundred twenty = 87720 = 4386 × 20\n\nSitemap" ]

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[ "## ARITHMETIC INSTRUTIONS", null, "Mnemonic\n\n A", null, "Description\n\nThe basic purpose of this instruction is to add two 16-bit operands. One of the operands must first be loaded into the accumulator, such as by means of execution of a load-accumulator instruction. The add instruction then provides the address of the other operand, which must be in main storage. Addition takes place, and the result is placed in the accumulator:\n\n(Sign bit 0 = 0 specifies + number.)\n\n```\n0 000 0000 1001 1101 = Contents of accumulator\n+0 000 0010 0011 0101 = Contents of storage location addressed by add instruction\n0 000 0010 1101 0010 = Result loaded into accumulator\n```\n\nAlthough the result replaces the contents of the accumulator, the contents of the addressed storage location remain unchanged.\n\nThe result of the addition is either positive or negative, depending upon the magnitude of the values used and whether the signs of the two operands are the same:\n\n+ plus a + = + - plus a - = - + plus a - = sign of the larger operand - plus a + = sign of the larger operand\n\nThe value in the accumulator is positive if the leftmost bit is at a value of 0; the value in the accumulator is negative if the leftmost bit is at a value of 1. Negative numbers are in two's-complement form.\n\nThere are no addressing exceptions for the add instruction; all forms of addressing that are described under \"Effective-Address Generation\" apply to the A instruction.\n\nIndicators: The carry indicator is automatically reset to 0 at the beginning of an add-instruction execution. If, during the add-instruction execution, a carry-out of the high-order (leftmost) position of the accumulator occurs, then the carry indicator is set to 1; if no such carry-out of the high-order position occurs, the carry indicator remains at its reset condition of 0. It can subsequently be set or reset by the various actions listed under \"Carry and Overflow Indicators\" (see Figure 13).\n\nThe overflow indicator must be reset to 0 if it is to be used during execution of an add instruction. If the overflow indicator is at a value of 1 at the start of an add operation, it is not changed regardless of the result of the add operation. If the overflow indicator is at a value of zero at the start of an add operation, it is set to a value of 1 if the addition produces a result that exceeds the capacity of the accumulator. For example, when the following two 16-bit operands are added together,\n\n```\nS\n\n0 100 0000 0000 0000 Operand in accumulator -- a positive number\n+0 100 0000 0000 0000 Operand in main storage -- a positive number\n1 000 0000 0000 0000 = Result in accumulator -- a negative number\n(S = Sign bit)\n```\n\nthe result is greater than the capacity of the accumulator because the accumulator specifies a negative result (the leftmost bit is at a value of 1). In this case, the overflow indicator is set to 1. The carry indicator, however, is not set to one because a carry-out of the high-order position of the accumulator does not occur. Refer to \"Carry and Overflow Indicators\" for a discussion of how these two indicators can be used together in certain arithmetic operations.\n\nThe maximum capacity of the accumulator is:\n\nPower-of-2 Notation Decimal Notation Hexadecimal Notation\n+215-1 +32,767 +7FFF\n-215 -32,768 -8000\n\nExamples\n\nAssembler Language Coding Hexadecimal Value Description of Instruction\nLabel   Operation   F T\n 21 25\n\n 27 30\n32 33   35..40..\nA         DISP 80XX Add contents of CSL at EA (I+DISP) to A\nA     1   DISP 81XX Add contents of CSL at EA (XR1+DISP) to A\nA     2   DISP 82XX Add contents of CSL at EA (XR2+DISP) to A\nA     3   DISP 83XX Add contents of CSL at EA (XR3+DISP) to A\nA   L     ADDR 8400XXXX Add contents of CSL at EA (Addr) to A\nA   L 1   ADDR 8500XXXX Add contents of CSL at EA (Addr+XR1) to A\nA   L 2   ADDR 8600XXXX Add contents of CSL at EA (Addr+XR2) to A\nA   L 3   ADDR 8700XXXX Add contents of CSL at EA (Addr+XR3) to A\nA   I     ADDR 8480XXXX Add contents of CSL at EA (V in CSL at Addr) to A\nA   I 1   ADDR 8580XXXX Add contents of CSL at EA (V in CSL at \"Addr+XR1\") to A\nA   I 2   ADDR 8680XXXX Add contents of CSL at EA (V in CSL at \"Addr+XR2\") to A\nA   I 3   ADDR 8780XXXX Add contents of CSL at EA (V in CSL at \"Addr+XR3\") to A\n\nBut wait, there's MORE...", null, "" ]

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[ "## 7.6 End-of-Chapter Material\n\n### Chapter Summary\n\nTo ensure that you understand the material in this chapter, you should review the meanings of the following bold terms in the following summary and ask yourself how they relate to the topics in the chapter.\n\nEnergy is the ability to do work. The transfer of energy from one place to another is heat. Heat and energy are measured in units of joules, calories, or kilocalories (equal to 1,000 calories). The amount of heat gained or lost when the temperature of an object changes can be related to its mass and a constant called the specific heat of the substance.\n\nThe transfer of energy can also cause a substance to change from one phase to another. During the transition, called a phase change, heat is either added or lost. Despite the fact that heat is going into or coming out of a substance during a phase change, the temperature of the substance does not change until the phase change is complete; that is, phase changes are isothermal. Analogous to specific heat, a constant called the heat of fusion of a substance describes how much heat must be transferred for a substance to melt or solidify (that is, to change between solid and liquid phases), while the heat of vaporization describes the amount of heat transferred in a boiling or condensation process (that is, to change between liquid and gas phases).\n\nEvery chemical change is accompanied by an energy change. This is because the interaction between atoms bonding to each other has a certain bond energy, the energy required to break the bond (called lattice energy for ionic compounds), and the bond energies of the reactants will not be the same as the bond energies of the products. Reactions that give off energy are called exothermic, while reactions that absorb energy are called endothermic. Energy-level diagrams can be used to illustrate the energy changes that accompany chemical reactions.\n\nEven complex biochemical reactions have to follow the rules of simple chemistry, including rules involving energy change. Reactions of carbohydrates and proteins provide our bodies with about 4 kcal of energy per gram, while fats provide about 9 kcal per gram.\n\n1. Sulfur dioxide (SO2) is a pollutant gas that is one cause of acid rain. It is oxidized in the atmosphere to sulfur trioxide (SO3), which then combines with water to make sulfuric acid (H2SO4).\n\n1. Write the balanced reaction for the oxidation of SO2 to make SO3. (The other reactant is diatomic oxygen.)\n2. When 1 mol of SO2 reacts to make SO3, 23.6 kcal of energy are given off. If 100 lb (1 lb = 454 g) of SO2 were converted to SO3, what would be the total energy change?\n2. Ammonia (NH3) is made by the direct combination of H2 and N2 gases according to this reaction:\n\nN2(g) + 3H2(g) → 2NH3(g) + 22.0 kcal\n1. Is this reaction endothermic or exothermic?\n2. What is the overall energy change if 1,500 g of N2 are reacted to make ammonia?\n3. A 5.69 g sample of iron metal was heated in boiling water to 99.8°C. Then it was dropped into a beaker containing 100.0 g of H2O at 22.6°C. Assuming that the water gained all the heat lost by the iron, what is the final temperature of the H2O and Fe?\n\n4. A 5.69 g sample of copper metal was heated in boiling water to 99.8°C. Then it was dropped into a beaker containing 100.0 g of H2O at 22.6°C. Assuming that the water gained all the heat lost by the copper, what is the final temperature of the H2O and Cu?\n\n5. When 1 g of steam condenses, 540 cal of energy is released. How many grams of ice can be melted with 540 cal?\n\n6. When 1 g of water freezes, 79.9 cal of energy is released. How many grams of water can be boiled with 79.9 cal?\n\n7. The change in energy is +65.3 kJ for each mole of calcium hydroxide [Ca(OH)2] according to the following reaction:\n\nCa(OH)2(s) → CaO(s) + H2O(g)\n\nHow many grams of Ca(OH)2 could be reacted if 575 kJ of energy were available?\n\n8. The thermite reaction gives off so much energy that the elemental iron formed as a product is typically produced in the liquid state:\n\n2Al(s) + Fe2O3(s) → Al2O3(s) + 2Fe(ℓ) + 204 kcal\n\nHow much heat will be given off if 250 g of Fe are to be produced?\n\n9. A normal adult male requires 2,500 kcal per day to maintain his metabolism.\n\n1. Nutritionists recommend that no more than 30% of the calories in a person’s diet come from fat. At 9 kcal/g, what is the maximum mass of fat an adult male should consume daily?\n2. At 4 kcal/g each, how many grams of protein and carbohydrates should an adult male consume daily?\n10. A normal adult male requires 2,500 kcal per day to maintain his metabolism.\n\n1. At 9 kcal/g, what mass of fat would provide that many kilocalories if the diet was composed of nothing but fats?\n2. At 4 kcal/g each, what mass of protein and/or carbohydrates is needed to provide that many kilocalories?\n11. The volume of the world’s oceans is approximately 1.34 × 1024 cm3.\n\n1. How much energy would be needed to increase the temperature of the world’s oceans by 1°C? Assume that the heat capacity of the oceans is the same as pure water.\n2. If Earth receives 6.0 × 1022 J of energy per day from the sun, how many days would it take to warm the oceans by 1°C, assuming all the energy went into warming the water?\n12. Does a substance that has a small specific heat require a small or large amount of energy to change temperature? Explain.\n\n13. Some biology textbooks represent the conversion of adenosine triphosphate (ATP) to adenosine diphosphate (ADP) and phosphate ions as follows:\n\nATP → ADP + phosphate + energy\n\nWhat is wrong with this reaction?\n\n14. Assuming that energy changes are additive, how much energy is required to change 15.0 g of ice at −15°C to 15.0 g of steam at 115°C? (Hint: you will have five processes to consider.)\n\n1. 2SO2 + O2 → 2SO3\n2. 16,700 kcal" ]

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[ "# JavaScript genrator generator\n\nGaby 2021-09-15 07:36:22\njavascript genrator generator\n\nIt should be noted that when I was young, lingyunzhi , Once the best in the world .  Pay attention to prevent getting lost ！   It is said that   give the thumbs-up + Collection == Learn to\n\n## generator (Generator) The concept of\n\nES6 Definition generator Standard guys learn from Python Of generator The concept and grammar of , If you are right about Python Of generator Familiar with , that ES6 Of generator Naturally .\n\nLet's review the concept of function first . A function is a complete piece of code , To call a function is to pass in parameters , And then return the result ：\n\n``````function foo(x) {\nreturn x + x;\n}\nvar r = foo(1); // call foo function\nCopy code ``````\n\nFunction in execution , If I don't meet `return` sentence （ If there is no at the end of the function `return`, It's implicit `return undefined;`）, Control cannot be returned to the called code .\n\ngenerator（ generator ） yes ES6 New data types introduced by the standard . One generator It looks like a function , But you can go back many times . perform Generator The function returns an iterator object . That is to say ,Generator Function is a function that generates an iterator object .\n\n1、ES6 Provides a solution to asynchronous programming\n2、cenerator The number of is a state machine , It encapsulates data in different states\n3、 Used to generate the traverser object\n4、 Pause function （ Lazy evaluation ）,yield Can pause ,next Method can start . Every time I return yield The result of the expression after\n\ncharacteristic ：\n\n1、function There is an asterisk between and the function name\n2、 For internal use yield Expressions to define different states\nfor example ：\n\n``````function* foo(){\nlet result = yield 'hello';// The status value is hello\nyield 'generator';// The status value is generator\n}\nCopy code ``````\n\n3、generator The function returns a pointer object （ Press 11 In Chapter iterator）, Instead of executing the internal logic of two numbers\n4、 call next The internal logic of the method function begins to execute , encounter yield The expression stops , return {value：yield The expression after\n5、 Call again next The method will start from the last stop yield Start at , Until the last\n6、yield The return result of the statement is usually undefined, When calling next Method will be used as the start time yield sentence\n\n## Create generator (Generator)\n\n### The way functions are declared\n\ngenerator It's like a function , The definition is as follows ：\n\n``````function* foo(x) {\nyield x + 1;\nyield x + 2;\nreturn x + 3;\n}\nCopy code ``````\n\ngenerator Unlike functions ,generator from `function*` Definition （ Pay attention to the extra `*` Number ）, keyword  `function`  And  ` Function name `  There is an asterisk between  `*`, also , except `return` sentence , You can also use `yield` Go back many times .\n\n`yield`  Keywords can only be used in generators  `generator`  Use in a function , Otherwise, an error will be reported\n\n### The way function expressions\n\nexcept Function declaration To create a generator ; also Function expression To create a generator ：\n\n``````let foo = function* (arr) {\nfor (let i = 0; i < arr.length; i++) {\nyield arr[i];\n}\n}\nlet g = foo([1, 2, 3]);\nconsole.log(g.next()); // {value: 1, done: false}\nconsole.log(g.next()); // {value: 2, done: false}\nconsole.log(g.next()); // {value: 3, done: false}\nconsole.log(g.next()); // {value: undefined, done: true}\nCopy code ``````\n\nThis is an anonymous function expression , therefore * stay function Between keywords and parentheses\n\nBe careful ： You cannot create a generator through an arrow function , After all * I don't know where to write, do I\n\n### ES6 Shorthand for object methods\n\nIt can also be used. ES6 Object method to create a generator , Just add an asterisk before the function name *\n\n``````let obj = {\n* createIterator(arr) {\nfor (let i = 0; i < arr.length; i++) {\nyield arr[i];\n}\n}\n};\nCopy code ``````\n\n## generator (Generator) How to invoke\n\n### 1. loop ：\n\nHere we will find , ordinary for Circulation and for..in Cycles are not appropriate , So use for..of loop Not traverse return Later\n\n``````function* foo() {\nyield \"a\";\nyield \"b\";\nreturn 'c';\n}\nlet g1 = foo();\nfor (let val of g1) {\nconsole.log(val); // a b\n}\nCopy code ``````\n\n### 2. deconstruction ：( Not traverse return Later )\n\n``````function* foo() {\nyield \"a\";\nyield \"b\";\nreturn 'c';\n};\nlet [g1, g2, g3] = foo();\nconsole.log(g1, g2, g3); // a b undefined\nCopy code ``````\n\n### 3. Extension operator ：( Not traverse return Later )\n\n``````function* show() {\nyield \"a\";\nyield \"b\";\nreturn 'c';\n};\nlet [...g1] = show();\nconsole.log(g1); // [\"a\", \"b\"]\nCopy code ``````\n\n### 4.Array.from()：( Not traverse return Later )\n\n``````function* show() {\nyield \"a\";\nyield \"b\";\nreturn 'c';\n};\nlet g1 = Array.from(show());\nconsole.log(g1); // [\"a\", \"b\"]\nCopy code ``````\n\n### 5. Object generator method ：\n\nThe generator itself is a function , So it can be added to the object , The method of becoming an object\n\n``````let obj = {\ncreateIterator: function* (arr) {\nfor (let i = 0; i < arr.length; i++) {\nyield arr[i];\n}\n}\n};\nlet iterator = obj.createIterator([10, 20, 30]);\nconsole.log(iterator.next()); // {value: 10, done: false}\nconsole.log(iterator.next()); // {value: 20, done: false}\nconsole.log(iterator.next()); // {value: 30, done: false}\nconsole.log(iterator.next()); // {value: undefined, done: true}\nCopy code ``````\n\n## generator Return multiple functions\n\ngenerator Can return multiple times “ function ”？ What's the use of returning multiple times ？\n\nLet's take a famous Fibonacci sequence as an example , It consists of `0`,`1` start ：\n\n``````0 1 1 2 3 5 8 13 21 34 ...\nCopy code ``````\n\nTo write a function that produces a Fibonacci sequence , It can be written like this ：\n\n``````function fib(max) {\nvar\nt,\na = 0,\nb = 1,\narr = [0, 1];\nwhile (arr.length < max) {\n[a, b] = [b, a + b];\narr.push(b);\n}\nreturn arr;\n}\n// test :\nfib(5); // [0, 1, 1, 2, 3]\nfib(10); // [0, 1, 1, 2, 3, 5, 8, 13, 21, 34]\nCopy code ``````\n\nFunction can only return once , So you have to return a `Array`. however , If replaced generator, You can return one number at a time , Go back and forth many times . use generator Rewrite as follows ：\n\n``````function* fib(max) {\nvar\nt,\na = 0,\nb = 1,\nn = 0;\nwhile (n < max) {\nyield a;\n[a, b] = [b, a + b];\nn ++;\n}\nreturn;\n}\nCopy code ``````\n\nTry calling directly ：\n\n``````fib(5); // fib {[[GeneratorStatus]]: \"suspended\", [[GeneratorReceiver]]: Window}\nCopy code ``````\n\nCall one directly generator Unlike calling a function ,`fib(5)` Just created a generator object , Haven't implemented it yet .\n\ncall generator There are two ways to object , One is to constantly call generator Object's `next()` Method ：\n\n``````var f = fib(5);\nf.next(); // {value: 0, done: false}\nf.next(); // {value: 1, done: false}\nf.next(); // {value: 1, done: false}\nf.next(); // {value: 2, done: false}\nf.next(); // {value: 3, done: false}\nf.next(); // {value: undefined, done: true}\nCopy code ``````\n\n`next()` Method will execute generator Code for , then , Every encounter `yield x;` Just return an object `{value: x, done: true/false}`, then “ Pause ”. Back to `value` Namely `yield` The return value of ,`done` Express this generator Whether the execution is over . If `done` by `true`, be `value` Namely `return` The return value of .\n\nWhen executed `done` by `true` when , This generator The object has been executed , Don't call on `next()` 了 .\n\nThe second method is to use `for ... of` Loop iteration generator object , This approach does not require our own judgment `done`\n\n``````'use strict'\nfunction* fib(max) {\nvar\nt,\na = 0,\nb = 1,\nn = 0;\nwhile (n < max) {\nyield a;\n[a, b] = [b, a + b];\nn ++;\n}\nreturn;\n}\n// adopt  `for`  loop , Batch processing  `yield`  sentence\nfor (var x of fib(10)) {\nconsole.log(x); // Output... In sequence 0, 1, 1, 2, 3, ...\n}\nCopy code ``````\n\n### generator Compared with ordinary functions , What's the usage? ？\n\nbecause generator You can return... Multiple times during execution , So it looks like a function that can remember the execution state , Take advantage of this , Write a generator You can realize the functions that can only be realized with object-oriented . for example , Use an object to save the State , That's how it's written ：\n\n``````var fib = {\na: 0,\nb: 1,\nn: 0,\nmax: 5,\nnext: function () {\nvar\nr = this.a,\nt = this.a + this.b;\nthis.a = this.b;\nthis.b = t;\nif (this.n < this.max) {\nthis.n ++;\nreturn r;\n} else {\nreturn undefined;\n}\n}\n};\nCopy code ``````\n\nUse the properties of the object to save the State , Quite complicated .\n\ngenerator There is another great benefit , It is to change the asynchronous callback code into “ Sync ” Code . This benefit will have to be learned later AJAX Only later can we realize .\n\nNo, generator The dark ages before , use AJAX You need to write code like this ：\n\n``````ajax('http://url-1', data1, function (err, result) {\nif (err) {\nreturn handle(err);\n}\najax('http://url-2', data2, function (err, result) {\nif (err) {\nreturn handle(err);\n}\najax('http://url-3', data3, function (err, result) {\nif (err) {\nreturn handle(err);\n}\nreturn success(result);\n});\n});\n});\nCopy code ``````\n\nMore callbacks , The more ugly the code is .\n\nWith generator A better time , use AJAX It can be written like this ：\n\n``````try {\nr1 = yield ajax('http://url-1', data1);\nr2 = yield ajax('http://url-2', data2);\nr3 = yield ajax('http://url-3', data3);\nsuccess(r3);\n}\ncatch (err) {\nhandle(err);\n}\nCopy code ``````\n\nLooks like synchronized code , The actual execution is asynchronous .\n\n### complete `ajax`  Request instance\n\n``````function ajax(url) {\nreturn new Promise((resolve, reject) => {\n\\$.ajax({\nurl,\ntype: 'get',\nsuccess: resolve,\nerror: reject\n});\n});\n}\nfunction* show() {\nyield ajax('https://jsonplacehouger.typicode.com/todos/1');\nyield ajax('https://jsonplacehouger.typicode.com/todos/2');\nyield ajax('https://jsonplacehouger.typicode.com/todos/3');\n};\nlet g1 = show();\ng1.next().value.then(res => {\nconsole.log(res);\nreturn g1.next().value;\n}).then(res => {\nconsole.log(res);\nreturn g1.next().value;\n}).then(res => {\nconsole.log(res);\nreturn g1.next().value;\n});\nCopy code ``````\n\n╭╮╱╭┳━━━┳╮╱╭╮\n┃┃╱┃┃╭━╮┃┃╱┃┃\n┃╰━╯┃┃┃┃┃╰━╯┃\n╰━━╮┃┃┃┃┣━━╮┃\n╱╱╱┃┃╰━╯┃╱╱┃┃\n\nWhen you come, you can't go until you like it , It is said that give the thumbs-up + Collection == Learn to\n\nhttps://javamana.com/2021/09/20210909131415443E.html" ]

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[ "Shortcuts\n\n# Source code for torch.nn.modules.normalization\n\nimport torch\nimport numbers\nfrom torch.nn.parameter import Parameter\nfrom .module import Module\nfrom ._functions import CrossMapLRN2d as _cross_map_lrn2d\nfrom .. import functional as F\nfrom .. import init\n\nfrom torch import Tensor, Size\nfrom typing import Union, List\n\n[docs]class LocalResponseNorm(Module):\nr\"\"\"Applies local response normalization over an input signal composed\nof several input planes, where channels occupy the second dimension.\nApplies normalization across channels.\n\n.. math::\nb_{c} = a_{c}\\left(k + \\frac{\\alpha}{n}\n\\sum_{c'=\\max(0, c-n/2)}^{\\min(N-1,c+n/2)}a_{c'}^2\\right)^{-\\beta}\n\nArgs:\nsize: amount of neighbouring channels used for normalization\nalpha: multiplicative factor. Default: 0.0001\nbeta: exponent. Default: 0.75\n\nShape:\n- Input: :math:(N, C, *)\n- Output: :math:(N, C, *) (same shape as input)\n\nExamples::\n\n>>> lrn = nn.LocalResponseNorm(2)\n>>> signal_2d = torch.randn(32, 5, 24, 24)\n>>> signal_4d = torch.randn(16, 5, 7, 7, 7, 7)\n>>> output_2d = lrn(signal_2d)\n>>> output_4d = lrn(signal_4d)\n\n\"\"\"\n__constants__ = ['size', 'alpha', 'beta', 'k']\nsize: int\nalpha: float\nbeta: float\nk: float\n\ndef __init__(self, size: int, alpha: float = 1e-4, beta: float = 0.75, k: float = 1.) -> None:\nsuper(LocalResponseNorm, self).__init__()\nself.size = size\nself.alpha = alpha\nself.beta = beta\nself.k = k\n\ndef forward(self, input: Tensor) -> Tensor:\nreturn F.local_response_norm(input, self.size, self.alpha, self.beta,\nself.k)\n\ndef extra_repr(self):\nreturn '{size}, alpha={alpha}, beta={beta}, k={k}'.format(**self.__dict__)\n\nclass CrossMapLRN2d(Module):\nsize: int\nalpha: float\nbeta: float\nk: float\n\ndef __init__(self, size: int, alpha: float = 1e-4, beta: float = 0.75, k: float = 1) -> None:\nsuper(CrossMapLRN2d, self).__init__()\nself.size = size\nself.alpha = alpha\nself.beta = beta\nself.k = k\n\ndef forward(self, input: Tensor) -> Tensor:\nreturn _cross_map_lrn2d.apply(input, self.size, self.alpha, self.beta,\nself.k)\n\ndef extra_repr(self) -> str:\nreturn '{size}, alpha={alpha}, beta={beta}, k={k}'.format(**self.__dict__)\n\n_shape_t = Union[int, List[int], Size]\n\n[docs]class LayerNorm(Module):\nr\"\"\"Applies Layer Normalization over a mini-batch of inputs as described in\nthe paper Layer Normalization <https://arxiv.org/abs/1607.06450>__\n\n.. math::\ny = \\frac{x - \\mathrm{E}[x]}{ \\sqrt{\\mathrm{Var}[x] + \\epsilon}} * \\gamma + \\beta\n\nThe mean and standard-deviation are calculated separately over the last\ncertain number dimensions which have to be of the shape specified by\n:attr:normalized_shape.\n:math:\\gamma and :math:\\beta are learnable affine transform parameters of\n:attr:normalized_shape if :attr:elementwise_affine is True.\nThe standard-deviation is calculated via the biased estimator, equivalent to\ntorch.var(input, unbiased=False).\n\n.. note::\nUnlike Batch Normalization and Instance Normalization, which applies\nscalar scale and bias for each entire channel/plane with the\n:attr:affine option, Layer Normalization applies per-element scale and\nbias with :attr:elementwise_affine.\n\nThis layer uses statistics computed from input data in both training and\nevaluation modes.\n\nArgs:\nnormalized_shape (int or list or torch.Size): input shape from an expected input\nof size\n\n.. math::\n[* \\times \\text{normalized\\_shape} \\times \\text{normalized\\_shape}\n\\times \\ldots \\times \\text{normalized\\_shape}[-1]]\n\nIf a single integer is used, it is treated as a singleton list, and this module will\nnormalize over the last dimension which is expected to be of that specific size.\neps: a value added to the denominator for numerical stability. Default: 1e-5\nelementwise_affine: a boolean value that when set to True, this module\nhas learnable per-element affine parameters initialized to ones (for weights)\nand zeros (for biases). Default: True.\n\nShape:\n- Input: :math:(N, *)\n- Output: :math:(N, *) (same shape as input)\n\nExamples::\n\n>>> input = torch.randn(20, 5, 10, 10)\n>>> # With Learnable Parameters\n>>> m = nn.LayerNorm(input.size()[1:])\n>>> # Without Learnable Parameters\n>>> m = nn.LayerNorm(input.size()[1:], elementwise_affine=False)\n>>> # Normalize over last two dimensions\n>>> m = nn.LayerNorm([10, 10])\n>>> # Normalize over last dimension of size 10\n>>> m = nn.LayerNorm(10)\n>>> # Activating the module\n>>> output = m(input)\n\"\"\"\n__constants__ = ['normalized_shape', 'eps', 'elementwise_affine']\nnormalized_shape: _shape_t\neps: float\nelementwise_affine: bool\n\ndef __init__(self, normalized_shape: _shape_t, eps: float = 1e-5, elementwise_affine: bool = True) -> None:\nsuper(LayerNorm, self).__init__()\nif isinstance(normalized_shape, numbers.Integral):\nnormalized_shape = (normalized_shape,)\nself.normalized_shape = tuple(normalized_shape)\nself.eps = eps\nself.elementwise_affine = elementwise_affine\nif self.elementwise_affine:\nself.weight = Parameter(torch.Tensor(*normalized_shape))\nself.bias = Parameter(torch.Tensor(*normalized_shape))\nelse:\nself.register_parameter('weight', None)\nself.register_parameter('bias', None)\nself.reset_parameters()\n\ndef reset_parameters(self) -> None:\nif self.elementwise_affine:\ninit.ones_(self.weight)\ninit.zeros_(self.bias)\n\ndef forward(self, input: Tensor) -> Tensor:\nreturn F.layer_norm(\ninput, self.normalized_shape, self.weight, self.bias, self.eps)\n\ndef extra_repr(self) -> Tensor:\nreturn '{normalized_shape}, eps={eps}, ' \\\n'elementwise_affine={elementwise_affine}'.format(**self.__dict__)\n\n[docs]class GroupNorm(Module):\nr\"\"\"Applies Group Normalization over a mini-batch of inputs as described in\nthe paper Group Normalization <https://arxiv.org/abs/1803.08494>__\n\n.. math::\ny = \\frac{x - \\mathrm{E}[x]}{ \\sqrt{\\mathrm{Var}[x] + \\epsilon}} * \\gamma + \\beta\n\nThe input channels are separated into :attr:num_groups groups, each containing\nnum_channels / num_groups channels. The mean and standard-deviation are calculated\nseparately over the each group. :math:\\gamma and :math:\\beta are learnable\nper-channel affine transform parameter vectors of size :attr:num_channels if\n:attr:affine is True.\nThe standard-deviation is calculated via the biased estimator, equivalent to\ntorch.var(input, unbiased=False).\n\nThis layer uses statistics computed from input data in both training and\nevaluation modes.\n\nArgs:\nnum_groups (int): number of groups to separate the channels into\nnum_channels (int): number of channels expected in input\neps: a value added to the denominator for numerical stability. Default: 1e-5\naffine: a boolean value that when set to True, this module\nhas learnable per-channel affine parameters initialized to ones (for weights)\nand zeros (for biases). Default: True.\n\nShape:\n- Input: :math:(N, C, *) where :math:C=\\text{num\\_channels}\n- Output: :math:(N, C, *) (same shape as input)\n\nExamples::\n\n>>> input = torch.randn(20, 6, 10, 10)\n>>> # Separate 6 channels into 3 groups\n>>> m = nn.GroupNorm(3, 6)\n>>> # Separate 6 channels into 6 groups (equivalent with InstanceNorm)\n>>> m = nn.GroupNorm(6, 6)\n>>> # Put all 6 channels into a single group (equivalent with LayerNorm)\n>>> m = nn.GroupNorm(1, 6)\n>>> # Activating the module\n>>> output = m(input)\n\"\"\"\n__constants__ = ['num_groups', 'num_channels', 'eps', 'affine']\nnum_groups: int\nnum_channels: int\neps: float\naffine: bool\n\ndef __init__(self, num_groups: int, num_channels: int, eps: float = 1e-5, affine: bool = True) -> None:\nsuper(GroupNorm, self).__init__()\nself.num_groups = num_groups\nself.num_channels = num_channels\nself.eps = eps\nself.affine = affine\nif self.affine:\nself.weight = Parameter(torch.Tensor(num_channels))\nself.bias = Parameter(torch.Tensor(num_channels))\nelse:\nself.register_parameter('weight', None)\nself.register_parameter('bias', None)\nself.reset_parameters()\n\ndef reset_parameters(self) -> None:\nif self.affine:\ninit.ones_(self.weight)\ninit.zeros_(self.bias)\n\ndef forward(self, input: Tensor) -> Tensor:\nreturn F.group_norm(\ninput, self.num_groups, self.weight, self.bias, self.eps)\n\ndef extra_repr(self) -> str:\nreturn '{num_groups}, {num_channels}, eps={eps}, ' \\\n'affine={affine}'.format(**self.__dict__)\n\n# TODO: ContrastiveNorm2d\n# TODO: DivisiveNorm2d\n# TODO: SubtractiveNorm2d", null, "## Docs\n\nAccess comprehensive developer documentation for PyTorch\n\nView Docs\n\n## Tutorials\n\nGet in-depth tutorials for beginners and advanced developers\n\nView Tutorials" ]

[ null, "https://www.googleadservices.com/pagead/conversion/795629140/", null ]

[ "## What are the combinations of 10?\n\nFor example, 4 + 6 and 0 + 10 are both combinations of 10.\n\n## What is make a ten in math?\n\nIn 1st grade, as students begin learning their basic addition facts, they apply that knowledge in a strategy known as “ make a ten ” to help make sense of facts that might otherwise be hard to memorize, such as 8 + 4 or 9 + 5. To use the strategy, students decompose one of the addends to make a ten from the other.\n\n## What are the number pairs of 7?\n\nThe number 7 can be made using two other numbers. Grades K-8 Worksheets.\n\n7 = 1 + 6 7 = 2 + 5 7 = 3 + 4\n7 = 4 + 3 7 = 5 + 2 7 = 6 + 1\n\n## What are number pairs?\n\nNumber pairs are all the different combinations of numbers that compose a specific number.The concept of number bonds is very basic, an important foundation for understanding how numbers work. A whole thing is made up of parts Number pairs for 1 can also be called friends of 1, number bonds for 1 and partners of 1.\n\n## How many combinations of 10 numbers are there?\n\nThe number of combinations that are possible with 10 numbers is 1,023.\n\n## What is a 10 fact?\n\nTwo children are napping.” Make Ten facts are pairs of numbers that equal 10. Being able to instantly recognize combinations that make 10 — for example, 3 + 7 = 10 — helps when adding 30 + 70 = 100 or 43 + 7 = 50. Add Ten facts ( 10 + 3, 7 + 10 ) apply when 10 is added to a single-digit number.\n\n## What does make ten mean?\n\nA strategy that uses combinations of numbers that add up to ten. Math Games for Kids. Multiplication Games.\n\n## What does a ten mean?\n\na very attractive person. A person who, on a scale of 0 to 10, is the best. You’ve been dating – at best – fives. But you’re hot enough to date tens. See more words with the same meaning: attractive person (either gender).\n\nYou might be interested:  FAQ: What causes an earthquake?\n\n## How do you explain a pair to a child?\n\nAsk your child, “Can you tell me which body parts come in twos?” He might list feet, hands, eyes and ears. You can explain, “If you have two things that look the same, they make a pair. So, you have a pair of eyes, ears, hands and feet. Things that go with those body parts also come in pairs.\n\n## How do I teach my child number bonds?\n\nHow are number bonds taught in primary school? Give your child ten counters (Lego bricks, past shapes, buttons, sweets) and ask them questions such as: What do you add to 3 to make 10? Print out number cards and ask your child to match them up into number pairs or number bonds (this can be done as a game of Snap).\n\n## What is a number bond to 100?\n\nWhat are Number Bonds to 100? Number Bonds to 100 are pairs of numbers that add together to make 100. To find a number bond to 100, first add on to reach the next multiple of ten and then add the multiples of ten needed to get to 100.\n\n## What is a number Bond to 20?\n\nWhat are Number Bonds to 20? Number bonds to 20 are the pairs of numbers that add together to make twenty.", null, "Related Posts" ]

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[ "# [Tex/LaTex] How to draw commutative diagrams in LaTeX?\n\ndiagramstikz-cd\n\nI would like to learn to make commutative rectangles using Tikz. How can I do that? I have tried\n\n$\\begin{tikzcd} A \\arrow{r}{\\varphi} \\arrow[swap]{dd}{g\\circ f} & B \\arrow{d}{g} \\\\ & C \\end{tikzcd}$\n\n\nbut it draws only a triangle.\n\nI don't know what you exactly wanted to draw, so I reproduce one of the diagrams from your link, showing how to do it with pst-node and with tikz-cd. One of the main differences is that in pstricks you first describe the nodes, then the arrows, while with tikz-cd, nodes and arrows are described simultaneously.\n\nI load auto-pst-pdf, as pdflatex doesn't support postscript instructions. You have to set the --enable-write18 compiler switch (MiKTeX) or -shell-escape (TeX Live, MacTeX). Alternatively, you can compile with xelatex.\n\n\\documentclass{article}\n\\usepackage{pst-node}\n\\uspackage{auto-pst-pdf}\n\\usepackage{tikz-cd}\n\n\\begin{document}\n%\n$\\psset{arrows=->, arrowinset=0.25, linewidth=0.6pt, nodesep=3pt, labelsep=2pt, rowsep=0.7cm, colsep = 1.1cm, shortput =tablr} \\everypsbox{\\scriptstyle} \\begin{psmatrix} A & B\\\\% A_f & B_g %%% \\ncline{1,1}{1,2}^{\\varphi} \\ncline{1,1}{2,1} <{\\varrho_f } \\ncline{1,2}{2,2} > {\\varrho_g} \\ncline{2,1}{2,2}^{\\varphi_f} \\end{psmatrix}$\n\n$\\begin{tikzcd} A \\arrow{r}{\\varphi} \\arrow[swap]{d}{\\varrho_f} & B \\arrow{d}{\\varrho_g} \\\\% A_f \\arrow{r}{\\varphi_f}& B_g \\end{tikzcd}$\n\\end{document}", null, "" ]

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[ "# Poster Presentation | Graphlet-based Filtering for High-Performance Subgraph Isomorphism Search\n\nI presented a poster on “Graphlet-based Filtering for High-Performance Subgraph Isomorphism Search” at the 19th International Summer School on Advanced Computer Architecture and Compilation for High-performance Embedded Systems organised by HiPEAC at Fiuggi, Italy between July 9 – 15, 2023.\n\nSummary\n\nIntroduction\n\nGraphs are powerful tools for representing complex relationships in various domains such as social networks, bioinformatics, and computer networks. The Subgraph Isomorphism (SI) search problem is crucial in graph analytics, involving finding instances of a pattern graph within a larger data graph. This problem has applications in pattern discovery and graph database queries.\n\nHowever, the SI problem is NP-complete, meaning that it becomes computationally intensive for larger graphs. To tackle this challenge, researchers have proposed heuristic algorithms that aim to speed up the SI search by pruning the search space through various techniques.\n\nThree Stages of Heuristic Algorithms\n\nThese heuristic algorithms can be divided into three stages:\n\n1. Filtering: In this stage, a candidate set of data graph vertices is generated for each vertex of the pattern graph. The goal is to select a subset of data graph vertices that are potential matches for each pattern vertex. Two common filtering techniques are Label and Degree Filtering (LDF) and Neighbourhood Label Filtering (NLF). LDF ensures that only vertices with matching labels and sufficient degrees are considered, while NLF adds further constraints based on the labels of neighbours.\n2. Ordering: The vertices of the pattern graph are ordered for mapping with the candidate data vertices. The Highest Degree First (HDF) strategy is commonly used.\n3. Backtracking: A backtracking search is performed based on the ordered vertices to find subgraph isomorphisms.\n\nProposed Approach: Graphlet Filtering (GLF)\n\nThe proposed approach, Graphlet Filtering (GLF), introduces an additional stage to the heuristic algorithms. Graphlets are recurring small subgraphs, and orbits represent groups of vertices within these graphlets. By counting the occurrences of orbits in both pattern and data graphs, we propose that the count of an orbit in the pattern graph must be less than or equal to the count of the same orbit in the candidate data vertices’ graphs. This idea enhances the filtering stage by providing more stringent filtering criteria.\n\nPreliminary Results\n\nWe conducted preliminary experiments on various datasets and found that GLF filtering provides additional filtering enhancements ranging from 4.2% to 15.38% depending on the dataset and pattern graph density. Across all datasets, the GLF technique improved filtering by 9.93% for sparse pattern graphs and 8.49% for dense pattern graphs.\n\nConclusion\n\nThe study suggests that incorporating graphlet-based filtering (GLF) into the existing heuristic algorithms for the Subgraph Isomorphism problem can lead to more effective filtering and pruning of the search space. We plan to explore the impact of GLF on the runtime of different heuristic algorithms. If successful, this technique could significantly reduce the execution time of algorithms used for tasks such as pattern discovery and graph database queries." ]

