vania-janet/multiturn-rag-retrieval-data huggingface dataset:
PID controller
K p ( \ displaystyle K_ ( \ text ( p ) ) ) is the proportional gain , a tuning parameter , K i ( \ displaystyle K_ ( \ text ( i ) ) ) is the integral gain , a tuning parameter , K d ( \ displaystyle K_ ( \ text ( d ) ) ) is the derivative gain , a tuning parameter , e ( t ) = S P − P V ( t ) ( \ displaystyle e ( t ) = \ mathrm ( SP ) - \ mathrm ( PV ) ( t ) ) is the error ( SP is the setpoint , and PV ( t ) is the process variable ) , t ( \ displaystyle t ) is the time or instantaneous time ( the present ) , τ ( \ displaystyle \ tau ) is the variable of integration ( takes on values from time 0 to the present t ( \ displaystyle t ) ) .
Root mean square
where t is time and ω is the angular frequency ( ω = 2π / T , where T is the period of the wave ) .
Normal distribution
Probability density function of a ground state in a quantum harmonic oscillator . The position of a particle that experiences diffusion . If initially the particle is located at a specific point ( that is its probability distribution is the dirac delta function ) , then after time t its location is described by a normal distribution with variance t , which satisfies the diffusion equation Template : Sfrac2 f ( x , t ) = Template : Sfrac2 Template : Sfrac2 f ( x , t ) . If the initial location is given by a certain density function g ( x ) , then the density at time t is the convolution of g and the normal PDF .
Magnetic field
Extending these experiments , Ampère published his own successful model of magnetism in 1825 . In it , he showed the equivalence of electrical currents to magnets and proposed that magnetism is due to perpetually flowing loops of current instead of the dipoles of magnetic charge in Poisson 's model . This has the additional benefit of explaining why magnetic charge can not be isolated . Further , Ampère derived both Ampère 's force law describing the force between two currents and Ampère 's law , which , like the Biot -- Savart law , correctly described the magnetic field generated by a steady current . Also in this work , Ampère introduced the term electrodynamics to describe the relationship between electricity and magnetism .
Bipolar junction transistor
Detailed transistor models of transistor action , such as the Gummel -- Poon model , account for the distribution of this charge explicitly to explain transistor behaviour more exactly . The charge - control view easily handles phototransistors , where minority carriers in the base region are created by the absorption of photons , and handles the dynamics of turn - off , or recovery time , which depends on charge in the base region recombining . However , because base charge is not a signal that is visible at the terminals , the current - and voltage - control views are generally used in circuit design and analysis .
Van de Graaff generator
Other classical electrostatic machines like a Wimshurst machine or a Bonetti machine can easily produce more current than a Van de Graaff generator for experiments with electrostatics and have positive and negative outputs . For these generators , however , corona discharge from exposed metal parts at high potentials and poorer insulation result in smaller voltages . In an electrostatic generator , the rate of charge transported ( current ) to the high - voltage electrode is very small , so the maximal voltage is obtained when the leakage current from the electrode equals the rate of charge transport . In the Van de Graaff generator , the belt allows the transport of charge into the interior of a large hollow spherical electrode . This is the ideal shape to minimize leakage and corona discharge , so the Van de Graaff generator can produce the greatest voltage . This is why the Van de Graaff design has been used for all electrostatic particle accelerators .
Forecasting
A variation on the naïve method is to allow the forecasts to increase or decrease over time , where the amount of change over time ( called the drift ) is set to be the average change seen in the historical data . So the forecast for time T + h ( \ displaystyle T + h ) is given by
PID controller
T i ( \ displaystyle T_ ( i ) ) is the integral time T d ( \ displaystyle T_ ( d ) ) is the derivative time
Circular motion
where i is the imaginary unit , and θ ( t ) ( \ displaystyle \ theta ( t ) ) is the argument of the complex number as a function of time , t .