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[ "", null, "By Wai-Kee Li, Gong-Du Zhou, Thomas Mak\n\nISBN-10: 0199216959\n\nISBN-13: 9780199216956\n\nA revised and up-to-date English model of a postgraduate textbook that has grown out of a number of years of lecture room improvement. The time period \"inorganic\" is utilized in a extensive experience because the booklet covers the structural chemistry of consultant parts (including carbon) within the Periodic desk, organometallics, coordination polymers, host-guest platforms and supramolecular assemblies.\nPart I of the e-book experiences the fundamental bonding theories, together with a bankruptcy on computational chemistry. half II introduces element teams and house teams and their chemical purposes. half III contains a succinct account of the structural chemistry of the weather within the periodic desk. It provides constitution and bonding, generalizations of structural traits, crystallographic info, in addition to highlights from the hot literature.\n\nQuality: Vector, Searchable, Bookmarked\n\nRead or Download Advanced Structural Inorganic Chemistry (International Union of Crystallography Texts on Crystallography) PDF\n\nSimilar crystallography books\n\nDownload PDF by Arthur S. Nowick: Crystal Properties via Group Theory\n\nThis ebook offers with the impact of crystal symmetry in deciding on the tensor houses of crystals. even if it is a well-established topic, the writer offers a brand new technique utilizing staff concept and, specifically, the tactic of symmetry coordinates, which has now not been utilized in any prior e-book.\n\nSandra E. Dann's Reactions and Characterization of Solids (Basic Concepts In PDF\n\nThe final 20 years or so has noticeable a transformation within the conception of reliable kingdom chemistry, particularly the clinical importance of realizing the connection among chemical constitution and actual houses. As such, it now types a big a part of either mainstream chemistry and fabric technology levels.\n\nRead e-book online Case Studies in Superconducting Magnets: Design and PDF\n\nDesigned for graduate scholars in mechanical engineering, this textbook discusses the elemental recommendations of superconducting magnet expertise. very important subject matters coated comprise box distribution, magnets, strength, thermal balance, dissipation, and defense. To aid the scholars excel within the box, every one bankruptcy comprises instructional difficulties, followed through strategies, using solenoidal magnets as examples.\n\nAdditional info for Advanced Structural Inorganic Chemistry (International Union of Crystallography Texts on Crystallography)\n\nExample text\n\n28) Dividing eq. 28) by XYZ yields. 1 X ∂ 2X ∂x2 + 1 Y ∂ 2Y ∂y2 + 1 Z ∂ 2Z ∂z 2 = −8π 2 mE . 29) Now it is obvious that each of the three terms on the left side of eq. 32) with the constraint on the constants being αx2 + αy2 + αz2 = 8π 2 mE . 34) Introduction to Quantum Theory and E = Ex + Ey + Ez . 35) Each of eqs. 32) is similar to that of the one-dimensional problem, eq. 3). Hence the solutions of eqs. 32) can be readily written Xj (x) = 2 a Yk (y) = 2 b Z (z) = 2 c 1 2 1 2 1 2 sin jπx , a j = 1, 2, 3, .\n\nE. ψ (0) = ψ (a) = 0. 6) 13 14 Fundamentals of Bonding Theory With ψ(0) = 0, we get B = 0. 8) Also, ψ(a) = 0 yields which means either A or sin α a vanishes. 9) or αa = nπ, n = 1, 2, 3, . .. 10) So, the wavefunctions have the form ψn (x) = A sin nπx , a n = 1, 2, 3, . .. 12) which leads to the following form for the wavefunctions: ψn (x) = 2 a 1 2 sin nπx . 13) Note that ψ has the unit of length−1/2 and ψ 2 has the unit of length−1 . By combining eqs. 14) or En = n2 h2 , 8ma2 n = 1, 2, 3, . .\n\nFrom statistics, the uncertainty of momentum, px , may be expressed in terms of and : px = 2 = h . 18) 16 Fundamentals of Bonding Theory In the following, again for the ground state, we calculate the mean value of position x as well as that of x2 : a 2 a = sin 0 πx πx x sin dx a a a = . 19) This result can be obtained by simply examining the function |ψ1 |2 shown in Fig. 1. Meanwhile, a 2 a = = a2 sin 0 πx 2 πx x sin dx a a 1 1 − 3 2π 2 . 20) Now we are ready to determine the uncertainty in x: x = 2 =a The product x px = a x· 1 12 1 12 − 1 2 1 2π 2 1 2 .\n\nDownload PDF sample\n\n### Advanced Structural Inorganic Chemistry (International Union of Crystallography Texts on Crystallography) by Wai-Kee Li, Gong-Du Zhou, Thomas Mak\n\nby David\n4.2\n\nRated 4.78 of 5 – based on 38 votes" ]

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[ "## SQL MOD Function\n\nSQL MOD function returns the remainder value which is a result of division of two numbers.\n\nThe syntax is\n\nMOD(number, divider)\n\nExamples:\nThe following SQL statements illustrate the use of SQL MOD function on couple different numbers:\n\nSELECT MOD (34, 6) FROM DUAL;\n\nOUTPUT:", null, "SELECT MOD (24, 4) FROM DUAL;\n\nOUTPUT:", null, "SELECT MOD (4,12) FROM DUAL;\n\nOUTPUT:", null, "SELECT MOD (-12,6) FROM DUAL;\n\nOUTPUT:", null, "" ]

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[ "# Calculating the power of a signal\n\nI'm trying to calculate the power of a signal and my tutor has given me this formula to do it", null, "I've spent the past while building a program and now the foundations are there it's time to implement the maths side of it. The problem is I can't actually read it. Would someone be able to transcribe it and explain it to me?\n\n• $P_x=\\dfrac{1}{T}\\sum_{t=1}^{T}x^2(t)$\n– jojek\nFeb 13 '15 at 17:23\n\nAs @jojek has already said in the comments, the formula reads $$P_\\mathrm{x} = \\dfrac{1}{T}\\sum_{t=1}^{T}x^2(t)$$ As $t$ usually denotes continous time I find this formulation a little bit odd. What your tutor probably actually meant is $$P_\\mathrm{x} = \\dfrac{1}{T}\\int_{t=0}^{T}x^2(t) \\mathrm{d}t$$ It calculates the average power of the (continous-time) signal $x(t)$ of length $T$. In computer programs we're dealing with discrete-time (and discrete valued) signals, of course and the average power of the digital signal $x_n$ is given by $$\\tilde P_\\mathrm{x} = \\dfrac{1}{N}\\sum_{n=1}^{N}x_n^2,$$ where $N$ is the length of $x_n$ in samples." ]

[ null, "https://i.stack.imgur.com/h1RN6.jpg", null ]

[ "# Time-Domain Specifications\n\nThis example gives a tour of available time-domain requirements for control system tuning with `systune` or `looptune`.\n\nThe `systune` and `looptune` functions tune the parameters of fixed-structure control systems subject to a variety of time- and frequency-domain requirements. To specify these requirements, use tuning goal objects.\n\n### Step Command Following\n\nThe `TuningGoal.StepTracking` requirement specifies how the tuned closed-loop system should respond to a step input. You can specify the desired response either in terms of first- or second-order characteristics, or as an explicit reference model. This requirement is satisfied when the relative gap between the actual and desired responses is small enough in the least-squares sense. For example,\n\n`R1 = TuningGoal.StepTracking('r','y',0.5);`\n\nstipulates that the closed-loop response from `r` to `y` should behave like a first-order system with time constant 0.5, while\n\n`R2 = TuningGoal.StepTracking('r','y',zpk(2,[-1 -2],-1));`\n\nspecifies a second-order, non-minimum-phase behavior. Use `viewGoal` to visualize the desired response.\n\n`viewGoal(R2)`", null, "This requirement can be used to tune both SISO and MIMO step responses. In the MIMO case, the requirement ensures that each output tracks the corresponding input with minimum cross-couplings.\n\n### Step Disturbance Rejection\n\nThe `TuningGoal.StepRejection` requirement specifies how the tuned closed-loop system should respond to a step disturbance. You can specify worst-case values for the response amplitude, settling time, and damping of oscillations. For example,\n\n`R1 = TuningGoal.StepRejection('d','y',0.3,2,0.5);`\n\nlimits the amplitude of $y\\left(t\\right)$ to 0.3, the settling time to 2 time units, and the damping ratio to a minimum of 0.5. Use `viewGoal` to see the corresponding time response.\n\n`viewGoal(R1)`", null, "You can also use a \"reference model\" to specify the desired response. Note that the actual and specified responses may differ substantially when better disturbance rejection is possible. Use the `TuningGoal.Transient` requirement when a close match is desired. For best results, adjust the gain of the reference model so that the actual and specified responses have similar peak amplitudes (see `TuningGoal.StepRejection` documentation for details).\n\n### Transient Response Matching\n\nThe `TuningGoal.Transient` requirement specifies the transient response for a specific input signal. This is a generalization of the `TuningGoal.StepTracking` requirement. For example,\n\n`R1 = TuningGoal.Transient('r','y',tf(1,[1 1 1]),'impulse');`\n\nrequires that the tuned response from $r$ to $y$ look like the impulse response of the reference model $1/\\left({s}^{2}+s+1\\right)$.\n\n`viewGoal(R1)`", null, "The input signal can be an impulse, a step, a ramp, or a more general signal modeled as the impulse response of some input shaping filter. For example, a sine wave with frequency ${\\omega }_{0}$ can be modeled as the impulse response of ${\\omega }_{0}^{2}/\\left({s}^{2}+{\\omega }_{0}^{2}\\right)$.\n\n```w0 = 2; F = tf(w0^2,[1 0 w0^2]); % input shaping filter R2 = TuningGoal.Transient('r','y',tf(1,[1 1 1]),F); viewGoal(R2)```", null, "### LQG Design\n\nUse the `TuningGoal.LQG` requirement to create a linear-quadratic-Gaussian objective for tuning the control system parameters. This objective is applicable to any control structure, not just the classical observer structure of LQG control. For example, consider the simple PID loop of Figure 2 where $d$ and $n$ are unit-variance disturbance and noise inputs, and ${S}_{d}$ and ${S}_{n}$ are lowpass and highpass filters that model the disturbance and noise spectral contents.", null, "Figure 2: Regulation loop.\n\nTo regulate $y$ around zero, you can use the following LQG criterion:\n\n`$J=li{m}_{T\\to \\infty }E\\left(\\frac{1}{T}{\\int }_{0}^{T}\\left({y}^{2}\\left(t\\right)+0.05{u}^{2}\\right)dt\\right)$`\n\nThe first term in the integral penalizes the deviation of $y\\left(t\\right)$ from zero, and the second term penalizes the control effort. Using `systune`, you can tune the PID controller to minimize the cost $J$. To do this, use the LQG requirement\n\n```Qyu = diag([1 0.05]); % weighting of y^2 and u^2 R4 = TuningGoal.LQG({'d','n'},{'y','u'},1,Qyu);```" ]

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[ "", null, "", null, "", null, "Next: Overall Comparison - What Up: Classical vs. Quantum Mechanics: Previous: Average Energy U and\n\n## Mean-Square Fluctuation\n\nOne physical quantity of great interest is the variance in the position of atoms at equilibrium,", null, ". For our model oscillator,", null, "; so", null, ". This mean-square fluctuation about the average position is related to the B factors of crystallography and is also measurable by neutron scattering and by Mössbauer spectroscopy . It is one of the most important quantities to keep an eye on in molecular dynamics simulations as well. What is this fluctuation for the harmonic oscillator in equilibrium at constant", null, "according to classical and quantum mechanics? We again use equations 2, 4, and 5, now with", null, ", and consider the same three frequencies of proton vibration. Because", null, "and", null, "for harmonic oscillation, the quantum and classical results are proportional to those obtained above for the average energy. That is,", null, ". Again, m is taken as the mass of a proton. (To plot the three frequencies on one scale, results have been scaled to the f = 100/ps values (green): Results for f = 10/ps (blue) were scaled by 0.01 ; results for f = 1/ps (cyan) were scaled by 0.0001. Consequently, the three classical curves (red),", null, ", coincide.)", null, "Mean-square fluctuation of H atom undergoing harmonic oscillation.", null, "", null, "", null, "Next: Overall Comparison - What Up: Classical vs. Quantum Mechanics: Previous: Average Energy U and\nSteinbach 2019-02-01" ]

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[ "# Influential Points\n\nSometimes in regression analysis, a few data points have disproportionate effects on the slope of the regression equation. In this lesson, we describe how to identify those influential points.\n\n## Outliers\n\nData points that diverge in a big way from the overall pattern are called outliers. There are four ways that a data point might be considered an outlier.\n\n• It could have an extreme X value compared to other data points.\n• It could have an extreme Y value compared to other data points.\n• It could have extreme X and Y values.\n• It might be distant from the rest of the data, even without extreme X or Y values.\n\nEach type of outlier is depicted graphically in the scatterplots below.\n\nExtreme X value", null, "Extreme Y value", null, "Extreme X and Y", null, "Distant data point", null, "## Influential Points\n\nAn influential point is an outlier that greatly affects the slope of the regression line. One way to test the influence of an outlier is to compute the regression equation with and without the outlier.\n\nThis type of analysis is illustrated below. The scatterplots are identical, except that one plot includes an outlier. When the outlier is present, the slope is flatter (-4.10 vs. -3.32); so this outlier would be considered an influential point.\n\nWithout Outlier", null, "Regression equation: ŷ = 104.78 - 4.10x\nCoefficient of determination: R2 = 0.94\n\nWith Outlier", null, "Regression equation: ŷ = 97.51 - 3.32x\nCoefficient of determination: R2 = 0.55\n\nThe charts below compare regression statistics for another data set with and without an outlier. Here, one chart has a single outlier, located at the high end of the X axis (where x = 24). As a result of that single outlier, the slope of the regression line changes greatly, from -2.5 to -1.6; so the outlier would be considered an influential point.\n\nWithout Outlier", null, "Regression equation: ŷ = 92.54 - 2.5x\nSlope: b0 = -2.5\nCoefficient of determination: R2 = 0.46\n\nWith Outlier", null, "Regression equation: ŷ = 87.59 - 1.6x\nSlope: b0 = -1.6\nCoefficient of determination: R2 = 0.52\n\nSometimes, an influential point will cause the coefficient of determination to be bigger; sometimes, smaller. In the first example above, the coefficient of determination is smaller when the influential point is present (0.94 vs. 0.55). In the second example, it is bigger (0.46 vs. 0.52).\n\nIf your data set includes an influential point, here are some things to consider.\n\n• An influential point may represent bad data, possibly the result of measurement error. If possible, check the validity of the data point.\n• Compare the decisions that would be made based on regression equations defined with and without the influential point. If the equations lead to contrary decisions, use caution.\n\nIn the context of regression analysis, which of the following statements are true?\n\nI. When the data set includes an influential point, the data set is nonlinear.\nII. Influential points always reduce the coefficient of determination.\nIII. All outliers are influential data points.\n\n(A) I only\n(B) II only\n(C) III only\n(D) All of the above\n(E) None of the above\n\nSolution\n\nThe correct answer is (E). Data sets with influential points can be linear or nonlinear. In this lesson, we went over an example in which an influential point increased the coefficient of determination. With respect to regression, outliers are influential only if they have a big effect on the regression equation. Sometimes, outliers do not have big effects. For example, when the data set is very large, a single outlier may not have a big effect on the regression equation." ]

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[ "# Quark", null, "", null, "Main Article Discussion Related Articles  [?] Bibliography  [?] External Links  [?] Citable Version  [?] This editable Main Article is under development and subject to a disclaimer. [edit intro]\nThe one exception to the confinement rule is the instance when a top quark decays with a lifetime less than $5\\times 10^{-25}{\\textrm {s}}$", null, ". This decay is so rapid that there is insufficient time for the quark to hadronize, i.e., form bound hadronic states. Thus top quarks are unique in decaying as free quarks and so offer a unique opportunity to measure the properties of free quarks directly.\n$V=\\left({\\begin{matrix}V_{ud}&V_{us}&V_{ub}\\\\V_{cd}&V_{cs}&V_{cb}\\\\V_{td}&V_{ts}&V_{tb}\\end{matrix}}\\right)=\\left({\\begin{matrix}1-\\lambda ^{2}/2&\\lambda &A\\lambda ^{3}(\\rho -i\\eta )\\\\-\\lambda &1-\\lambda ^{2}/2&A\\lambda ^{2}\\\\A\\lambda ^{3}(1-\\rho -i\\eta )&-A\\lambda ^{2}&1\\end{matrix}}\\right)$", null, "" ]

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[ "## Resonant Pendulum", null, "Here we have six pendulums that form three pairs of equal lengths. All are suspended from the same supporting rod, which is free to move back and forth. Now, set one of the pendulums in to motion. You will notice that another pendulum of the same length starts oscillating with maximum displacement.\n\nThis is because of the maximum transfer of energy of motion of one pendulum to the other of same length. This is the principle of resonance.\n\nIn this model three pairs of pendulums each of different lengths are suspended from a supporting rod. If one of the pendulum is set into oscillation, its pair, whose length is same as the former also starts to oscillate. This is all because of the supporting rod which itself starts to move back and forth when the pendulum is set into oscillation. This motion of the supporting rod transfers the energy of motion of one pendulum to another pendulum of the same length to a maximum extent. Due to this transfer, the other pendulum is set into oscillation, gradually covers greater distances from its rest position and reaches maximum when there is a maximum transfer of energy. By that time, the first pendulum would have almost come to rest. Now the transfer takes place from the second pendulum to the first one and this goes on till the second pendulum comes to rest. Thus, the cycle continues.\n\nThe scientific phenomenon behind the transfer of energy is known as \"Resonance\".\n\nIf the pendulum is pulled to one extreme and released without pushing, it makes a certain number of oscillations in a unit time. This number is a constant for a given pendulum and is known as its natural frequency or resonant frequency. This resonant frequency depends on the length of the pendulum. Longer the pendulum, lower the natural frequency.\n\nIf there is a connecting medium between two objects of same length, the motion of one object brings about motion in the other. This is resonance. The transfer of energy is then complete and maximum. The transfer takes place even between the objects of different natural frequencies. But, it will not be maximum.\n\n### Current Shows", null, "", null, "", null, "" ]

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[ "# A Diagonalizable Matrix which is Not Diagonalized by a Real Nonsingular Matrix", null, "## Problem 584\n\nProve that the matrix\n$A=\\begin{bmatrix} 0 & 1\\\\ -1& 0 \\end{bmatrix}$ is diagonalizable.\nProve, however, that $A$ cannot be diagonalized by a real nonsingular matrix.\nThat is, there is no real nonsingular matrix $S$ such that $S^{-1}AS$ is a diagonal matrix.", null, "Add to solve later\n\nContents\n\n## Proof.\n\nWe first find the eigenvalues of $A$ by computing its characteristic polynomial $p(t)$.\nWe have\n\\begin{align*}\np(t)=\\det(A-tI)=\\begin{vmatrix}\n-t & 1\\\\\n-1& -t\n\\end{vmatrix}=t^2+1.\n\\end{align*}\nSolving $p(t)=t^2+1=0$, we obtain two distinct eigenvalues $\\pm i$ of $A$.\nHence the matrix $A$ is diagonalizable.\n\nTo prove the second statement, assume, on the contrary, that $A$ is diagonalizable by a real nonsingular matrix $S$.\nThen we have\n$S^{-1}AS=\\begin{bmatrix} i & 0\\\\ 0& -i \\end{bmatrix}$ by diagonalization.\nAs the matrices $A, S$ are real, the left-hand side is a real matrix.\nTaking the complex conjugate of both sides, we obtain\n$\\begin{bmatrix} -i & 0\\\\ 0& i \\end{bmatrix}=\\overline{\\begin{bmatrix} i & 0\\\\ 0& -i \\end{bmatrix}}=\\overline{S^{-1}AS}=S^{-1}AS=\\begin{bmatrix} i & 0\\\\ 0& -i \\end{bmatrix}.$ This equality is clearly impossible.\nHence the matrix $A$ cannot be diagonalized by a real nonsingular matrix.", null, "Add to solve later\n\n### More from my site\n\n#### You may also like...\n\nThis site uses Akismet to reduce spam. Learn how your comment data is processed.\n\n###### More in Linear Algebra", null, "##### Diagonalize the Upper Triangular Matrix and Find the Power of the Matrix\n\nConsider the $2\\times 2$ complex matrix $A=\\begin{bmatrix} a & b-a\\\\ 0& b \\end{bmatrix}.$ (a) Find the eigenvalues of $A$. (b)...\n\nClose" ]

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[ "## Tuesday, January 29, 2013\n\n### Best-systems accounts of laws and second-order laws\n\nOn best-systems accounts of laws, p is a law provided that p is a theorem of the best system, where the best system is the one that optimizes informativeness and simplicity (and maybe fit, if we want probabilistic laws). But we also seem to have second-order laws, such as symmetry principles like Lorentz-invariance. Can we fit such second-order laws into a best-systems account?\n\nSay that a symmetry S is a permutation of the collection of worlds. Given a proposition p, let pS be a proposition that is true at a world w if and only if p is true at S(w). Say that a propositon is invariant under a class U of symmetries provided that p is true at w if and only if pS true at w for all S in U. A nice way to formulate invariance principles is then to say that the conjunction of the laws is invariant under U, for some appropriate class of symmetries U.\n\nOn a best systems analysis, then, U-invariance holds in a world w if and only if the conjunction of the axioms of w's best system is U-invariant. But that's not enough for us to have a second-order invariance law. To have a second-order invariance law, we need that it be a theorem of the best system that the conjunction of the axioms of the best system is U-invariant.\n\nSuppose w is some world with deterministic first-order Newtonian laws, an absolute distinction between rest and motion, and a second-order laws that says that the laws are Galileian-invariant. Is this likely to work out on a best-systems analysis? Let the first-order Newtonian axioms be N1,...,Nn. These will be all part of the best-system. Now, N1,...,Nn do not entail that the laws are Galileian-invariant. For there will be worlds where N1,...,Nn are laws, but on a best-systems analysis there is a further law, L0, where L0 is not Galilean-invariant (perhaps all of the particles initially are at rest, and it that they are all at rest might then make it in as an axiom of the best system). Since the second-order claim that the laws are Galileian-invariant does not follow from N1,...,Nn, it follows that for the second-order claim to be a law, the best system needs something more than N1,...,Nn. But it seems possible that (a) it is a second-order law that the laws are Galileian-invariant and yet (b) the best system is just N1,...,Nn as adding stuff that entails the second-order law to the axioms does not add enough predictive value beyond that N1,...,Nn already have to justify the loss of simplicity." ]

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[ "# Search the Community\n\nShowing results for tags 'entmake'.\n\n• ### Search By Tags\n\nType tags separated by commas.\n\n### Forums\n\n• News, Announcements & FAQ\n• Feedback\n• AutoCAD 2D Drafting, Object Properties & Interface\n• AutoCAD Drawing Management & Output\n• AutoCAD 3D Modelling & Rendering\n• AutoCAD Bugs, Error Messages & Quirks\n• The CUI, Hatches, Linetypes, Scripts & Macros\n• AutoLISP, Visual LISP & DCL\n• .NET, ObjectARX & VBA\n• Application Beta Testing\n• Application Archive\n• Other Autodesk Products\n• Autodesk 3ds Max\n• Autodesk Revit\n• Autodesk Inventor\n• Autodesk Software General\n• SketchUp\n• Rhino\n• SolidWorks\n• MicroStation\n• Design Software\n• Catch All\n• Resources\n• Tutorials & Tips'n'Tricks\n• Blocks, Images, Models & Materials\n• Community\n• Introduce Yourself\n• Showcase\n• Work In Progress\n• Jobs & Training\n• Chat\n• Competitions\n\n### Categories\n\n• Programs and Scripts\n• Images\n• Backgrounds\n\n### Filter by number of...\n\n• 0 Replies\n\n• 0 Reviews\n\n• 0 Views\n\n#### Minimum number of views\n\nFound 10 results\n\n1.", null, "## select the 4 points on each line and entmake pline\n\nCan someone help me to find the solution for some doubts. If someone will make one lisp for this, so I think I will get answer for few doubts I need to draw a pline inside this 4 line using line point like this My doubts 1 how to get “line point” with window selection (4 line all pints not in window only 4 line 4 point) (setq p1 (getpoint \"\\nSelect object...\")) (setq p2 (getcorner p1)) (setq mp (polar p1 (angle p1 p2) (/ (distance p1 p2) 2))) (setq p1 (list (nth 0 p1) (nth 1 p1))) (setq p2 (list (nth 0 p2) (nth 1 p2))) (if (not (equal '(nil nil) (sssetfirst nil (ssget \"_C\" p1 p2 '((0 . \"LINE\")))))) (setq lines (ssget \"_:L\"))) (if (/= (sslength lines) 4) (alert \"4 lines need to be selected\") 2 how to segregate the entity (which one is first which one is last) 3 how to entmake pline\n2.", null, "## entmake Inserting and orienting with entmake\n\nIn continuation of this thread I would like to continue this interesting story about UCSs and transformed entities. So far I have understood ( I am thankful to the community here) that An OCS is an coordinate system that most of the Autocad entities use instead of any other CS An OCS share the same origin with the WCS, however its x,y,z may be other than the one of the WCS However, it seems that something still eludes me and I cannot fully grasp it. I made a very simple model with a line drawn in WCS from 0,0,0 to 1,2,3. I would like to insert the same model on this one, that is having this line sitting on the end point (1,2,3) of the other as an extension. That means the lines need to be collinear. Let's assume I mirror3d this line on the xy plane, so the extrusion vector now becomes 0.0 0.0 -1.0. Using the following snippet the line comes on the correct placement but the orientation is wrong. What am I missing? ; clicking the mirrored entity from 0,0,0 to 1,2,-3 (setq pt (cdr (assoc 11 (setq ent (entget (car (entsel))))))) (setq v (cdr (assoc 210 ent))) ; inserting the drawing (entmakex (list (cons 0 \"INSERT\") (cons 2 \"Dwg\") (cons 8 \"0\") (cons 10 (trans (trans pt 0 1) 1 v)) (cons 70 0) (cons 66 1) (cons 50 0) (cons 210 v) ) ) Any suggestions appreciated.\n3.", null, "## Set the property \"InsUnits\" in a block generated by ENTMAKE.\n\nHi. I am generating a block using ENTMAKE, but I have noticed that the property \"InsUnits (RO)\" indicates \"Unitless\". The variable \"INSUNITS of the document (drawing) is set to \"6\" for Meters, but when generating the Block the property is set as Unitless. How do I assign the property to the BLOCK as this is the INSUNITS variable? (defun ent-block (nameBlock pto-ins atrib-var / ) (entmake (list '(0 . \"BLOCK\") '(100 . \"AcDbEntity\") '(100 . \"AcDbBlockBegin\") '(8 . \"0\") (cons 2 nameBlock) (cons 10 pto-ins) (cons 70 (if atrib-var 2 0)) ) ) ) (defun makeBlockGMM (listaEntNames nameBlock pto-ins atrib-var / msg ciclo) (defun ciclo ( listaEntNames / X) (foreach X listaEntNames (entmake (entget X)) ) ) (if (vl-catch-all-error-p (setq resultado01 (vl-catch-all-apply 'ent-block (list nameBlock pto-ins atrib-var)))) (progn (prompt (setq msg (strcat \"**ERROR en Cabecera, mensage de error: \" (vl-catch-all-error-message resultado01)))) ) ) (if (and (not msg ) (vl-catch-all-error-p (setq resultado02 (vl-catch-all-apply 'ciclo (list listaEntNames))))) (progn (prompt (setq msg (strcat \"**ERROR en creacion de entidades, mensage de error: \" (vl-catch-all-error-message resultado02)))) ) ) (if (and (equal resultado1 nil) (equal resultado2 nil)) (progn (ent-endblock) ) ) ) (defun ent-endblock ( / ) (entmake (list '(0 . \"ENDBLK\") '(100 . \"AcDbEntity\") '(100 . \"AcDbBlockEnd\") '(8 . \"0\") ) ) ) Regards.\n4.", null, "## Create a line with Corresponding Dimension\n\nHi, I was wondering if i could use two commands, line and dimlinear, in a single lisp file. this one i have measures a line you set with two points and creates a line that is a 1/3 in length of the distance between the two points. I want to add dimension line that will be 500 units above the created line. Any help would be very much appreciated. Thank you in advance. (defun c:aa () (setq po1 (getpoint \"Pick first point:\") po2 (getpoint po1 \"Pick second point:\") le (/ (distance po1 po2) 3) po3 (polar po1 (angle po1 po2) le)) (entmake (list '(0 . \"LINE\") (cons 10 po1) (cons 11 po3))) )\n5.", null, "## entmake block with attributes, scale and rotation issue\n\nI have done quite a search and have not found any good explanation to use entmake to insert a defined block, and scale or rotate that block upon insertion. The idea is to tag a line (pipe), and add the diameter, length, and cut-length of that pipe using attributes. I have the code to get the line information ready, and was working on the entmake for the attribute block to label the \"pipes\". Here is the code for the attribute block: (defun c:apd (/ LAY1 LAY2 LAY3 LAY4 CLR1 CLR2 CLR3 CLR4 LTP1 LTP2 LTP3 LTP4 FONT value1 value2 value3 rotation p) ;;; Change layer names and colors to suit user. (setq LAY1 \"S-Pipe-Detail\" LAY2 \"S-Pipe-Dia\" LAY3 \"S-Pipe-Length\" LAY4 \"S-Pipe-Cut\" CLR1 1 CLR2 2 CLR3 3 CLR4 4 LTP1 \"Continuous\" LTP2 \"Continuous\" LTP3 \"Continuous\" LTP4 \"Continuous\" FONT \"Standard\" ) ;;;======================== Block Definition ====================== (defun DEF_PipeDetail () ;generated using EntMaker CAB 04- MakeEntmake.lsp (entmake '((0 . \"BLOCK\") (100 . \"AcDbEntity\") (67 . 0) (8 . \"0\") (100 . \"AcDbBlockReference\") (66 . 1) (2 . \"PipeDetail\") (10 0.0 0.0 0.0) (70 . 2) ) ) (entmake '((0 . \"ATTDEF\") (100 . \"AcDbEntity\") (67 . 0) (8 . \"S-Pipe-Dia\") (100 . \"AcDbText\") (10 0.0 0.0 0.0) (40 . 0.095833333333331) (1 . \"-DIA-\") (50 . 0.0) (41 . 0. (51 . 0.0) (7 . \"Standard\") (71 . 0) (72 . 1) (100 . \"AcDbAttributeDefinition\") (280 . 0) (3 . \"PIPE DIAMETER:\") (2 . \"DIA\") (70 . 0) (74 . 1) (280 . 0) ) ) (entmake '((0 . \"ATTDEF\") (100 . \"AcDbEntity\") (67 . 0) (8 . \"S-Pipe-Length\") (100 . \"AcDbText\") (10 0.0 0.0 0.0) (40 . 0.095833333333331) (1 . \"-LENGTH-\") (50 . 0.0) (41 . 0. (51 . 0.0) (7 . \"Standard\") (71 . 0) (72 . 1) (100 . \"AcDbAttributeDefinition\") (280 . 0) (3 . \"PIPE LENGTH:\") (2 . \"PIPELENGTH\") (70 . 0) (74 . 3) (280 . 0) ) ) (entmake '((0 . \"ATTDEF\") (100 . \"AcDbEntity\") (67 . 0) (8 . \"S-Pipe-Cut\") (100 . \"AcDbText\") (10 0.0 0.0 0.0) (40 . 0.095833333333331) (1 . \"-LENGTH-\") (50 . 0.0) (41 . 0. (51 . 0.0) (7 . \"Standard\") (71 . 0) (72 . 1) (100 . \"AcDbAttributeDefinition\") (280 . 0) (3 . \"CUT LENGTH:\") (2 . \"CUTLENGTH\") (70 . 0) (74 . 3) (280 . 0) ) ) (entmake '((0 . \"ENDBLK\") (100 . \"AcDbBlockEnd\") (8 . \"0\"))) (princ) ) ; end DEF_PipeDetail ;;;======================== Insert Block ====================== (defun insert_PipeDetail (p lay rot d_lay pl_lay cl_lay font value1 value2 value3) (entmake (list (cons 0 \"INSERT\") (cons 2 \"PipeDetail\") (cons 10 p) (cons 8 lay) (cons 66 1) (cons 62 256) (cons 39 0) (cons 6 \"BYLAYER\") (cons 50 rot);block rotation (radians) ) ) (entmake (list (cons 0 \"ATTRIB\") (cons 8 d_lay) (cons 10 (mapcar '* (mapcar '+ p '(0.0 0.046875 0.0)) (list (getvar \"textsize\")(getvar \"textsize\")(getvar \"textsize\")))) (cons 11 (mapcar '+ p '(0.0 0.140625 0.0))) (cons 40 (getvar \"textsize\"));text height (cons 1 Value1) (cons 2 \"DIA\") (cons 70 0);attr flag (cons 50 0);text rot (cons 41 1);relative x-factor, width ;;; (cons 51 0);oblique angle (default 0) (cons 7 font) ;;; (cons 71 0);text flag (def 0, bkwrd 2, upside dn 4) (cons 74 1);1 BCenter (cons 72 1);1 Center (cons 210 (list 0 0 1));extrusion (def 0,0,1) ;;; (cons 73 0) (cons 62 256);color (bylayer 256) ;;; (cons 39 0);thickness (def 0) (cons 6 \"BYLAYER\") ) ) (entmake (list (cons 0 \"ATTRIB\") (cons 8 pl_lay) (cons 10 (mapcar '* (mapcar '+ p '(-0.046875 -0.140625 0.0)) (list (getvar \"textsize\")(getvar \"textsize\")(getvar \"textsize\")))) (cons 11 (mapcar '+ p '(-0.046875 -0.140625 0.0))) (cons 40 (getvar \"textsize\"));text height (cons 1 Value2) (cons 2 \"PIPELENGTH\") (cons 70 0);attr flag (cons 50 0);text rot (cons 41 1);relative x-factor, width ;;; (cons 51 0);oblique angle (default 0) (cons 7 font) ;;; (cons 71 0);text flag (def 0, bkwrd 2, upside dn 4) (cons 74 3);3 TCenter (cons 72 1);1 Center (cons 210 (list 0 0 1));extrusion (def 0,0,1) ;;; (cons 73 0) (cons 62 256);color (bylayer 256) ;;; (cons 39 0);thickness (def 0) (cons 6 \"BYLAYER\");linetype name ) ) (entmake (list (cons 0 \"ATTRIB\") (cons 8 cl_lay) (cons 10 (mapcar '* (mapcar '+ p '(0.046875 -0.28125 0.0)) (list (getvar \"textsize\")(getvar \"textsize\")(getvar \"textsize\")))) (cons 11 (mapcar '+ p '(0.046875 -0.28125 0.0))) (cons 40 (getvar \"textsize\"));text height (cons 1 Value3) (cons 2 \"CUTLENGTH\") (cons 70 0);attr flag (cons 50 0);text rot (cons 41 1);relative x-factor, width ;;; (cons 51 0);oblique angle (default 0) (cons 7 font) ;;; (cons 71 0);text flag (def 0, bkwrd 2, upside dn 4) (cons 74 3);3 TCenter (cons 72 1);1 Center (cons 210 (list 0 0 1));extrusion (def 0,0,1) ;;; (cons 73 0) (cons 62 256);color (bylayer 256) ;;; (cons 39 0);thickness (def 0) (cons 6 \"BYLAYER\");linetype name ) ) (entmake (list (cons 0 \"SEQEND\") (cons 8 lay) ) ) ) ;;;======================== Make Layers ====================== (defun make_layer (MyLayer MyColor MyLtype) (entmake (list (cons 0 \"LAYER\") (cons 100 \"AcDbSymbolTableRecord\") (cons 100 \"AcDbLayerTableRecord\") (cons 2 MyLayer) (cons 6 MyLtype) (cons 62 MyColor) (cons 70 0) ) ) ) ;;;======================== Main Function ======================= (if (not (tblsearch \"layer\" LAY1)) (make_layer LAY1 CLR1 LTP1) ) (if (not (tblsearch \"layer\" LAY2)) (make_layer LAY2 CLR2 LTP2) ) (if (not (tblsearch \"layer\" LAY3)) (make_layer LAY3 CLR3 LTP3) ) (if (not (tblsearch \"layer\" LAY4)) (make_layer LAY4 CLR4 LTP4) ) (if (not (tblsearch \"block\" \"PipeDetail\")) (DEF_PipeDetail) ) ;;; temporary setq (setq value1 \"MyDiameter\" value2 \"MyLength\" value3 \"MyCut\" rotation 1.5708 ) ;;; end temporary setq (setvar \"osmode\" 512) (while (setq p (getpoint \"\\nPick insertion point >> \")) (insert_PipeDetail p LAY1 rotation LAY2 LAY3 LAY4 FONT value1 value2 value3) ) ;;;end while (princ) ) This code works, but I cannot get the lower two attributes to offset from the line (by half the text height), nor can I get the entire block to rotate (I used rotation 1.5708, or 90 degrees). If anyone can enlighten me, or kick me in the right direction it would be much appreciated. Thanks, CHL\n6.", null, "## Help shading a circular area with entmake hatch\n\nI am working off of this code cadpanacea.com/node/186, but when I try to run the following, the radius of the circular hatch varies based on the 'ctr' variable's distance from the origin. I would like it to depend solely on the 'ctr' and 'edge' points. (defun c:test()(setvar \"osmode\" 0) (setq ctr (getpoint \"\\nCenter of Circle: \")) (setq edge (getpoint \"\\nEdge of Circle: \")) (entmakex (list (cons 0 \"HATCH\") (cons 100 \"AcDbEntity\") (cons 8 \"E-GRND\") (cons 100 \"AcDbHatch\") (cons 10 ctr) (cons 210 (list 0 0 1)) (cons 2 \"SOLID\") (cons 70 1) (cons 71 0) (cons 91 1) (cons 92 1) (cons 93 1) (cons 72 3) ;the \"3\" designates this is an elliptical shape, 1 for circle (cons 10 ctr) ;center point of ellipse (cons 11 edge) ;point of top quad (cons 40 1) ;ratio of width to height (cons 50 0.0) ;start angle (cons 51 (* pi 2.0)) ;end angle (full ellipse) (cons 73 1) ;counterclockwise flag (cons 97 0) (cons 75 0) (cons 76 1) (cons 98 1) (cons 10 (list 0 0 0)) ))\n7.", null, "## Displaying variables and characters in an entmake dimension\n\nHello! I just stared working in AutoLISP a few days ago, and I've come across a problem. I need to create a dimension line where the dimension value is dependent on an input value. So if the input is y, then the text on the dimension line should equal 4.5*(y+1) inches, and it also needs to have a character width of 0.75. Currently, it just displays 4 1/2\". As I understand it, this would be a real number, meaning I can't concatenate it with the inches symbol. Any help would be greatly appreciated! (defun c:retan (/ p1 p2 p3 p4 x y i j)(setvar \"osmode\" 0) (setq p1 (getpoint \"\\nfirst corner of rectangle: \")) (setq x (getint \"\\nEnter Horizontal Count: \")) (setq y (getint \"\\nEnter Vertical Count: \")) (setq p3 (list (+ (+ 1.625 (* 0.8125 (- x 1))) (car p1))(+ (+ 1.625 (* 0.8125 (- y 1))) (cadr p1)))) (setq p2 (list (car p1)(cadr p3))) (setq p4 (list (car p3)(cadr p1))) (command \"pline\" p1 p2 p3 p4 \"c\") ;c closes the rectangle's fourth side (entmakex (list (cons 0 \"DIMENSION\") (cons 100 \"AcDbEntity\") (cons 8 \"E-DIMS\") ;; 8 Layer (cons 100 \"AcDbDimension\") (cons 10 (list (- (car P1) 0.7) (cadr P2) 0)) ;; 10 Arrow Node (cons 11 (list (- (car P1) 0.9) (/ (+ (cadr P2)(cadr P1)) 2) 0)) ;; 11 Text Position (cons 70 160) (cons 1 \"{\\\\W0.75;4 1/2\\\"}\") ;; 1 Contents of Dimension Textbox (cons 71 5) ;; 71 Text Alignment (5=centered) (cons 42 0.8125) (cons 53 1.5708) ;; 53 Text Rotation (cons 3 \"REW-1_.125txt\") (cons 100 \"AcDbAlignedDimension\") (cons 13 P1) ;; 13 point on line (cons 14 P2) ;; 14 point on line (cons 50 1.5708) ;; 50 Angle (radians) 1.5708 (cons 100 \"AcDbRotatedDimension\"))) (setvar \"osmode\" 16383)(princ) )\n8.", null, "## entmake - why \"too few arguments\"\n\nWhy \"too few arguments\"? (defun c:mci (cp) (setq cp (getpoint \"\\nCenter point:\")) (entmake (list (cons 0 \"CIRCLE\");;Entity (cons 62 5);;Color (cons 10 cp);;Center point (cons 40 2);;Radius ) ) (princ) )\n9.", null, "## DCL Ignore Blank Values MText\n\nI am trying to write a routine that allows users to input items and weights in a dialog box, and outputs a formatted MText (among other things). I allow the user to input up to 10 items, but I only want the MText to use the values that are filled in. Here's what my dialog box looks like: And here's what my output looks like: Here's my code for the Mtext: (setq val (strcat \"\\\\pxtr18,c20,r30;\\t\" eq1 \"\\t=\\t\" wt1 \" LB \\\\P\\t\" eq2 \"\\t=\\t\" wt2 \" LB \\\\P\\t\" eq3 \"\\t=\\t\" wt3 \" LB \\\\P\\t\" eq4 \"\\t=\\t\" wt4 \" LB \\\\P\\t\" eq5 \"\\t=\\t\" wt5 \" LB \\\\P\\t\" eq6 \"\\t=\\t\" wt6 \" LB \\\\P\\t\" eq7 \"\\t=\\t\" wt7 \" LB \\\\P\\t\" eq8 \"\\t=\\t\" wt8 \" LB \\\\P\\t\" eq9 \"\\t=\\t\" wt9 \" LB \\\\P\\t\" eq10 \"\\t=\\t\" wt10 \" LB\" )) (entmake (list (cons 0 \"MTEXT\") (cons 100 \"AcDbEntity\") (cons 100 \"AcDbMText\") (cons 10 pt1) (cons 1 val) (cons 8 \"NOTES\") (cons 40 0.09375) (cons 7 \"ROMANS\") (cons 41 4))) Any suggestions how to make it ignore the \"0\" values? Thanks in advance!\n10.", null, "## Annotative text style\n\nHi guys, I'm learning to use LISP functions and came across an problem. Maybe it has been asked thousand times, but I couldn't find an relative thread here. I want to create a function that checks if there is an text style named \"Tekst 2.5\". Now, the problem is that i can't get the text style to be annotative This is what I have: (defun c:test (/) (if (null (tblsearch \"style\" \"tekst 2.5\")) (entmake (list '(0 . \"STYLE\") '(100 . \"AcDbSymbolTableRecord\") '(100 . \"AcDbTextStyleTableRecord\") '(2 . \"Tekst 2.5\") ; Style name '(70 . 0) ; Standard flag values (bit-coded values) '(40 . 2.5) ; text height '(41 . 1.0) ; width factor '(50 . 0.0) ; oblique angle '(71 . 1) ; text generation \"0\" normal text '(42 . 0) ; last height used '(3 . \"Arial.ttf\") ; font file name '(4 . \"\") ; bigfont (blank for no) ) ; end list ) ; end entmake ) ; end if (princ) ) Does any of you know hou to get it annotative using entmake?\n×\n×\n• Create New..." ]

[ null, "https://www.cadtutor.net/forum/uploads/monthly_2020_05/kiMLa7yij.thumb.jpg.3af93db9bb610f33ec8630e6861f8181.jpg", null, "data:image/svg+xml,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20viewBox%3D%220%200%201024%201024%22%20style%3D%22background%3A%239bc462%22%3E%3Cg%3E%3Ctext%20text-anchor%3D%22middle%22%20dy%3D%22.35em%22%20x%3D%22512%22%20y%3D%22512%22%20fill%3D%22%23ffffff%22%20font-size%3D%22700%22%20font-family%3D%22-apple-system%2C%20BlinkMacSystemFont%2C%20Roboto%2C%20Helvetica%2C%20Arial%2C%20sans-serif%22%3EM%3C%2Ftext%3E%3C%2Fg%3E%3C%2Fsvg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20viewBox%3D%220%200%201024%201024%22%20style%3D%22background%3A%2362a5c4%22%3E%3Cg%3E%3Ctext%20text-anchor%3D%22middle%22%20dy%3D%22.35em%22%20x%3D%22512%22%20y%3D%22512%22%20fill%3D%22%23ffffff%22%20font-size%3D%22700%22%20font-family%3D%22-apple-system%2C%20BlinkMacSystemFont%2C%20Roboto%2C%20Helvetica%2C%20Arial%2C%20sans-serif%22%3EG%3C%2Ftext%3E%3C%2Fg%3E%3C%2Fsvg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20viewBox%3D%220%200%201024%201024%22%20style%3D%22background%3A%2371c462%22%3E%3Cg%3E%3Ctext%20text-anchor%3D%22middle%22%20dy%3D%22.35em%22%20x%3D%22512%22%20y%3D%22512%22%20fill%3D%22%23ffffff%22%20font-size%3D%22700%22%20font-family%3D%22-apple-system%2C%20BlinkMacSystemFont%2C%20Roboto%2C%20Helvetica%2C%20Arial%2C%20sans-serif%22%3EI%3C%2Ftext%3E%3C%2Fg%3E%3C%2Fsvg%3E", null, "https://www.cadtutor.net/forum/uploads/monthly_2018_08/avatar53440_2.thumb.gif.939acc9fa3708069035942c7dc67894f.gif", null, "data:image/svg+xml,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20viewBox%3D%220%200%201024%201024%22%20style%3D%22background%3A%239e62c4%22%3E%3Cg%3E%3Ctext%20text-anchor%3D%22middle%22%20dy%3D%22.35em%22%20x%3D%22512%22%20y%3D%22512%22%20fill%3D%22%23ffffff%22%20font-size%3D%22700%22%20font-family%3D%22-apple-system%2C%20BlinkMacSystemFont%2C%20Roboto%2C%20Helvetica%2C%20Arial%2C%20sans-serif%22%3EP%3C%2Ftext%3E%3C%2Fg%3E%3C%2Fsvg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20viewBox%3D%220%200%201024%201024%22%20style%3D%22background%3A%239e62c4%22%3E%3Cg%3E%3Ctext%20text-anchor%3D%22middle%22%20dy%3D%22.35em%22%20x%3D%22512%22%20y%3D%22512%22%20fill%3D%22%23ffffff%22%20font-size%3D%22700%22%20font-family%3D%22-apple-system%2C%20BlinkMacSystemFont%2C%20Roboto%2C%20Helvetica%2C%20Arial%2C%20sans-serif%22%3EP%3C%2Ftext%3E%3C%2Fg%3E%3C%2Fsvg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20viewBox%3D%220%200%201024%201024%22%20style%3D%22background%3A%23a462c4%22%3E%3Cg%3E%3Ctext%20text-anchor%3D%22middle%22%20dy%3D%22.35em%22%20x%3D%22512%22%20y%3D%22512%22%20fill%3D%22%23ffffff%22%20font-size%3D%22700%22%20font-family%3D%22-apple-system%2C%20BlinkMacSystemFont%2C%20Roboto%2C%20Helvetica%2C%20Arial%2C%20sans-serif%22%3ET%3C%2Ftext%3E%3C%2Fg%3E%3C%2Fsvg%3E", null, "data:image/svg+xml,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20viewBox%3D%220%200%201024%201024%22%20style%3D%22background%3A%23c4bb62%22%3E%3Cg%3E%3Ctext%20text-anchor%3D%22middle%22%20dy%3D%22.35em%22%20x%3D%22512%22%20y%3D%22512%22%20fill%3D%22%23ffffff%22%20font-size%3D%22700%22%20font-family%3D%22-apple-system%2C%20BlinkMacSystemFont%2C%20Roboto%2C%20Helvetica%2C%20Arial%2C%20sans-serif%22%3EP%3C%2Ftext%3E%3C%2Fg%3E%3C%2Fsvg%3E", null, "https://www.cadtutor.net/forum/uploads/monthly_2018_08/avatar71214_2.thumb.gif.ebfb5bf69dd372e9773b1fae3557fbee.gif", null ]

[ "", null, "", null, "Try the Free Math Solver or Scroll down to Tutorials!\n\n Depdendent Variable\n\n Number of equations to solve: 23456789\n Equ. #1:\n Equ. #2:\n\n Equ. #3:\n\n Equ. #4:\n\n Equ. #5:\n\n Equ. #6:\n\n Equ. #7:\n\n Equ. #8:\n\n Equ. #9:\n\n Solve for:\n\n Dependent Variable\n\n Number of inequalities to solve: 23456789\n Ineq. #1:\n Ineq. #2:\n\n Ineq. #3:\n\n Ineq. #4:\n\n Ineq. #5:\n\n Ineq. #6:\n\n Ineq. #7:\n\n Ineq. #8:\n\n Ineq. #9:\n\n Solve for:\n\n Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:\n\n# Systems of Linear Equations\n\nPLEASE NOTE THAT YOU CANNOT USE A CALCULATOR ON THE ACCUPLACER -\nELEMENTARY ALGEBRA TEST! YOU MUST BE ABLE TO DO THE FOLLOWING PROBLEMS\nWITHOUT A CALCULATOR!\n\nSystems of Linear Equations\n\nYou already studied the linear equation in two variables Ax + By = C whose graph is a\nstraight line. Many applied problems are modeled by two or more linear equations.\nWhen this happens, we talk about a System of Linear Equations.\n\nSystems of Linear Equations can be solved graphically, or by using the Substitution Method or the\n\nThe following is a pictorial representation of the system consisting of the linear equations", null, "The point of intersection is considered the solution of the\nsystem.", null, "Solving a System of Linear Equations graphically often does not give use the correct solution. For\nexample, in the picture above we might believe that the solution is", null, ".\n\nActually, the solution is", null, "as you will see later, but this is difficult to see on a graph.\nTherefore, we will consider two methods for solving linear systems that do NOT depend on finding\nsolutions visually.\n\nStrategy for Solving Systems of Equations by the Substitution Method\n\nStep 1: Solve any one of the equations for one variable in terms of the other. If one of\nthe equations is already in this form, you can skip this step.\n\nStep 2: Substitute the expression found in Step 1 into the other equation. You should\nnow have an equation in one variable. Find its value.\n\nPlease note that ONLY at the point of intersection two equations are equal to\neach other. By setting the x- or y-value of one equation equal to the x- or yvalue\nof the other equation, we are in effect finding the point of intersection.\n\nStep 3: To find the value of the second variable, back-substitute the value of the variable\nfound in Step 2 into one of the original equations.\n\nStep 4: Form an ordered pair with the values found in Step 3 and Step 4. This is the\nsolution to your system of equations.\n\nStrategy for Solving Systems of Equations by the Addition Method\n\nStep 1: If necessary, rewrite both equations in the same form so that the variables and\nthe constants match up when one equation is beneath the other.\n\nStep 2: If necessary, multiply either equation or both equations by appropriate numbers\nso that the coefficient of either x or y will be opposite in sign giving a sum of 0.\n\nStep 3: Write the equations one below the other, draw a horizontal line, then add each of\ntheir terms. The sum should be an equation in one variable. Find its value.\n\nStep 4: To find the value of the second variable, back-substitute the value of the variable\nfound in Step 3 into one of the original equations.\n\nStep 5: Form an ordered pair with the values found in Step 4 and Step 5. This is the\nsolution to your system of equations.\n\nNOTE: Solving Systems of Linear Equations with the Substitution Method is often quicker than\nwhen using the Addition Method. However, the Substitution Method is most useful if one of the given\nequations has a variable with coefficient 1 or -1. Such a variable can easily be isolated without\nintroducing fractions. As soon as isolating either of the two variables in both equations produces\nALL fractions, the Addition Method becomes a better choice.\n\nProblem 1:\nSolve the following system:", null, "Let's use both the Substitution Method and the Addition Method.\n\nSubstitution Method:\n\nStep 1:\n\nSolve any one of the equations for one variable in terms of the other. By\nsolving", null, "for y, we find", null, "Step 2:\nNext, we back-substitute into the equation", null, "as follows", null, "Step 3:\nNow, we have to find the y-coordinate of the point of intersection of the two\nlines. Back-substituting into the equation", null, ", we get", null, "Therefore, the solution to the linear system of equations or the point of intersection\nof the two lines is", null, ".", null, "Step 1:\n\nThe equations are already rewritten in the same form so that the variables and\nthe constants match up when one equation is beneath the other.\n\nStep 2:\nWe multiply both sides of the first equation by -5 so that the coefficient of y in\nboth equations will be opposite in sign giving a sum of 0.", null, "Step 3:\nNow, we will write the \"new\" first equation below the second equation, draw a\nhorizontal line, then add each of their terms.", null, "The x-coordinate of the point of intersection.\n\nStep 4:\nTo find the y-coordinate of the point of intersection of the two lines, we back-substitute\nthe value found for x into the equation", null, "to get", null, "The solution to the system of linear equations or their point of intersection is", null, ".\n\nProblem 2:\nSolve the following system:", null, "We will use the Substitution Method because both variables in the second equation have\na coefficient of 1.\n\nSolve the second equation for one variable in terms of the other. It does not matter which\none you solve for!\n\nBy solving the equation", null, "for x, we find", null, ".\nBack-substituting into the equation", null, ", we get", null, "", null, ", which is, of course, impossible.\n\nIn this case, we can conclude that the System of Linear Equations has NO solutions. This\nindicates that the two lines are parallel to each other. Remember that parallel lines have\nthe same slope!\n\nProblem 3:\nSolve the following system:", null, "We will use the Substitution Method because both equations have variables with a\ncoefficient of 1.\n\nIn this case, both equations are already solved for y. This is a perfect case for the\nSubstitution Method. We just have to substitute the right side of the first equation for y in\nthe second equation. That is,", null, "Solving for the y-coordinate using the equation", null, ", we get", null, "Therefore, the solution to the linear system of equations or the point of intersection\nof the two lines is", null, ".\n\nProblem 4:\nSolve the following system:", null, "We will use the Substitution Method because one variable in the second equation has a\ncoefficient of 1.\n\nFurthermore, the second equation is already solved for y.\n\nBack-substituting into the equation", null, ", we get", null, "Solving for the y-coordinate using the equation", null, ", we get", null, "Therefore, the solution to the linear system of equations or the point of intersection\nof the two lines is", null, ".\n\nProblem 5:\nSolve the following system:", null, "In this case, we will use the Addition Method because none of the variables have a\ncoefficient of 1.\n\nLet's eliminate x by multiplying the first equation by 3 and the second equation by -5.\nThen we'll add the two new equations to find x.", null, "To find the y-coordinate of the point of intersection of the two lines, we back-substitute the\nvalue found for y into the equation", null, "to get", null, "The solution to the system of linear equations or their point of intersection is", null, ".\n\nProblem 6:\nSolve the following system.", null, "First we must arrange the system so that the variable terms appear on one side of the\nequation and constants on the other side. Then we will use the Addition Method because\nnone of the variables have a coefficient of 1. However, note that we could have divided\nthe first equation by 2 and the second one by 3 to produce variables with coefficient 1.", null, "Let's eliminate y by multiplying the first equation by 3 and the second equation by 2.\nThen we'll add the two new equations to find x.", null, "Since we not only eliminated y but also x, we have to conclude that this System of Linear\nEquations has infinitely many solutions. Graphically, you will find that both equations\nhave the same graph. If you divide the first equation by 2 and the second equation by -3\nyou can convince yourself of this!\n\nProblem 7:\n\nA grocer plans to mix candy that sells for \\$1.20 a pound with candy that sells for \\$2.40 a\npound to get a mixture that he plans to sell for \\$1.65 a pound. How much of the \\$1.20\nand \\$2.40 candy should he use if he wants 80 pounds of the mix?\n\nHere we have enough information to make two equation in two variables. Let's call the\ncandy that sells for \\$1.20 per pound x and the candy that sells for \\$2.40 per pound y.\n\nThe first equation is an income equation: 1.20x + 2.40y = 1.65(80)\nThe second equation shows the total number of pounds in the mixture: x + y = 80\nTherefore, we are solving the following system.\n\n1.20x + 2.40y = 132\nx + y = 80\n\nWe'll divide the first equation by -1.20 and then use the Addition Method.", null, "To find the value of x, we back-substitute the value found for y into the equation x + y =\n80 to get\n\nx + 30 = 80\nx = 50\n\nThe grocer needs 50 lb of candy that sells for \\$1.20 and 30 lb of candy that sells for\n\\$2.40 to make an 80-lb mixture of candy that sells for \\$1.65.\n\nProblem 8:\n\nA charity has been receiving donations of dimes and quarters. They have 94 coins in all.\nIf the total value is \\$19.30, how many dimes and how many quarters do they have?\n\nHere we again have enough information to make two equation in two variables. Let's call\nthe number of dimes x and the number of quarters y.\n\nThe first equation is an income equation: 0.10x + 0.25y = 19.30\n\nThe second equation shows the total number of coins: x + y = 94\n\nTherefore, we are solving the following system.\n\n0.10x - 0.25y = 19.30\nx + y = 94\n\nWe'll divide the first equation by -0.10 and then use the Addition Method.", null, "To find the value of x, we back-substitute the value found for y into the equation x + y =\n94 to get\n\nx + 66 = 94\nx = 28\n\nThe charity has 28 dimes and 66 quarters.\n\nProblem 9:\n\nAn apartment building contains 12 units consisting of one- and two-bedroom apartments\nthat rent for \\$360 and \\$450 per months respectively. When all units are rented, the total\nmonthly rent is \\$4,950. What is the number of one- and two bedroom apartments?\n\nHere we again have enough information to make two equation in two variables. Let's call\nthe number of one-bedroom apartments x and the number of two-bedroom apartments y.\n\nThe first equation is an income equation: 360x + 450y = 4950\nThe second equation shows the total number of apartments: x + y = 12\nTherefore, we are solving the following system.\n\n360x + 450y = 4950\nx + y = 12\n\nWe'll multiply the second equation by -360 and then use the Addition Method.", null, "To find the value of x, we back-substitute the value found for y into the equation x + y =\n12 to get\n\nx + 7 = 12\nx = 5\n\nThe apartment building has 5 one-bedroom apartments and 7 two-bedroom\napartments." ]

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[ "# Difference between revisions of \"Description of output files\"\n\n## Default output files\n\nThe following output files are always produced.\n\n### Main output file\n\nThe main output file contains all results calculated by default during the transport cycle. The file is written in Matlab-readable format in file:\n\n```[input]_res.m\n```\n\nWhere:\n\n [input] : is the name of the input file\n\nIn calculations involving multiple transport cycles (such burnup calculation) the file is appended after each cycle. When the file is read into Matlab, each parameter is read into a variable (scalar or vector). A run index “idx” is assigned to each block of results, and the output data from different cycles are read into different rows (turning scalar variables into vectors and vector variables into matrices).\n\nThe list of parameters is provided separately here.\n\n### Nuclide and material data\n\nNuclear and material data is collected in in file:\n\n```[input].out\n```\n\nWhere:\n\n [input] : is the name of the input file\n\nBasically the file lists all nuclides and their reactions as they are read from the nuclear data libraries. The material data includes isotopic compositions and densities, as well as volumes and masses if available. The list of tables included in the file can be handled in the set dataout option. The format is self-explanatory.\n\nThe data is divided into two sections: nuclear data (Tables 1-4) and material data (Table 5), as follows:\n\n• Table 1: Summary of nuclide data\n• Table 2: Reaction and decay data\n• Table 3: Fission yield data\n• Table 4: Lost transmutation paths\n• Table 5: Summary of material compositions\n\n### Burnup calculation output\n\nOutput from burnup calculations is printed in file:\n\n``` [input]_dep.m\n```\n\nThis file contains Matlab format data in several variables of form:\n\n``` MAT_[material]_[data]\n```\n\nWhere:\n\n [material] : is the name of a material in the calculation [data] : is the data type\n\nEvery variable is a matrix with rows corresponding to the nuclides requested in the set inventory option and columns corresponding to different burnup steps. The list of variables included in the file can be handled in the set deppara option. The data types are:\n\n ADENS : Atom density in b-1 cm-1 MDENS : mass density in g/cm3 A : Activity in becquerels H : Decay heat in Watts SF : Spontaneous fission rate in fissions per second GSRC : Photon emission rate in photons per second ING_TOX : Ingestion toxicity in sieverts INH_TOX : Inhalation toxicity in sieverts VOLUME : Material volume in cm3 BURNUP : Burnup in MWd/kgU\n\nNotes:\n\n• For 2D geometries, values are on a per axial length basis.\n• To additional rows are printed for each data array: data for lost nuclides (reaction products without nuclide data) and total.\n\nThe following output files are produced by invoking various input options.\n\n### Group constant output\n\nGroup constant data is printed separately in file:\n\n```[input].coe\n```\n\nWhere:\n\n [input] : is the name of the input file\n\nThe file is designed to be read by post-processing scripts, and the format is described together with the automated burnup sequence.\n\n### Reaction rate output\n\nCalculation of analog reaction rates by counting the number of sampled interactions is invoked using the set arr option. The output is printed in file:\n\n```[input]_arr[n].m\n```\n\nWhere:\n\n [input] : is the name of the input file [n] : is the burnup index (zero for first step or if no burnup calculation is run)\n\nThe data is printed in Matlab format in two variables: string array \"nuc\", which contains the nuclide identifiers (ZA.id), and table \"rr\", consisting one row for each reaction and 7 columns:\n\n```IDX ZAI MT EMIN EMAX RR ERR\n```\n\nwhere the values are:\n\n IDX : Nuclide index corresponding to the entries in the nuc array ZAI : Nuclide identifier (ZAI) MT : ENDF reaction MT EMIN : Minimum energy of the reaction mode EMAX : Maximum energy of the reaction mode RR : Reaction rate ERR : Relative statistical error\n\nNotes:\n\n• The values are normalized microscopic reaction rates integrated over all materials and energies.\n• Neutron transport mode includes either reactions that affect neutron balance (absorption, fission, neutron-multiplying scattering) or all reactions, depending on the value of the input option.\n• All reaction modes are included in photon transport mode.\n\n### Micro depletion output\n\nMicroscopic few-group cross sections calculated for the purpose of micro-depletion (set mdep) option are printed in file:\n\n```[input]_mdx[n].m\n```\n\nWhere:\n\n [input] : is the name of the input file [n] : is the burnup index (zero for first step or if no burnup calculation is run)\n\nor in branch calculation:\n\n```[input]_mdx[n]b[m].m\n```\n\nWhere:\n\n [input] : is the name of the input file [n] : is the burnup index [m] : is the branch index\n\n#### Cross sections\n\nThe data includes few-group cross sections printed in table XS_[u], where [u] is the universe for which the calculation is carried out. The columns are:\n\n```ZAI MT I N ERRN XS1 ERR1 XS2 ERR2 ..\n```\n\nwhere the values are:\n\n ZAI : Nuclide identifier (ZAI) MT : ENDF reaction MT I : Special flag (isomeric state or fission yield distribution number) N : Nuclide density smeared to homogenized volume ERRN : Associated relative statistical error XSg : Microscopic cross section ERRg : Associated relative statistical error RR : Reaction rate ERR : Relative statistical error\n\n#### Fission yields\n\nActinide fission yields are additionally printed in variables NFY_[ZAI]_[n], where [ZAI] is the nuclide identifier and [n] is the yield distribution number. Each yield corresponds to an energy, printed in variable NFY_[ZAI]_[n]E. The columns in the fission yield distribution are:\n\n```ZAI FI FC\n```\n\nwhere the values are:\n\n ZAI : Product identifier FI : Independent yield FC : Cumulative yield\n\n#### Decay data\n\nDecay data of decaying nuclides are additionally printed in variable dec. The columns in the decay data table are:\n\n```1. ZAI\n2. decay constant (1/s)\n3. specific decay energy (J)\n4. reaction type\n5. branch fraction\n6. product ZAI\n```\n\nNotes:\n\n• For fission reactions the special flag corresponds to a fission product yield distribution, which are tabulated for different energies.\n• For transmutation reactions the special flag indicates the isomeric state of the product nuclide (0 = ground state, 1 = isomeric state).\n• Nuclide densities were not present before 2.1.32.\n• Additional product nuclides (e.g. H-1) can be determined from the reaction type. Each number in the reaction type corresponds to one simultaneous reaction.\n\n### History output\n\nCertain cycle-wise results are stored when the the set his option is invoked. The results are printed in file:\n\n```[input]_his[n].m\n```\n\nWhere:\n\n [input] : is the name of the input file [n] : is the burnup index (zero for first step or if no burnup calculation is run)\n\nThe output consists of tables corresponding to different parameters. The first column lists the cycle index, which is then followed by the results grouped in three columns that provide the cycle-wise value, the cumulative mean and the corresponding relative statistical error. If the parameter has two values, the number of columns is 7 (cycle index + two groups of three columns of results), and so on.\n\nBy default the output includes the following variables:\n\nParameter Description\nHIS_IMP_KEFF Implicit estimator of keff\nHIS_ANA_KEFF Analog estimator of keff (total, prompt and delayed)\nHIS_COL_KEFF Collision estimator of keff\nHIS_MEAN_POP_SIZE Mean simulated population size\nHIS_MEAN_POP_WGT Mean simulated population weight\nHIS_TRANSPORT_RUNTIME Transport cycle running time (wall-clock and CPU time)\nHIS_TRANSPORT_CPU_USAGE Mean CPU usage (ratio of CPU and wall-clock time)\nHIS_ENTR_SPT Shannon entropy of source point distribution (total, x, y and z)\nHIS_ENTR_SWG Shannon entropy of source weight distribution (total, x, y and z)\n\n### Burned material output\n\nBurned materials' isotopic compositions and densities at each burnup step can be printed using the set printm option. The output will be in files of the form:\n\n```[input].bumat[n]\n```\n\nWhere:\n\n [input] : is the name of the input file [n] : is the burnup index (zero for first step or if no burnup calculation is run)\n\nThe data will be printed in a serpent-compatible material definition format." ]

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[ "# Professor Andrew Archer, University of Loughborough\n\n#### Professor Andrew Archer, University of Loughborough. Part of the applied mathematics seminar series.\n\nIntroduction to classical density functional theory (DFT) and dynamical density functional theory (DDFT)\n\nIn this talk I will give an introduction to classical^** density functional theory (DFT) and dynamical density functional theory (DDFT). DFT is a statistical-mechanical theory for the average density distribution of a system of classical particles in the presence of an external field. It is a microscopic theory, able to describe the structure even down to the scale of the individual particles. A typical problem that can be solved using DFT is to determine the density distribution of molecules in a liquid in the presence of a container wall. It can also describe solid phases of matter and the density distribution at the interface between a crystal coexisting with the liquid phase. In addition to yielding particle density distributions, DFT can also be used to obtain thermodynamic quantities such as free energies and interfacial tensions. DDFT is a generalisation of DFT, able to describe the non-equilibrium time evolution of the density profile. Originally developed for systems of Brownian particles with stochastic equations of motion, the formalism has been extended to describe many body systems evolving under Newton's equations of motion and also underdamped stochastic equations of motion.\n\n^** Classical DFT should not be confused with quantum DFT, a related theory for the density distribution of electrons in matter. I will not discuss quantum DFT.\n\n#### Related events\n\nSee all Applied Mathematics events" ]

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[ "", null, "Community Primary School\n\nTogether We Thrive\n\n# Maths\n\nHere are some of the number facts that you should know by now:\n\n• Number bonds for 10 and 20 (eg. 5 + 5 = 10, 15 + 5 = 20) Don't forget that you also need to learn the subtraction facts: 10 - 5 = 5, 20 - 15 = 5\n• Number bonds to 10 related to number facts up to 100, e.g. 4+6=10 is related to  40+60=100.\n• Multiplication and division for the 2, 5 and 10 x tables (but we are only focusing on addition and subtraction facts this week).\n\n1. Practice recalling your number facts through a variety of games / videos\n\n2. Complete some sheets/booklets with Word Problems\n\n## Relate number bonds to 100 to number bonds to 10\n\nMaths Games for recalling of Year 2 Number Facts:\n\n• Target! Write out the numbers from 0-20 in a line.  Throw a bean-bag. If you land on, say, 5, then you have to shout out 15 (since 5 + 15 =20).\n\n• Write the multiples of 10 from 10-90 on square pieces of paper.  Your opponent chooses a card and you must say what you would add onto that number to make 100.  So, if my opponent chooses 20, I would shout out \"80!\".  (I know this because I know that 2 + 8 =10 so therefore 20 + 80 = 100).\n\n• 'I SAY, YOU SAY' Up to 10:  I say 4, you say 6   Up to 20: I say 12, you say 8  Up to 100: I say 20, you say 80.\n\nActivities to Print out and Complete\n\nBelow, there are a variety of activities to suit your different needs.  If you are really confident with your number bonds to 20, then you don't have to complete that task.\n\nTop" ]