Houston Astros
In April 1977 the Houston Astros introduced their very first mascot , Chester Charge . Created by Ed Henderson , Chester Charge was a Texas cavalry soldier on a horse . Chester appeared on the field at the beginning of each home game , during the seventh inning stretch and then ran around the bases at the conclusion of each win . At the blast of a bugle , the scoreboard would light up and the audience would yell , `` Charge ! ''
Circular motion
Because the radius of the circle is constant , the radial component of the velocity is zero . The unit vector u ^ R ( t ) ( \ displaystyle ( \ hat ( u ) ) _ ( R ) ( t ) ) has a time - invariant magnitude of unity , so as time varies its tip always lies on a circle of unit radius , with an angle θ the same as the angle of r → ( t ) ( \ displaystyle ( \ vec ( r ) ) ( t ) ) . If the particle displacement rotates through an angle dθ in time dt , so does u ^ R ( t ) ( \ displaystyle ( \ hat ( u ) ) _ ( R ) ( t ) ) , describing an arc on the unit circle of magnitude dθ . See the unit circle at the left of Figure 4 . Hence :
History of Vietnam
The Tây Sơn army commanded by Nguyễn Huệ marched north in 1786 to fight the Trịnh Lord , Trịnh Khải . The Trịnh army failed and Trịnh Khải committed suicide . The Tây Sơn army captured the capital in less than two months . The last Lê emperor , Lê Chiêu Thống , fled to Qing China and petitioned the Qianlong Emperor for help . The Qianlong Emperor supplied Lê Chiêu Thống with a massive army of around 200,000 troops to regain his throne from the usurper . Nguyễn Huệ proclaimed himself Emperor Quang Trung and defeated the Qing troops with 100,000 men in a surprise 7 day campaign during the lunar new year ( Tết ) . There was even a rumor saying that Quang Trung had also planned to conquer China , although it was unclear . During his reign , Quang Trung envisioned many reforms but died by unknown reason on the way march south in 1792 , at the age of 40 . During the reign of Emperor Quang Trung , Đại Việt was in fact divided into three political entities . The Tây Sơn leader , Nguyễn Nhạc , ruled the centre of the country from his capital Qui Nhơn . Emperor Quang Trung ruled the north from the capital Phú Xuân Huế . In the South , Nguyễn Ánh , assisted by many talented recruits from the South , captured Gia Định ( present - day Saigon ) in 1788 and established a strong base for his force .
Articles of Confederation
The Congress from time to time during the Revolutionary War requisitioned troops from the states . Any contributions were voluntary , and in the debates of 1788 the Federalists ( who supported the proposed new Constitution ) claimed that state politicians acted unilaterally , and contributed when the Continental army protected their state 's interests . The Anti-Federalists claimed that state politicians understood their duty to the Union and contributed to advance its needs . Dougherty ( 2009 ) concludes that generally the States ' behavior validated the Federalist analysis . This helps explain why the Articles of Confederation needed reforms .
Time dilation
Let t be the time in an inertial frame subsequently called the rest frame . Let x be a spatial coordinate , and let the direction of the constant acceleration as well as the spaceship 's velocity ( relative to the rest frame ) be parallel to the x-axis . Assuming the spaceship 's position at time t = 0 being x = 0 and the velocity being v and defining the following abbreviation
Transport in London
In February 2003 , TfL introduced a radical scheme to charge motorists £ 5 per day for driving vehicles within a designated area of central London during peak hours , the congestion charge . The politicians behind the scheme claim that it has significantly reduced traffic congestion and hence improved reliability of bus and taxi services , but this is strongly contested by the scheme 's critics . The charge was increased to £ 8 per day on 4 July 2005 . In 2007 the zone was extended into west London . On 4 January 2011 several changes were implemented based on the public consultation conducted in 2008 , which included the removal of the Western Extension and a charge increase from £ 8 to £ 10 ,
T cell
About 98 % of thymocytes die during the development processes in the thymus by failing either positive selection or negative selection , whereas the other 2 % survive and leave the thymus to become mature immunocompetent T cells . Increasing evidence indicates microRNAs , which are small noncoding regulatory RNAs , could impact the clonal selection process during thymic development . For example , miR - 181a was found to play a role in the positive selection of T lymphocytes .
Electromagnetic radiation
Any electric charge that accelerates , or any changing magnetic field , produces electromagnetic radiation . Electromagnetic information about the charge travels at the speed of light . Accurate treatment thus incorporates a concept known as retarded time , which adds to the expressions for the electrodynamic electric field and magnetic field . These extra terms are responsible for electromagnetic radiation .