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[ "First Principles Calculation of Elastic Moduli of Early-Late Transition Metal Alloys\n\n# First Principles Calculation of Elastic Moduli of Early-Late Transition Metal Alloys\n\nWilliam Paul Huhn Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213    Michael Widom Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213    Andrew M. Cheung Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA 22904    S. Joseph Poon Department of Physics, University of Virginia, Charlottesville, VA 22904    Gary J. Shiflet Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA 22904    John Lewandowski Department of Materials Science and Engineering, Case Western Reserve University, Cleveland, OH 44106\n###### Abstract\n\nMotivated by interest in the elastic properties of high strength amorphous metals, we examine the elastic properties of select crystalline phases. Using first principles methods, we calculate elastic moduli in various chemical systems containing transition metals, specifically early (Ta,W) and late (Co,Ni). Theoretically predicted alloy elastic properties are verified for Ni-Ta by comparison with experimental measurements using resonant ultrasound spectroscopy. Comparison of our computed elastic moduli with effective medium theories shows that alloying leads to enhancement of bulk moduli relative to averages of the pure elements, and considerable deviation of predicted and computed shear moduli. Specifically, we find an enhancement of bulk modulus relative to effective medium theory and propose a candidate system for high strength, ductile amorphous alloys. Trends in the elastic properties of chemical systems are analyzed using force constants, electronic densities of state and Crystal Overlap Hamilton Populations. We interpret our findings in terms of the electronic structure of the alloys.\n\n## I Introduction\n\nElastic moduli are important for understanding various properties of amorphous metals. Bulk moduli, shear moduli, and their ratio correlate to glass transition temperature Egami (1997); Egami et al. (2007), glass forming ability Wang (2006), brittleness Poon et al. (2008); Chen et al. (1975); Lewandowski et al. (2005), Grüneisen parameters Wang and Bai (2009), maximum resolved shear stress at yielding Johnson and Samwer (2005), chemical bonding type Wang (2012), and possibly fragility Wang (2012). Knowledge of the bulk and shear moduli is thus important for materials design. However, amorphous materials commonly contain at least 4 chemical species, making exhaustive experimental evaluation of candidate materials impossible. Empirical methods for predicting stoichiometries with desired properties are therefore necessary.\n\nFirst principles computational methods prove fruitful, owing to their chemical specificity and absence of adjustable parameters, as well as the insight they yield into electronic structure. However, amorphous metals pose computational difficulties, as they lack both spatial periodicity and a unique structure. While the first problem can be practically overcome by imposing suitably large periodic boundary conditions, this requires hundreds of atoms per computational cell, straining computational resources, and requiring averaging over multiple samples to remove sample dependence. The second problem can be partially overcome by running molecular dynamics on a liquid sample then rapidly quenching the sample. However the requirement for equilibration further increases the computational time necessary. Hence we adopt a different strategy.\n\nFrank Kasper phases Frank and Kasper (1958, 1959); Sinha (1972) are complex but otherwise ordinary crystalline phases. Due to their topological close packing they exhibit local icosahedral ordering similar to that found in many amorphous metals. Fig. 1 shows the standard Voronoi polyhedra of Frank-Kasper structures. We expect that the similar local chemical environments of the Frank Kasper phases can be used to mimic amorphous metals, yielding “amorphous approximants”, similar in concept to “quasicrystal approximants”. These crystalline phases will be used to understand trends in the elastic properties of amorphous metals. It is observed that in amorphous metals, shear moduli are typically 20%-30% lower, and bulk moduli 5%-10% lower, compared to crystalline phases of similar composition Chen et al. (1975). Many crystalline phases have small unit cells compared to system sizes required to reproduce amorphous structures.\n\nAmorphous metals can exhibit high strength Telford (2004), but often at the cost of a lack of ductility owing to the absence of dislocations. Designing amorphous alloys for high ductility is impeded both by the challenge of formulating accurate amorphous structural models, and by the lack of a valid predictive theory of ductility even for the case of crystalline compounds, though there are empirical rules based on the Poisson ratio, or equivalently the shear/bulk modulus ratio. We hypothesize that relatively ductile crystalline compounds will tend to create relatively ductile amorphous compounds. Further, metallic glass composites, consisting of crystalline grains embedded in an amorphous matrix, have been shown to increase the toughness, impact resistance and plastic strain to failure Hays et al. (2000), further motivating the investigation into elastic properties of crystalline phases in metallic glass-forming alloy systems.\n\n## Ii Background and Methods\n\n### ii.1 Elasticity\n\nThe fundamental equation of linearized elasticity is , where is the stress tensor, is the strain tensor, and the stiffness tensor relating the two. Here we employ Voigt notation, converting the tensors and into vectors with 6 components . For crystals depends on the symmetry of the material in question Landau and Lifshitz (1986) and contains at least three independent parameters. For the special case of isotropic materials has only two independent parameters, the bulk modulus and the shear modulus . The non-vanishing elements are , , and . An additional elastic quantity of interest is the Poisson ratio , defined to be the negative of the ratio of axial strain to transverse strain. For crystals depends on the direction of applied stress, but in the isotropic case it reduces to\n\n ν=3−2G/K6+2G/K. (1)\n\nNotice that is a function of the shear to bulk modulus ratio , also known as the Pugh ratio Pugh (1954).\n\nDuctility and Poisson’s ratio are positively correlated in both polycrystalline Pugh (1954) and amorphous Poon et al. (2008) solids, with (equivalently ) proposed as a empirical criterion for good ductility  Gu et al. (2006). Seeking simultaneously high strength and ductility, it is natural to choose chemical species which in elemental form have large . The species chosen must also be known good glass formers. Early-late transition metal alloys fit both criteria, as the transition metals from Group IV to XI all have GPa, and they are one of the most frequently examined classes of amorphous metals, . Size mismatch criteria favor using transition metals from different rows and columns of the periodic table, e.g. Ta and W for early transition metals (ETMs), and Co and Ni as late transition metals (LTMs). Co and W are of particular interest for materials design as Co-based glasses exhibit ultrahigh fracture strength, W-based glasses have the highest known glass transition temperature for bulk metallic glasses, and both have high Young’s modulus Inoue et al. (2003); Wang (2012); Ohtsuki et al. (2004).\n\nOrdinary crystalline materials contain randomly orientated microscopic grains and appear macroscopically isotropic. To compute the elastic properties for these “polycrystals”, orientational averaging is required. Each grain is described microscopically by the same stiffness matrix, which contains between 3 (cubic) and 21 (triclinic) independent parameters Nye (1985), but macroscopically the crystal is isotropic with only two independent parameters and . In the Voigt average, the stiffness matrix is averaged over orientations Zeller and Dederichs (1973), which is exact if stress is uniform throughout space. In the Reuss average, the compliance matrix is averaged over orientations, which is exact if strain is uniform throughout space. The Voigt average systematically overestimates the isotropic moduli, while the Reuss average systematically underestimates the moduli. Empirically, the arithmetic mean of the two, known as the Hill average Hill (1952), gives improved agreement with experiment, and this is what we will report.\n\nThe polycrystalline average assumes the stiffness matrices of various grains are identical to the perfect crystal, differing only by relative orientation. To obtain macroscopic elastic moduli in materials where chemical environment spatially varies, in particular in materials containing chemically distinct grains, it is necessary to include effects arising from fluctuations in the local stiffness matrices. A general class of approximation schemes known as “effective medium theories” exists where each grain with its local stiffness matrix interacts with an effective medium characterized by a background stiffness matrix incorporating the interactions of all other grains. A popular effective medium theory is the coherent potential approximation (CPA) Nan (1993), a self-consistent formalism in which the background stiffness matrix is taken as the macroscopic average itself. The self-consistent interaction of grains yields a pair of coupled non-linear equations,\n\n ∑iϕiKi−K3Ki+4G=0 (2)\n\nand\n\n ∑iϕiGi−G5G(3K+4G)+6(K+2G)(Gi−G)=0, (3)\n\nwhich can be solved numerically for the effective and , where denotes the volume fraction of grain type in the material. and denote the bulk and shear modulus of grain type , respectively.\n\nAlthough intended for mixtures of crystalline grains, we will apply CPA in the limit where each grain shrinks to a single atom, to estimate the elastic moduli of compounds using the self-consistent average of properties of the constituent pure elements. Our usage of CPA may be viewed as a higher-order correction to the well-known but highly empirical “rule of mixtures” paradigm common in materials design, which has already been applied to bulk metallic glasses Zhang and Greer (2007). CPA takes into account the pure elemental properties but lacks information about interspecies bonding and specific alloy crystal structure. Thus we take CPA as a convenient, physically motivated interpolation to establish a baseline for comparison with the computed alloy moduli revealing the specific contributions of structure and bonding, though we note that metallic glasses exist where trace changes in composition yield relatively large changes in K and G due to alteration of chemical bonding type Zhang et al. (2006).\n\n### ii.2 First principles methods\n\nOur first principles calculations use the Vienna Ab-Initio Simulation Package (VASP) Kresse and Hafner (1993); Kresse and Furthmüller (1996), a plane wave ab-initio package implementing PAW pseudopotentials Blöchl (1994) in the PW91 Perdew and Wang (1992) generalized gradient approximation to density functional theory (DFT). VASP calculates total energies, forces, elastic moduli, and electronic structure. All structures are relaxed until the maximum ionic force is below 0.01 eV/Å, and the k-point density is subsequently increased until total energy per atom has converged to within 0.1 meV/atom. Default plane wave energy cutoffs are used for total energy calculations. In structures containing Co and Ni, spin polarization has been included. However, we do not include spin-orbit coupling despite the presence of 5d elements Ta and W. Total energies are converted to enthalpies of formation by subtracting from the tie-line joining the total energies of pure elements in their stable crystalline forms Mihalkovic and Widom (2004).\n\nWe perform elastic calculations using a finite difference method internal to VASP. To ensure proper convergence of elastic moduli, we increase the k-point density until the all polycrystalline averages converge to within 2%, then increase the energy cutoff until the polycrystalline averages converge. Convergence in energy cutoff occurs at 360 eV, with the exception of NiTa and NiW where 400 eV and 440 eV respectively were required. All structures were tested for mechanical stability, and elastic constants were not calculated for structures that were found to be mechanically unstable, though they were included in the enthalpy of formation plots, as it is possible for the stabilizing distortions to affect the calculated total energy only weakly.\n\nTo quantify bond strength between individual atoms in structures, we calculate interatomic force constants and the Crystal Overlap Hamilton Population (COHP). To calculate the force constant between atoms at position , separated by a bond in the direction , we calculate the Hessian matrix . We use density functional perturbation theory internal to VASP to calculate within a supercell of sufficient size that atoms lie at least 4.2 Å  away from their own repeated images. Restricting our attention to longitudinal (bond stretching) interactions and assuming central forces, we define\n\n kαβ≡^γαβ⋅Hαβ⋅^γαβ (4)\n\nas the projection of the Hessian along . must be positive for the force to be stabilizing.\n\nThe COHP provides an electronic structure-based characterization of interatomic bond strength Dronskowski and Blöchl (1993). One calculates matrix elements of the density functional theory Hamiltonian between localized atomic orbitals and on a pair of atoms and , then multiplies by the density of states projected onto the two orbitals. We calculate wave functions using a TB-LMTO method Jepsen and Andersen (1995) then calculate an integrated COHP for a pair of atoms , summing over atomic orbitals and integrating over energies up to the Fermi energy.\n\n### ii.3 Experimental Methods\n\nTo check the validity of our first principles calculations we have prepared samples of single phase alloys of Ni-Ta by arc melting the pure element constituents (Ni 99.995% and Ta 99.95%) under an argon atmosphere. The alloys were then suction cast into water cooled copper molds to form rods of 2mm diameter. Single phases of the rod samples were verified by x-ray powder diffraction (XRD) (Figure 2). Cylindrical samples were obtained by sectioning the rods with a diamond saw into 4mm segments. The ends of the segments were polished to a 3 micron finish. The elastic constants of the cylinders were calculated using data obtained from a Magnaflux Quasar Resonant Ultrasound Spectrometer. RUS involves placing the cylindrical samples diagonally between two ultrasonic transceivers and recording the natural modes of vibration Migliori and Sarrao (1997). A Levenberg-Marquardt algorithm is then used to determine the elastic constants by finding the best fit solution through minimization of the difference between measured and calculated natural modes through iterative changes to the values of elastic constants.", null, "The RUS measurement technique is limited to nonmagnetic samples. The study using the RUS measurements for comparison to theory is limited to the Ni-Ta system where single phases of NiTa, NiTa, NiTa and NiTa, which are nonmagnetic, can be produced, allowing for RUS measurements. Rods of the pure elements Ni and Ta can also be cast, but of the two only Ta produces nonmagnetic rods.\n\n## Iii Results\n\nIn this section we first discuss atomistic structure, then present results on thermodynamic stability for each alloy system considered, finally we address the elastic moduli.\n\n### iii.1 Structure\n\nBecause we consider a large number of specific structures, we establish a numbering scheme to unambiguously identify them (see Table 1). In the text we refer to a given crystalline material using the notation Compound.Pearson (e.g. CoTa.cF24). Of particular interest are the Frank-Kasper structures, which we take as amorphous approximants owing to the prevalence of their coordination polyhedra in many metallic glasses Sheng et al. (2006); Fang et al. (2011). Canonical Frank-Kasper polyhedra have coordination numbers CN=12, 14, 15 and 16. However, we include the Bernal holes Bernal (1964); Nelson (1983), notably CN=10, as tetrahedral but non-canonical Frank-Kasper polyhedra Sheng et al. (2006) suitable for smaller atoms. Also, the tetrahedral close-packing of the Frank Kasper phases matches the packing properties expected in bulk metallic glasses Miracle (2012).\n\nTo justify use of crystalline phases as amorphous approximants, we compare Honeycutt-Andersen common neighbor statistics Honeycutt and Andersen (1987); Ganesh and Widom (2008), of crystalline and amorphous structures. Amorphous structures were simulated by quenching 100 atom liquid structures in NPT ensembles from T = 2500 K down to 300 K over runs of more than 15ps. All simulations were performed at the gamma point with default energy cutoffs. Shown in Figure 3 is the number of common neighbors between two bonded atoms of given types. We show results for Co-Ta, but Ni-Ta, Ni-W, and Co-W were also simulated and generated similar results, with the exception of one Ni-W amorphous sample which was likely out of equilibrium.\n\nAll structures have many bonds with common neighbors, especially between unlike atomic species, reflecting the prevalence of icosahedral ordering in Frank-Kasper phases and amorphous materials. Very few Co-Co bonds have common neighbors, and very few Ta-Ta bonds have common neighbors, reflecting the relative sizes of Co and Ta atoms. Because hR13 is a canonical Frank-Kasper phase with no bonds sharing common neighbors, we utilize tI12 to capture the role of Co-Co bonds.\n\n### iii.2 Stability\n\nFigure 4 summarizes our calculated enthalpies of formation. Vertices of the convex hull of enthalpy as a function of composition are predicted to be stable phases at low temperature Mihalkovic and Widom (2004). We employ special plotting symbols to indicate phases claimed experimentally to be stable at low temperature (heavy circles) and high temperature (light circles). Phases whose stability or existence is in question are shown as squares. From the prevalence of heavy circles on or near the convex hull we see general (though imperfect) agreement with the experimentally reported phase diagrams. We briefly summarize our findings for the four alloy systems of primary interest.\n\n#### iii.2.1 Co-Ta\n\nFor Co-Ta (Fig. 4a), at , we find that cP4 and hR12 (reference numbers 6 and 7) are nearly degenerate, with cP4 (stability not reported experimentally) favored by 1 meV/atom, which is closer than DFT can reliably distinguish. At , three different Laves phases have been reported (reference numbers 8-10), with conflicting claims of stability and uncertain composition. We find that none of these phases lies on the convex hull. Further, all of their structures are mechanically unstable to deformation, casting doubt on the reported structure and stability of this phase. In our plot, we show the energy of a distorted cF24 structure which is mechanically stable, for comparison with the undistorted hP12 and hP24. In the vicinity of lies the Frank-Kasper phase. This phase is common to many alloy systems containing fourth and fifth row early transition metals with third row late transition metals. In most cases the phase shows a broad composition range at high temperature but favors an ETM-rich low temperature limit (i.e. with the mixed occupancy site occupied by an ETM). This feature is correctly reproduced by our calculation. At , the tI12 phase (reference number 5) is a non-canonical Frank-Kasper phase, as it contains a CN=10 Bernal Hole, in addition to a canonical CN=15 Kasper polyhedron.\n\n#### iii.2.2 Ni-Ta\n\nFor Ni-Ta (Figure 4b) at we find NiTa.tI18 to be low-temperature stable. The experimental phase diagram has a tI36 structure stable, however no crystallographic refinement exists, so we use the known tI18 phase instead. There is disagreement on recent phase diagrams concerning the stable structure at , and we find three different structures have nearly identical enthalpies (tI8 is the lowest). The main source of disagreement between our T = 0 K phase diagram and experimental phase diagrams is the stability of NiTa.hR13, with even the ETM-rich variant lying 7 meV/atom above the convex hull. Fig. 2 shows the diffraction patterns of our experimentally cast rods, verifying the existence of the expected phases in our own samples.\n\n#### iii.2.3 (Co,Ni)-W\n\nOur calculations verify the known CoW and NiW phase stabilities. However, the reported CoW phase lies above the convex hull, and additionally favors the ETM-rich limit contrary to experimental report. This phase has not been reported in the Ni-W alloy system, and we indeed find it lies well above the convex hull. However, we will study the electronic and elastic properties of this hypothetical phase in order to elucidate trends with respect to composition. Notice that enthalpies of formation for alloys with W are lower than enthalpies with Ta. This does not necessarily reflect lower mechanical stability or melting points for the compounds, as the greater cohesive energy of tungsten compared to tantalum contributes to a reduction of the alloy formation enthalpies. An equiatomic Ni-W phase with orthorhombic symmetry has been observed low temperature stable Walsh and M. J. Donachie (1973), however no atomic structural data exists. Owing to similar chemical identity and Bravais lattice, we attempted to use the Frank-Kasper phase MoNi.oP56 with Mo substituted for W, but found that this structure lies 66 meV/atom above the convex hull and likely is not the correct phase. It was also too computationally expensive to compute elastic moduli for this phase.\n\n### iii.3 Binary Elastic Moduli\n\nWe examine the effect of alloying on the elastic moduli by using CPA to approximate a hypothetical alloy where no interspecies interactions exist. That is, for a well-ordered phase with stoichiometry AB, we compare its elastic moduli to a hypothetical solution of pure specie A and pure specie B with a stoichiometric ratio x:(1-x) in the CPA approximation. As input for CPA, we use our computed elemental elastic moduli. These agree closely with experimental moduli for Ta and W but are relatively high for Co and Ni. Note that our calculation are valid at 0 K, while the experimental values are room temperature, so it is expected that our values should be high, especially for non-refractory elements. As the CPA approximation only incorporates elemental elastic moduli with no atomic environmental details, the deviation of computed polycrystalline moduli from the CPA approximation yields a measure of the relative importance of atomic environment and alloying species for elastic moduli.\n\nAll crystal structures are elastically anisotropic, and it is of interest to characterize the anisotropy of our amorphous approximants. We define three anisotropies Nye (1985); Tromans (2011): (Zener), (shear) and (Young’s) as\n\n AZ=2C44C11−C12,\n AG=S44+S662S44,\n\nand\n\n AE=S11S33,\n\nall of which are 1 for isotropic structures, where are elements of the compliance matrix. Table 2 compares calculated anisotropies of our hR13 and tI12 structures with the four pure elements. Our anisotropies are close to one, similar to those seen in the pure metals, with hR13 exhibiting less anisotropy than tI12. These anisotropies can be taken as estimates of the local anisotropy expected at the atomic level in actual amorphous structures. Recall that the polycrystalline averages are expected to reflect the globally isotropic properties of the bulk amorphous structures.\n\nShown in Figure 5 are our calculated K values, compared with CPA estimates. All CPA estimates are indicated by lines, all calculated moduli by individual data points, and for Ni-Ta asterisks indicate experimental results. Our calculated Ni-Ta bulk moduli show excellent agreement with our experimental results. For all four chemical families, CPA gives reasonable estimates for bulk moduli, with at most a 16% deviation between estimated and calculated bulk moduli. However, in all alloy systems and for all structures examined, CPA underestimates the bulk modulus. This suggests the dominant correction to the bulk moduli is chemical bonding and not atomic environmental details such as the prevalence of tetrahedra. Shear moduli show relatively larger and less regular deviations from CPA, suggesting that bond topology plays a significant role. Nonetheless, our calculated Ni-Ta shear moduli are in good agreement with experiment (crosses).\n\nShown in Table 3 are the correlation coefficient for various linear regressions across all calculated CoTa, CoW, NiTa, and NiW alloys, where the sign of the correlation coefficient denotes the sign of the slope. Here K and G (units GPa) are deviations of calculated bulk and shear moduli from CPA estimates, v (units Å per atom) the deviation of volume per atom from a linear interpolation of pure elements, and h (units eV per atom) the enthalpy of formation per atom as illustrated in Fig. 4. Correlations of elastic moduli with v and h reflect structure and bonding effects that are missing from CPA. There is only a weak correlation between h and v, though the associated slope is positive, expected as increased bond strength (more negative h) draws atoms closer together (more negative v). G and K are both correlated to v, with K in particular strongly correlated. This is line with other work that shows that K and G correlate with V and that the correlation for K is particularly strong Wang (2012). This is also true for individual chemical families, and for K all chemical families’ regressions have similar slopes. This strong correlation of K with v explains why all structures have CPA underestimating the bulk moduli (positive K), as all structures were also observed to have negative v, as expected. The slopes of G and K are both negative, as decreasing v draws atoms closer together, shortening bonds and enhancing interatomic force constants. The observed correlation of G with K is likely due to the underlying correlation of each with v.\n\nA goal of metallic glass design is to predict glass-forming compounds with high ductility. Thus, as a guide, we plot the Poisson ratio’s of the various alloys under discussion. Our computed T = 0 K crystalline Poisson ratios are expected to be systematically low relative to the corresponding glasses, as G decreases more rapidly than K as temperature increases Liu et al. (2010), and amorphous G and K are lower relative to crystalline values by around 30% and 10%, respectively. Here we see no systematic trend in the choice of Ta versus W (empty versus filled plotting symbols) but Ni generally has higher Poisson’s ratio than Co (red versus blue). Empirically, it has been observed that serves as a rough criterion for separating ductile and brittle behavior in amorphous materials Lewandowski et al. (2005). The majority of our Ni alloys lie above this criterion and Co alloy below. In particular, all Ni-W alloys satisfy this criterion, and Ni-W in the amorphous approximant structure hR13 shows particularly large Poisson’s ratios. Combined with the large bulk modulus due to the presence of tungsten, we propose that Ni-W is a candidate system for future research into strong amorphous materials with high ductility.\n\n## Iv Analysis and Discussion\n\nTo understand trends in elastic constants of these alloys we now look into the interatomic interactions. Within a first principles approach there is no unique decomposition of interactions into pairwise and many-body forces, and no simple notion of a chemical bond, especially for metals. However some heuristic measures are available. Here we examine the interatomic force constants, which can be regarded as springs connecting the atoms, and the crystal overlap Hamilton populations (COHPs) which are a measure of the covalency of electronic wave functions.\n\n### iv.1 Force Constants and COHP\n\nTo compare different ETM and LTM substitutions, Table 4 shows k, the mean force constants for the near neighbor bonds of a given species combination, , the total iCOHP per unit volume for bonds of a given species combination up to 4 Å, and K, the bulk moduli in the structural prototype tI12. To calculate the mean force constant, we sum force constants for all bonds up to 4 Å  for a given cell then divide by the number of atoms.\n\nBoth the mean force constant and correlate with the bulk moduli. This is especially notable in the mean force constant, where there is a large increase in mean force constant performing a Ta W substitution and a relatively small increase performing a Ni Co substitution, but the effect is also present in . As a force constant gives a measure of the stiffness of an individual bond, this mean force constant gives a measure of the total stiffness of all bonds, and bulk modulus is increased under chemical substitution by an overall increase in the interatomic force constant. We also see in Table 4 that performing a Ni Co or a Ta W substitution enhances . Thus these substitutions have enhanced the bonding nature of the electronic states.\n\nTo further understand the enhancement of bonding, we calculate electronic densities of state (Fig. 7). The low-energy peak near -4 or -5 eV consists of -hybrid orbitals, followed by a series of higher-energy peaks consisting solely of orbitals, with the Fermi level lying in the middle of the ETM -band and at or above the top of the LTM -band. For Co-W, the Co and W bands are closely aligned, inducing strong hybridization of Co and W orbitals. This effect is present in all structures we have examined. Performing a W Ta substitution shifts the ETM -band up relative to the LTM -band, decreasing the -band overlap and diminishing hybridization. Performing a Co Ni substitution shifts the LTM -band down relative to the ETM -band, also decreasing the -band overlap. Both of these induce an decrease in the hybridization of the ETM-LTM -bands. As hybridization generally creates bonding states below the Fermi level, this reduction in hybridization going from W Ta and Co Ni decreases the overall bonding characteristic of the occupied states, leading to the observed trends in , and hence in bulk modulus.\n\n### iv.2 Microstructural Details: Ternaries and Quaternaries\n\nElemental properties provide the dominant contribution to the elasticity of these ETM-LTM intermetallic compounds, as can be seen in the qualitative agreement of calculated alloy moduli with the CPA predictions shown in Fig. 5. In Table 5 we see that the small decreases in modulus from Co to Ni, and the large increases from Ta to W, are echoed in the moduli of the hR13 Frank-Kasper structure.\n\nWhile binary amorphous metals exist, size mismatch criteria and material property tuning favor the usage of multiple constituent species in amorphous metals for practical applications, and thus the question of transferability of binary results to structures with 3 or more constituent species must be addressed. In addition, there is still the lingering need to quantify how atomic environment affects the elastic moduli. To answer both these questions, we perform chemical substitutions in a binary structure to yields ternaries and quaternary structures. This changes the chemical identities of formerly equivalent sites, altering local chemical ordering.\n\nShown in Table 6 is a comparison of binary hR13 structures (including also alloys with Nb, an ETM) with nearly equiatomic composition quaternary variants of hR13 and six associated ternaries. Site occupancies in the quaternary has been chosen to maintain the ETM/LTM nature of sites and minimize energy, and the ternaries were formed by keeping the early/late site identity fixed.\n\nTo compare our binary results to ternaries and quaternaries, we here use a simple chemical environment averaging scheme between ETM and LTM, with a equiatomic ABCD mixture with A and B LTM and C and D ETM approximated by 1/4*(AC+AD+BC+BD), and an ABC mixture (with C having near 50% concentration) approximated by 1/2*(AC+BC). Here AC, AD, BC and BD refer to the relevant binary hR13 structure with the associated chemical formula. As an example, the predicted bulk moduli of CoTaW would be the average bulk modulus of CoTa and CoW. While this ignores interspecies ETM-ETM and LTM-LTM bonds present (i.e. AB and CD), binary enthalpies of formation for ETM-ETM and LTM-LTM families are weak compared to ETM-LTM families, suggesting that as a first approximation we may assume the differences in interspecies ETM-ETM and LTM-LTM bond strength average out.\n\nDifferences between our predicted interpolated elastic moduli and computed elastic moduli follow the trends previously reported for CPA. Again we see bulk moduli negligibly affected by atomic environment and predominately determined by the alloying species, with deviations in bulk moduli below 2.6% for all structures. For shear moduli, the structures can be placed into two categories: those structures that have only one ETM species or else two ETM species from the same group (here Nb and Ta belong to group IV) which have deviations in shear moduli below 3.7%, and those that have ETM species from different groups (here W from group V together with Nb or Ta from group IV) which have deviations in shear moduli between 10.0% and 18.7%. In all cases where predicted shear moduli deviate significantly from calculated shear moduli, the computed shear moduli have been enhanced.\n\nThat mixing Co and Ni or Nb and Ta causes little deviation in shear modulus, but mixing Ta and W does, is further evidence for the dependence of shear modulus on atomic environment. Co and Ni have similar atomic radii and electronegativity, as do Nb and Ta. For a topologically close packed structure like hR13, substitution of these chemical species should not noticeably affect bond lengths and ionic charges, yielding similar calculated and averaged results. However, Nb and Ta have larger atomic radii and lower electronegativity than W, leading to larger charge transfers and changes in bond length, reducing the accuracy of our averaging scheme while generally increasing bonding strength.\n\n## V Conclusions\n\nIn this paper we examine the elasticity of various early transition metal-late transition metal crystalline binary alloys using first principles calculations and comparison with various averaging schemes. Calculated bulk moduli were reasonably close to the coherent potential approximation using pure elemental species, but CPA predictions were systematically low. This deviation correlates strongly with volume per atom. Larger and less regular deviations were observed for shear moduli, suggesting structural distortion being responsible for the deviation. Select ternary and quaternary structures were examined and confirmed these trends. To explain the dependence of elastic moduli on chemical bonding, force constants and electronic densities of state were calculated and it was found early transition metals are responsible for the strongest bonding, which agrees with observed trends in the bulk moduli. We find that Ni-W alloys have the largest Poisson ratios among the compositions studied and hence hold promise as the basis for design of ductile metallic glasses.\n\n## Vi Acknowledgements\n\nWe would like to give special thanks to DOD-DTRA for funding this research under contract number DTRA-11-1-0064.\n\n## References\n\n• Egami (1997) T. Egami, Mat. Sci. Eng. A 2260228, 261 (1997).\n• Egami et al. (2007) T. Egami, S. J. Poon, Z. Zhang,  and V. Keppens, Phys. Rev. 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(2010) X. F. Liu, R. J. Wang,  and W. H. Wang, Scripta Mater. 62, 254 (2010).\nYou are adding the first comment!\nHow to quickly get a good reply:\n• Give credit where it’s due by listing out the positive aspects of a paper before getting into which changes should be made.\n• Be specific in your critique, and provide supporting evidence with appropriate references to substantiate general statements.\n• Your comment should inspire ideas to flow and help the author improves the paper.\n\nThe better we are at sharing our knowledge with each other, the faster we move forward.\nThe feedback must be of minimum 40 characters and the title a minimum of 5 characters", null, "", null, "", null, "" ]

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[ "## PRACTICE PROBLEMS\n\n(Note: Problem solutions are available at http://sites.google.com/site/automatedmanufacturingsystems/)\n\n1. Is the ladder logic in the figure below for an AND or an OR gate?", null, "2. Draw a ladder diagram that will cause output D to go true when switch A and switch B are closed or when switch C is closed.\n\n3. Draw a ladder diagram that will cause output D to be on when push button A is on, or either B or C are on.\n\n4. Design ladder logic for a car that considers the variables below to control the motor M. Also add a second output that uses any outputs not used for motor control.", null, "5. a) Explain why a stop button must be normally closed and a start button must be normally open.\n\nb) Consider a case where an input to a PLC is a normally closed stop button. The contact used in the ladder logic is normally open, as shown below. Why are they both not the same? (i.e., NC or NO)", null, "6. Make a simple ladder logic program that will turn on the outputs with the binary patterns when the corresponding buttons are pushed.", null, "7. Convert the following Boolean equation to the simplest possible ladder logic.", null, "8. Simplify the following boolean equations.", null, "9. Simplify the following Boolean equations,", null, "10. Simplify the Boolean expression below.", null, "11. Given the Boolean expression a) draw a digital circuit and b) a ladder diagram (do not simplify), c) simplify the expression.", null, "12. Simplify the following Boolean equation and write corresponding ladder logic.", null, "13. For the following Boolean equation,", null, "a) Write out the logic for the unsimplified equation.\n\nb) Simplify the equation.\n\nc) Write out the ladder logic for the simplified equation.\n\n14. a) Write a Boolean equation for the following truth table. (Hint: do this by writing an expression for each line with a true output, and then ORing them together.)", null, "b) Write the results in a) in a Boolean equation.\n\nc) Simplify the Boolean equation in b)\n\n15. Simplify the following Boolean equation, and create the simplest ladder logic.", null, "16. Simplify the following boolean equation with Boolean algebra and write the corresponding ladder logic.", null, "17. Convert the following ladder logic to a Boolean equation. Then simplify it, and convert it back to simpler ladder logic.", null, "18. a) Develop the Boolean expression for the circuit below.\n\nb) Simplify the Boolean expression.\n\nc) Draw a simpler circuit for the equation in b).", null, "19. Given a system that is described with the following equation,", null, "a) Simplify the equation using Boolean Algebra.\n\nb) Implement the original and then the simplified equation with a digital circuit.\n\nc) Implement the original and then the simplified equation in ladder logic.\n\n20. Simplify the following and implement the original and simplified equations with gates and ladder logic.", null, "21. Convert the following ladder logic to a Boolean equation. Simplify the equation and convert it back to ladder logic.", null, "22. Use Boolean equations to develop simplified ladder logic for the following truth table where A, B, C and D are inputs, and X and Y are outputs.", null, "" ]

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[ "June Lester - Curriculum Vitae - Home\n\nMathematical Publications\n\n Note: some of the papers listed below appear in more than one section. There are 39 distinct papers. Follow the links to see papers on\n\n Metric Vector Spaces A metric vector space is a vector space which has a (usually indefinite) scalar product. I first became fascinated with these spaces as a beginning master's student. Geometrically interesting in their own right (as Euclidean n-space or Minkowski spacetime, for example), they are also invaluable as coordinate spaces: it's quite extraordinary just how many classical geometries can be coordinatized by n-tuples subject to some indefinite scalar product. And looking at these geometries through their coordinate spaces often makes obvious the isomorphisms between different models of the same geometry, or even between different geometries: the same coordinate space implies the same or related geometries. On Null-Cone Preserving Mappings. (with M. A. McKiernan) Math. Proc. Camb. Phil. Soc. 81 (1977) 455 - 462 Cone Preserving Mappings for Quadratic Cones over Arbitrary Fields. Canad. J. Math. 29 (1977) 1247 - 1253 Some Properties of Non-Positive Definite Real Metric Vector Spaces. Utilitas Math. 12 (1977) 327 - 333 A Characterization of Non-Euclidean, Non-Minkowskian Inner Product Space Isometries. Utilitas Math. 16 (1979) 101 - 109 Transformations of n-Space Which Preserve a Fixed Square-Distance. Canad. J. Math. 31 (1979) 392 - 395 Conformal Spaces. J. Geom. 14 (1980) 108 - 117 Transformations Preserving Null Line Sections of a Domain: the Arbitrary Signature Case. Resultate Math. 9 (1986) 107 - 118 A Metric Vector Space Proof of Miquel's Theorem. C. R. Math. Rep. Acad. Sci. Canada 9 (1987) 59 - 62 The Octahedron Theorem in Minkowski Three-Space: A Metric Vector Space Proof of Miquel's Theorem in the Laguerre Plane. J. Geom. 30 (1987) 196 - 202 Back to the top of this page\n\n Geometric Characterization Problems The basic characterization problem: determine those transformations of a geometric space which preserve some particular feature or measurement of the space, without recourse to regularity assumptions (linearity, continuity, ... ) or even without assuming bijectivity. The classical example is the Beckman-Quarles theorem: functions from the Euclidean plane to itself preserving pairs of points a distance 1 apart must be Euclidean motions (the functions need not be assumed bijective, or even single valued). There are characterization theorems for many other spaces and spacetimes: for a survey, see a book chapter I wrote: Distance Preserving Transformations. Chapter 16 of Handbook of Incidence Geometry, p. 921 - 944, ed. F. Buekenhout, Elsevier Science B. V., 1995. On Null-Cone Preserving Mappings. (with M. A. McKiernan) Math. Proc. Camb. Phil. Soc. 81 (1977) 455 - 462 Cone Preserving Mappings for Quadratic Cones over Arbitrary Fields. Canad. J. Math. 29 (1977) 1247 - 1253 A Characterization of Non-Euclidean, Non-Minkowskian Inner Product Space Isometries. Utilitas Math. 16 (1979) 101 - 109 Transformations of n-Space Which Preserve a Fixed Square-Distance. Canad. J. Math. 31 (1979) 392 - 395 On Distance Preserving Transformations of Lines in Euclidean Three-Space. Aequationes Math. 28 (1985) 69 - 72 Euclidean Plane Point Transformations Preserving Unit Area or Unit Perimeter. Archiv Math. (Basel) 45 (1985) 561 - 564 Transformations Preserving Null Line Sections of a Domain: the Arbitrary Signature Case. Resultate Math. 9 (1986) 107 - 118 A Characterization of Motions as Bijections Preserving Circumradius or Inradius 1. Monatsh. Math. 101 (1986) 151 - 158 Martin's Theorem for Euclidean n-Space and a Generalization to the Perimeter Case. J. Geom. 27 (1986) 29 - 35 Orthogonal Spheres. C. R. Math. Rep. Acad. Sci. Canada. 8 (1986) 231 - 235 On Line Mappings Which Preserve Unit Triangles. Utilitas Math. 31 (1987) 81 - 84 Angle-preserving Transformations of Spheres. Aequationes Math. 32 (1987) 52 - 57 A Beckman-Quarles-Type Theorem for Coxeter's Inversive Distance. Canad. Math. Bull. 34 (1991) 492 - 498 Many of my characterization theorems are also discussed in two books by Walter Benz: Geometrische Transformationen unter besonderer Berücksichtigung der Lorentztransformationen. B.I. Wissenschaftsverlag, Mannheim 1992 Real Geometries. B.I. Wissenschaftsverlag, Mannheim 1994 Back to the top of this page\n\n Spacetime Geometry Both of the previous topics come together here: the simplest spacetime, Minkowski spacetime is an example of a metric vector space, while Alexandrov's theorem characterizes its transformations (Lorentz transformations) by the fact that they preserve pairs of points connected by light signals. Another example: Zeeman's theorem characterizes the causality-preserving transformations of Minkowski spacetime, for example. I've done generalizations of these and other theorems for several other spacetimes. In another, disjoint spacetime direction, my favourite paper Does Matter Matter? uses some ideas from classical inversive geometry to construct a spacetime model in which the location of infinity is relative (i.e. observer-dependent). Under some very natural assumptions about proper time, the model predicts cosmological redshifts with unexpectedly realistic properties. It also predicts an age for the universe of about 25 billion years (comfortably more than the stars in it, unlike the situation in more classical theories). The Beckman-Quarles Theorem in Minkowski Space for a Spacelike Square-Distance. Arch. Math. (Basel) 37 (1981) 561 - 568 [summary in C. R. Math. Rep. Acad. Sci. Canada 3 (1981) 59 - 61] Alexandrov-type Transformations on Einstein's Cylinder Universe. C. R. Math.Rep. Acad. Sci. Canada 4 (1982) 175 - 178 Transformations of Robertson-Walker Spacetimes Preserving Separation Zero. Aequationes Math. 25 (1982) 216 - 232 A Physical Characterization of Conformal Transformations of Minkowski Spacetime. Ann. Discrete Math. 18 (1983) 567 - 574 Conformal Minkowski Spacetime I: Relative Infinity and Proper Time. Il Nuovo Cimento 72B (1982) 261 - 272 Conformal Minkowski Spacetime II: A Cosmological Model. Il Nuovo Cimento 73B (1983) 139 - 149 Separation Preserving Transformations of de Sitter Spacetime. Abh. Math. Sem. Univ. Hamburg 53 (1983) 217 - 224 The Causal Automorphisms of de Sitter and Einstein Cylinder Spacetimes. J. Math. Phys. 25 (1984) 113 - 116 Relative Infinity in Projective de Sitter Spacetime and its Relation to Proper Time. Ann. Discrete Math. 37 (1988) 257 - 264 Zeeman's Lemma on Robertson-Walker Spacetimes. J. Math. Phys. 30 (1989) 1296 - 1300 The Effect of a Relative Infinity on Cosmological Redshifts. Astrophysics and Space Science 207 (1993) 231 - 248 Does Matter Matter? Physics Essays 11 (1998) 481 - 491 Back to the top of this page\n\n Complex Triangle and Polygon Geometry This topic began as a minor recreational problem and expanded into a major research project. Basically what I've done is to develop a rather productive complex cross ratio formalism for triangle geometry. First, I use a single complex number, called shape, to describe Euclidean triangles and prove theorems about similar triangles. Second, I use another complex number to coordinatize the plane relative to a given triangle and to prove theorems about it. Third, I relate the two: the coordinate of any special point of a triangle is a corresponding function of its shape. This function can be used to discover and prove theorems about special points by reducing the proofs to complex algebra. Triangles I: Shape. Aequationes Math. 52 (1996) 30 - 54 Triangles II: Complex Triangle Coordinates. Aequationes Math.52 (1996) 215 - 245 Triangles III: Complex Triangle Functions. Aequationes Math. 53 (1997) 4 - 35 A generalization of Napoleon's Theorem to n-gons. C. R. Math. Soc. Canada 16 (1994) 253 - 257 My triangles work has been extended to other planes: see for example Shapes of Polygons, R. Artzy, J. Geom. 50 (1994) 11 - 15 and Shape-Regular Polygons in Finite Planes, R. Artzy and G. Kiss, J. Geom. 57 (1996) 20 - 26. The discover of the circle that has come to be known as the Lester circle was one of many theorems in Triangles III. For details of this theorem and a bibliography of papers it has inspired, please see the Lester Circle website. Back to the top of this page\n\n Miscellaneous Topics This includes some pre-Ph.D work on functional equations and various other work. A Canonical Form for a System of Quadratic Functional Equations. Colloq. Math. 35 (1976) 105 - 108 The Solution of a System of Quadratic Functional Equations. Ann. Polon. Math. 37 (1980) 113 - 117 Points of Difference: Relative Infinity in the Euclidean Plane. J. Geom. 46 (1993) 92 - 118 Worlds of Difference: Relative Infinity in the Hyperbolic Plane. Mitt. Math. Ges. Hamburg 13 (1993) 93 - 117 Orthochronous Subgroups of O(p, q). Linear and Mulitlinear Algebra 36 (1993) 111 - 113 Back to the top of this page" ]

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[ "# D語言變數\n\nType 描述\nchar 通常一個八位位元組(1位元組)。這是一個整數型別。\nint 最自然的機器的整數大小。\nfloat 單精度浮點值。\ndouble 雙精度浮點值。\nvoid 表示不存在型別。\n\nD程式設計語言還允許定義各種其他型別的變數，我們將覆蓋像列舉，指標，陣列，結構，聯合，等後面的章節對於本章中，我們只學習基本的變數型別。\n\n## 在D語言中變數定義：\n\n`type variable_list;`\n\n```int i, j, k;\nchar c, ch;\nfloat f, salary;\ndouble d;```\n\n`type variable_name = value;`\n\n```extern int d = 3, f = 5; // declaration of d and f.\nint d = 3, f = 5; // definition and initializing d and f.\nbyte z = 22; // definition and initializes z.\nchar x = 'x'; // the variable x has the value 'x'.```\n\n## 範例\n\n```import std.stdio;\n\nint a = 10, b =10;\nint c;\nfloat f;\n\nint main ()\n{\nwriteln(\"Value of a is : \", a);\n/* variable re definition: */\nint a, b;\nint c;\nfloat f;\n\n/* Initialization */\na = 30;\nb = 40;\nwriteln(\"Value of a is : \", a);\nc = a + b;\nwriteln(\"Value of c is : \", c);\n\nf = 70.0/3.0;\nwriteln(\"Value of f is : \", f);\nreturn 0;\n}\n```\n\n```Value of a is : 10\nValue of a is : 30\nValue of c is : 70\nValue of f is : 23.3333\n```\n\n## 在D語言中左值和右值：\n\nD中有兩種型別的表示式：\n\n1. lvalue : 這是一個左值的表示式可能會出現無論是左值或右值。\n\n2. rvalue : 這是一個右值表示式可以出現在賦值的右值而不是左值。\n\n`int g = 20;`\n\n`10 = 20;`" ]

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[ "hex\n\n## Class Distribution\n\n• All Implemented Interfaces:\njava.io.Externalizable, java.io.Serializable, java.lang.Cloneable, Freezable<Distribution>\n\n```public abstract class Distribution\nextends Iced<Distribution>```\nDistribution functions to be used by ML Algos\nSerialized Form\n• ### Field Summary\n\nFields\nModifier and Type Field and Description\n`hex.genmodel.utils.DistributionFamily` `_family`\n`double` `_huberDelta`\n`LinkFunction` `_linkFunction`\n`double` `_quantileAlpha`\n`double` `_tweediePower`\n• ### Constructor Summary\n\nConstructors\nConstructor and Description\n`Distribution(hex.genmodel.utils.DistributionFamily family)`\n```Distribution(hex.genmodel.utils.DistributionFamily family, LinkFunction lf)```\n`Distribution(Model.Parameters params)`\n```Distribution(Model.Parameters params, LinkFunction lf)```\n• ### Method Summary\n\nAll Methods\nModifier and Type Method and Description\n`double` ```deviance(double w, double y, double f)```\nDeviance of given distribution function at predicted value f\n`double` ```gammaDenom(double w, double y, double z, double f)```\nContribution to denominator for GBM's leaf node prediction\n`double` ```gammaNum(double w, double y, double z, double f)```\nContribution to numerator for GBM's leaf node prediction\n`double` ```initFDenom(double w, double o, double y)```\nContribution to denominator for initial value computation\n`double` ```initFNum(double w, double o, double y)```\nContribution to numerator for initial value computation\n`double` `link(double f)`\n`double` `linkInv(double f)`\n`java.lang.String` `linkInvString(java.lang.String f)`\nString version of link inverse (for POJO scoring code generation)\n`double` ```negHalfGradient(double y, double f)```\n(Negative half) Gradient of deviance function at predicted value f, for actual response y This assumes that the deviance(w,y,f) is w*deviance(y,f), so the gradient is w * d/df deviance(y,f)\n`double` ```negHalfGradient(double y, double f, int l)```\n(Negative half) Gradient of deviance function at predicted value f, for actual response y This assumes that the deviance(w,y,f) is w*deviance(y,f), so the gradient is w * d/df deviance(y,f)\n`void` `reset()`\nMethod useful for custom distribution only.\n`void` `setHuberDelta(double huberDelta)`\nSetter of huber delta.\n• ### Methods inherited from class water.Iced\n\n`asBytes, clone, copyOver, frozenType, read, readExternal, readJSON, reloadFromBytes, toJsonString, write, writeExternal, writeJSON`\n• ### Methods inherited from class java.lang.Object\n\n`equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`\n• ### Field Detail\n\n• #### _tweediePower\n\n`public final double _tweediePower`\n• #### _quantileAlpha\n\n`public final double _quantileAlpha`\n• #### _huberDelta\n\n`public double _huberDelta`\n\n`public LinkFunction _linkFunction`\n• #### _family\n\n`public final hex.genmodel.utils.DistributionFamily _family`\n• ### Constructor Detail\n\n• #### Distribution\n\n```public Distribution(hex.genmodel.utils.DistributionFamily family,\n• #### Distribution\n\n`public Distribution(hex.genmodel.utils.DistributionFamily family)`\n• #### Distribution\n\n```public Distribution(Model.Parameters params,\n• #### Distribution\n\n`public Distribution(Model.Parameters params)`\n• ### Method Detail\n\n• #### setHuberDelta\n\n`public void setHuberDelta(double huberDelta)`\nSetter of huber delta. Required for Huber aka M-regression.\nParameters:\n`huberDelta` -\n\n`public double link(double f)`\nParameters:\n`f` - value in original space, to be transformed to link space\nReturns:\n\n`public double linkInv(double f)`\nParameters:\n`f` - value in link space, to be transformed back to original space\nReturns:\n\n`public java.lang.String linkInvString(java.lang.String f)`\nString version of link inverse (for POJO scoring code generation)\nParameters:\n`f` - value to be transformed by link inverse\nReturns:\nString that turns into compilable expression of linkInv(f)\n• #### deviance\n\n```public double deviance(double w,\ndouble y,\ndouble f)```\nDeviance of given distribution function at predicted value f\nParameters:\n`w` - observation weight\n`y` - (actual) response\n`f` - (predicted) response in original response space (including offset)\nReturns:\ndeviance\n\n```public double negHalfGradient(double y,\ndouble f)```\n(Negative half) Gradient of deviance function at predicted value f, for actual response y This assumes that the deviance(w,y,f) is w*deviance(y,f), so the gradient is w * d/df deviance(y,f)\nParameters:\n`y` - (actual) response\n`f` - (predicted) response in link space (including offset)\nReturns:\n\n```public double negHalfGradient(double y,\ndouble f,\nint l)```\n(Negative half) Gradient of deviance function at predicted value f, for actual response y This assumes that the deviance(w,y,f) is w*deviance(y,f), so the gradient is w * d/df deviance(y,f)\nParameters:\n`y` - (actual) response\n`f` - (predicted) response in link space (including offset)\n`l` - (class label) label of a class (converted lexicographically from original labels to 0-number of class - 1)\nReturns:\n• #### initFNum\n\n```public double initFNum(double w,\ndouble o,\ndouble y)```\nContribution to numerator for initial value computation\nParameters:\n`w` - weight\n`o` - offset\n`y` - response\nReturns:\nweighted contribution to numerator\n• #### initFDenom\n\n```public double initFDenom(double w,\ndouble o,\ndouble y)```\nContribution to denominator for initial value computation\nParameters:\n`w` - weight\n`o` - offset\n`y` - response\nReturns:\nweighted contribution to denominator\n• #### gammaNum\n\n```public double gammaNum(double w,\ndouble y,\ndouble z,\ndouble f)```\nContribution to numerator for GBM's leaf node prediction\nParameters:\n`w` - weight\n`y` - response\n`z` - residual\n`f` - predicted value (including offset)\nReturns:\nweighted contribution to numerator\n\n```public double gammaDenom(double w,\ndouble y,\ndouble z,\ndouble f)```\nContribution to denominator for GBM's leaf node prediction\nParameters:\n`w` - weight\n`y` - response\n`z` - residual\n`f` - predicted value (including offset)\nReturns:\nweighted contribution to denominator\n• #### reset\n\n`public void reset()`\nMethod useful for custom distribution only. It resets custom function to be loaded again." ]

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[ "# Systems Of Equations Elimination Worksheet Doc Worksheets Solving By Graphing Kuta Software", null, "systems of equations elimination worksheet doc worksheets solving by graphing kuta software.\n\nsolving systems of linear equations elimination method lesson by worksheet doc kuta answers with work algebra 2,solving systems of equations elimination worksheet pdf by answers kuta software using word problems,to review these matrix methods for solving systems of linear equations by substitution and elimination worksheet pdf method answers graphing kuta software,solving systems of equations by elimination worksheet kuta software answers with work algebra 2 method frog topic algebraically,solving systems of linear equations by elimination worksheet doc instructional unit kuta easy,solving systems of equations by elimination worksheet kuta software algebra 2 graphing solve the system,equations solving systems of by elimination worksheet answers with work algebra 2 graphing kuta,chapter 4 classroom solving systems of equations by elimination worksheets with answers graphing worksheet kuta software substitution and pdf,systems of equations elimination worksheet kuta solving independent practice method answers with work by worksheets pdf,solving systems of equations elimination worksheet answers lesson teaching point students will be able to write by graphing kuta software pdf." ]

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[ "", null, "# Is 52 Odd Or Even?\n\n## Is 13 an odd number?\n\nOdd numbers always end with a digit of 1, 3, 5, 7, or 9.\n\n1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31 are odd numbers..\n\n## Is 99 odd or even?\n\nYou can divide 99 by two and if the result is an integer (whole number) then it is an even number. Otherwise, it is an odd number. 99 divided by 2 is 49.5, which is not an integer. Therefore, 99 is an odd number.\n\n## Is 56 an odd number?\n\nQ: Is 56 an Odd Number? A: No, the number 56 is not an odd number – it is an even number.\n\n## Is 50 an odd or even?\n\nTo find out if 50 is an odd number, we divided 50 by two. … If you divide any number, such as 50, by two and you don’t get a whole number, it means that the number is an odd number. 50 divided by two is a whole number. Thus, 50 is not an odd number and the answer to the question “Is 50 an odd number?” is NO.\n\n## Is 55 an odd number?\n\nYou can divide 55 by two and if the result is an integer (whole number) then it is an even number. Otherwise, it is an odd number. 55 divided by 2 is 27.5, which is not an integer. Therefore, 55 is an odd number.\n\n## Is 49 odd or even?\n\nHow is 49 an odd number? An odd number is any integer (a whole number) that cannot be divided by 2 evenly. … That means the number is an odd number because it cannot be divided by 2 without a remainder.\n\n## Is 45 odd or even?\n\nYou can divide 45 by two and if the result is an integer (whole number) then it is an even number. Otherwise, it is an odd number. 45 divided by 2 is 22.5, which is not an integer. Therefore, 45 is an odd number.\n\n## Is 53 an odd or even number?\n\nNotice the number is not a whole number and has a remainder (the . 5)? That means the number is an odd number because it cannot be divided by 2 without a remainder.\n\n## Is 56 an even number?\n\nTo find out if 56 is an even number, we divided 56 by two. … If you divide any number, such as 56, by two and you get a whole number, it means that the number is an even number. 56 divided by two is a whole number. Thus, 56 is an even number and the answer to the question “Is 56 an even number?” is YES.\n\n## Is 96 odd or even?\n\nQ: Is 96 an Odd Number? A: No, the number 96 is not an odd number – it is an even number.\n\n## Is 42 a odd or even?\n\nA: No, the number 42 is not an odd number – it is an even number.\n\n## Is 0.5 odd or even?\n\nA number is divisible by other number if their quotient is an integer. Extending this definition to all real numbers, 0.5 / 2 = 0.25 is clearly not an integer, so 0.5 is odd. … Since (1/2) is not a whole number,it is not an integer and therefore there is no question its oddity or even nature. It is neither Even nor Odd !\n\n## Can 3 odd numbers make an even?\n\nWithout cheating, it’s not possible because sum of three odd numbers can’t be even. Let k be any real number. So, 2k+1 will be an odd number & 2k will be an even number.\n\n## Is 65 an odd or even number?\n\nHow is 65 an odd number? … Notice the number is not a whole number and has a remainder (the . 5)? That means the number is an odd number because it cannot be divided by 2 without a remainder.\n\n## Is the number 1 2 odd or even?\n\n1/2 is neither even nor odd. Since the terms only apply to natural numbers (positive integers), that rules it out. There are multiple things that can also determine whether a number is even or odd. … Therefore, 1/2 is neither even nor odd.\n\n## Which are even number?\n\nTo find an even number, look at the ones digit, or the digit to the very right of the number. (the ones digit in 5382 would be 2.) If the ones digit is either 0, 2, 4, 6, or 8, then the number is even. If the ones digit is either1, 3, 5, 7, or 9, then the number is odd.\n\n## Is 72 an even or odd number?\n\nIf you divide any number, such as 72, by two and you get a whole number, it means that the number is an even number. 72 divided by two is a whole number. Thus, 72 is an even number and the answer to the question “Is 72 an even number?” is YES." ]

[ null, "https://mc.yandex.ru/watch/66675283", null ]

[ "# Submission f80bb946...\n\nChallenge Hex decoder ricmoo.firefly.eth 2018-21-01 30654\n``````pragma solidity 0.4.24;\n\ncontract HexDecoder {\n\nfunction decode(string /* input */) pure public returns(bytes) {\nassembly {\n\n// WARNING! This is NOT safe. For the purpose of this contest I\n// am assuming the ABI pointer to the dynamic slot is\n// 32, but that is not, in general, safe to assume\nlet offset := 68\n\n// Output length\nlength := div(length, 2)\n\n// Allocate memory for the response\nlet outputLength := and(add(length, 95), 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe0)\n\n// Should do this, to update free-memory pointer, but since we aren't using any Solidity\n// this is safe to leave\n\n// Pointer to the dynamic slot for the bytes\nmstore(output, 0x20)\n\n// Length of the bytes (half the length)\n\nfor { } lt(offset, end) { } {\n\n// For letters, the 7th bit is high; n0 is 0x90 for letters 0x00 for numbers\nlet n0 := and(data, 0x5050505050505050505050505050505050505050505050505050505050505050)\nn0 := and(n0, 0x9090909090909090909090909090909090909090909090909090909090909090)\n\n// Move the data over 1 nibble\ndata := mul(data, 0x10)\n\n// Take the lowest nibble from each ascii character (upper nibble since we shifted)\n// 0-9: already the correct value\n// A-F: add 9 to the value to offset A (1) -> 10, etc\ndata := and(data, 0xf0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0f0)\n\n// Shift all nibbles over to the left and odd nibbles into their neighbour\n// (odd bytes become junk)\ndata := or(data, mul(data, 0x10))\n\n// Remove the spaces in the output by chunking\ndata := and(data, 0xff00ff00ff00ff00ff00ff00ff00ff00ff00ff00ff00ff00ff00ff00ff00ff00)\ndata := or(data, mul(data, 0x100))\ndata := and(data, 0xffff0000ffff0000ffff0000ffff0000ffff0000ffff0000ffff0000ffff0000)\ndata := or(data, mul(data, 0x10000))\ndata := and(data, 0xffffffff00000000ffffffff00000000ffffffff00000000ffffffff00000000)\ndata := or(data, mul(data, 0x100000000))\ndata := and(data, 0xffffffffffffffff0000000000000000ffffffffffffffff0000000000000000)\ndata := or(data, mul(data, 0x10000000000000000))\n\nmstore(outOffset, data)" ]

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[ "Flowdock\nclass\n\n# Vector", null, "v1_9_2_180 - Show latest stable - 0 notes - Superclass: Object\n\nThe Vector class represents a mathematical vector, which is useful in its own right, and also constitutes a row or column of a Matrix.\n\n## Method Catalogue\n\nTo create a Vector:\n\n• Vector.[](*array)\n\n• Vector.elements(array, copy = true)\n\nTo access elements:\n\n• [](i)\n\nTo enumerate the elements:\n\n• #each2(v)\n\n• #collect2(v)\n\nVector arithmetic:\n\n• *(x) \"is matrix or number\"\n\n• +(v)\n\n• -(v)\n\nVector functions:\n\nConversion to other data types:\n\nString representations:\n\nShow files where this class is defined (1 file)" ]

[ null, "https://d2vfyqvduarcvs.cloudfront.net/images/importance_2.png", null ]

[ "# State Function Approximation: Linear Function\n\nIn the previous posts, we use different techniques to build and keep updating State-Action tables. But it is impossible to do the same thing when the number of states and actions get huge. So this post we gonna discuss about using a parameterized function to approximate the value function.\n\nBasic Idea of State Function Approximation\n\nInstead of looking up on a State-Action table, we build a black box with weights inside it. Just tell the blackbox whose value functions we want, and then it will calculate and output the value. The weights can be learned by data, which is a typical supervised learning problem.", null, "The input of the system is actually the feature of state S, so we need to do Feature Engineering (Feature Extraction) to represent the state S. X(s) is the feature vectore of state S.", null, "Linear Function Approximation with an Oracle\n\nFor the black box, we can use different models. In this post, we use Linear Function: inner product of features and weights", null, "Assume we are cheatingnow, knowing the true value of the State Value function, then we can do Gradient Descent using Mean Square Error:", null, "", null, "and SGD sample the gradient:", null, "Model-Free Value Function Approximation\n\nThen we go back to reality, realizing the oracle does not help us, which means the only method we can count on is Model-Free algorithm. So we firstly use Monte Carlo, modifying the SGD equation to the following form:", null, "We can also use TD(0) Learning, the Cost Function is:", null, "the gradient is:", null, "The algorithm can be described as:", null, "Model-Free Control Based on State-Action Value Function Approximation\n\nSame as state value function approximation, we extract features from our target problem, building a feature vector:", null, "Then the linear estimation for the Q-function is :", null, "To minimize the MSE cost function, we can get Monte Carlo gradient by taking derivative:", null, "SARSA gradient:", null, "Q-Learning gradient:", null, "References:\n\nhttps://www.youtube.com/watch?v=buptHUzDKcE\n\nhttps://www.youtube.com/watch?v=UoPei5o4fps&list=PLqYmG7hTraZDM-OYHWgPebj2MfCFzFObQ&index=6\n\n0\n0\n\n91 发布于 2019-08-14 07:11 评论(0) 阅读(14)\n\n• 博客[ 6429 ]\n• 评论[ 4 ]\n• 阅读[ 142460 ]" ]

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[ "*> \\brief \\b DPFTRF * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \\htmlonly *> Download DPFTRF + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \\endhtmlonly * * Definition: * =========== * * SUBROUTINE DPFTRF( TRANSR, UPLO, N, A, INFO ) * * .. Scalar Arguments .. * CHARACTER TRANSR, UPLO * INTEGER N, INFO * .. * .. Array Arguments .. * DOUBLE PRECISION A( 0: * ) * * *> \\par Purpose: * ============= *> *> \\verbatim *> *> DPFTRF computes the Cholesky factorization of a real symmetric *> positive definite matrix A. *> *> The factorization has the form *> A = U**T * U, if UPLO = 'U', or *> A = L * L**T, if UPLO = 'L', *> where U is an upper triangular matrix and L is lower triangular. *> *> This is the block version of the algorithm, calling Level 3 BLAS. *> \\endverbatim * * Arguments: * ========== * *> \\param[in] TRANSR *> \\verbatim *> TRANSR is CHARACTER*1 *> = 'N': The Normal TRANSR of RFP A is stored; *> = 'T': The Transpose TRANSR of RFP A is stored. *> \\endverbatim *> *> \\param[in] UPLO *> \\verbatim *> UPLO is CHARACTER*1 *> = 'U': Upper triangle of RFP A is stored; *> = 'L': Lower triangle of RFP A is stored. *> \\endverbatim *> *> \\param[in] N *> \\verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \\endverbatim *> *> \\param[in,out] A *> \\verbatim *> A is DOUBLE PRECISION array, dimension ( N*(N+1)/2 ); *> On entry, the symmetric matrix A in RFP format. RFP format is *> described by TRANSR, UPLO, and N as follows: If TRANSR = 'N' *> then RFP A is (0:N,0:k-1) when N is even; k=N/2. RFP A is *> (0:N-1,0:k) when N is odd; k=N/2. IF TRANSR = 'T' then RFP is *> the transpose of RFP A as defined when *> TRANSR = 'N'. The contents of RFP A are defined by UPLO as *> follows: If UPLO = 'U' the RFP A contains the NT elements of *> upper packed A. If UPLO = 'L' the RFP A contains the elements *> of lower packed A. The LDA of RFP A is (N+1)/2 when TRANSR = *> 'T'. When TRANSR is 'N' the LDA is N+1 when N is even and N *> is odd. See the Note below for more details. *> *> On exit, if INFO = 0, the factor U or L from the Cholesky *> factorization RFP A = U**T*U or RFP A = L*L**T. *> \\endverbatim *> *> \\param[out] INFO *> \\verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, the leading minor of order i is not *> positive definite, and the factorization could not be *> completed. *> \\endverbatim * * Authors: * ======== * *> \\author Univ. of Tennessee *> \\author Univ. of California Berkeley *> \\author Univ. of Colorado Denver *> \\author NAG Ltd. * *> \\ingroup doubleOTHERcomputational * *> \\par Further Details: * ===================== *> *> \\verbatim *> *> We first consider Rectangular Full Packed (RFP) Format when N is *> even. We give an example where N = 6. *> *> AP is Upper AP is Lower *> *> 00 01 02 03 04 05 00 *> 11 12 13 14 15 10 11 *> 22 23 24 25 20 21 22 *> 33 34 35 30 31 32 33 *> 44 45 40 41 42 43 44 *> 55 50 51 52 53 54 55 *> *> *> Let TRANSR = 'N'. RFP holds AP as follows: *> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last *> three columns of AP upper. The lower triangle A(4:6,0:2) consists of *> the transpose of the first three columns of AP upper. *> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first *> three columns of AP lower. The upper triangle A(0:2,0:2) consists of *> the transpose of the last three columns of AP lower. *> This covers the case N even and TRANSR = 'N'. *> *> RFP A RFP A *> *> 03 04 05 33 43 53 *> 13 14 15 00 44 54 *> 23 24 25 10 11 55 *> 33 34 35 20 21 22 *> 00 44 45 30 31 32 *> 01 11 55 40 41 42 *> 02 12 22 50 51 52 *> *> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the *> transpose of RFP A above. One therefore gets: *> *> *> RFP A RFP A *> *> 03 13 23 33 00 01 02 33 00 10 20 30 40 50 *> 04 14 24 34 44 11 12 43 44 11 21 31 41 51 *> 05 15 25 35 45 55 22 53 54 55 22 32 42 52 *> *> *> We then consider Rectangular Full Packed (RFP) Format when N is *> odd. We give an example where N = 5. *> *> AP is Upper AP is Lower *> *> 00 01 02 03 04 00 *> 11 12 13 14 10 11 *> 22 23 24 20 21 22 *> 33 34 30 31 32 33 *> 44 40 41 42 43 44 *> *> *> Let TRANSR = 'N'. RFP holds AP as follows: *> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last *> three columns of AP upper. The lower triangle A(3:4,0:1) consists of *> the transpose of the first two columns of AP upper. *> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first *> three columns of AP lower. The upper triangle A(0:1,1:2) consists of *> the transpose of the last two columns of AP lower. *> This covers the case N odd and TRANSR = 'N'. *> *> RFP A RFP A *> *> 02 03 04 00 33 43 *> 12 13 14 10 11 44 *> 22 23 24 20 21 22 *> 00 33 34 30 31 32 *> 01 11 44 40 41 42 *> *> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the *> transpose of RFP A above. One therefore gets: *> *> RFP A RFP A *> *> 02 12 22 00 01 00 10 20 30 40 50 *> 03 13 23 33 11 33 11 21 31 41 51 *> 04 14 24 34 44 43 44 22 32 42 52 *> \\endverbatim *> * ===================================================================== SUBROUTINE DPFTRF( TRANSR, UPLO, N, A, INFO ) * * -- LAPACK computational routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. CHARACTER TRANSR, UPLO INTEGER N, INFO * .. * .. Array Arguments .. DOUBLE PRECISION A( 0: * ) * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D+0 ) * .. * .. Local Scalars .. LOGICAL LOWER, NISODD, NORMALTRANSR INTEGER N1, N2, K * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA, DSYRK, DPOTRF, DTRSM * .. * .. Intrinsic Functions .. INTRINSIC MOD * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 NORMALTRANSR = LSAME( TRANSR, 'N' ) LOWER = LSAME( UPLO, 'L' ) IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'T' ) ) THEN INFO = -1 ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DPFTRF', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) \\$ RETURN * * If N is odd, set NISODD = .TRUE. * If N is even, set K = N/2 and NISODD = .FALSE. * IF( MOD( N, 2 ).EQ.0 ) THEN K = N / 2 NISODD = .FALSE. ELSE NISODD = .TRUE. END IF * * Set N1 and N2 depending on LOWER * IF( LOWER ) THEN N2 = N / 2 N1 = N - N2 ELSE N1 = N / 2 N2 = N - N1 END IF * * start execution: there are eight cases * IF( NISODD ) THEN * * N is odd * IF( NORMALTRANSR ) THEN * * N is odd and TRANSR = 'N' * IF( LOWER ) THEN * * SRPA for LOWER, NORMAL and N is odd ( a(0:n-1,0:n1-1) ) * T1 -> a(0,0), T2 -> a(0,1), S -> a(n1,0) * T1 -> a(0), T2 -> a(n), S -> a(n1) * CALL DPOTRF( 'L', N1, A( 0 ), N, INFO ) IF( INFO.GT.0 ) \\$ RETURN CALL DTRSM( 'R', 'L', 'T', 'N', N2, N1, ONE, A( 0 ), N, \\$ A( N1 ), N ) CALL DSYRK( 'U', 'N', N2, N1, -ONE, A( N1 ), N, ONE, \\$ A( N ), N ) CALL DPOTRF( 'U', N2, A( N ), N, INFO ) IF( INFO.GT.0 ) \\$ INFO = INFO + N1 * ELSE * * SRPA for UPPER, NORMAL and N is odd ( a(0:n-1,0:n2-1) * T1 -> a(n1+1,0), T2 -> a(n1,0), S -> a(0,0) * T1 -> a(n2), T2 -> a(n1), S -> a(0) * CALL DPOTRF( 'L', N1, A( N2 ), N, INFO ) IF( INFO.GT.0 ) \\$ RETURN CALL DTRSM( 'L', 'L', 'N', 'N', N1, N2, ONE, A( N2 ), N, \\$ A( 0 ), N ) CALL DSYRK( 'U', 'T', N2, N1, -ONE, A( 0 ), N, ONE, \\$ A( N1 ), N ) CALL DPOTRF( 'U', N2, A( N1 ), N, INFO ) IF( INFO.GT.0 ) \\$ INFO = INFO + N1 * END IF * ELSE * * N is odd and TRANSR = 'T' * IF( LOWER ) THEN * * SRPA for LOWER, TRANSPOSE and N is odd * T1 -> A(0,0) , T2 -> A(1,0) , S -> A(0,n1) * T1 -> a(0+0) , T2 -> a(1+0) , S -> a(0+n1*n1); lda=n1 * CALL DPOTRF( 'U', N1, A( 0 ), N1, INFO ) IF( INFO.GT.0 ) \\$ RETURN CALL DTRSM( 'L', 'U', 'T', 'N', N1, N2, ONE, A( 0 ), N1, \\$ A( N1*N1 ), N1 ) CALL DSYRK( 'L', 'T', N2, N1, -ONE, A( N1*N1 ), N1, ONE, \\$ A( 1 ), N1 ) CALL DPOTRF( 'L', N2, A( 1 ), N1, INFO ) IF( INFO.GT.0 ) \\$ INFO = INFO + N1 * ELSE * * SRPA for UPPER, TRANSPOSE and N is odd * T1 -> A(0,n1+1), T2 -> A(0,n1), S -> A(0,0) * T1 -> a(n2*n2), T2 -> a(n1*n2), S -> a(0); lda = n2 * CALL DPOTRF( 'U', N1, A( N2*N2 ), N2, INFO ) IF( INFO.GT.0 ) \\$ RETURN CALL DTRSM( 'R', 'U', 'N', 'N', N2, N1, ONE, A( N2*N2 ), \\$ N2, A( 0 ), N2 ) CALL DSYRK( 'L', 'N', N2, N1, -ONE, A( 0 ), N2, ONE, \\$ A( N1*N2 ), N2 ) CALL DPOTRF( 'L', N2, A( N1*N2 ), N2, INFO ) IF( INFO.GT.0 ) \\$ INFO = INFO + N1 * END IF * END IF * ELSE * * N is even * IF( NORMALTRANSR ) THEN * * N is even and TRANSR = 'N' * IF( LOWER ) THEN * * SRPA for LOWER, NORMAL, and N is even ( a(0:n,0:k-1) ) * T1 -> a(1,0), T2 -> a(0,0), S -> a(k+1,0) * T1 -> a(1), T2 -> a(0), S -> a(k+1) * CALL DPOTRF( 'L', K, A( 1 ), N+1, INFO ) IF( INFO.GT.0 ) \\$ RETURN CALL DTRSM( 'R', 'L', 'T', 'N', K, K, ONE, A( 1 ), N+1, \\$ A( K+1 ), N+1 ) CALL DSYRK( 'U', 'N', K, K, -ONE, A( K+1 ), N+1, ONE, \\$ A( 0 ), N+1 ) CALL DPOTRF( 'U', K, A( 0 ), N+1, INFO ) IF( INFO.GT.0 ) \\$ INFO = INFO + K * ELSE * * SRPA for UPPER, NORMAL, and N is even ( a(0:n,0:k-1) ) * T1 -> a(k+1,0) , T2 -> a(k,0), S -> a(0,0) * T1 -> a(k+1), T2 -> a(k), S -> a(0) * CALL DPOTRF( 'L', K, A( K+1 ), N+1, INFO ) IF( INFO.GT.0 ) \\$ RETURN CALL DTRSM( 'L', 'L', 'N', 'N', K, K, ONE, A( K+1 ), \\$ N+1, A( 0 ), N+1 ) CALL DSYRK( 'U', 'T', K, K, -ONE, A( 0 ), N+1, ONE, \\$ A( K ), N+1 ) CALL DPOTRF( 'U', K, A( K ), N+1, INFO ) IF( INFO.GT.0 ) \\$ INFO = INFO + K * END IF * ELSE * * N is even and TRANSR = 'T' * IF( LOWER ) THEN * * SRPA for LOWER, TRANSPOSE and N is even (see paper) * T1 -> B(0,1), T2 -> B(0,0), S -> B(0,k+1) * T1 -> a(0+k), T2 -> a(0+0), S -> a(0+k*(k+1)); lda=k * CALL DPOTRF( 'U', K, A( 0+K ), K, INFO ) IF( INFO.GT.0 ) \\$ RETURN CALL DTRSM( 'L', 'U', 'T', 'N', K, K, ONE, A( K ), N1, \\$ A( K*( K+1 ) ), K ) CALL DSYRK( 'L', 'T', K, K, -ONE, A( K*( K+1 ) ), K, ONE, \\$ A( 0 ), K ) CALL DPOTRF( 'L', K, A( 0 ), K, INFO ) IF( INFO.GT.0 ) \\$ INFO = INFO + K * ELSE * * SRPA for UPPER, TRANSPOSE and N is even (see paper) * T1 -> B(0,k+1), T2 -> B(0,k), S -> B(0,0) * T1 -> a(0+k*(k+1)), T2 -> a(0+k*k), S -> a(0+0)); lda=k * CALL DPOTRF( 'U', K, A( K*( K+1 ) ), K, INFO ) IF( INFO.GT.0 ) \\$ RETURN CALL DTRSM( 'R', 'U', 'N', 'N', K, K, ONE, \\$ A( K*( K+1 ) ), K, A( 0 ), K ) CALL DSYRK( 'L', 'N', K, K, -ONE, A( 0 ), K, ONE, \\$ A( K*K ), K ) CALL DPOTRF( 'L', K, A( K*K ), K, INFO ) IF( INFO.GT.0 ) \\$ INFO = INFO + K * END IF * END IF * END IF * RETURN * * End of DPFTRF * END" ]

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[ "# OECD Discriminatory family code data analysis 5 - Linear regression using R. Attitudes Towards Working Mother, Early Marriage and Per Capita GDP", null, "Photo by Bjorn Pierre on Unsplash\n\nThis post is following of above post.\nIn this post, I will do linear regression analysis with R.\n\nFirst, I make a data frame which have \"atwm\": Attitudes Towards Working Mothers only.", null, "Second, I make a data frame which have \"em\": Early Marriage only.", null, "Then, I merge those two data frames with merge() function.", null, "Now we have 80 observations in df2.\n\nLet's make a scatter plot for \"atwm\" and \"em\".", null, "", null, "I use lm() function for linear regression.", null, "p-value is less than 0.05, so I say this model is statistically significant.\n\nLet's make plot for scatter plot and regression line.", null, "", null, "We see the higer \"atwm\", the higher \"em\".\n\nLet's test for Heteroskedasticity.", null, "atwm, I(atwm^2) and entire model's p-value are all greater than 0.05, 0.206, 0.263 and 0.363 respectively. So this model is not Heteroskedasticiy.\n\nI have per capita GDP file which is downloaded from OECD web site.\nI will load this GDP data file.", null, "I merge this pcgdp data frame and df2 data frame.", null, "I make log(pc_gdp) for linear regression analysis and make two scatter plots.", null, "", null, "I wee \"atwm\" and \"em\" have negative relationship to \"lpc_gdp\": log(per capita GDP).\n\nSo, the lower \"atwm\" and \"em\", the higher per capita GDP.\n\nLet's do linear regression with lm() function.", null, "\"atwm\" and \"em\" has statistically significant coefficient. The both coefficients signs are negative.\n\nLastly, let's make a 3D scatter plot with scatterplot3d() function in scatterplor3d package.", null, "", null, "That's it. Thank you!\n\nNext post is" ]

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[ "# #00200f Color Information\n\nIn a RGB color space, hex #00200f is composed of 0% red, 12.5% green and 5.9% blue. Whereas in a CMYK color space, it is composed of 100% cyan, 0% magenta, 53.1% yellow and 87.5% black. It has a hue angle of 148.1 degrees, a saturation of 100% and a lightness of 6.3%. #00200f color hex could be obtained by blending #00401e with #000000. Closest websafe color is: #003300.\n\n• R 0\n• G 13\n• B 6\nRGB color chart\n• C 100\n• M 0\n• Y 53\n• K 87\nCMYK color chart\n\n#00200f color description : Very dark (mostly black) cyan - lime green.\n\n# #00200f Color Conversion\n\nThe hexadecimal color #00200f has RGB values of R:0, G:32, B:15 and CMYK values of C:1, M:0, Y:0.53, K:0.87. Its decimal value is 8207.\n\nHex triplet RGB Decimal 00200f `#00200f` 0, 32, 15 `rgb(0,32,15)` 0, 12.5, 5.9 `rgb(0%,12.5%,5.9%)` 100, 0, 53, 87 148.1°, 100, 6.3 `hsl(148.1,100%,6.3%)` 148.1°, 100, 12.5 003300 `#003300`\nCIE-LAB 9.541, -16.437, 7.494 0.603, 1.067, 0.626 0.262, 0.465, 1.067 9.541, 18.065, 155.492 9.541, -8.37, 6.346 10.332, -7.668, 3.639 00000000, 00100000, 00001111\n\n# Color Schemes with #00200f\n\n• #00200f\n``#00200f` `rgb(0,32,15)``\n• #200011\n``#200011` `rgb(32,0,17)``\nComplementary Color\n• #012000\n``#012000` `rgb(1,32,0)``\n• #00200f\n``#00200f` `rgb(0,32,15)``\n• #00201f\n``#00201f` `rgb(0,32,31)``\nAnalogous Color\n• #200001\n``#200001` `rgb(32,0,1)``\n• #00200f\n``#00200f` `rgb(0,32,15)``\n• #1f0020\n``#1f0020` `rgb(31,0,32)``\nSplit Complementary Color\n• #200f00\n``#200f00` `rgb(32,15,0)``\n• #00200f\n``#00200f` `rgb(0,32,15)``\n• #0f0020\n``#0f0020` `rgb(15,0,32)``\n• #112000\n``#112000` `rgb(17,32,0)``\n• #00200f\n``#00200f` `rgb(0,32,15)``\n• #0f0020\n``#0f0020` `rgb(15,0,32)``\n• #200011\n``#200011` `rgb(32,0,17)``\n• #000000\n``#000000` `rgb(0,0,0)``\n• #000000\n``#000000` `rgb(0,0,0)``\n• #000703\n``#000703` `rgb(0,7,3)``\n• #00200f\n``#00200f` `rgb(0,32,15)``\n• #003a1b\n``#003a1b` `rgb(0,58,27)``\n• #005327\n``#005327` `rgb(0,83,39)``\n• #006d33\n``#006d33` `rgb(0,109,51)``\nMonochromatic Color\n\n# Alternatives to #00200f\n\nBelow, you can see some colors close to #00200f. Having a set of related colors can be useful if you need an inspirational alternative to your original color choice.\n\n• #002007\n``#002007` `rgb(0,32,7)``\n• #00200a\n``#00200a` `rgb(0,32,10)``\n• #00200c\n``#00200c` `rgb(0,32,12)``\n• #00200f\n``#00200f` `rgb(0,32,15)``\n• #002012\n``#002012` `rgb(0,32,18)``\n• #002014\n``#002014` `rgb(0,32,20)``\n• #002017\n``#002017` `rgb(0,32,23)``\nSimilar Colors\n\n# #00200f Preview\n\nThis text has a font color of #00200f.\n\n``<span style=\"color:#00200f;\">Text here</span>``\n#00200f background color\n\nThis paragraph has a background color of #00200f.\n\n``<p style=\"background-color:#00200f;\">Content here</p>``\n#00200f border color\n\nThis element has a border color of #00200f.\n\n``<div style=\"border:1px solid #00200f;\">Content here</div>``\nCSS codes\n``.text {color:#00200f;}``\n``.background {background-color:#00200f;}``\n``.border {border:1px solid #00200f;}``\n\n# Shades and Tints of #00200f\n\nA shade is achieved by adding black to any pure hue, while a tint is created by mixing white to any pure color. In this example, #000c06 is the darkest color, while #f8fffb is the lightest one.\n\n• #000c06\n``#000c06` `rgb(0,12,6)``\n• #00200f\n``#00200f` `rgb(0,32,15)``\n• #003418\n``#003418` `rgb(0,52,24)``\n• #004721\n``#004721` `rgb(0,71,33)``\n• #005b2b\n``#005b2b` `rgb(0,91,43)``\n• #006e34\n``#006e34` `rgb(0,110,52)``\n• #00823d\n``#00823d` `rgb(0,130,61)``\n• #009646\n``#009646` `rgb(0,150,70)``\n• #00a94f\n``#00a94f` `rgb(0,169,79)``\n• #00bd59\n``#00bd59` `rgb(0,189,89)``\n• #00d162\n``#00d162` `rgb(0,209,98)``\n• #00e46b\n``#00e46b` `rgb(0,228,107)``\n• #00f874\n``#00f874` `rgb(0,248,116)``\n• #0cff7e\n``#0cff7e` `rgb(12,255,126)``\n• #20ff89\n``#20ff89` `rgb(32,255,137)``\n• #34ff93\n``#34ff93` `rgb(52,255,147)``\n• #47ff9d\n``#47ff9d` `rgb(71,255,157)``\n• #5bffa8\n``#5bffa8` `rgb(91,255,168)``\n• #6effb2\n``#6effb2` `rgb(110,255,178)``\n• #82ffbd\n``#82ffbd` `rgb(130,255,189)``\n• #96ffc7\n``#96ffc7` `rgb(150,255,199)``\n• #a9ffd1\n``#a9ffd1` `rgb(169,255,209)``\n• #bdffdc\n``#bdffdc` `rgb(189,255,220)``\n• #d1ffe6\n``#d1ffe6` `rgb(209,255,230)``\n• #e4fff1\n``#e4fff1` `rgb(228,255,241)``\n• #f8fffb\n``#f8fffb` `rgb(248,255,251)``\nTint Color Variation\n\n# Tones of #00200f\n\nA tone is produced by adding gray to any pure hue. In this case, #0f1110 is the less saturated color, while #00200f is the most saturated one.\n\n• #0f1110\n``#0f1110` `rgb(15,17,16)``\n• #0e1210\n``#0e1210` `rgb(14,18,16)``\n• #0c1410\n``#0c1410` `rgb(12,20,16)``\n• #0b1510\n``#0b1510` `rgb(11,21,16)``\n• #0a1610\n``#0a1610` `rgb(10,22,16)``\n• #091710\n``#091710` `rgb(9,23,16)``\n• #07190f\n``#07190f` `rgb(7,25,15)``\n• #061a0f\n``#061a0f` `rgb(6,26,15)``\n• #051b0f\n``#051b0f` `rgb(5,27,15)``\n• #041c0f\n``#041c0f` `rgb(4,28,15)``\n• #021e0f\n``#021e0f` `rgb(2,30,15)``\n• #011f0f\n``#011f0f` `rgb(1,31,15)``\n• #00200f\n``#00200f` `rgb(0,32,15)``\nTone Color Variation\n\n# Color Blindness Simulator\n\nBelow, you can see how #00200f is perceived by people affected by a color vision deficiency. This can be useful if you need to ensure your color combinations are accessible to color-blind users.\n\nMonochromacy\n• Achromatopsia 0.005% of the population\n• Atypical Achromatopsia 0.001% of the population\nDichromacy\n• Protanopia 1% of men\n• Deuteranopia 1% of men\n• Tritanopia 0.001% of the population\nTrichromacy\n• Protanomaly 1% of men, 0.01% of women\n• Deuteranomaly 6% of men, 0.4% of women\n• Tritanomaly 0.01% of the population" ]

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[ "# How to reduce any number not equal to 0 to 1 and any number equal to 0 kept at 0 in Python? [closed]\n\nThe first behaviour you list is mathematically called the signum operation. If you are allowed to use numpy, i’d simply do:\n\nimport numpy\nsign = numpy.sign(x)\n\n\nWith regard to your 2nd question, that’s quite easy.\n\nSimply use:\n\nint(bool(x))\n\n\n## Edit:\n\nWith some tinkering i found a solution for your first question, too:\n\nnegsign = int(int(num) >> 31)\npossign = int(num > 0)\n\nsign = negsign + possign\n\n\nNote that i did not thoroughly test this for special cases like -0." ]

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[ "Get instant live expert help with Excel or Google Sheets\n“My Excelchat expert helped me in less than 20 minutes, saving me what would have been 5 hours of work!”\n\n#### Post your problem and you'll get expert help in seconds\n\nYour message must be at least 40 characters\nOur professional experts are available now. Your privacy is guaranteed.\n\n# Filter values in array formula\n\nExcel allows us to filter values in an array with the IF, ISNUMBER and MATCH functions. This step by step tutorial will assist all levels of Excel users in filtering in or out some specific values in a data set.\n\nFigure 1. Final result: Filter values in array\n\nFinal formula: `=COUNT(IF(ISNUMBER(MATCH(B3:D5,G2:G3,0)),B3:D5))`\n\n## Syntax of the IF function\n\nIF function evaluates a given logical test and returns a TRUE or a FALSE.\n\n### Syntax\n\n`=IF(logical_test, [value_if_true], [value_if_false])`\n\n• The arguments “value_if_true” and “value_if_false” are optional.  If left blank, the function will return TRUE if the logical test is met, and FALSE if otherwise.\n\n## Syntax of the ISNUMBER function\n\nThe ISNUMBER function tests whether a value is a number and returns TRUE; FALSE if otherwise\n\n### Syntax\n\n`=ISNUMBER(value)`\n\n• Value – any value that we want to test if a number or not\n\n## Syntax of the MATCH function\n\nMATCH function is used to search for a specific value in a range of cells.  It returns the #N/A error value if the search is unsuccessful.\n\n### Syntax\n\n`=MATCH(lookup_value, lookup_array, [match_type])`\n\nThe parameters are:\n\n• lookup_value – a value which we want to find in the lookup_array\n• lookup_array – the range of cells containing the value we want to match\n• [match_type] optional; the type of match; if omitted, the default value is 1; We use 0 to find an exact match\n\n## Setting up Our Data\n\nOur data shows a 3×3 table with values 0, 1, 2 and 3.  In cells G2 and G3, we specify the values we want to filter, which are numbers 0 and 3.\n\nFigure 2. Sample data to filter values in array\n\n## Filter Values in Array\n\nWe want to filter the values 0 and 3 in our data.\n\nFigure 3. Entering the formula to filter values in array\n\nTo filter values in an array, we follow these steps:\n\nStep 1.  Select cell G5.\n\nStep 2.  Enter the formula: `=COUNT(IF(ISNUMBER(MATCH(B3:D5,G2:G3,0)),B3:D5))`\n\nStep 3.  Press Ctrl + Shift + ENTER because this is an array formula.\n\nFirst, the formula matches our data with the filter values 0 and 3 through the MATCH function “`MATCH(B3:D5,G2:G3,0)`”. The ISNUMBER evaluates the matched values and returns TRUE if there is a match. Otherwise it returns FALSE.\n\nThe result is an array with these values:  `{TRUE,TRUE,FALSE;TRUE,FALSE,FALSE;FALSE,FALSE,TRUE}`\n\nFigure 4. Resulting array after the matched values are evaluated if a number or not\n\nThe COUNT and IF functions return the count for the filtered values. As a final result, the value in cell G5 is 4, which is the count of all values 0 and 3 in our data.\n\n## Exclude Filters in Array\n\nThere are instances when we want to exclude the filtered values from our data.\n\nFigure 5. Entering the formula to exclude filtered values in array\n\nTo exclude filtered values in an array, we follow these steps:\n\nStep 1.  Select cell G5.\n\nStep 2.  Enter the formula: `=COUNT(IF(1-ISNUMBER(MATCH(B3:D5,G2:G3,0)),B3:D5))`\n\nStep 3.  Press Ctrl + Shift + ENTER .\n\nThe result in cell G5 is the reverse of the result in our previous example. Out of the 9 data points, we excluded the filtered values 0 and 3, and came up with 5 values.\n\nMost of the time, the problem you will need to solve will be more complex than a simple application of a formula or function. If you want to save hours of research and frustration, try our live Excelchat service! Our Excel Experts are available 24/7 to answer any Excel question you may have. We guarantee a connection within 30 seconds and a customized solution within 20 minutes.\n\n### Did this post not answer your question? Get a solution from connecting with the expert.", null, "" ]

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[ "# Stabilized FEM solution of MHD duct flow with conducting cracks in the insulation\n\n2023-05-15\nTezer, Münevver\nAYDIN, SALİM TUTGUN\n© 2022 Elsevier B.V.In this paper, the numerical solution of the fully developed liquid–metal magnetohydrodynamic (MHD) flow is given in a rectangular duct under an external oblique magnetic field with no-slip and insulated walls containing crack regions. The coupled MHD flow equations are transformed first into decoupled convection–diffusion equations in terms of the velocity and induced magnetic field. Thus, we apply the SUPG stabilization in the finite element method (FEM) solution procedure for high values of Hartmann number which determine the convection dominant case. Numerical solutions for high values of Hartmann number and several orientation angles of external magnetic field as well as different crack configurations depict the effects of these parameters on the flow, flowrate and induced current. The SUPG in the FEM solution of MHD equations enables one to display the well-known characteristics of MHD pipe flow for large values of Hartmann number in which wall insulation is faced to several cracks. It is found that, the flowrate drops with an increase in the Hartmann number, and the increase in the number and lengths of the cracks which are located on one Hartmann wall. The flowrate is minimum if the crack is located at the center of the Hartmann wall. If the crack is located on the side layer, it does not significantly affect the flowrate. The case of each Hartmann wall contains one crack, significantly drops the flowrate compared to two cracks on the same Hartmann wall. Also, the breakdowns and peaks are sharpened when the Hartmann wall is a curved boundary. The FEM with SUPG stabilization is capable of capturing flow changes for high values of Hartmann number even in the vicinity of small-sized crack regions.\nJournal of Computational and Applied Mathematics\n\n# Suggestions\n\n Stabilizing subgrid FEM solution of the natural convection flow under high magnitude magnetic field on sinusoidal corrugated enclosure Aydın, S. H.; Tezer, Münevver (Informa UK Limited, 2019-7-7) This study deals with the stabilized finite element solution of the steady, natural convection flow in an enclosure under a magnetic field applied perpendicular to the sinusoidal corrugated vertical walls of the enclosure, in terms of primitive variables. Several vertical sinusoidal functions are selected for the comparison. A stabilized FEM scheme called SSM is proposed in order to obtain a stable solution for the high values of problem parameters with a cheap computational cost. Proposed numerical scheme ...\n A DRBEM solution for MHD pipe flow in a conducting medium Han Aydın, S.; Tezer, Münevver (Elsevier BV, 2014-3) Numerical solutions are given for magnetohydrodynamic (MHD) pipe flow under the influence of a transverse magnetic field when the outside medium is also electrically conducting. Convection-diffusion-type MHD equations for inside the pipe are coupled with the Laplace equation defined in the exterior region, and the continuity requirements for the induced magnetic fields are also coupled on the pipe wall. The most general problem of a conducting pipe wall with thickness, which also has magnetic induction gene...\n Controlling the power law fluid flow and heat transfer under the external magnetic field using the flow index and the Hartmann number Evcin, Cansu; Uğur, Ömür; Tezer, Münevver (2018-10-01) The direct and optimal control solution of laminar fully developed, steady Magnetohydrodynamics (MHD) flow of an incompressible, electrically conducting power-law non-Newtonian fluid in a square duct is considered with the heat transfer. The fluid is subjected to an external uniform magnetic field as well as a constant pressure gradient. The apparent fluid viscosity is both a function of the unknown velocity and the flow index which makes the momentum equation nonlinear. Viscous and Joule dissipation terms ...\n Controlling the power law fluid flow and heat transfer under the external magnetic field using the flow index and the Hartmann number Evcin, Cansu; Uğur, Ömür; Tezer, Münevver (2018-10-01) The direct and optimal control solution of laminar fully developed, steady Magnetohydrodynamics (MHD) flow of an incompressible, electrically conducting power-law non-Newtonian fluid in a square duct is considered with the heat transfer. The fluid is subjected to an external uniform magnetic field as well as a constant pressure gradient. The apparent fluid viscosity is both a function of the unknown velocity and the flow index which makes the momentum equation nonlinear. Viscous and Joule dissipation terms ...\n Numerical solution of magnetohydrodynamic flow problems using the boundary element method Tezer, Münevver (2005-03-18) A boundary element solution is given for a magnetohydrodynamic (MHD) flow problem in a rectangular duct having insulating walls, in terms of velocity and induced magnetic field. The coupled velocity and magnetic field equations are first transformed into decoupled nonhomogeneous convection-diffusion type equations and then finding particular solutions, the homogeneous equations are solved using the boundary element method (BEM). The fundamental solutions of the decoupled homogeneous equations themselves are...\nCitation Formats\nM. Tezer and S. T. AYDIN, “Stabilized FEM solution of MHD duct flow with conducting cracks in the insulation,” Journal of Computational and Applied Mathematics, vol. 423, pp. 0–0, 2023, Accessed: 00, 2023. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85142894649&origin=inward.", null, "" ]