Lagrangian mechanics
Kinetic energy is the energy of the system 's motion , and v = v v is the magnitude squared of velocity , equivalent to the dot product of the velocity with itself . The kinetic energy is a function only of the velocities v , not the positions r nor time t , so T = T ( v , v , ... ) .
Magnetic field
( T ) he command , `` Measure the direction and magnitude of the vector B at such and such a place , '' calls for the following operations : Take a particle of known charge q . Measure the force on q at rest , to determine E. Then measure the force on the particle when its velocity is v ; repeat with v in some other direction . Now find a B that makes the Lorentz force law fit all these results -- that is the magnetic field at the place in question .
Seafloor spreading
Due to the large velocity , the temperature dependence on the horizontal direction is negligible , and the height at time t ( i.e. of sea floor of age t ) can be calculated by integrating the thermal expansion over z :
Lagrangian mechanics
If T or V or both depend explicitly on time due to time - varying constraints or external influences , the Lagrangian L ( r , r , ... v , v , ... t ) is explicitly time - dependent . If neither the potential nor the kinetic energy depend on time , then the Lagrangian L ( r , r , ... v , v , ... ) is explicitly independent of time . In either case , the Lagrangian will always have implicit time - dependence through the generalized coordinates .
Samurai
In the early Heian period , during the late 8th and early 9th centuries , Emperor Kanmu sought to consolidate and expand his rule in northern Honshū , and sent military campaigns against the Emishi , who resisted the governance of the Kyoto - based imperial court . Emperor Kanmu introduced the title of sei'i - taishōgun ( 征夷 大 将軍 ) , or shōgun , and began to rely on the powerful regional clans to conquer the Emishi . Skilled in mounted combat and archery ( kyūdō ) , these clan warriors became the Emperor 's preferred tool for putting down rebellions ; the most well - known of which was Sakanoue no Tamuramaro . Though this is the first known use of the title shōgun , it was a temporary title and was not imbued with political power until the 13th century . At this time ( the 7th to 9th centuries ) , the Imperial Court officials considered them to be merely a military section under the control of the Imperial Court . Samurai
Bohr effect
When hemoglobin is in its T state , the N - terminal amino groups of the α - subunits and the C - terminal histidine of the β - subunits are protonated , giving them a positive charge and allowing these residues to participate in ionic interactions with carboxyl groups on nearby residues . These interactions help hold the haemoglobin in the T state . Decreases in pH ( increases in acidity ) stabilize this state even more , since a decrease in pH makes these residues even more likely to be protonated , strengthening the ionic interactions . In the R state , the ionic pairings are absent , meaning that the R state 's stability increases when the pH increases , as these residues are less likely to stay deprotonated in a more basic environment . The Bohr effect works by simultaneously destabilizing the high - affinity R state and stabilizing the low - affinity T state , which leads to an overall decrease in oxygen affinity . This can be visualized on an oxygen - haemoglobin dissociation curve by shifting the whole curve to the right .
Battle of Tippecanoe
Lieutenants Nuge and Klaus , the other two Yellow Jacket commanding officers , were also soon shot and killed . The Yellow Jackets began to fall back from the main line , retreating with the sentinels . The warriors followed the retreating unit and entered the camp . Colonel Bartholomew requested a detachment of 25 regular troops and led a bayonet charge that repulsed the warriors . During the charge Bartholomew was shot through the lower arm , breaking both bones . He was still clutching his sword when he was treated hours later . For his leadership during the Battle of Tippecanoe , Bartholomew was promoted to brigadier general. ( 7 )
Time dilation
In addition to the light clock used above , the formula for time dilation can be more generally derived from the temporal part of the Lorentz transformation . Let there be two events at which the moving clock indicates t a ( \ displaystyle t_ ( a ) ) and t b ( \ displaystyle t_ ( b ) ) , thus
Sundial
where H is the height of the style above the plane , and t is the time ( in hours ) before or after the center - time for the polar dial . The center time is the time when the style 's shadow falls directly down on the plane ; for an East - facing dial , the center time will be 6am , for a West - facing dial , this will be 6pm , and for the inclined dial described above , it will be noon . When t approaches ± 6 hours away from the center time , the spacing X diverges to + ∞ ; this occurs when the sun 's rays become parallel to the plane .