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[ "# D.R.Kaprekar: Indian Mathematician\n\nThe readers may recall that I talked about Ramanujan sometime back. Today I introduce to my readers, a much less known Indian Mathematician.", null, "Kaprekar constantDattaraya Ramchandra Kaprekar, born 1905 worked on the number theory. He had no formal postgraduate training and worked as a schoolteacher in Nasik, India.\n\nHis claim to fame is the Kaprekar constant 6174. Start with any four digit number, with no repeating digits – say Z. Let A and B be two numbers formed by rearranging the digits of Z, such that A is the highest number that is possible, and B the smallest. Subtract B from A. If this is not 6174, continue the same way now taking this number to be Z. For example, starting with Ramanujan number 1729:\n``` 9721-1279 = 8442 8442-2448 = 5994 9954-4599 = 5355 5553-3555 = 1998 9981-1899 = 8082 8820-0288 = 8532 8532-2358 = 6174 7641-1467 = 6174```\n\nHe also gave the world Harshad numbers: numbers that can be divided by the sum of their digits – for example 12, which is divisible by 3." ]

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[ "# Bert Simonovich's Design Notes\n\nInnovative Signal Integrity & Backplane Solutions\n\n## Characteristic Impedance – Where SI/PI Worlds Collide\n\nwith one comment\n\nOriginally published Signal Integrity Journal, February 23, 2021\n\nSignal and power integrity (SI/PI) simulations, measurements, and analysis usually live in two different worlds, but occasionally these worlds collide. One such collision occurs when we refer to characteristic impedance, Z0. Traditionally the PI world lives in the frequency domain while the SI world lives in the time domain.\n\nWhen designing a power distribution network (PDN) in the PI world, we are mostly interested in engineering a flat impedance below a target impedance from DC to the highest frequency components of the transient current. Practically this is achieved with a network of capacitors with different values connected to the respective power planes as shown in Figure 1.", null, "Figure 1 A simplified model of a typical PDN courtesy .\n\nIn the real world, there is no such thing as an ideal capacitor. There are always parasitic elements known as equivalent series inductance (ESL) and equivalent series resistance (ESR). Physical characteristics of the PCB, like component mounting inductance, plane spreading inductance, via and BGA ball inductance, along with voltage regulator module (VRM) characteristics also contribute to the impedance profile. When connected together, the interaction of capacitors and parasitic inductance and resistance create a transfer impedance profile with resonant peaks and anti-resonant nulls as shown in Figure 2.\n\nThe transfer impedance between the VRM and the load is calculated and plotted in the frequency domain with a log-log scale. The resulted impedance curve is then compared to the target impedance (Ztarget), which is estimated based on the allowed noise ripple and maximum transient current. The flat target impedance is frequency independent in the analysis.", null, "Figure 2 Impedance profile of the PDN as viewed from the pads on the die power rail courtesy .\n\nResonant peaks are due to ESL of one capacitor connected in parallel with another capacitor. Anti-resonant nulls are due to the series combination of ESR, ESL, and C for each capacitor. Different capacitor values will have anti-resonant nulls at different frequencies.\n\nBut in the PI world, there is a rarely talked about characteristic impedance, Z0. In this case, it refers to the geometric average of the reactive impedance of a capacitor (XC) and reactive impedance of an inductor (XL).\n\nEquation 1", null, "At resonance, XL and XC intersect at the characteristic impedance and are equal as shown in Figure 3.", null, "Figure 3 Inductive and capacitive reactance plot of ideal inductor and capacitor versus frequency. At resonance, XL and XC are equal and intersect at the characteristic impedance, Z0. Simulated with Pathwave ADS .\n\nThis is a very important observation, and it is where the SI/PI worlds collide.\n\nIn the SI world, characteristic impedance, Z0 refers to the instantaneous ratio of the voltage to current of a wave front traveling along a uniform transmission line without reflections. For an infinitely long uniform transmission line, Z0 equals the input impedance.\n\nThe characteristic impedance of a lossy transmission line is defined as:\n\nEquation 2", null, "Where R is resistance per unit length; G is conductance per unit length; L is inductance per unit length; and C is capacitance per unit length. For a lossless uniform transmission line, R and G are assumed to be zero and thus the characteristic impedance is reduced to:\n\nEquation 3", null, "#### Time Domain Reflectometer\n\nIn the SI world, we usually use a time domain reflectometer (TDR) to measure characteristic impedance, but more often than not, the measured impedance we get is not what we predicted with a 2D field solver. Many 2D field solvers used by most PCB FAB shops only calculate the lossless characteristic impedance of the cross-sectional geometry at a single frequency, defined by the dielectric constant (Dk). It has no input for conductor resistivity, dielectric loss, or how long the conductor(s) is.\n\nSo the issue is: we design the stackup, then do our SI modeling analysis based on stackup parameters and matching characteristic impedance. But the PCB FAB shop will often adjust the line width(s), over and above normal process variation, so that when measured, the impedance will fall within the specified tolerance, usually +/-10 percent.\n\nPart of the problem lies with the method used to take the measurements. Most PCB FAB shops follow IPC-TM-650 Test Methods Manual . But it has limitations because Z0 measured is derived and cannot be directly measured. The reason is the measurements include resistive and dielectric losses, up to the point where the measurement takes place along the TDR plot.\n\nResistive loss often results in a slow monotonic rise in the impedance profile, shown in the example TDR plot of Figure 4. IPC-TM-650 specifies a measurement zone between 30-70 percent to avoid probing induced ringing affecting the measurements. Most PCB FAB shops will measure an average impedance over this range, usually in the center region.\n\nDepending on the linewidth, thickness and dielectric dissipation factor (Df), the slope of the monotonic rise will vary.", null, "Figure 4 Example TDR plot showing slow monotonic rise in impedance due to resistive losses and IPC-TM-650 measurement zone.\n\nThe problem is that the IPC-TM-650 test method was last updated back in 2004, when higher dielectric loss, along with wider line widths and thicker copper weights, were used more often. A higher Df tends to compensate for resistive loss by flattening the slope as shown in Figure 5.\n\nOn the bottom left is a simulated TDR plot using a high loss dielectric with Df = 0.024. The right side has the exact same geometry properties except Df = 0.004. The average impedance, when measured at the 50 percent point, is 49.8 Ohms on the left side vs. 51.4 Ohms on the right side. We also confirm flatter slope for high loss material.\n\nThe actual characteristic impedance predicted by a Polar SI9000 2D field solver in Figure 5 is 49 Ohms. For higher loss material, measuring within the measurement zone would pass without any issues. But for lower loss material, the resistive loss dominates and measuring within the measurement zone will give ~5 percent higher impedance reading compared to the higher loss material. The correct measurement point for Z0 is, in fact, the initial dip, equivalent to the field solver prediction. Depending on the tolerance specified, this may affect yield and cost.", null, "Figure 5 Characteristic impedance prediction by Polar SI9000 2D field solver (top). Simulated 2 inch TDR plots using a high loss dielectric (bottom left) vs. low loss dielectric with exactly the same geometry (bottm right). A higher Df compensates for higher resistive loss thereby flattening the curve. Simulated with Pathwave ADS .\n\nToday, with the push to low loss dielectric and finer line widths with thinner copper weights, measuring the true transmission line characteristic impedance using a TDR becomes more challenging. This is even more so when measuring differential impedance, because a change in line width space geometry can have a more profound effect on measured differential impedance.\n\nUsing the first article build of a new design, as an example, let’s assume the correct characteristic impedance, when measured at the beginning of the slow monotonic rise of a TDR plot, is on the high end of nominal +10 percent tolerance. Let’s say it’s 54 Ohms.  But because of the low loss dielectric and high resistive loss, the TDR measurement at the midpoint is now reading 5% higher at 57 Ohms. This would imply the impedance is now out of spec over nominal and the board would be scrapped.\n\nThe PCB fab shop will then go back and adjust the linewidth accordingly for the next build to bring the measurement within range to their measurement set up. Doing this effectively lowers the true nominal characteristic impedance!\n\nIf subsequent manufacturing variations pushes the measured impedance within the measurement zone on the low end of the -10 percent tolerance, say 44 Ohms, then the true characteristic impedance, if measured at the initial dip, will be 5 percent lower at 42 Ohms and be out of spec. But the board will pass because it was measured following IPC-TM-650 test method.\n\n#### 2-port Shunt Measurement\n\nBut what if there were another way? What if we could borrow impedance measuring techniques from the PI world to determine the true transmission line characteristic impedance in the SI world?  Well there is. Enter the 2-port shunt measurement technique.\n\nFor example, in the PI world, to measure ESL and ESR of a chip capacitor, of a device under test (DUT), a 2-port shunt measurement is often used. It is much like the 4-point Kelvin measurement technique used to measure very low DC resistance.\n\nThe 2-port shunt measurement is usually done with a 2-port vector network analyzer (VNA). Port 1 of the VNA sends out a calibrated signal, and port 2 measures the voltage signal across the DUT. Often an isolation transformer is also used to break the inherent ground loop when measuring ultra-low impedances .\n\nOnce the measurements have been completed and S-parameters saved in touchstone format, further analysis can be done in your favorite SPICE simulator. Figure 6 is a generic schematic using popular Pathwave ADS that can be used for 2-port shunt analysis.\n\nWhen port 1 and port 2 are connected to port 1 of the DUT and port 2 of the DUT is grounded, the impedance of the DUT can be determined by ;\n\nEquation 4", null, "", null, "Figure 6 Generic Pathwave ADS schematic used for 2-port shunt analysis on a S2P file for DUT.\n\nIf we replace the DUT in Figure 6 with a capacitor and inductor, we get an impedance plot shown in Figure 7.  As we saw earlier, when we take the geometric average of the inductive and capacitive reactance using Equation 1, we get the characteristic impedance. If we apply Equation 4 to the results of a 2-port shunt measurements of a capacitor and inductor, we get exactly the same results as shown in the top of Figure 7.\n\nWhen we replace the capacitor and inductor with a S-parameter file of a transmission line model from Figure 5, we get the plot shown at the bottom of Figure 7. Except for the resonant nulls and peaks, up to a certain frequency, the impedance of a transmission line looks like the impedance of a capacitor when the far-end is open, and looks like the impedance of an inductor when the far-end is shorted. And because of that, this is where the two worlds collide!\n\nIf we take the geometric average of the impedance when the far-end is open (Zopen) or shorted (Zshort), we get the characteristic impedance at that frequency. We note where the red and blue impedance lines first intersect, is exactly the geometric average characteristic impedance at that frequency.\n\nAlso worth noting, the lines intersect at half of the frequency between the peaks and valleys at higher frequencies as well.", null, "Figure 7 Impedance of inductive and capacitive reactance vs. frequency (top) and impedance of a transmission line vs. frequency (bottom) when the far-end is open (solid red) compared to when the far-end is shorted (solid blue). The intersection of the red and blue lines is exactly the characteristic impedance. Simulated with Pathwave ADS .\n\nWe can see this more clearly if we replot Figure 7 bottom using a linear scale for the x-axis, as shown in Figure 8. This is a very powerful observation. What this means is that when we measure the impedance half way between a peak and adjacent valley, of either the red or blue plot, it is the characteristic impedance of the transmission line at that frequency.\n\nThus, only an open or shorted end measurement is all that is needed to determine the characteristic impedance. For example, if we look at the red curve alone, then measure the first resonant null (m14) and adjacent peak (m15), the characteristic impedance (mag(Zopen) is measured exactly at one half the frequency between the two (m16).", null, "Figure 8 Impedance of a transmission line vs. frequency on a linear scale when the far-end is open (solid red) compared to when the far-end is shorted (solid blue). The intersection of the red and blue lines half way between respective peaks and valleys is the characteristic impedance. Simulated with Pathwave ADS .\n\nThe first resonant red null and blue peak represent the quarter-wave resonant frequency due to open and shorted end. Each respective red null and blue peak following are the odd harmonics of the first quarter-wave resonant frequency.\n\nKnowing this, we can now determine the phase or time delay (TD) of the transmission line as being one quarter of the period of the resonant frequency (f0).\n\nEquation 5", null, "Because resonant nulls and peaks occur at the resonant frequency, we can also determine the effective dielectric constant (Dkeff). Given the speed of light (c) = 11.8 in. per nanosecond, the length of the transmission line (len) in in. and quarter-wave resonant frequency (f0), Dkeff can be determined by:\n\nEquation 6", null, "#### CMP28 Case Study", null, "Figure 9 Photo of a portion of CMP-28 test platform courtesy of Wildriver Technology used for measurement validation.\n\nTo test the accuracy of this method, measured data from a CMP28 test platform, shown in Figure 9, was used for measurement validation. S-parameter (s2p) files from 2 inch and 8 inch single-ended stripline traces were provided as part of CMP-28 design kit courtesy of Wildriver Technologies . The 6-inch transmission line segment S-parameter data was de-embedded courtesy of AtaiTec Corporation .\n\nThe characteristic impedance, based on trace geometry and stackup parameters, was modeled in Polar SI9000 . Using Dk from data sheet tables @ 10GHz, and correcting for conductor roughness , the characteristic impedance predicted was 49.66 Ohms, as shown in Figure 10.", null, "Figure 10 Polar SI9000 field-solver characteristic impedance prediction of CMP28 trace geometry.\n\nTouchstone S-parameter DUT files were connected with far-end open, shorted, and terminated as shown in Figure 11. The TDR plot, with far-end terminated, shows an impedance of 50.57 Ohms, when measured at the initial peak. Then it takes an immediate dip to approximately 50 Ohms before continuing with a slow monotonic rise with some ripples. If the DUT was a uniform trace, with connector discontinuity de-embedded, we would not see the initial peak followed by the dip.  This signature strongly suggests that the DUT is not uniform and thus it is very difficult to determine the actual characteristic impedance using IPC-TM-650 test method alone.\n\nBut only after taking 2-port shunt measurements can we confirm the true characteristic impedance. As shown, Zoavg is 50.68 Ohms where the red and blue curves cross at 122.5 MHz, and confirms the true measurement point in the TDR plot is the initial peak. Both are about 1 Ohm higher compared with 2-D field solver results in Figure 10.\n\nIf the length of the transmission line simulated above is 6 in. and f0 =248.2 MHz, then TD = 1 ns and Dkeff = 3.92, using Equation 5 and Equation 6 respectively.", null, "Figure 11 Measured results from a CMP28 test platform design kit, courtesy of Wildriver Technology .\n\nBut wait a minute. Why is Dkeff is higher than what was used in the 2-D field solver in Figure 10?\n\nOne reason is due to process variation of the material and fabrication. The actual Dkeff is determined by the final thickness of dielectric and the roughness of the copper, which also increases inductance affecting TD . But the main reason is Dk is frequency dependent and the value used in the field solver was at 10 GHz, based on laminate supplier’s Dk/Df tables.\n\nSince TD, ultimately determines Dkeff, it does not represent the intrinsic property of the dielectric material. Because Dkeff varies with frequency, it was calculated at the first resonant null of 248.2 MHz, which is at a much lower frequency for Dk than the frequency originally used to select Dk in the field solver.\n\nAs can be seen in Figure 12, a simulated vs. measured 2-port shunt frequency plot, with far-end open and shorted, we get exactly the same information, compared to the traditional method used to validate characteristic impedance and Dkeff.\n\nIf we measure the 39th odd harmonic frequency (H) at 9.884GHz for the resonant null closest to 10GHz, equating to the value of Dk used in Polar Si9000 2D field solver, Dkeff can be calculated with Equation 7:\n\nEquation 7", null, "The bottom right plot of Figure 12, shows Dkeff simulated (blue) vs. measured (red). As we can see, the measured Dkeff at 248.7 MHz is 3.94; pretty much agreeing with our earlier calculation of 3.92 using Equation 6. Furthermore, when we compare Dkeff = 3.76 at 9.884 GHz, it agrees with our calculation for the 39th harmonic frequency from Equation 7. The reason there is still a slight difference in Dkeff is because the added delay due to inductance due to roughness was not factored into the simulated model.\n\nThe bottom left is a TDR plot that shows measured impedance (red) vs. simulated (blue) over time. The marker at the beginning of the initial dip (m6) represents the characteristic impedance with highest frequency harmonics included in the incident step edge of TDR waveform. The marker at the end (m16) represents the impedance at twice the TD with high frequency harmonics attenuated due to dispersion of the lossy dielectric and resistance of trace length.\n\nWhen we measure Zoavg_meas impedance of DUT at 9.884GHz, at the top plot of Figure 12, it agrees pretty well with the simulated and measured TDR plot at the initial step.", null, "Figure 12 Comparison of PI world 2-port shunt measurement results for transmission line characteristic impedance and Dkeff compared to traditional SI world measurement results. Top plot is the 2-port shunt simulated vs. DUT impedance measurements at the fundamental and 39th harmonic frequencies. Bottom left is beginning and end impedance measurements on TDR plot. Bottom right measuring equivalent Dkeff at fundamental and 39th harmonic frequencies.\n\n#### Summary and Conclusion\n\nSometimes, when SI and PI worlds collide, we get the best of both worlds. By borrowing a simple 2-port shunt impedance measuring technique from the PI world, we have another tool at our disposal to measure true characteristic impedance, TD, and effective Dk from a uniformly designed transmission line in the SI world. The advantage is, unlike a TDR measurement, measuring true characteristic impedance using 2-port shunt method is not influenced by resistive or dielectric losses.\n\n#### References\n\n1. L. Smith, S. Sandler, E. Bogatin, “Target Impedance Is Not Enough,” Signal Integrity Journal, Vol. 1, Issue 1, January 2019; URL: https://www.signalintegrityjournal.com/ext/resources/MEDIA-KIT-2019/January-2019-Print-Issue/SIJ-January-2019-Issue_eBook_-V2.pdf\n2. IPC-TM-650 Test methods Manual, Number 2.5.5.7, “Characteristic Impedance of Lines on Printed Boards by TDR”, Rev. A, March, 2004\n3. I. Novak, J. Millar, “Frequency-Domain Characterization of Power Distribution Networks,” Artech House, 685 Canton St., Norwood, MA, 02062, 2007." ]

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[ "#", null, "0\n\n## SQL語法\n\nA1表欄位結構同B1,且KEY為A11，B11\n\n### 1 個回答\n\n18\n\nUPDATE b.b1, a.a1 SET b.b1.b13=a.a1.a13,b.b1.b14=a.a1.a14 WHERE b.b1.b11=a.a1.a11\n\nMicrosoft SQL Server的寫法：\nUPDATE b.dbo.b1 SET b13=a.dbo.a1.a13,b14=a.dbo.a1.a14 FROM b.dbo.b1 inner join a.dbo.a1 ON a.dbo.a1.a11=b.dbo.b1.b11\n\nMB057=COST_TEST_A.dbo.INVMB.MB057\n\nFROM 子句中的物件 \"COST_TEST_A.dbo.INVMB\" 和 \"Leader.dbo.INVMB\" 具有相同的公開名稱。請使用相互關聯名稱加以區別。\n\nUPDATE L SET L.MB057=A.MB057 FROM Leader.dbo.INVMB L INNER JOIN COST_TEST_A.dbo.INVMB A ON L.MB001=A.MB001 WHERE L.MB001='4602100504500550'" ]

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[ "# Sin(x)=5/13 and x is in quadrant 1: find sin 2x, cos 2x, and tan 2x.?\n\nI know this is trigonometric double angle formula, but beyond that I’m stumped.\n\n• Identities needed:\n\n1) sin 2x = 2 sin x cos x\n\n2) cos 2x = 2cos^2 x -1\n\n3) cos x = √1-sin^2 x\n\n4) tan x = sin x / cos x\n\nsince sin x = 5/13, using identity (3) gives:\n\ncos x = √(1-25/169) = 12/13\n\nUsing identity (2), it can be found that:\n\n>>>cos 2x = 2*(12/13)^2 -1\n\nusing identity (1):\n\n>>>sin 2x = 2* 5/13 * 12/13 = 120/169\n\nusing identity (4):\n\n>>>tan 2x = [120/169] / [2*(12/13)^2 -1]\n\n• If sin x = 5/13 then cos x= 12/13\n\nNow, just apply the formulae and substitute the values of Sin x and Cos x\n\nSin 2x = 2*Sin x*Cos x= 120/169\n\nCos 2x = Cos^2 x – Sin^2 x = 144/169 – 25/169 =119/169\n\nTan 2x = Sin 2x/Cos 2x = 120/119.\n\n• cos x = 12/13\n\nsin 2x = 2 sin x cos x = 2 x 5/13 x 12/13 = 120/169\n\ncos 2x = 2 cos ² x – 1 = 119/169\n\ntan 2x = 120/119\n\n• You’ll also need cos(x), which you can get by using sin^2(x) + cos^2(x) = 1. Solve for cos(x). You’ll have a choice of a positive or negative answer. The info that it’s in quadrant 1 tells you whether the cosine should be positive or negative.\n\nOnce you have those, plug them into the formulas for sin(2x) and cos(2x), which are in terms of sin(x) and cos(x).\n\nAnd then tan(2x) = sin(2x)/cos(2x)." ]

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[ "July 14, 2020", null, "### Trading with Alpari: currency pairs, spot metals, and CFDs\n\nHow this formula works. The formula in this example converts amounts in USD to other currencies using currency codes. Available currencies and exact conversion rates can be adjusted by editing the values in the table on the right. The core of this formula is the VLOOKUP function, configured like this: =", null, "### FOREX Pip Calculation | Profit and Loss - P/L Calculation\n\nForex Gain Formula Trading System was designed to be very simple and at the same time very powerful. And unlike most trading systems, the system is checked for prolonged testing and proved profitable even in the worst market conditions.", null, "### How to Calculate the Perfect Forex Position Size\n\nMoney › Forex How to Calculate Leverage, Margin, and Pip Values in Forex. Although most trading platforms calculate profits and losses, used margin and useable margin, and account totals, it helps to understand how these things are calculated so that you can plan transactions and can determine what your potential profit or loss could be.", null, "### How to Calculate Leverage, Margin, and Pip Values in Forex\n\nFinancing fees for forex trades Find out how we calculate our financing charges, so you can better understand the cost/credit and other associated potential charges when you trade with us.", null, "### Use a formula in a Word or Outlook table - Office Support\n\nHow to Calculate Risk in Forex. A common question that I see in Forex forums is \"How do I calculate my risk in Forex trading?\" Then usually, someone goes into a big long calculation that factors in leverage, price per pip and any other random information that they want to include.", null, "### Trader's calculator - FBS - online broker on the Forex market\n\nMargin Pip Calculator Use our pip and margin calculator to aid with your decision-making while trading forex. Maximum leverage and available trade size varies by product. If you see a tool tip next to the leverage data, it is showing the max leverage for that product. FOREX.com is a registered FCM and RFED with the CFTC and member of the", null, "### MT4 Position Size Calculator Excel Spreadsheets @ Forex\n\n2019/06/25 · How to Calculate an Exchange Rate using U.S. dollars use the following formula: 1/exchange rate. currency it takes to buy one unit of the first currency. From there you can calculate …", null, "### Forex Calculators - Margin, Lot Size, Pip Value, and More\n\n2014/12/09 · How to Calculate Pips in JPY Currency Pairs. In the trading platform you will also find JPY pairs and crosses. One pip is these currency pairs and crosses is not 0.0001 but 0.01, the third decimal point. The formula to calculate the value of the pip is the …", null, "### ROI Formula, Calculation, and Examples of Return on Investment\n\nWhile exchange rate quotes are relatively easy to find, reading and making calculations based on them can be a little more challenging. Investors can use many different online resources to help calculate exchanges rates on the spot or familiarize themselves with the basic mathematics needed to calculate exchanges rates by hand.", null, "### Add a calculated field to a table - Access\n\nThe Position Size Calculator will calculate the required position size based on your currency pair, risk level (either in terms of percentage or money) and the stop loss in pips.", null, "### Position Size Calculator, Forex Position Size Calculator\n\nFull currency converter. Has a database of historical values, and also allows bank commissions in the calculation.", null, "### Margin Pip Calculator | FOREX.com\n\nUsually, the forex trading account is funded in US dollars. So if the quote currency is not the dollar, the pip value will be multiplied by the exchange rate for the quote currency against the US dollar. What information do we need to make forex position size calculator formula? Account Currency: USD Account Balance: \\$5000 for example", null, "### HOW TO CALCULATE PIPS, PROFIT & PIP VALUE IN FOREX\n\nFOREX.com is a trading name of GAIN Global Markets Inc. which is authorized and regulated by the Cayman Islands Monetary Authority under the Securities Investment Business Law of the Cayman Islands (as revised) with License number 25033.", null, "### How to Determine Lot Size for Day Trading\n\n2011/06/13 · To calculate arbitrage in Forex, first find the current exchange rates for each of your currency pairs on your broker’s software or on websites that list current exchange rates. Next, convert your starting currency into your second, second to third, and then back into your starting currency.", null, "### Pip & Margin Calculator | Forex Calculator | FOREX.com\n\nBesides real time rates, your profit and loss is calculated on real time basis by the forex trading software and is displayed live online. Even though this is an important advantage in forex trading account but I strongly recommend that you must be aware about the methodology to calculate your profit and loss from forex trading.", null, "", null, "" ]

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[ "### Courses\n\n##### Last Updated:\n29/11/2019 - 15:23\n\n## IAM564 - Basic Algorithms and Programming\n\nCredit: 0(0-4); ECTS: 4.0\nInstructor(s): Consent of IAM\nPrerequisites: Consent of Instructor(s)\n\n#### Course Catalogue Description\n\nBasics of programming, introducing MATLAB, programming with MATLAB, basic algorithms and problem solving in Linear Algebra, Differential Equations, Optimization, and so an. Reporting and presenting problems and their solutions, introducing LATEX and/or Scientific Workplace, Typesetting text and mathematical formulae,graphing, making bibliography and index, packages and defining your own styles.\n\n#### Course Objectives\n\nThe aim of this course is to help students acquire basic programming techniques and various fundamental algorithms in applied sciences. Also in this course, students are hoped to learn both programming using MATLAB and reporting their work using LATEX/ ScientificWorkplace.\n\n#### Course Learning Outcomes\n\nAt the end of the course students should have a basic knowledge on programming their own algorithms and documenting them. Also, they are expected to be qualified in typesetting using Latex packages.\n\n#### Tentative (Weekly) Outline\n\nBasics of programming, introducing MATLAB, programming with MATLAB, basic algorithms and problem solving in Linear Algebra, Differential Equations, Optimization, and so an. Reporting and presenting problems and their solutions, introducing LATEX and/or Scientific Workplace, Typesetting text and mathematical formulae,graphing, making bibliography and index, packages and defining your own styles." ]

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[ "", null, "How to calculate exponention | Sololearn: Learn to code for FREE!\n\n0\n\n# How to calculate exponention\n\nDid you know that there are more bacteria cells in your body than cells that make up your body? Weird! A bacteria culture starts with 500 bacteria and doubles in size every hour. Which means, after 1 hour the number of bacteria is 1000, after 2 hours - 2000, and so on. Let’s calculate and output the number of bacteria that will be in the culture after 24 hours\n\n-1\n\nPRINT(500*2**24) BACTERIA DOUBLE EVERY HOURS SO = 500*2 ,AND THE IT IS HAPPEING FOR 24 HOUR S0=500*2**24 FINAL STEP=PRINT(500*2**24)\n\n+5\n\nExponentiation is explained in lesson 5 of the Python for Beginners course. Re-read the lesson\n\n+2\n\nPower calculation need is 2**24, =>2 power 24 here ** is 'power of' operator in python. hope it helps in complete task.\n\n+1\n\n+1\n\nYou can use ** operator, but be aware with its predence, exponent operator has right to left associativity" ]

[ null, "https://www.facebook.com/tr", null ]

[ "## Trigonometry (11th Edition) Clone\n\n$\\dfrac{\\sqrt3}{3}$\nConvert the angle measure to degrees to obtain: $=-\\frac{2\\pi}{3} \\cdot \\frac{180^o}{\\pi} = -2(60^o)=-120^o$ Thus, $\\cot{(-\\frac{2\\pi}{3})} = \\cot{(-120^o)}$ $-120^o$ is co-terminal with $-120^o+360^o=240^o$. $240^o$ is in Quadrant III so its reference angle is $=240^o-180^o=60^o$. Note that the cotangent function is positive in Quadrant III. From Section 2.1 (page 50) , we learned that: $\\cot{60^o} = \\dfrac{\\sqrt3}{3}$ This means that: $\\cot{(-\\frac{2\\pi}{3})} \\\\=\\cot{(-120^o)} \\\\=\\cot{60^o} \\\\= \\dfrac{\\sqrt3}{3}$" ]

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[ "# T-H Example\n\nThis example appears in the Accelerated Life Testing Data Analysis Reference book.\n\nThe following data were collected after testing twelve electronic devices at different temperature and humidity conditions:\n\nUsing ALTA, the following results were obtained:\n\n\\begin{align} \\widehat{\\beta }=\\ & 5.874395 \\\\ & & \\\\ \\widehat{A}=\\ & 0.000060 \\\\ & & \\\\ \\widehat{b}=\\ & 0.280599 \\\\ & & \\\\ \\widehat{\\phi}=\\ & 5630.329851 \\end{align}\\,\\!\n\nA probability plot for the entered data is shown next.\n\nNote that three lines are plotted because there are three combinations of stresses, namely, (398K, 0.4), (378K, 0.8) and (378K, 0.4).\n\nGiven the use stress levels, time estimates can be obtained for a specified probability. A Life vs. Stress plot can be obtained if one of the stresses is kept constant. For example, the following picture shows a Life vs. Temperature plot at a constant humidity of 0.4." ]

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[ "Note\n\n*TODO* Freshen up this old documentation\n\n# `io` - defines pytensor.function [TODO]#\n\n## Inputs#\n\nThe `inputs` argument to `pytensor.function` is a list, containing the `Variable` instances for which values will be specified at the time of the function call. But inputs can be more than just Variables. `In` instances let us attach properties to `Variables` to tell function more about how to use them.\n\nclass pytensor.compile.io.In(object)[source]#\n__init__(variable, name=None, value=None, update=None, mutable=False, strict=False, autoname=True, implicit=None)[source]#\n\n`variable`: a Variable instance. This will be assigned a value before running the function, not computed from its owner.\n\n`name`: Any type. (If `autoname_input==True`, defaults to `variable.name`). If `name` is a valid Python identifier, this input can be set by `kwarg`, and its value can be accessed by `self.<name>`. The default value is `None`.\n\n`value`: literal or `Container`. The initial/default value for this\n\ninput. If update is`` None``, this input acts just like an argument with a default value in Python. If update is not `None`, changes to this value will “stick around”, whether due to an update or a user’s explicit action.\n\n`update`: Variable instance. This expression Variable will replace `value` after each function call. The default value is `None`, indicating that no update is to be done.\n\n`mutable`: Bool (requires value). If `True`, permit the compiled function to modify the Python object being used as the default value. The default value is `False`.\n\n`strict`: Bool (default: `False` ). `True` means that the value you pass for this input must have exactly the right type. Otherwise, it may be cast automatically to the proper type.\n\n`autoname`: Bool. If set to `True`, if `name` is `None` and the Variable has a name, it will be taken as the input’s name. If autoname is set to `False`, the name is the exact value passed as the name parameter (possibly `None`).\n\n`implicit`: Bool or `None` (default: `None`)\n\n`True`: This input is implicit in the sense that the user is not allowed to provide a value for it. Requires `value` to be set.\n\n`False`: The user can provide a value for this input. Be careful when `value` is a container, because providing an input value will overwrite the content of this container.\n\n`None`: Automatically choose between `True` or `False` depending on the situation. It will be set to `False` in all cases except if `value` is a container (so that there is less risk of accidentally overwriting its content without being aware of it).\n\n### Value: initial and default values#\n\nA non-None `value` argument makes an In() instance an optional parameter of the compiled function. For example, in the following code we are defining an arity-2 function `inc`.\n\n```>>> import pytensor.tensor as at\n>>> from pytensor import function\n>>> from pytensor.compile.io import In\n>>> u, x, s = at.scalars('u', 'x', 's')\n>>> inc = function([u, In(x, value=3), In(s, update=(s+x*u), value=10.0)], [])\n```\n\nSince we provided a `value` for `s` and `x`, we can call it with just a value for `u` like this:\n\n```>>> inc(5) # update s with 10+3*5\n[]\n>>> print(inc[s])\n25.0\n```\n\nThe effect of this call is to increment the storage associated to `s` in `inc` by 15.\n\nIf we pass two arguments to `inc`, then we override the value associated to `x`, but only for this one function call.\n\n```>>> inc(3, 4) # update s with 25 + 3*4\n[]\n>>> print(inc[s])\n37.0\n>>> print(inc[x]) # the override value of 4 was only temporary\n3.0\n```\n\nIf we pass three arguments to `inc`, then we override the value associated with `x` and `u` and `s`. Since `s`’s value is updated on every call, the old value of `s` will be ignored and then replaced.\n\n```>>> inc(3, 4, 7) # update s with 7 + 3*4\n[]\n>>> print(inc[s])\n19.0\n```\n\nWe can also assign to `inc[s]` directly:\n\n```>>> inc[s] = 10\n>>> inc[s]\narray(10.0)\n```\n\n### Input Argument Restrictions#\n\nThe following restrictions apply to the inputs to `pytensor.function`:\n\n• Every input list element must be a valid `In` instance, or must be upgradable to a valid `In` instance. See the shortcut rules below.\n\n• The same restrictions apply as in Python function definitions: default arguments and keyword arguments must come at the end of the list. Un-named mandatory arguments must come at the beginning of the list.\n\n• Names have to be unique within an input list. If multiple inputs have the same name, then the function will raise an exception. [*Which exception?]\n\n• Two `In` instances may not name the same Variable. I.e. you cannot give the same parameter multiple times.\n\nIf no name is specified explicitly for an In instance, then its name will be taken from the Variable’s name. Note that this feature can cause harmless-looking input lists to not satisfy the two conditions above. In such cases, Inputs should be named explicitly to avoid problems such as duplicate names, and named arguments preceding unnamed ones. This automatic naming feature can be disabled by instantiating an In instance explicitly with the `autoname` flag set to False.\n\nFor each input, `pytensor.function` will create a `Container` if `value` was not already a `Container` (or if `implicit` was `False`). At the time of a function call, each of these containers must be filled with a value. Each input (but especially ones with a default value or an update expression) may have a value between calls. The function interface defines a way to get at both the current value associated with an input, as well as the container which will contain all future values:\n\n• The `value` property accesses the current values. It is both readable and writable, but assignments (writes) may be implemented by an internal copy and/or casts.\n\n• The `container` property accesses the corresponding container. This property accesses is a read-only dictionary-like interface. It is useful for fetching the container associated with a particular input to share containers between functions, or to have a sort of pointer to an always up-to-date value.\n\nBoth `value` and `container` properties provide dictionary-like access based on three types of keys:\n\n• integer keys: you can look up a value/container by its position in the input list;\n\n• name keys: you can look up a value/container by its name;\n\n• Variable keys: you can look up a value/container by the Variable it corresponds to.\n\nIn addition to these access mechanisms, there is an even more convenient method to access values by indexing a Function directly by typing `fn[<name>]`, as in the examples above.\n\nTo show some examples of these access methods…\n\n```>>> from pytensor import tensor as at, function\n>>> a, b, c = at.scalars('xys') # set the internal names of graph nodes\n>>> # Note that the name of c is 's', not 'c'!\n>>> fn = function([a, b, ((c, c+a+b), 10.0)], [])\n```\n```>>> # the value associated with c is accessible in 3 ways\n>>> fn['s'] is fn.value[c]\nTrue\n>>> fn['s'] is fn.container[c].value\nTrue\n```\n```>>> fn['s']\narray(10.0)\n>>> fn(1, 2)\n[]\n>>> fn['s']\narray(13.0)\n>>> fn['s'] = 99.0\n>>> fn(1, 0)\n[]\n>>> fn['s']\narray(100.0)\n>>> fn.value[c] = 99.0\n>>> fn(1,0)\n[]\n>>> fn['s']\narray(100.0)\n>>> fn['s'] == fn.value[c]\nTrue\n>>> fn['s'] == fn.container[c].value\nTrue\n```\n\n### Input Shortcuts#\n\nEvery element of the inputs list will be upgraded to an In instance if necessary.\n\n• a Variable instance `r` will be upgraded like `In(r)`\n\n• a tuple `(name, r)` will be `In(r, name=name)`\n\n• a tuple `(r, val)` will be `In(r, value=value, autoname=True)`\n\n• a tuple `((r,up), val)` will be `In(r, value=value, update=up, autoname=True)`\n\n• a tuple `(name, r, val)` will be `In(r, name=name, value=value)`\n\n• a tuple `(name, (r,up), val)` will be `In(r, name=name, value=val, update=up, autoname=True)`\n\nExample:\n\n```>>> import pytensor\n>>> from pytensor import tensor as at\n>>> from pytensor.compile.io import In\n>>> x = at.scalar()\n>>> y = at.scalar('y')\n>>> z = at.scalar('z')\n>>> w = at.scalar('w')\n```\n```>>> fn = pytensor.function(inputs=[x, y, In(z, value=42), ((w, w+x), 0)],\n... outputs=x + y + z)\n>>> # the first two arguments are required and the last two are\n>>> # optional and initialized to 42 and 0, respectively.\n>>> # The last argument, w, is updated with w + x each time the\n>>> # function is called.\n```\n```>>> fn(1) # illegal because there are two required arguments\nTraceback (most recent call last):\n...\nTypeError: Missing required input: y\n>>> fn(1, 2) # legal, z is 42, w goes 0 -> 1 (because w <- w + x)\narray(45.0)\n>>> fn(1, y=2) # legal, z is 42, w goes 1 -> 2\narray(45.0)\n>>> fn(x=1, y=2) # illegal because x was not named\nTraceback (most recent call last):\n...\nTypeError: Unknown input or state: x. The function has 3 named inputs (y, z, w), and 1 unnamed input which thus cannot be accessed through keyword argument (use 'name=...' in a variable's constructor to give it a name).\n>>> fn(1, 2, 3) # legal, z is 3, w goes 2 -> 3\narray(6.0)\n>>> fn(1, z=3, y=2) # legal, z is 3, w goes 3 -> 4\narray(6.0)\n>>> fn(1, 2, w=400) # legal, z is 42 again, w goes 400 -> 401\narray(45.0)\n>>> fn(1, 2) # legal, z is 42, w goes 401 -> 402\narray(45.0)\n```\n\nIn the example above, `z` has value 42 when no value is explicitly given. This default value is potentially used at every function invocation, because `z` has no `update` or storage associated with it.\n\n## Outputs#\n\nThe `outputs` argument to function can be one of\n\n• `None`, or\n\n• a Variable or `Out` instance, or\n\n• a list of Variables or `Out` instances.\n\nAn `Out` instance is a structure that lets us attach options to individual output `Variable` instances, similarly to how `In` lets us attach options to individual input `Variable` instances.\n\nOut(variable, borrow=False) returns an `Out` instance:\n\n• `borrow`\n\nIf `True`, a reference to function’s internal storage is OK. A value returned for this output might be clobbered by running the function again, but the function might be faster.\n\nDefault: `False`\n\nIf a single `Variable` or `Out` instance is given as argument, then the compiled function will return a single value.\n\nIf a list of `Variable` or `Out` instances is given as argument, then the compiled function will return a list of their values.\n\n```>>> import numpy\n>>> from pytensor.compile.io import Out\n>>> x, y, s = at.matrices('xys')\n```\n```>>> # print a list of 2 ndarrays\n>>> fn1 = pytensor.function([x], [x+x, Out((x+x).T, borrow=True)])\n>>> fn1(numpy.asarray([[1,0],[0,1]]))\n[array([[ 2., 0.],\n[ 0., 2.]]), array([[ 2., 0.],\n[ 0., 2.]])]\n```\n```>>> # print a list of 1 ndarray\n>>> fn2 = pytensor.function([x], [x+x])\n>>> fn2(numpy.asarray([[1,0],[0,1]]))\n[array([[ 2., 0.],\n[ 0., 2.]])]\n```\n```>>> # print an ndarray\n>>> fn3 = pytensor.function([x], outputs=x+x)\n>>> fn3(numpy.asarray([[1,0],[0,1]]))\narray([[ 2., 0.],\n[ 0., 2.]])\n```" ]