Ranger's Apprentice
The Emperor of Nihon - Ja begins with Horace and George ( from the Ward ) in Nihon - Ja , speaking with their Emperor , Shigeru . Meanwhile , Will , Halt , Selethen , and Alyss are watching a Toscan general demonstrate his military tactics while at a treaty signing between the Toscans and the Arridi , both allies of Araluen . During a ride in which the Emperor of Nihon - Ja accompanies Horace and George back to the city in which they could sail back home , they are told by the Emperor 's Cousin , Shuikin , that there has been a coup against the Emperor . Furthermore , a Senshi ( Skilled Nihon - Jan swordsmen ) ambush nearly succeeds in killing the Emperor , but Horace intervenes and decides to help the seemingly ill - fated Emperor find a legendary , impenetrable fortress known as Ran - Koshi while George goes to the nearest city and sends word to the famous Ranger duo . Back in Toscana , the Crown Princess of Araluen , Cassandra , appears and enlists the help of the two Rangers , Alyss , and Selethen to go after Horace , using Gundar Hardstriker 's ship ( From Books 5 and 6 ) . En route to Ran - Koshi , Horace 's party befriends the local woodworkers known as the Kikori . For Halt 's party , they encounter a pirate ship but make short work of it . After paying a Kikori village for their hospitality , people from that village catch up and tell the Emperor that a Senshi scouting party destroyed their village . From then on , Kikori of various villages came to join Horace 's group on the trek to Ran - Koshi . Halt 's group hits Nihon - Ja and they arrive at an inn , making a rendezvous with an ally of the Emperor . Horace , on the other hand , allows Shuikin and a few Senshi delay Arisaka 's enormous Senshi party of around five - hundred while they buy more time by crossing a bridge and destroying it . In this encounter , Horace drops his sword into a ravine . Halt 's group learns of Horace 's whereabouts and Horace 's group hits Ran - Koshi -- .
Russian culture
Famous Russian battle tanks include T - 34 , the best tank design of World War II , and further tanks of T - series , including T - 54 / 55 , the most produced tank in history , first fully gas turbine tank T - 80 and the most modern Russian tank T - 90 . The AK - 47 and AK - 74 by Mikhail Kalashnikov constitute the most widely used type of assault rifle throughout the world -- so much so that more AK - type rifles have been produced than all other assault rifles combined . With these and other weapons Russia for a long time has been among the world 's top suppliers of arms .
Microphone
A nearly constant charge is maintained on the capacitor . As the capacitance changes , the charge across the capacitor does change very slightly , but at audible frequencies it is sensibly constant . The capacitance of the capsule ( around 5 to 100 pF ) and the value of the bias resistor ( 100 MΩ to tens of GΩ ) form a filter that is high - pass for the audio signal , and low - pass for the bias voltage . Note that the time constant of an RC circuit equals the product of the resistance and capacitance .
Radioactive decay
the equation indicates that the decay constant λ has units of t , and can thus also be represented as 1 / τ , where τ is a characteristic time of the process called the time constant .
Circular motion
where u ^ R ( t ) ( \ displaystyle ( \ hat ( u ) ) _ ( R ) ( t ) ) is the unit vector parallel to the radius vector at time t and pointing away from the origin . It is convenient to introduce the unit vector orthogonal to u ^ R ( t ) ( \ displaystyle ( \ hat ( u ) ) _ ( R ) ( t ) ) as well , namely u ^ θ ( t ) ( \ displaystyle ( \ hat ( u ) ) _ ( \ theta ) ( t ) ) . It is customary to orient u ^ θ ( t ) ( \ displaystyle ( \ hat ( u ) ) _ ( \ theta ) ( t ) ) to point in the direction of travel along the orbit .
Bayonet
In 1995 , during the Siege of Sarajevo , French Marine infantrymen from the 3rd RIMA carried out a bayonet charge against the Serbian forces at the Battle of Vrbanja bridge .
Lagrangian mechanics
If the entire Lagrangian is explicitly independent of time , it follows the partial time derivative of the Lagrangian is zero , ∂ L / ∂ t = 0 , so the quantity under the total time derivative in brackets
Horn of Africa
In the early 15th century , Ethiopia sought to make diplomatic contact with European kingdoms for the first time since Aksumite times . A letter from King Henry IV of England to the Emperor of Abyssinia survives . In 1428 , the Emperor Yeshaq sent two emissaries to Alfonso V of Aragon , who sent return emissaries who failed to complete the return trip .
New Year
The Islamic New Year occurs on Muharram . Since the Islamic calendar is based on 12 lunar months amounting to about 354 days , its New Year occurs about eleven days earlier each year in relation to the Gregorian calendar , with two Islamic New Years falling in Gregorian year 2008 . The `` Opening of the Year '' ( Egyptian : Wp ( t ) Rnpt ) , usually transcribed as Wep Renpet , was the ancient Egyptian New Year . It appears to have originally been set to occur upon Sirius 's return to the night sky ( 19 July OS ) during the initial stages of former annual flood of the Nile but the Egyptian calendar 's lack of leap years until its reform by the Roman emperor Augustus meant that the celebration slowly cycled through the entire solar year over the course of two or three 1460 - year Sothic cycles . Northern
Spanish Inquisition
The entire process was undertaken with the utmost secrecy , as much for the public as for the accused , who were not informed about the accusations that were levied against them . Months or even years could pass without the accused being informed about why they were imprisoned . The prisoners remained isolated , and , during this time , the prisoners were not allowed to attend Mass nor receive the sacraments . The jails of the Inquisition were no worse than those of secular authorities , and there are even certain testimonies that occasionally they were much better .
Australian Army during World War II
The third and final stage of the campaign was the capture of Balikpapan on the central east coast of Borneo . This operation had been opposed by Blamey , who believed that it was unnecessary , but went ahead on the orders of MacArthur . After a 20 - day preliminary air and naval bombardment the 7th Division landed near the town on 1 July . Balikpapan and its surrounds were secured after some heavy fighting on 21 July but mopping up continued until the end of the war as isolated pockets of Japanese resistance remained . The capture of Balikpapan was the last large - scale land operation conducted by the Western Allies during World War II . Although the Borneo campaign was criticised in Australia at the time , and in subsequent years , as pointless or a waste of soldiers ' lives , it did achieve a number of objectives , such as increasing the isolation of significant Japanese forces occupying the main part of the NEI , capturing major oil supplies and freeing Allied prisoners of war , who were being held in deteriorating conditions .
Execution of the Romanov family
According to the presumption of innocence , no one can be held criminally liable without guilt being proven . In the criminal case , an unprecedented search for archival sources taking all available materials into account was conducted by authoritative experts , such as Sergey Mironenko , the director of the largest archive in the country , the State Archive of the Russian Federation . The study involved the main experts on the subject -- historians and archivists . And I can confidently say that today there is no reliable document that would prove the initiative of Lenin and Sverdlov . --
PID controller
These gains apply to the ideal , parallel form of the PID controller . When applied to the standard PID form , only the integral and derivative time parameters T i ( \ displaystyle T_ ( i ) ) and T d ( \ displaystyle T_ ( d ) ) are dependent on the oscillation period T u ( \ displaystyle T_ ( u ) ) . Please see the section `` Alternative nomenclature and PID forms '' .
Emperor of Japan
The Emperor 's powers are limited only to important ceremonial functions . Article 4 of the Constitution stipulates that the Emperor `` shall perform only such acts in matters of state as are provided for in the Constitution and he shall not have powers related to government . '' It also stipulates that `` the advice and approval of the Cabinet shall be required for all acts of the Emperor in matters of state '' ( Article 3 ) . Article 4 also states that these duties can be delegated by the Emperor as provided for by law .
Floyd Mayweather Jr. vs. Manny Pacquiao
The Telegraph reported on December 20 , that Mayweather said Pacquiao 's association with promoter Bob Arum is the reason why the bout will not happen . `` We all know the Pacquiao fight , at this particular time , will never happen , and the reason why the fight wo n't happen is because I will never do business with Bob Arum again in life , and Pacquiao is Bob Arum 's fighter , '' Mayweather said .
Lagrangian mechanics
and time is scaled by a factor β , t ′ = βt , then the velocities v are scaled by a factor of α / β and the kinetic energy T by ( α / β ) . The entire Lagrangian has been scaled by the same factor if
Ramcharitmanas
During the Bālakāṇḍa , it is mentioned that Shiva is retelling the story of Rama ( Rama Katha ) to his spouse Parvati . During this retelling , Shiva explains as many as five reasons why Rama incarnated on earth .