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[ "# averagePooling1dLayer\n\n1-D average pooling layer\n\nSince R2021b\n\n## Description\n\nA 1-D average pooling layer performs downsampling by dividing the input into 1-D pooling regions, then computing the average of each region.\n\nThe dimension that the layer pools over depends on the layer input:\n\n• For time series and vector sequence input (data with three dimensions corresponding to the `\"C\"` (channel), `\"B\"` (batch), and `\"T\"` (time) dimensions), the layer pools over the `\"T\"` (time) dimension.\n\n• For 1-D image input (data with three dimensions corresponding to the `\"S\"` (spatial), `\"C\"` (channel), and `\"B\"` (batch) dimensions), the layer pools over the `\"S\"` (spatial) dimension.\n\n• For 1-D image sequence input (data with four dimensions corresponding to the `\"S\"` (spatial), `\"C\"` (channel), `\"B\"` (batch), and `\"T\"` (time) dimensions), the layer pools over the `\"S\"` (spatial) dimension.\n\n## Creation\n\n### Syntax\n\n``layer = averagePooling1dLayer(poolSize)``\n``layer = averagePooling1dLayer(poolSize,Name=Value)``\n\n### Description\n\nexample\n\n````layer = averagePooling1dLayer(poolSize)` creates a 1-D average pooling layer and sets the `PoolSize` property.```\n\nexample\n\n````layer = averagePooling1dLayer(poolSize,Name=Value)` also specifies the padding or sets the `Stride` and Name properties using one or more optional name-value arguments. For example, `averagePooling1dLayer(3,Padding=1,Stride=2)` creates a 1-D average pooling layer with a pool size of `3`, a stride of `2`, and padding of size `1` on both the left and right of the input.```\n\n### Input Arguments\n\nexpand all\n\nName-Value Arguments\n\nSpecify optional pairs of arguments as `Name1=Value1,...,NameN=ValueN`, where `Name` is the argument name and `Value` is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.\n\nExample: `averagePooling1dLayer(3,Padding=1)` creates a 1-D average pooling layer with a pool size of 3 and padding of size 1 on the left and right of the layer input.\n\nPadding to apply to the input, specified as one of the following:\n\n• `\"same\"` — Apply padding such that the output size is `ceil(inputSize/stride)`, where `inputSize` is the length of the input. When `Stride` is `1`, the output is the same size as the input.\n\n• Nonnegative integer `sz` — Add padding of size `sz` to both ends of the input.\n\n• Vector `[l r]` of nonnegative integers — Add padding of size `l` to the left and `r` to the right of the input.\n\nExample: `Padding=[2 1]` adds padding of size 2 to the left and size 1 to the right.\n\nData Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64` | `char` | `string`\n\n## Properties\n\nexpand all\n\n### Average Pooling\n\nWidth of the pooling regions, specified as a positive integer.\n\nThe width of the pooling regions `PoolSize` must be greater than or equal to the padding dimensions `PaddingSize`.\n\nData Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64`\n\nStep size for traversing the input, specified as a positive integer.\n\nData Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64`\n\nSize of padding to apply to each side of the input, specified as a vector ```[l r]``` of two nonnegative integers, where `l` is the padding applied to the left and `r` is the padding applied to the right.\n\nWhen you create a layer, use the `Padding` name-value argument to specify the padding size.\n\nData Types: `double`\n\nMethod to determine padding size, specified as one of the following:\n\n• `'manual'` – Pad using the integer or vector specified by `Padding`.\n\n• `'same'` – Apply padding such that the output size is `ceil(inputSize/Stride)`, where `inputSize` is the length of the input. When `Stride` is `1`, the output is the same as the input.\n\nTo specify the layer padding, use the `Padding` name-value argument.\n\nData Types: `char`\n\nValue used to pad input, specified as `0` or `\"mean\"`.\n\nWhen you use the `Padding` option to add padding to the input, the value of the padding applied can be one of the following:\n\n• `0` — Input is padded with zeros at the positions specified by the `Padding` property. The padded areas are included in the calculation of the average value of the pooling regions along the edges.\n\n• `\"mean\"` — Input is padded with the mean of the pooling region at the positions specified by the `Padding` option. The padded areas are effectively excluded from the calculation of the average value of each pooling region.\n\n### Layer\n\nLayer name, specified as a character vector or a string scalar. For `Layer` array input, the `trainNetwork`, `assembleNetwork`, `layerGraph`, and `dlnetwork` functions automatically assign names to layers with the name `''`.\n\nData Types: `char` | `string`\n\nNumber of inputs of the layer. This layer accepts a single input only.\n\nData Types: `double`\n\nInput names of the layer. This layer accepts a single input only.\n\nData Types: `cell`\n\nNumber of outputs of the layer. This layer has a single output only.\n\nData Types: `double`\n\nOutput names of the layer. This layer has a single output only.\n\nData Types: `cell`\n\n## Examples\n\ncollapse all\n\nCreate a 1-D average pooling layer with a pool size of 3.\n\n`layer = averagePooling1dLayer(3)`\n```layer = AveragePooling1DLayer with properties: Name: '' Hyperparameters PoolSize: 3 Stride: 1 PaddingMode: 'manual' PaddingSize: [0 0] PaddingValue: 0 ```\n\nInclude a 1-D average pooling layer in a layer array.\n\n```layers = [ sequenceInputLayer(12,MinLength=40) convolution1dLayer(11,96) reluLayer averagePooling1dLayer(3) convolution1dLayer(11,96) reluLayer globalMaxPooling1dLayer fullyConnectedLayer(10) softmaxLayer classificationLayer]```\n```layers = 10x1 Layer array with layers: 1 '' Sequence Input Sequence input with 12 dimensions 2 '' 1-D Convolution 96 11 convolutions with stride 1 and padding [0 0] 3 '' ReLU ReLU 4 '' 1-D Average Pooling average pooling with pool size 3, stride 1, and padding [0 0] 5 '' 1-D Convolution 96 11 convolutions with stride 1 and padding [0 0] 6 '' ReLU ReLU 7 '' 1-D Global Max Pooling 1-D global max pooling 8 '' Fully Connected 10 fully connected layer 9 '' Softmax softmax 10 '' Classification Output crossentropyex ```\n\nexpand all\n\n## Version History\n\nIntroduced in R2021b" ]

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[ "# Texas Go Math Grade 4 Lesson 11.4 Answer Key Multi-Step Division Problems\n\nRefer to our Texas Go Math Grade 4 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 4 Lesson 11.4 Answer Key Multi-Step Division Problems.\n\n## Texas Go Math Grade 4 Lesson 11.4 Answer Key Multi-Step Division Problems\n\nEssential Question\n\nHow can you use the strategy draw a diagram to solve multi-step division problems?\nIn solving multi-step division problems, the total to be found first,\nThen the total should be divided in to the required equal parts.\n\nUnlock the Problem", null, "Lucia and her dad will prepare corn for a community picnic. There are 3 bags of corn. Each bag holds 32 ears of corn. When the corn is cooked, they want to divide the corn equally among B serving plates. How many ears of corn should they put on each of 8 serving plates?\n12 ears of corn.\nExplanation:\nThere are 3 bags of corn.\nEach bag holds 32 ears of corn.\n3 x 32 = 96\nWhen the corn is cooked, they want to divide the corn equally among 8 serving plates.\nTotal ears of corn should they put on each of 8 serving plates\n96÷8 = 12\n\nWhat do I need to find?\nI need to find the number of ________________ that will go on each plate.\nEar corns\n\nWhat information am I given?\n______________ bags with ______________ ears in each bag. The total ears arc divided equally into ______________ groups.\n3 bags with 32 ears in each bag.\n8 groups.\n\nPlan\n\nWhat is my plan or strategy?\n\nI will make a strip diagram for each step and use equations. Then I will ______________ to find the total and ___________ to find the number for each plate.", null, "I will multiply 32 x3  to find the total and divide 96 to find the number for each plate.\n\nSolve\n\nI can draw strip diagrams and use equations and then decide how to find how many ears of corn should go on a plate.\n\nFirst, I will find the total number of ears of corn.", null, "32 × __________ = e\n___________ = e\nThen I will find how many ears of corn should go on each plate.", null, "96 ÷ __________ = c\n___________ = c", null, "96 ÷ 8 = c\n12 = c\n\nQuestion 1.\nHow many ears of corn should go on each plate?\n12 ears of corn\n\nQuestion 2.\n32 × 3 = e\n96 = e\n96 ÷ 8 = c\n12 = c\nExplanation:\nDivision is opposite to multiplication and multiplication is opposite to division vice-versa.\n\nTry Another Problem\n\nThere are 8 dinner rolls in a package. How many packages will be needed to feed 64 people if each person has 2 dinner rolls?", null, "What do I need to find?\nTotal packages will be needed to feed 64 people if each person has 2 dinner rolls.\n\nWhat information am I given?\nEach package contains 8 dinner rolls.\nTotal number of people to feed 64.\n\nPlan\n\nWhat is my plan or strategy?\nI will make a strip diagram for each step and use equations.\n\nSolve\n64 x 2 = 128 dinner rolls required\n128 ÷ 8 = p\n16 = p\nQuestion 3.\nHow many packages of rolls will he needed?\n16 packages of rolls needed for 64 people for dinner\n\nQuestion 4.\nStrip Drawing helps to break the whole into small parts to slove.", null, "Math Talk\n\nMathematical Processes\nDescribe another method you could have used to solve the problem.\nEquation method\nExplanation:\n64 x 2 =128\n128 ÷ 8 = 16\n\nShare and Show\n\nQuestion 1.\nA firehouse pantry has 52 cans of vegetables and 74 cans of soup. Each shelf holds 9 cans. What is the the least number of shelves needed for all the cans?\n\nFirst, draw a strip diagram for the total number of cans.\nNext, add to find the total number of cans.\nThen, draw a strip diagram to show the number of shelves needed.\nFinally, divide to find the number of shelves needed.", null, "So, _________ Shelves are needed to hold all of the cans.\n14 shelves are needed to hold all of the cans.\nExplanation:\nA firehouse pantry has 52 cans of vegetables and 74 cans of soup.\nEach shelf holds 9 cans.\nThe least number of shelves needed for all the cans\n(52 + 74) ÷ 9 = n\n126 ÷ 9 = n\n14 = n\n\nQuestion 2.\nH.O.T. Multi-Step What if 18 cans fit on a shelf? What is the least number of shelves needed? Describe how your answer would be different.\n7 shelves are needed to hold all of the cans\nExplanation:\nA firehouse pantry has 52 cans of vegetables and 74 cans of soup.\nEach shelf holds 18 cans.\nThe least number of shelves needed for all the cans\n(52 + 74) ÷ 18 = n\n126 ÷ 18 = n\n7 = n\n\nProblem-Solving\n\nQuestion 3.", null, "H.O.T. Multi-Step Ms. Johnson bought 6 bags of balloons. Each hag has 25 balloons. She fills all the balloons and puts 5 balloons in each bunch. How many bunches can she make?\n30 bunches.\nExplanation:\nMs. Johnson bought 6 bags of balloons.\nEach bag has 25 balloons.\nShe fills all the balloons and puts 5 balloons in each bunch.\nTotal bunches she can make\n(6 x 25) ÷ 5 = n\n150 ÷ 5 = n\n30 = n\n\nQuestion 4.\nBasketball jerseys are shipped in packages of 6. How many packages of jerseys are needed for 12 players if each player gets 4 jerseys?\n(A) 3 packages\n(B) 2 packages\n(C) 8 packages\n(D) 48 packages\nOption(B)\nExplanation:\nBasketball jerseys are shipped in packages of 6,\nif each player gets 4 jerseys.\nTotal packages of jerseys are needed for 12 players, if each player gets 4 jerseys\n(6 x 4) ÷ 12 = n\n24 ÷ 12 = n\n2 = n\n\nQuestion 5.\nRobin and her grandmother bake muffins. Each batch of hatter makes 36 mini muffins. They make 4 batches. They divide the muffins equally into bags of 3 muffins for a bake sale. How many bags of 3 muffins do they have?\n(A) 9 bags\n(B) 48 bags\n(C) 12 bags\n(D) 3 bags\nOption(B)\nExplanation:\nRobin and her grandmother bake muffins.\nEach batch of batter makes 36 mini muffins.\nThey make 4 batches.\nThey divide the muffins equally into bags of 3 muffins for a bake sale.\nTotal bags of 3 muffins they have\n(36 x 4) ÷ 3 = n\n144 ÷ 3 = n\n48 = n\n\nQuestion 6.\nMulti-Step The fourth graders at Sunshine School go to the Museum of Nature and Science. The school pays $671 for the trip. The adult tickets are$10 each and the student tickets are $7 each. There are 9 adults going on the trip. How many students go on the trip? (A) 74 students (B) 86 students (C) 95 students (D) 83 students Answer: Option(D) Explanation: The school pays$671 for the trip.\nThe adult tickets are $10 each and the student tickets are$7 each.\nThere are 9 adults going on the trip.\nTotal students go on the trip\n671 – (10 x 9) ÷ 7  = n\n90 – 671 ÷ 7= n\n581 ÷ 7 = n\n83 = n\n\nTEXAS Test Prep\n\nQuestion 7.\nBen collected 43 cans and some bottles. He received 5 for each can or bottle. If Ben received a total of $4.95, how many bottles did he collect? (A) 56 (B) 99 (C) 560 (D) 990 Answer: Option(A) Explanation: Ben collected 43 cans and some bottles. He received 5 for each can or bottle. If Ben received a total of$4.95,\nNumber of bottles he collect\n(43 + x) x 0.0 5 = 2.15 + 0.05x\n4.95 = 2.15 + 0.05x\n4.95 – 2.15 = 0.05x\n2.80 = 0.05x\n2.80 ÷ 0.05 = x\nx = 56\n\n#### Texas Go Math Grade 4 Lesson 11.4 Homework and Practice Answer Key\n\nProblem Solving\n\nQuestion 1.\nMarco bought 2 bottles of juice. Each bottle is 48 ounces. How many 8-ounce glasses of juice can Marco pour from the two bottles?\n12 glasses.\nExplanation:\n48 + 48 = 96 ounces\n96 ÷ 8 = 12 glasses\n\na. Draw a strip diagram for the number of ounces of juice in the two bottles.", null, "b. Write an equation to find the total number of ounces of juice in the two bottles.\nn = 2 x 48 = 96 ounces\n\nc. Draw a strip diagram to show the number of 8-ounce glasses of juice that can be poured.", null, "d. Write an equation to find the number of glasses of juice.\n\nMarco can pour ________ glasses of juice.\n12 glasses.\nExplanation:\nx = 96 ÷ 8 = 12 glasses\nMarco can pour 12 glasses of juice\n\nQuestion 2.\nDescribe another method you could have used to solve the problem.\nAlgebraic equation method\nn=48 x 2 = 96\nx = 96 ÷ 8 = 12\n\nQuestion 3.\nWhat if Marco poured 10-ounce glasses of juice? What is the greatest number of full glasses of juice he could have poured? Explain.\nx = 96 ÷ 10 = 9.6\n\nLesson Check\n\nQuestion 4.\nMulti-Step Orlando has a bag of 37 apples and a bag of 29 apples. He can hake 6 apples in a pan. How many pans of apples can Orlando make?\n(A) 66\n(B) 33\n(C) 11\n(D) 22\nOption(C)\nExplanation:\nOrlando has a bag of 37 apples and a bag of 29 apples.\nHe can bake 6 apples in a pan.\nTotal pans of apples Orlando can make\n(37 + 29) ÷ 6 = n\n66 ÷ 6 = n\n11 = n\n\nQuestion 5.\nMulti-Step Anna has 5 bunches of flowers with 12 flowers in each bunch. She has 4 bunches of flowers with 10 flowers in each bunch. How many vases can Anna fill if she puts 10 flowers in each vase?\n(A) 10\n(B) 100\n(C) 9\n(D) 15\nOption(A)\nExplanation:\nAnna has 5 bunches of flowers with 12 flowers in each bunch.\nShe has 4 bunches of flowers with 10 flowers in each bunch.\nTotal vases Anna can fill if she puts 10 flowers in each vase\n(5 x 12) + (4 x 10) ÷ 10 = n\n60 + 40 ÷ 10 = n\n100 ÷ 10 = n\n10 = n\n\nQuestion 6.\nMulti-Step Five friends are going to share the cost of two gifts. One gift costs $39 and the other gift costs$26. What is each person’s share of the cost?\n(A) $7 (B)$15\n(C) $18 (D)$13\nOption(D)\nExplanation:\nFive friends are going to share the cost of two gifts.\nOne gift costs $39 and the other gift costs$26.\nEach person’s share of the cost\n39 + 26 ÷ 5 = n\n65 ÷ 5 = n\n13 = n\n\nQuestion 7.\nMulti-Step There are 14 chairs in each of 6 rows. There are 18 chairs in each of 4 rows. How many rows of 13 chairs can be made from all of the chairs?\n(A) 13\n(B) 12\n(C) 14\n(D) 18\nOption(B)\nExplanation:\nThere are 14 chairs in each of 6 rows.\nThere are 18 chairs in each of 4 rows.\nTotal rows of 13 chairs can be made from all of the chairs\n(14 x 6) + (18 x 4) ÷ 13 = n\n(84 + 72 ) ÷ 13 = n\n156 ÷ 13 = n\n12 = n\n\nQuestion 8.\nMulti-Step Justin collected 26 shells, Amy collected 31 shells. Jose collected 21 shells, If they share all of the shells equally, how many shells will each person get?\n(A) 24\n(B) 78\n(C) 26\n(D) 19\nOption(C)\nExplanation:\nJustin collected 26 shells,\nAmy collected 31 shells.\nJose collected 21 shells,\nIf they share all of the shells equally,\nNumber of shells will each person get\n(26 + 31 + 21) ÷ 3 = n\n78 ÷ 3 = n\n26 = n\n\nQuestion 9.\nMulti-Step Taylor has 2 packages of 36 tacks each and 16 tacks. How many garage sale posters can she put up if she uses 4 tacks for each poster?\n(A) 13\n(B) 22\n(C) 17\n(D) 21" ]

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[ "# New inequalities for operator convex functions\n\n## Abstract\n\nThe aim of this paper is to present some new inequalities of Hermite-Hadamard type inequalities for operator convex functions. In this paper, we use elementary operations and give some inequalities related to the Hermite-Hadamard type. We conclude that the results given in this work are the generalization of the recent results.\n\nMSC:26D15, 47A63.\n\n## 1 Introduction\n\nLet $f:\\left[a,b\\right]⟶\\mathbb{R}$ be a convex function, then the inequality\n\n$f\\left(\\frac{a+b}{2}\\right)\\le \\frac{1}{b-a}{\\int }_{a}^{b}f\\left(x\\right)\\phantom{\\rule{0.2em}{0ex}}dx\\le \\frac{f\\left(a\\right)+f\\left(b\\right)}{2},\\phantom{\\rule{1em}{0ex}}a,b\\in \\mathbb{R},$\n(1)\n\nLet X be a vector space, $x,y\\in X$, $x\\ne y$ and $\\left[x,y\\right]=\\left\\{\\left(1-t\\right)x+ty,t\\in \\left[0,1\\right]\\right\\}$. We consider the function $f:\\left[x,y\\right]⟶\\mathbb{R}$ and the associated function\n\n$g\\left(x,y\\right):\\left[0,1\\right]⟶\\mathbb{R},\\phantom{\\rule{2em}{0ex}}g\\left(x,y\\right)\\left(t\\right):=f\\left[\\left(1-t\\right)x+ty\\right],\\phantom{\\rule{1em}{0ex}}t\\in \\left[0,1\\right].$\n\nNote that f is convex on $\\left[x,y\\right]$ if and only if $g\\left(x,y\\right)$ is convex on $\\left[0,1\\right]$.\n\nFor any convex function defined on a segment $\\left[x,y\\right]\\subset X$, we have the Hermite-Hadamard integral inequality\n\n$f\\left(\\frac{x+y}{2}\\right)\\le {\\int }_{0}^{1}f\\left[\\left(1-t\\right)x+ty\\right]\\phantom{\\rule{0.2em}{0ex}}dt\\le \\frac{f\\left(x\\right)+f\\left(y\\right)}{2},$\n(2)\n\nwhich can be derived from the classical Hermite-Hadamard inequality (1) for the convex function $g\\left(x,y\\right):\\left[0,1\\right]⟶\\mathbb{R}$.\n\nA real-valued continuous function f on an interval I is said to be operator convex (operator concave) if\n\n$f\\left(\\left(1-\\lambda \\right)A+\\lambda B\\right)\\le \\left(\\ge \\right)\\phantom{\\rule{0.25em}{0ex}}\\left(1-\\lambda \\right)f\\left(A\\right)+\\lambda f\\left(B\\right)$\n\nin the operator order for all $\\lambda \\in \\left[0,1\\right]$ and for every self-adjoint operator A and B on a Hilbert space H whose spectra are contained in I. Notice that a function f is operator concave if −f is operator convex.\n\nIn recent years, many authors have been interested in giving some refinements and extensions of the Hermite-Hadamard inequality in (1). For more about convex functions and the Hermite-Hadamard inequality, see .\n\nThe author in shows some new integral inequalities analogous to the well-known Hermite-Hadamard inequality. We give a general form of the second of these inequalities and show that the inequalities therein are satisfied for operator convex functions.\n\nThe author in shows some new Hermite-Hadamard inequalities similar to Pachpatte’s results.\n\nPachpatte (2003) gives some integral inequalities analogous to the well-known Hermite-Hadamard inequality by using a fairly elementary analysis in .\n\nTheorem 1 Let f and g be real-valued, nonnegative and convex functions on $\\left[a,b\\right]$. Then\n\n1. (i)\n$\\frac{1}{b-a}{\\int }_{a}^{b}f\\left(x\\right)g\\left(x\\right)\\phantom{\\rule{0.2em}{0ex}}dx\\le \\frac{1}{3}M\\left(a,b\\right)+\\frac{1}{6}N\\left(a,b\\right),$\n(3)\n2. (ii)\n$2f\\left(\\frac{a+b}{2}\\right)g\\left(\\frac{a+b}{2}\\right)\\le \\frac{1}{b-a}{\\int }_{a}^{b}f\\left(x\\right)g\\left(x\\right)\\phantom{\\rule{0.2em}{0ex}}dx+\\frac{1}{6}M\\left(a,b\\right)+\\frac{1}{3}N\\left(a,b\\right),$\n(4)\n\nwhere $M\\left(a,b\\right)=f\\left(a\\right)g\\left(a\\right)+f\\left(b\\right)g\\left(b\\right)$, $N\\left(a,b\\right)=f\\left(a\\right)g\\left(b\\right)+f\\left(b\\right)g\\left(a\\right)$.\n\nTunç (2012) gives an inequality for convex functions in as follows.\n\nTheorem 2 Let $f,g:\\left[a,b\\right]⟶\\mathbb{R}$ be two convex functions. Then", null, "(5)\n\nwhere $M\\left(a,b\\right)=f\\left(a\\right)g\\left(a\\right)+f\\left(b\\right)g\\left(b\\right)$, $N\\left(a,b\\right)=f\\left(a\\right)g\\left(b\\right)+f\\left(b\\right)g\\left(a\\right)$.\n\nTunç (2012) gives another inequality for convex functions in , too.\n\nTheorem 3 Let $f,g:\\left[a,b\\right]⟶\\mathbb{R}$ be two convex functions. Then\n\n$\\begin{array}{r}\\frac{1}{b-a}{\\int }_{a}^{b}\\left(f\\left(\\frac{a+b}{2}\\right)g\\left(x\\right)+g\\left(\\frac{a+b}{2}\\right)f\\left(x\\right)\\right)\\phantom{\\rule{0.2em}{0ex}}dx\\\\ \\phantom{\\rule{1em}{0ex}}\\le \\frac{1}{2\\left(b-a\\right)}{\\int }_{a}^{b}f\\left(x\\right)g\\left(x\\right)\\phantom{\\rule{0.2em}{0ex}}dx+\\frac{1}{12}M\\left(a,b\\right)+\\frac{1}{6}N\\left(a,b\\right)+f\\left(\\frac{a+b}{2}\\right)g\\left(\\frac{a+b}{2}\\right),\\end{array}$\n(6)\n\nwhere $M\\left(a,b\\right)=f\\left(a\\right)g\\left(a\\right)+f\\left(b\\right)g\\left(b\\right)$, $N\\left(a,b\\right)=f\\left(a\\right)g\\left(b\\right)+f\\left(b\\right)g\\left(a\\right)$.\n\nGhazanfari (2012) gives an inequality for two operator convex functions in as follows.\n\nTheorem 4 Let $f,g:I⟶\\mathbb{R}$ be operator convex functions on the interval I. Then for any self-adjoint operators A and B on a Hilbert space H with spectra in I, the inequality", null, "(7)\n\nholds for any $x\\in H$ with $\\parallel x\\parallel =1$, where", null, "For further inequalities, see .\n\n## 2 Main results\n\nIn this section, we give some new Hermite-Hadamard type inequalities for operator convex functions and mention the differences related to the results in recent papers. We emphasize the difference by giving an example.\n\nThe following theorem is a generalization for the product of two operator convex functions.\n\nTheorem 5 Let $f,g:I⟶\\mathbb{R}$ be operator convex, nonnegative functions on the interval I. Then for any self-adjoint operators A and B with spectra in I, we have the inequality", null, "(8)\n\nwhere", null, "(9)", null, "(10)\n\nand k is the number of steps.\n\nProof Let $x\\in H$, $\\parallel x\\parallel =1$ and A, B be two self-adjoint operators with spectra in I. Using the convexity of f, g and the change of variable $u=kt$, we have\n\n$\\begin{array}{rl}〈f\\left(\\left(1-t\\right)A+tB\\right)x,x〉& =〈f\\left(\\left(1-\\frac{u}{k}\\right)A+\\frac{u}{k}B\\right)x,x〉\\\\ =〈f\\left(\\left(1-u\\right)A+u\\frac{\\left(k-1\\right)A+B}{k}\\right)x,x〉\\\\ \\le \\left(1-u\\right)〈f\\left(A\\right)x,x〉+u〈f\\left(\\frac{\\left(k-1\\right)A+B}{k}\\right)x,x〉\\end{array}$\n(11)\n\nand\n\n$\\begin{array}{rl}〈f\\left(tA+\\left(1-t\\right)B\\right)x,x〉& =〈f\\left(\\frac{u}{k}A+\\left(1-\\frac{u}{k}\\right)B\\right)x,x〉\\\\ =〈f\\left(u\\frac{A+\\left(k-1\\right)B}{k}+\\left(1-u\\right)B\\right)x,x〉\\\\ \\le u〈f\\left(\\frac{A+\\left(k-1\\right)B}{k}\\right)x,x〉+\\left(1-u\\right)〈f\\left(B\\right)x,x〉.\\end{array}$\n(12)\n\nBy the change of variable $u=kt-1$, we have\n\n$\\begin{array}{rcl}〈f\\left(\\left(1-t\\right)A+tB\\right)x,x〉& =& 〈f\\left(\\left(1-\\frac{u+1}{k}\\right)A+\\frac{u+1}{k}B\\right)x,x〉\\\\ =& 〈f\\left(\\left(1-u\\right)\\frac{\\left(k-1\\right)A+B}{k}+u\\frac{\\left(k-2\\right)A+2B}{k}\\right)x,x〉\\\\ \\le & \\left(1-u\\right)〈f\\left(\\frac{\\left(k-1\\right)A+B}{k}\\right)x,x〉+u〈f\\left(\\frac{\\left(k-2\\right)A+2B}{k}\\right)x,x〉\\end{array}$\n\nand\n\n$\\begin{array}{rcl}〈f\\left(tA+\\left(1-t\\right)B\\right)x,x〉& =& 〈f\\left(\\frac{u+1}{k}A+\\left(1-\\frac{u+1}{k}\\right)B\\right)x,x〉\\\\ =& 〈f\\left(u\\frac{2A+\\left(k-2\\right)B}{k}+\\left(1-u\\right)\\frac{A+\\left(k-1\\right)B}{k}\\right)x,x〉\\\\ \\le & u〈f\\left(\\frac{2A+\\left(k-2\\right)B}{k}\\right)x,x〉+\\left(1-u\\right)〈f\\left(\\frac{A+\\left(k-1\\right)B}{k}\\right)x,x〉.\\end{array}$\n\nSimilarly, by using the change of variables $u=kt-2,u=kt-3,\\dots ,u=kt-\\left(k-2\\right)$, we have some inequalities. By the change of variable $u=kt-\\left(k-1\\right)$, we get\n\n$\\begin{array}{rcl}〈f\\left(\\left(1-t\\right)A+tB\\right)x,x〉& =& 〈f\\left(\\left(1-\\frac{u+k-1}{k}\\right)A+\\frac{u+k-1}{k}B\\right)x,x〉\\\\ =& 〈f\\left(\\left(1-u\\right)\\frac{A+\\left(k-1\\right)B}{k}+uB\\right)x,x〉\\\\ \\le & \\left(1-u\\right)〈f\\left(\\frac{A+\\left(k-1\\right)B}{k}\\right)x,x〉+u〈f\\left(B\\right)x,x〉\\end{array}$\n\nand\n\n$\\begin{array}{rcl}〈f\\left(tA+\\left(1-t\\right)B\\right)x,x〉& =& 〈f\\left(\\frac{u+k-1}{k}A+\\left(1-\\frac{u+k-1}{k}\\right)B\\right)x,x〉\\\\ =& 〈f\\left(uA+\\left(1-u\\right)\\frac{\\left(k-1\\right)A+B}{k}x,x\\right)〉\\\\ \\le & u〈f\\left(A\\right)x,x〉+\\left(1-u\\right)〈f\\left(\\frac{\\left(k-1\\right)A+B}{k}\\right)x,x〉.\\end{array}$\n\nUsing the convexity of f, g, we have\n\n$\\begin{array}{rl}〈f\\left(\\frac{A+B}{2}\\right)x,x〉& =〈f\\left(\\frac{tA+\\left(1-t\\right)B}{2}+\\frac{\\left(1-t\\right)A+tB}{2}\\right)x,x〉\\\\ \\le \\frac{〈f\\left(tA+\\left(1-t\\right)B\\right)x,x〉+〈f\\left(\\left(1-t\\right)A+tB\\right)x,x〉}{2}\\end{array}$\n(13)\n\nand\n\n$\\begin{array}{rl}〈g\\left(\\frac{A+B}{2}\\right)x,x〉& =〈g\\left(\\frac{tA+\\left(1-t\\right)B}{2}+\\frac{\\left(1-t\\right)A+tB}{2}\\right)x,x〉\\\\ \\le \\frac{〈g\\left(tA+\\left(1-t\\right)B\\right)x,x〉+〈g\\left(\\left(1-t\\right)A+tB\\right)x,x〉}{2}.\\end{array}$\n(14)\n\nFirstly, if we write the values obtained from the change of variable $u=kt$ in (13) and (14), we get\n\n$\\begin{array}{rcl}〈f\\left(\\frac{A+B}{2}\\right)x,x〉& \\le & \\frac{〈f\\left(tA+\\left(1-t\\right)B\\right)x,x〉+〈f\\left(\\left(1-t\\right)A+tB\\right)x,x〉}{2}\\\\ =& \\frac{〈f\\left(u\\frac{A+\\left(k-1\\right)B}{k}+\\left(1-u\\right)B\\right)x,x〉+〈f\\left(\\left(1-u\\right)A+u\\frac{\\left(k-1\\right)A+B}{k}\\right)x,x〉}{2}\\end{array}$\n(15)\n\nand\n\n$\\begin{array}{r}〈g\\left(\\frac{A+B}{2}\\right)x,x〉\\\\ \\phantom{\\rule{1em}{0ex}}\\le \\frac{〈g\\left(tA+\\left(1-t\\right)B\\right)x,x〉+〈g\\left(\\left(1-t\\right)A+tB\\right)x,x〉}{2}\\\\ \\phantom{\\rule{1em}{0ex}}=\\frac{〈g\\left(u\\frac{A+\\left(k-1\\right)B}{k}+\\left(1-u\\right)B\\right)x,x〉+〈g\\left(\\left(1-u\\right)A+u\\frac{\\left(k-1\\right)A+B}{k}\\right)x,x〉}{2}.\\end{array}$\n(16)\n\nIf we multiply (15) and (16) and suppose $\\left(1-u\\right)A+u\\frac{\\left(k-1\\right)A+B}{k}={X}_{1}$ and $u\\frac{A+\\left(k-1\\right)B}{k}+\\left(1-u\\right)B={Y}_{1}$, we get", null, "(17)\n\nIf we integrate both sides of inequality (17) over $\\left[0,1\\right]$, we reach\n\n$\\begin{array}{r}〈f\\left(\\frac{A+B}{2}\\right)x,x〉〈g\\left(\\frac{A+B}{2}\\right)x,x〉\\\\ \\phantom{\\rule{1em}{0ex}}\\le \\frac{k}{4}\\left[{\\int }_{0}^{1/k}〈f\\left(tA+\\left(1-t\\right)B\\right)x,x〉〈g\\left(tA+\\left(1-t\\right)B\\right)x,x〉\\phantom{\\rule{0.2em}{0ex}}dt\\right]\\\\ \\phantom{\\rule{2em}{0ex}}+\\frac{k}{4}\\left[{\\int }_{0}^{1/k}〈f\\left(\\left(1-t\\right)A+tB\\right)x,x〉〈g\\left(\\left(1-t\\right)A+tB\\right)x,x〉\\phantom{\\rule{0.2em}{0ex}}dt\\right]\\\\ \\phantom{\\rule{2em}{0ex}}+\\frac{1}{24}\\left[〈f\\left(\\frac{A+\\left(k-1\\right)B}{k}\\right)x,x〉〈g\\left(A\\right)x,x〉+〈f\\left(B\\right)x,x〉〈g\\left(\\frac{\\left(k-1\\right)A+B}{k}\\right)x,x〉\\right]\\\\ \\phantom{\\rule{2em}{0ex}}+\\frac{1}{12}\\left[〈f\\left(\\frac{A+\\left(k-1\\right)B}{k}\\right)x,x〉〈g\\left(\\frac{\\left(k-1\\right)A+B}{k}\\right)x,x〉+〈f\\left(B\\right)x,x〉〈g\\left(A\\right)x,x〉\\right]\\\\ \\phantom{\\rule{2em}{0ex}}+\\frac{1}{24}\\left[〈f\\left(A\\right)x,x〉〈g\\left(\\frac{A+\\left(k-1\\right)B}{k}\\right)x,x〉+〈f\\left(\\frac{\\left(k-1\\right)A+B}{k}\\right)x,x〉〈g\\left(B\\right)x,x〉\\right]\\\\ \\phantom{\\rule{2em}{0ex}}+\\frac{1}{12}\\left[〈f\\left(A\\right)x,x〉〈g\\left(B\\right)x,x〉+〈f\\left(\\frac{\\left(k-1\\right)A+B}{k}\\right)x,x〉〈g\\left(\\frac{A+\\left(k-1\\right)B}{k}\\right)x,x〉\\right].\\end{array}$\n\nIf we continue the same operations as above until the change of variable $u=kt-\\left(k-1\\right)$, we have some inequalities. And then, if we sum these obtained inequalities, we get the desired inequality. □\n\nRemark 6 In inequality (8), if we take $k=1$, we get the inequality in (7).\n\nNow, we show the comparison between Theorems 4 and 5 utilizing self-adjoint operators (Hermitian matrices) as follows.\n\nExample 7 Let $A=\\left[\\begin{array}{cc}1& 0\\\\ 0& 2\\end{array}\\right]$, $B=\\left[\\begin{array}{cc}-0.4& 1\\\\ 1& 1\\end{array}\\right]$. Let our operator convex functions be $f\\left(X\\right)={X}^{2}$ and $g\\left(X\\right)=X$. Since $x\\in H$ and $\\parallel x\\parallel =1$, then we can choose x as $x=\\left[\\begin{array}{c}1\\\\ 0\\end{array}\\right]$. From the information given above, for $k=3$, Theorem 5 gives\n\n$\\begin{array}{r}\\left({x}^{\\ast }f\\left(\\frac{A+B}{2}\\right)x\\right)\\left({x}^{\\ast }g\\left(\\frac{A+B}{2}\\right)x\\right)\\\\ \\phantom{\\rule{1em}{0ex}}\\le \\frac{1}{2}{\\int }_{0}^{1}〈f\\left(tA+\\left(1-t\\right)B\\right)x,x〉〈g\\left(tA+\\left(1-t\\right)B\\right)x,x〉\\phantom{\\rule{0.2em}{0ex}}dt\\\\ \\phantom{\\rule{2em}{0ex}}+\\frac{1}{24}\\left[\\left({x}^{\\ast }f\\left(A\\right)x\\right)\\left({x}^{\\ast }g\\left(\\frac{A+B}{2}\\right)x\\right)+\\left({x}^{\\ast }f\\left(B\\right)x\\right)\\left({x}^{\\ast }g\\left(\\frac{A+B}{2}\\right)x\\right)\\\\ \\phantom{\\rule{2em}{0ex}}+\\left({x}^{\\ast }f\\left(\\frac{A+B}{2}\\right)x\\right)\\left({x}^{\\ast }f\\left(A\\right)x\\right)+\\left({x}^{\\ast }f\\left(\\frac{A+B}{2}\\right)x\\right)\\left({x}^{\\ast }g\\left(B\\right)x\\right)\\right]\\\\ \\phantom{\\rule{2em}{0ex}}+\\frac{1}{12}\\left[\\left({x}^{\\ast }f\\left(A\\right)x\\right)\\left({x}^{\\ast }g\\left(B\\right)x\\right)+2\\left({x}^{\\ast }f\\left(\\frac{A+B}{2}\\right)x\\right)\\left({x}^{\\ast }g\\left(\\frac{A+B}{2}\\right)x\\right)\\\\ \\phantom{\\rule{2em}{0ex}}+\\left({x}^{\\ast }f\\left(B\\right)x\\right)\\left({x}^{\\ast }g\\left(A\\right)x\\right)\\right].\\end{array}$\n\nPutting the values of the functions in the above inequality, we get\n\n$\\begin{array}{r}0,102\\le \\frac{1}{2}{\\int }_{0}^{1}〈f\\left(tA+\\left(1-t\\right)B\\right)x,x〉〈g\\left(tA+\\left(1-t\\right)B\\right)x,x〉\\phantom{\\rule{0.2em}{0ex}}dt+0.1158\\\\ \\phantom{\\rule{1em}{0ex}}⟹\\phantom{\\rule{1em}{0ex}}{\\int }_{0}^{1}〈f\\left(tA+\\left(1-t\\right)B\\right)x,x〉〈g\\left(tA+\\left(1-t\\right)B\\right)x,x〉\\phantom{\\rule{0.2em}{0ex}}dt\\ge -0.0276.\\end{array}$\n\nTheorem 4 gives\n\n$\\begin{array}{rcl}\\left({x}^{\\ast }f\\left(\\frac{A+B}{2}\\right)x\\right)\\left({x}^{\\ast }g\\left(\\frac{A+B}{2}\\right)x\\right)& \\le & \\frac{1}{2}{\\int }_{0}^{1}〈f\\left(tA+\\left(1-t\\right)B\\right)x,x〉〈g\\left(tA+\\left(1-t\\right)B\\right)x,x〉\\phantom{\\rule{0.2em}{0ex}}dt\\\\ +\\frac{1}{12}\\left[\\left({x}^{\\ast }f\\left(A\\right)x\\right)\\left({x}^{\\ast }g\\left(A\\right)x\\right)+\\left({x}^{\\ast }f\\left(B\\right)x\\right)\\left({x}^{\\ast }g\\left(B\\right)x\\right)\\right]\\\\ +\\frac{1}{6}\\left[\\left({x}^{\\ast }f\\left(A\\right)x\\right)\\left({x}^{\\ast }g\\left(B\\right)x\\right)+\\left({x}^{\\ast }f\\left(B\\right)x\\right)\\left({x}^{\\ast }g\\left(A\\right)x\\right)\\right].\\end{array}$\n\nPutting the values of the functions in the above inequality, we obtain\n\n$\\begin{array}{r}0,102\\le \\frac{1}{2}{\\int }_{0}^{1}〈f\\left(tA+\\left(1-t\\right)B\\right)x,x〉〈g\\left(tA+\\left(1-t\\right)B\\right)x,x〉\\phantom{\\rule{0.2em}{0ex}}dt+0.1713\\\\ \\phantom{\\rule{1em}{0ex}}⟹\\phantom{\\rule{1em}{0ex}}{\\int }_{0}^{1}〈f\\left(tA+\\left(1-t\\right)B\\right)x,x〉〈g\\left(tA+\\left(1-t\\right)B\\right)x,x〉\\phantom{\\rule{0.2em}{0ex}}dt\\ge -0.1386.\\end{array}$\n\nSo, we can conclude that our result, Theorem 5, is more strict than Theorem 4 in this case.\n\nThe following theorem is a lower bound for the product of two operator convex functions.\n\nTheorem 8 Let $f,g:I⟶\\mathbb{R}$ be operator convex, nonnegative functions on the interval I. Then for any self-adjoint operators A and B with spectra in I, we have the inequality", null, "(18)\n\nwhere\n\n$\\begin{array}{r}M\\left(A,B\\right)=〈f\\left(A\\right)x,x〉〈g\\left(A\\right)x,x〉+〈f\\left(B\\right)x,x〉〈g\\left(B\\right)x,x〉,\\\\ N\\left(A,B\\right)=〈f\\left(A\\right)x,x〉〈g\\left(B\\right)x,x〉+〈f\\left(B\\right)x,x〉〈g\\left(A\\right)x,x〉.\\end{array}$\n\nProof Let $x\\in H$, $\\parallel x\\parallel =1$ and A, B be two self-adjoint operators with spectra in I. Define the real-valued functions ${\\phi }_{x,A,B}:\\left[0,1\\right]⟶\\mathbb{R}$ given by ${\\phi }_{x,A,B}\\left(t\\right)=〈f\\left(\\left(1-t\\right)A+tB\\right)x,x〉$ and ${\\psi }_{x,A,B}:\\left[0,1\\right]⟶\\mathbb{R}$ given by ${\\psi }_{x,A,B}\\left(t\\right)=〈g\\left(\\left(1-t\\right)A+tB\\right)x,x〉$. Since f and g are operator convex functions, then for every $t\\in \\left[0,1\\right]$, we have", null, "(19)", null, "(20)\n\nIf $a\\le b$ and $c\\le d$ for $a,b,c,d\\in \\mathbb{R}$, we have $ad+bc\\le ac+bd$. Using this inequality analogous to (19) and (20), we get", null, "(21)\n\nSince ${\\phi }_{x,A,B}\\left(t\\right)$ and ${\\psi }_{x,A,B}\\left(t\\right)$ are operator convex on $\\left[0,1\\right]$, they are integrable on $\\left[0,1\\right]$ and consequently ${\\phi }_{x,A,B}\\left(t\\right){\\psi }_{x,A,B}\\left(t\\right)$ is also integrable on $\\left[0,1\\right]$. Integrating both sides of inequality (21) over $\\left[0,1\\right]$, we get", null, "(22)\n\nIt can be easily controlled that\n\n${\\int }_{0}^{1}{\\left(1-t\\right)}^{2}\\phantom{\\rule{0.2em}{0ex}}dt={\\int }_{0}^{1}{t}^{2}\\phantom{\\rule{0.2em}{0ex}}dt=\\frac{1}{3},\\phantom{\\rule{2em}{0ex}}{\\int }_{0}^{1}t\\left(1-t\\right)\\phantom{\\rule{0.2em}{0ex}}dt=\\frac{1}{6}.$\n\nWhen the above equalities are taken into account, the proof is complete. □\n\nRemark 9 In inequality (18), if we take $x=\\left(1-t\\right)A+tB$, $a=0$ and $b=1$, we get the inequality in (5). Our result is more general than (5).\n\nIn Theorem 8, we give a lower bound. But now we give both lower and upper bounds for the product of two operator convex functions.\n\nTheorem 10 Let $f,g:I⟶\\mathbb{R}$ be operator convex, nonnegative functions on the interval I. Then for any self-adjoint operators A and B with spectra in I, we have the inequality", null, "(23)\n\nwhere ${Z}_{1}$ and ${T}_{2}$ are defined in (9) and (10) and k is the number of steps.\n\nProof Let $x\\in H$, $\\parallel x\\parallel =1$ and A, B be two self-adjoint operators with spectra in I. Using the convexity of f, g and the change of variable $u=kt$, we have (11) and (12). Using the analogous condition that, if $a\\le b$ and $c\\le d$ for $a,b,c,d\\in \\mathbb{R}$, we have $ad+bc\\le ac+bd$, we obtain", null, "(24)\n\nIf we continue the same operations as above until the change of variable $u=kt-\\left(k-1\\right)$, we have some inequalities. And then, if we integrate the multiplication inequalities, we get k inequalities. These inequalities are defined on $\\left[0,\\frac{1}{k}\\right),\\left(\\frac{1}{k},\\frac{2}{k}\\right),\\dots ,\\left(\\frac{k-1}{k},1\\right]$, respectively. The sum of the integration parts of these k inequalities yields ${\\int }_{0}^{1}〈f\\left(\\left(1-t\\right)A+tB\\right)x,x〉〈g\\left(\\left(1-t\\right)A+tB\\right)x,x〉\\phantom{\\rule{0.2em}{0ex}}dt$. Thus, the proof is complete. □\n\nRemark 11 Inequality (23) is a general form of inequality (18). When $k=1$ in inequality (23), we get inequality (18).\n\nTheorem 12 Let $f,g:I⟶\\mathbb{R}$ be operator convex, nonnegative functions on the interval I. Then for any self-adjoint operators A and B with spectra in I, we have the inequality", null, "(25)\n\nwhere ${Z}_{1}$, ${Z}_{2}$, ${T}_{1}$ and ${T}_{2}$ are defined in (9) and (10) and k is the number of steps.\n\nProof The proof is obvious from the proofs of Theorem 3 and Theorem 5. □\n\nRemark 13 In Theorem 12, if we take $k=1$, we get (6). Theorem 12 is a generalization of Theorem 3. If we take k as the largest number we can take in Theorem 12, we near the exact solution.\n\n## References\n\n1. Pecaric JE, Proschan F, Tong YL: Convex Functions, Partial Orderings and Statistical Applications. Academic Press, New York; 1991.\n\n2. Hadamard J: Étude sur les proprietes des fonctions entieres en particulier d’une fonction considérée par Riemann. J. Math. Pures Appl. 1893, 58: 171–215.\n\n3. Dragomir SS: Hermite-Hadamard’s type inequalities for convex functions of selfadjoint operators in Hilbert spaces. Linear Algebra Appl. 2012, 436: 1503–1515. 10.1016/j.laa.2011.08.050\n\n4. Dragomir SS: Operator inequalities of the Jensen, Cebysev and Grüss type. Springer Briefs Math. 2012. doi:10.1007/978–1-4614–1521–3_2\n\n5. Dragomir SS: New Hermite-Hadamard-type inequalities for convex functions (II). Comput. Math. Appl. 2011, 62: 401–418. 10.1016/j.camwa.2011.05.023\n\n6. Dragomir SS: New refinements of the Hermite-Hadamard integral inequality for convex functions and applications. Soochow J. Math. 2002, 28(4):357–374.\n\n7. Pachpatte, BG: On some inequalities for convex functions. RGMIA Res. Rep. Coll. 6(E) (2003)\n\n8. Tunç M: On some new inequalities for convex functions. Turk. J. Math. 2012, 36: 245–251.\n\n9. Ghazanfari, AG: Some new Hermite-Hadamard type inequalities for two operator convex functions (4 July 2012). http://arxiv.org/pdf/1207.0928.pdf\n\n10. Dragomir SS: Hermite-Hadamard’s type inequalities for operator convex functions. Appl. Math. Comput. 2011, 218: 766–772. 10.1016/j.amc.2011.01.056\n\n11. Zabandan G: A new refinement of the Hermite-Hadamard inequality for convex functions. J. Inequal. Pure Appl. Math. 2009., 10(2): Article ID 45\n\n12. Mitrinovic DS: Analytic Inequalities. Springer, Berlin; 1970.\n\n## Acknowledgements\n\nThis study was supported by the Coordinatorship of Selçuk University’s Scientific Research Project (BAP) and the Scientific and Technical Research Council of Turkey (TÜBİTAK). The authors would like to thank the referees for the very helpful comments and suggestions to improve this paper.\n\n## Author information\n\nAuthors\n\n### Corresponding author\n\nCorrespondence to Vildan Bacak.\n\n### Competing interests\n\nThe authors declare that they have no competing interests.\n\n### Authors’ contributions\n\nThe paper is a joint work of all the authors who contributed equally to the final version of the paper. All authors read and approved the final manuscript.\n\n## Rights and permissions\n\nReprints and Permissions\n\nBacak, V., Türkmen, R. New inequalities for operator convex functions. J Inequal Appl 2013, 190 (2013). https://doi.org/10.1186/1029-242X-2013-190", null, "" ]

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[ "", null, "# Get and Sign Adding and Subtracting Scientific Notation Worksheet with Answer Key PDF Form\n\nUse a adding and subtracting scientific notation worksheet with answer key pdf template to make your document workflow more streamlined.\n\nName _____________________ Date _________________________ Scientific Notation Addition and Subtraction - Independent Practice Worksheet Complete all the problems. 1. 9 × 103 + 2.3 × 104 2. 15 × 102 + 5.2 × 105 3. 10 × 104 + 2.8 × 106 4. 7 × 103 + 8.6 × 104 5. 3 × 104 + 14.5 × 105 6. 8 x 104 – 2.7 x 102 7. 5 x 103 – 8.9 x 104 8. 7 x 103 – 8.20 x 102 9. 9 x 102 – 5.54 x 104 10. 10 x 102 – 7.79 x 103 Tons of Free Math Worksheets at: © www.mathworksheetsland.com ...\nShow details\n\n#### How it works\n\nEdit & sign adding and subtracting scientific notation worksheet pdf from anywhere\n\n4.6\n\n## Quick guide on how to complete adding and subtracting scientific notation worksheet\n\nForget about scanning and printing out forms. Use our detailed instructions to fill out and eSign your documents online.\n\nsignNow's web-based service is specially designed to simplify the arrangement of workflow and improve the whole process of proficient document management. Use this step-by-step guide to complete the Scientific notation addition and subtraction independent practice worksheet answers form swiftly and with excellent precision.\n\n### How you can complete the Scientific notation addition and subtraction independent practice worksheet answers form online:\n\n1. To begin the blank, use the Fill camp; Sign Online button or tick the preview image of the blank.\n2. The advanced tools of the editor will direct you through the editable PDF template.\n3. Enter your official contact and identification details.\n4. Utilize a check mark to indicate the choice where necessary.\n5. Double check all the fillable fields to ensure complete accuracy.\n6. Use the Sign Tool to create and add your electronic signature to signNow the Scientific notation addition and subtraction independent practice worksheet answers form.\n7. Press Done after you complete the blank.\n8. Now it is possible to print, save, or share the document.\n9. Follow the Support section or get in touch with our Support group in case you have got any concerns.\n\nBy utilizing signNow's complete solution, you're able to carry out any needed edits to Scientific notation addition and subtraction independent practice worksheet answers form, make your customized digital signature in a couple of quick steps, and streamline your workflow without leaving your browser.\n\n### Video instructions and help with filling out and completing Adding And Subtracting Scientific Notation Worksheet With Answer Key PDF Form\n\nFind a suitable template on the Internet. Read all the field labels carefully. Start filling out the blanks according to the instructions:\n\nIn this lesson I want to focus on adding and subtracting two numbers using scientific notation so consider this example 9 times 10 to 3 minus 5 times 10 to the 3 what's the answer now what is 9x minus 5 × 9x minus 5 X is 4x because both terms contain X the same variable you can simply subtract the coefficient in this case the 9 and the 5 they're attached to the same thing 10 to 3 so all you need to do is subtract the coefficient so 9 minus 5 is 4, so this is simply going to be 4 times 10 to the 3 you can do that if these two are the same so go ahead and try these examples what's 7 plus what's 7 times 10 to the 4 plus 2 times 10 to the 4 and 5 times 10 to the 6 minus 3 times 10 to the 6 so 7 plus 2 is 9 and then the 10th the 4 will be carried over, so that's the first answer 5 minus 3 is 2, and so we're going to carry over the 10 to the 6 and so that's a simple way to add or subtract two numbers in scientific notation now what will you do if the exponents are different so what is 12 ti\n\n### FAQs adding and subtracting scientific notation practice\n\nHere is a list of the most common customer questions. If you can’t find an answer to your question, please don’t hesitate to reach out to us.\n\nNeed help? Contact support\n\n### Related searches to adding and subtracting scientific notation pdf\n\nmultiplying and dividing scientific notation worksheet with answer key pdf\nadding and subtracting scientific notation worksheet kuta\nstandard and scientific notation worksheet answers\nadding and subtracting scientific notation practice\nscientific notation worksheet 8th grade pdf\noperations with scientific notation worksheet\nadding and subtracting scientific notation worksheet doc\n\n#### Create this form in 5 minutes!\n\nUse professional pre-built templates to fill in and sign documents online faster. Get access to thousands of forms.\n\n## How to create an eSignature for the adding and subtracting scientific notation\n\nSpeed up your business’s document workflow by creating the professional online forms and legally-binding electronic signatures.", null, "" ]

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[ "Related Articles\nDistinct adjacent elements in a binary array\n• Last Updated : 01 Aug, 2019\n\nGiven a binary array arr[] of 1’s and 0’s of length N. The task is to find the number of elements which are different with respect to their neighbors.\nNote:At least one of the neighbors should be distinct.\n\nExamples:\n\nInput : N = 4 , arr=[1, 0, 1, 1]\nOutput : 3\narr=1 is distinct since it’s neighbor arr=0 is different.\narr=0 is also distinct, as it has two different neighbors i.e, arr=1 & arr=1.\narr=1 has same neighbor in arr=1 but has different neighbor in arr=0. So it’s distinct.\nBut arr=1 is not distinct as it’s neighbor arr=1 is the same.\nSo total distinct elements are 1+1+1+0=3\n\nInput : N = 2 , arr=[1, 1]\nOutput : 0\n\n## Recommended: Please try your approach on {IDE} first, before moving on to the solution.\n\nApproach:\n\n• Run a loop for all the elements of list and compare every element with its previous and next neighbors. Increment count by 1 if the element is distinct.\n• The first element has to be compared only with its next neighbor and similarly the last element has to be compared only with its previous element.\n• The remaining elements have two neighbors . If anyone of two neighbors is different then it is considered distinct.\n\nBelow is the implementation of the above approach:\n\n## C++\n\n `// C++ implementation of``// the above approach``#include `` ` `using` `namespace` `std;`` ` `int` `distinct(``int` `arr[], ``int` `n)``{``    ``int` `count = 0;`` ` `    ``// if array has only one element, return 1``    ``if` `(n == 1)``        ``return` `1;`` ` `    ``for` `( ``int` `i = 0; i < n - 1; i++)``    ``{``  ` `        ``// For first element compare``        ``// with only next element``        ``if``(i == 0)``        ``{``            ``if``(arr[i] != arr[i + 1])``                ``count += 1;``        ``}`` ` `        ``// For remaining elements compare with``        ``// both prev and next elements``        ``else``        ``{``            ``if``(arr[i] != arr[i + 1] || ``               ``arr[i] != arr[i - 1])``                ``count += 1;``        ``}``    ``}``     ` `    ``// For last element compare``    ``// with only prev element``    ``if``(arr[n - 1] != arr[n - 2])``        ``count += 1;`` ` `    ``return` `count;``}`` ` `// Driver code``int` `main()``{``    ``int` `arr[] = {0, 0, 0, 0, 0, 1, 0};``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr);``    ``cout << distinct(arr, n);``     ` `    ``return` `0;``}`\n\n## Java\n\n `// Java implementation of``// the above approach``class` `GFG ``{``static` `int` `distinct(``int` `[]arr, ``int` `n)``{``    ``int` `count = ``0``;`` ` `    ``// if array has only one element, ``    ``// return 1``    ``if` `(n == ``1``)``        ``return` `1``;`` ` `    ``for` `(``int` `i = ``0``; i < n - ``1``; i++)``    ``{`` ` `        ``// For first element compare``        ``// with only next element``        ``if``(i == ``0``)``        ``{``            ``if``(arr[i] != arr[i + ``1``])``                ``count += ``1``;``        ``}`` ` `        ``// For remaining elements compare with``        ``// both prev and next elements``        ``else``        ``{``            ``if``(arr[i] != arr[i + ``1``] || ``               ``arr[i] != arr[i - ``1``])``                ``count += ``1``;``        ``}``    ``}``     ` `    ``// For last element compare``    ``// with only prev element``    ``if``(arr[n - ``1``] != arr[n - ``2``])``        ``count += ``1``;`` ` `    ``return` `count;``}`` ` `// Driver code``public` `static` `void` `main(String[] args) ``{``    ``int` `arr[] = {``0``, ``0``, ``0``, ``0``, ``0``, ``1``, ``0``};``    ``int` `n = arr.length;``    ``System.out.println(distinct(arr, n));``}``}`` ` `// This code is contributed by Rajput-Ji`\n\n## Python3\n\n `# Python3 implementation of ``# the above approach``def` `distinct(arr):``    ``count ``=` `0`` ` `    ``# if array has only one element, return 1``    ``if` `len``(arr) ``=``=` `1``:``        ``return` `1``     ` `    ``for` `i ``in` `range``(``0``, ``len``(arr) ``-` `1``):`` ` `        ``# For first element compare``        ``# with only next element``        ``if``(i ``=``=` `0``):``            ``if``(arr[i] !``=` `arr[i ``+` `1``]):``                ``count ``+``=` `1`` ` `        ``# For remaining elements compare with``        ``# both prev and next elements``        ``elif``(i > ``0` `& i < ``len``(arr) ``-` `1``):``            ``if``(arr[i] !``=` `arr[i ``+` `1``] ``or` `               ``arr[i] !``=` `arr[i ``-` `1``]):``                ``count ``+``=` `1`` ` `    ``# For last element compare ``    ``# with only prev element``    ``if``(arr[``len``(arr) ``-` `1``] !``=` `arr[``len``(arr) ``-` `2``]):``        ``count ``+``=` `1``    ``return` `count`` ` `# Driver code``arr ``=` `[``0``, ``0``, ``0``, ``0``, ``0``, ``1``, ``0``]`` ` `print``(distinct(arr))`` ` `# This code is contributed by Mohit Kumar`\n\n## C#\n\n `// C# implementation of``// the above approach``using` `System;``     ` `class` `GFG ``{``static` `int` `distinct(``int` `[]arr, ``int` `n)``{``    ``int` `count = 0;`` ` `    ``// if array has only one element, ``    ``// return 1``    ``if` `(n == 1)``        ``return` `1;`` ` `    ``for` `(``int` `i = 0; i < n - 1; i++)``    ``{`` ` `        ``// For first element compare``        ``// with only next element``        ``if``(i == 0)``        ``{``            ``if``(arr[i] != arr[i + 1])``                ``count += 1;``        ``}`` ` `        ``// For remaining elements compare with``        ``// both prev and next elements``        ``else``        ``{``            ``if``(arr[i] != arr[i + 1] || ``               ``arr[i] != arr[i - 1])``                ``count += 1;``        ``}``    ``}``     ` `    ``// For last element compare``    ``// with only prev element``    ``if``(arr[n - 1] != arr[n - 2])``        ``count += 1;`` ` `    ``return` `count;``}`` ` `// Driver code``public` `static` `void` `Main(String[] args) ``{``    ``int` `[]arr = {0, 0, 0, 0, 0, 1, 0};``    ``int` `n = arr.Length;``    ``Console.WriteLine(distinct(arr, n));``}``}`` ` `// This code is contributed by Princi Singh`\nOutput:\n```3\n```\n\nTime Complexity: O(N)\n\nAttention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.\n\nIn case you wish to attend live classes with industry experts, please refer Geeks Classes Live and Geeks Classes Live USA\n\nMy Personal Notes arrow_drop_up" ]

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[ "Solutions by everydaycalculation.com\n\nAdd 6/2 and 1/12\n\n1st number: 3 0/2, 2nd number: 1/12\n\n6/2 + 1/12 is 37/12.\n\nSteps for adding fractions\n\n1. Find the least common denominator or LCM of the two denominators:\nLCM of 2 and 12 is 12\n2. For the 1st fraction, since 2 × 6 = 12,\n6/2 = 6 × 6/2 × 6 = 36/12\n3. Likewise, for the 2nd fraction, since 12 × 1 = 12,\n1/12 = 1 × 1/12 × 1 = 1/12\n4. Add the two fractions:\n36/12 + 1/12 = 36 + 1/12 = 37/12\n5. In mixed form: 31/12\n\nMathStep (Works offline)", null, "Download our mobile app and learn to work with fractions in your own time:\nAndroid and iPhone/ iPad" ]

[ null, "https://answers.everydaycalculation.com/mathstep-app-icon.png", null ]

[ "Order the positive and negative numbers Find the sum of the positive numbers Find the sum of the negative numbers Get the total result", null, "Click on  new  to create a new problem.\n\nCan you top 295 points?\n\n#### Add and subtract integerswith strategy -level 5-\n\nNote the calculation strategy.\n = = =\n\nrealmath.de\n\n... more than just practicing", null, "" ]

[ null, "https://realmath.de/english/integers/addsubint/loes002.png", null, "https://realmath.de/bilder/donate.png", null ]

[ "yum install -y lm-sensors sensors-applet\n\n[root@iz2zecibr4bozfdvtbnvfkz ~]# sensors\nw83627dhg-isa-0290\nVCore: +1.13 V (min = +0.00 V, max = +1.74 V)\nin1: +11.30 V (min = +0.90 V, max = +0.05 V) ALARM\nAVCC: +3.28 V (min = +2.11 V, max = +2.40 V) ALARM\n3VCC: +3.28 V (min = +2.05 V, max = +0.37 V) ALARM\nin4: +1.41 V (min = +0.00 V, max = +1.57 V)\nin5: +1.65 V (min = +0.02 V, max = +0.14 V) ALARM\nin6: +4.45 V (min = +3.28 V, max = +1.64 V) ALARM\nVSB: +3.28 V (min = +0.14 V, max = +3.07 V) ALARM\nVBAT: +3.22 V (min = +2.06 V, max = +1.02 V) ALARM\nCase Fan: 0 RPM (min = 2636 RPM, div = 128) ALARM\nCPU Fan: 1117 RPM (min = 1591 RPM, div = 8) ALARM\nAux Fan: 0 RPM (min = 1171 RPM, div = 128) ALARM\nfan5: 0 RPM (min = 659 RPM, div = 128) ALARM\nSys Temp: +31.0°C (high = +18.0°C, hyst = +96.0°C) sensor = thermistor\nCPU Temp: +33.0°C (high = +80.0°C, hyst = +75.0°C) sensor = diode\nAUX Temp: +124.5°C (high = +80.0°C, hyst = +75.0°C) ALARM sensor = thermistor\ncpu0_vid: +1.163 V\n\ncoretemp-isa-0000\nCore 0: +43.0°C (high = +82.0°C, crit = +100.0°C)\n\ncoretemp-isa-0001" ]

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[ "This is the fourth part of the solutions for interval queries in SQL Server. For an introduction, please refer to the blog post Interval Queries in SQL Server Part 1. You can find the second part of the solutions in the blog post Interval Queries in SQL Server Part 2, and the third part in the blog post Interval Queries in SQL Server Part 3. Note that you also need to read an excellent article by Itzik Ben-Gan wrote on interval queries in SQL Server (http://sqlmag.com/t-sql/sql-server-interval-queries) by using the Relational Interval Tree model. I am using the tables and data Itzik has prepared. In order to test the solutions, you can download the code from Itzik’s article by using the link in this paragraph.\n\nIn this post, I am introducing a solution that uses my interval on a countably\ninfinite discrete set called IntervalCID CLR user defined type. For more in-depth knowledge about intervals, interval operators, and interval forms, please refer to the Inside Microsoft® SQL Server® 2008: T-SQL Programming book by Itzik Ben-Gan , Dejan Sarka, Roger Wolter, Greg Low , Ed Katibah, and Isaac Kunen, Microsoft Press, 2009 (http://www.amazon.com/gp/product/0735626022/ref=s9_simh_gw_p14_d0_i1?pf_rd_m=ATVPDKIKX0DER&pf_rd_s=center-2&pf_rd_r=1AEWTQ7GTY1XS1R68R2M&pf_rd_t=101&pf_rd_p=1389517282&pf_rd_i=507846). I explain a lot of details in chapter 12, Temporal Support in the Relational Model.\n\nI am showing the C# definition of the IntervalCID type here, as a block comment inside T-SQL code. As I mentioned, please refer to the book for the details of this type, Allen’s operators, and more. If you want to test this code, just create a C# CLR UDT project, copy the code, and compile it.\n\n— IntervalCID C# code\n/*\nusing System;\nusing System.Data;\nusing System.Data.SqlClient;\nusing System.Data.SqlTypes;\nusing Microsoft.SqlServer.Server;\nusing System.Text.RegularExpressions;\nusing System.Globalization;\n\n[Serializable]\n[Microsoft.SqlServer.Server.SqlUserDefinedType(\nFormat.Native,\nIsByteOrdered = true,\nValidationMethodName = “ValidateIntervalCID”)]\npublic struct IntervalCID : INullable\n{\n//Regular expression used to parse values of the form (intBegin,intEnd)\nprivate static readonly Regex _parser\n= new Regex\n(@”A(s*(?-?d+?)s*:s*(?-?d+?)s*)Z”,\nRegexOptions.Compiled | RegexOptions.ExplicitCapture);\n\n// Begin, end of interval\nprivate Int32 _begin;\nprivate Int32 _end;\n\n// Internal member to show whether the value is null\nprivate bool _isnull;\n\n// Null value returned equal for all instances\nprivate const string NULL = “<>”;\nprivate static readonly IntervalCID NULL_INSTANCE\n= new IntervalCID(true);\n\n// Constructor for a known value\npublic IntervalCID(Int32 begin, Int32 end)\n{\nthis._begin = begin;\nthis._end = end;\nthis._isnull = false;\n}\n\n// Constructor for an unknown value\nprivate IntervalCID(bool isnull)\n{\nthis._isnull = isnull;\nthis._begin = this._end = 0;\n}\n\n// Default string representation\npublic override string ToString()\n{\nreturn this._isnull ? NULL : (“(“\n+ this._begin.ToString(CultureInfo.InvariantCulture) + “:”\n+ this._end.ToString(CultureInfo.InvariantCulture)\n+ “)”);\n}\n\n// Null handling\npublic bool IsNull\n{\nget\n{\nreturn this._isnull;\n}\n}\n\npublic static IntervalCID Null\n{\nget\n{\nreturn NULL_INSTANCE;\n}\n}\n\n// Parsing input using regular expression\npublic static IntervalCID Parse(SqlString sqlString)\n{\nstring value = sqlString.ToString();\n\nif (sqlString.IsNull || value == NULL)\nreturn new IntervalCID(true);\n\n// Check whether the input value matches the regex pattern\nMatch m = _parser.Match(value);\n\n// If the input’s format is incorrect, throw an exception\nif (!m.Success)\nthrow new ArgumentException(\n“Invalid format for complex number. “\n+ “Format is (intBegin:intEnd).”);\n\n// If everything is OK, parse the value;\n// we will get two Int32 type values\nIntervalCID it = new IntervalCID(Int32.Parse(m.Groups.Value,\nCultureInfo.InvariantCulture), Int32.Parse(m.Groups.Value,\nCultureInfo.InvariantCulture));\nif (!it.ValidateIntervalCID())\nthrow new ArgumentException(“Invalid begin and end values.”);\n\nreturn it;\n}\n\n// Begin and end separately\npublic Int32 BeginInt\n{\n[SqlMethod(IsDeterministic = true, IsPrecise = true)]\nget\n{\nreturn this._begin;\n}\nset\n{\nInt32 temp = _begin;\n_begin = value;\nif (!ValidateIntervalCID())\n{\n_begin = temp;\nthrow new ArgumentException(“Invalid begin value.”);\n}\n\n}\n}\n\npublic Int32 EndInt\n{\n[SqlMethod(IsDeterministic = true, IsPrecise = true)]\nget\n{\nreturn this._end;\n}\nset\n{\nInt32 temp = _end;\n_end = value;\nif (!ValidateIntervalCID())\n{\n_end = temp;\nthrow new ArgumentException(“Invalid end value.”);\n}\n\n}\n}\n\n// Validation method\nprivate bool ValidateIntervalCID()\n{\nif (_end >= _begin)\n{\nreturn true;\n}\nelse\n{\nreturn false;\n}\n}\n\n// Allen’s operators\npublic bool Equals(IntervalCID target)\n{\nreturn ((this._begin == target._begin) &\n(this._end == target._end));\n}\n\npublic bool Before(IntervalCID target)\n{\nreturn (this._end < target._begin);\n}\n\npublic bool After(IntervalCID target)\n{\nreturn (this._begin > target._end);\n}\n\npublic bool Includes(IntervalCID target)\n{\nreturn ((this._begin <= target._begin) &\n(this._end >= target._end));\n}\n\npublic bool ProperlyIncludes(IntervalCID target)\n{\nreturn ((this._begin < target._begin) &\n(this._end > target._end));\n}\n\npublic bool Meets(IntervalCID target)\n{\nreturn ((this._end + 1 == target._begin) |\n(this._begin == target._end + 1));\n}\n\npublic bool Overlaps(IntervalCID target)\n{\nreturn ((this._begin <= target._end) &\n(target._begin <= this._end));\n}\n\npublic bool Merges(IntervalCID target)\n{\nreturn (this.Meets(target) |\nthis.Overlaps(target));\n}\n\npublic bool Begins(IntervalCID target)\n{\nreturn ((this._begin == target._begin) &\n(this._end <= target._end));\n}\n\npublic bool Ends(IntervalCID target)\n{\nreturn ((this._begin >= target._begin) &\n(this._end == target._end));\n}\n\npublic IntervalCID Union(IntervalCID target)\n{\nif (this.Merges(target))\nreturn new IntervalCID(\nSystem.Math.Min(this.BeginInt, target.BeginInt),\nSystem.Math.Max(this.EndInt, target.EndInt));\nelse\nreturn new IntervalCID(true);\n}\n\npublic IntervalCID Intersect(IntervalCID target)\n{\nif (this.Merges(target))\nreturn new IntervalCID(\nSystem.Math.Max(this.BeginInt, target.BeginInt),\nSystem.Math.Min(this.EndInt, target.EndInt));\nelse\nreturn new IntervalCID(true);\n}\n\npublic IntervalCID Minus(IntervalCID target)\n{\nif (this.Merges(target) &\n(this.BeginInt < target.BeginInt) &\n(this.EndInt <= target.EndInt))\nreturn new IntervalCID(\nthis.BeginInt,\nSystem.Math.Min(target.BeginInt – 1, this.EndInt));\nelse\nif (this.Merges(target) &\n(this.BeginInt >= target.BeginInt) &\n(this.EndInt > target.EndInt))\nreturn new IntervalCID(\nSystem.Math.Max(target.EndInt + 1, this.BeginInt),\nthis.EndInt);\nelse\nreturn new IntervalCID(true);\n}\n}\n*/\n\nAs mentioned, I am not going into a detailed explanation of the data type. Let me just point out that it uses native serialization, which is byte ordered (see the attributes of the structure), and that the two private variables which denote the begin and the end of the interval appear in the order begin, end. This means that the order of the intervals when serialized is (begin, end), like the following list example shows:\n\n(1, 3)\n(1, 5)\n(2, 2)\n(3, 4)\n(3, 7)\n(4, 5)\n\nTo show this graphically, the following picture denotes the order of the intervals.\n\nBlack color denotes the intervals in the table. The blue colored interval is the one I am checking for the overlaps. The intervals are sorted by the lower boundary, representing SQL Server’s usage of the idx_lower index. Eliminating intervals from the right side of the given (blue) interval is simple: just eliminate all intervals where the beginning is at least one unit bigger (more to the right) of the end of the given interval. You can see this boundary in the figure denoted with yellow line. However, eliminating from the left is more complex. In order to use the same index, the index which I will create on the column of my IntervalCID data type for eliminating from the left, I need to use the beginning of the intervals in the table in the WHERE clause of the query. I have to go to the left side away from the beginning of the given (blue) interval at least for the length of the longest interval in the table, which is marked with red color in the figure. Of course, this picture is taken from the first blog post in this series, the Interval Queries in SQL Server Part 1 post. I could just provide the link; however, I spent quite a few time for drawing this picture in Visio, and therefore I want to publish it more than onceJ Don’t you agree that it is very nice?\n\nIn order to use a CLR data type, you need to enable CLR on your SQL Server instance.\n\nUSE\nmaster;\n\nEXEC\nsp_configure\n‘clr enabled’, 1;\n\nRECONFIGURE;\n\nGO\n\nUSE\nIntervalsDB;\nGO\n\nThe next step is to deploy the assembly and create the data type.\n\n— Deploy assembly\n— Replace the path with your path to the .dll file\nCREATE\nASSEMBLY\nIntervalCID\nFROM\n‘C:TempIntervalCID.dll’\n\nWITH\nPERMISSION_SET\n=\nSAFE;\nGO\n\n— Type\nCREATE\nTYPE\ndbo.IntervalCID\n\nEXTERNAL NAME\n\nIntervalCID.IntervalCID;\nGO\n\nNow I can create and populate a table that uses the IntervalCID data type to store the intervals. Note that I am also creating an index on my IntervalCID column called during.\n\nCREATE\nTABLE\ndbo.IntervalsCID\n(\n\nid\nINT\nNOT\nNULL,\nduring\nIntervalCID\nNOT\nNULL\n);\n\nINSERT\nINTO\ndbo.IntervalsCID\nWITH(TABLOCK)\n(id, during)\n\nSELECT\nid,\nN'(‘\n+\nCAST(lower\nAS\nNVARCHAR(10))\n+‘:’ +\n\nCAST(upper\nAS\nNVARCHAR(10))\n+\n‘)’\n\nFROM\ndbo.Stage;\n\nALTER\nTABLE\ndbo.IntervalsCID\nADD\nCONSTRAINT\nPK_IntervalsCID\n\nPRIMARY\nKEY(id);\n\nCREATE\nINDEX\nidx_IntervalCID\nON\ndbo.IntervalsCID(during);\nGO\n\nExecuting this part of code took approximately 80 second on my notebook. Therefore, the performance is pretty good, nearly the same as with the fastest solution I tested so far.\n\nFor querying, the query is quite similar to the query introduced in the part 1 of this series. I find the maximal length of the intervals in advance and then store it in a variable (OK, this time I already know the maximal length is 20, so I store this as a constant and don’t query for it anymore). The query that checks for the overlaps in the middle of the data uses just slightly different WHERE clause than the query in the part 1; instead of just using the @l and @u variables that define the given, the searched interval, I need to create three variables of IntervalCID data type:\n\n• An interval whose sort value is low enough to filter out the intervals before the given one\n• An interval whose sort value is high enough to filter out the intervals after the given one\n• An interval to filter exactly the intervals needed, the ones that really overlap with the given one\n\nHere is the code for the query the middle of the data:\n\n— query\nSET\nSTATISTICS\nIO\nON;\nSET\n\nSTATISTICS\nTIME\nON;\nGO\n\n— middle of data\nDECLARE\n@l\nAS\nINT\n= 5000000,\n@u\nAS\nINT\n= 5000020;\nDECLARE\n@max\nAS\nINT\n= 20;\n— max length in the data is 20\nDECLARE\n@b\nAS\nIntervalCID, @e\nAS\nIntervalCID, @i\nAS\nIntervalCID;\n— An interval whose sort value is low enough to filter out\n— the intervals before the given one\nSET @b\n\n=\nN'(‘\n+\nCAST((@l 1\n@max)\nAS\nNVARCHAR(10))\n+\n‘:’\n\n+\nCAST((@l1)\nAS\nNVARCHAR(10))\n+\n‘)’;\n— An interval whose sort value is high enough to filter out\n— the intervals after the given one\nSET\n@e\n= N'(‘\n\n+\nCAST((@u+1)\nAS\nNVARCHAR(10))\n+\n‘:’\n\n+\nCAST((@u +1)\nAS\nNVARCHAR(10))\n+\n‘)’;\n— An interval to filter exactly the intervals needed,\n— the ones that really overlap with the given one\nSET\n@i\n= N'(‘\n\n+\nCAST(@l\nAS\nNVARCHAR(10))\n+‘:’\n\n+\nCAST(@u\nAS\nNVARCHAR(10))\n+\n‘)’;\n\nSELECT\n\nid\nFROM\ndbo.IntervalsCID\nAS\nI\nWHERE\nduring <\n@e\nAND\n\nduring\n>\n@b\n\nAND\n@i.Overlaps(I.during)\n= 1\n\nOPTION (RECOMPILE);\n\nGO\n— logical reads: 4, CPU time: 0 ms\n\nAs you can see, the code is extremely efficient. The query performs perfectly. However, the query has the same problem as the query introduced in part 1. If there would be only one long interval in the table, the code would become much less efficient, because SQL Server would not be able to eliminate a lot of rows from the left side of the given interval.\n\nNevertheless, using the IntervalCID data type is my preferred solution so far. First of all, because the knowledge built in the data type, for example Allen’s operators, the T-SQL code becomes simple and less prone to errors. You can quickly change the query to check for the included intervals, intervals that begin other intervals, and similar. Just select the operator you need. In addition, the during column is now a scalar column, which eliminates problems with normalization. Note that in Itzik’s demo data, the id column is unique. However, imagine a real world case, for example a table of the products supplied. This table would have in the classical solution at least these four columns: supplierid, productid, lower, upper. Because the same supplier can supply the same product in different time periods, the combination supplierid, productid cannot be a key for this table. There are two candidate keys: supplierid, productid, lower and supplierid, productid, upper. Two composite candidate keys with overlapping columns violate the Boyce-Codd normal form. This problem disappears when the only candidate key is supplierid, productid, during.\n\nBesides this kind of optimization of the interval queries I just introduced in this post, it is possible to use all other optimizations I know and I have introduced in the previous posts in this series, including the RI tree model introduced in Itzik’s article, and except the geometry data type solution by Davide Mauri (of course, a single column cannot be of two data types). You can create persisted calculated columns from the IntervalCID data type properties to get a single lower and upper boundary values, to calculate the fork node for the RI tree model, or to create an indexed view or an additional table in the unpacked form.\n\nAgain, I have to rant about Microsoft. It is not possible to use CLR UDT properties directly in indexes, constraints like foreign keys, and more. That’s why I need to add persisted computed columns and thus denormalize my table. This lowers the usability of the CLR UDTs.\n\nHere is the code that creates the dbo.IntervalsCID table with all computed persisted columns you might need:\n\nCREATE\nTABLE\ndbo.IntervalsCID\n(\n\nid\nINT\nNOT\nNULL,\nduring\nIntervalCID\nNOT\nNULL,\nlower\nAS\nduring.BeginInt\nPERSISTED,\n\nupper\nAS\nduring.EndInt\nPERSISTED,\n\nilen\nAS\nduring.EndInt during.BeginInt\nPERSISTED,\n\nnode\nAS\nduring.EndInt during.EndInt %\n\nPOWER(2, FLOOR(LOG((during.BeginInt 1)\n^ during.EndInt, 2)))\n\nPERSISTED\n);\n\nNow you can just pick up the optimized interval queries solution that suits you and your data the best." ]

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