darklight03/StackMIAsub huggingface dataset:
Wikipedia asserts that The rays represent luminous intensity, which varies according to Lambert's cosine law for an ideal diffuse reflector. Describing this figure: I understand this is a perceptual phenomenon, and we are observing the light coming from an object that is diffusely - and isotropically - reflecting light. and that the Lambert Cosine has to do with how stretching a circle on one axis increase its area. However, I do not understand how or why this stretch happens, since (in my mental representation) we are always looking at small cylinders of light that come straight (normal) to the eye surface. Can you explain, or maybe include a simple draw of how you image this?
I understand that our main supporting evidence for dark matter is the anomalous speed of objects orbiting around the edges of distant galaxies. Is there a reason why dark matter solves this problem better than say, the strength of gravity simply being stronger in the region? My idea is that maybe these galaxies don't seem to be large scale attractors, but it also seems to me that they could be attracted themselves to areas of space where gravity is EVEN stronger.
With Compton scattering the total momentum and the total energy of the photon electron system is conserved, so it has to be ELASTIC Collision/Scattering. But an argument is that just because the kinetic energy of the incoming photon is different than the outgoing photon, it is INELASTIC Collision/Scattering. However, I thought we had to look at the system, which is the photon and electron interaction; not just the scattered photon itself. So, what is the real issue here?
If one plate of an isolated charged parallel plate capacitor is earthed, then that plate must have a potential zero after being earthed as that is what earthing an isolated conductor does, but potential on each plate is only due to the charges on the other plate. Since the other plate(the one which is not earthed) is isolated and non-neutral, potential due to it on the earthed plate should not change. As surface charge density on the unearthed plate cannot be zero... how on earth will I manage to get the potential of the earthed plate to be zero without changing the charge on the other plate?
In the dimensional analysis, relationship of dimensionless parameter is? Above is the previous question I asked. I kinda understand that relationship of dimensionless group can be more complex. However, I was taught using the above method to determine dimensionless groups. Then how should I interpret the last equation? It seems to me that the groups are related by multiplication. Is the method wrong or does the above equation doesn't actually mean equity but shows the fact that they are somewhat related?
So I've heard that all finite abelian groups are isomorphic to direct sums of the integers or of integers modulo a power of a prime, then you get that all extensions of reals are basically the real numbers or the p-adic number. Is there any such theorem for the rationals? Any other way of creating numbers that is not some vector space or an algebra over the reals? The way the complex numbers are just two dimensional real numbers and the grassman algebra is just an algebra of the complex numbers. I gues what I am saying is, is there any other way to do multiplication that is really new? Not having a copy of the natural numbers embedded inside?
Zenithal perspective projections are generated from a point P and carried through the sphere to the plane of projection as illustrated in the figure below. By a simple geometric relationship, we can show that the radius satisfies the following: with . The inverse equation is given by: where I could reproduce the first equation but not the second one. I think the derivation is purely based on algebraic operation of the first one but I have no idea how. Does anyone have any idea how to derive the second equation?
Okay so by the definition of a wave i.e The osciallatory disturbance in a medium which propogates energy is called as wave..the stationary wave contradicts both the crieteria as it doesnt propogate nor does it transmit any energy. Now one may say that a stationary wave is made by two progressive waves with same phase, frequency and amplitude superimposing in opposite direction..and we know that compsition of two waves is also a new wave..by that conclusion the stationary wave must be a wave..but it contradicts the definition of a wave So what do we call the Stationary Wave as? this was asked to me by a physics proffessor and i am pondering since. wave
In my physics high school lecture my teacher taught the concept of electromagnetic induction under diamagnetic materials (though not completely disregarded it in ferromagnetic substance but as a characteristic property of diamagnetic substance) but the typical high school numericals that are in my textbook consist of conducting ring (as resistance will be low so due to induced emf an induced current is easy to imagine). So is electromagnetic induction possible in ferromagnetic ,antiferromagnetic substances etc (ie it is a universal phenomenon, independent of magnetic properties of material) or is it dominant (or observable) only in diamagnetic substances (ie depending on the magnetic properties of material)??
We know that volume is cubicly proportional to radius of a sphere. But if the radius is become half due to relativistic Length contraction, it's being reduced from only one dimension, not three. And the object is not a sphere any more . Does it mean that the volume in that case is directly proportional to radius? And is density inversely proportional to the square of radius? (Since the mass is increasing by same multiple as the radius decreasing?
Usually, when we study algebraic topology, we learn a lot of theory with just a few examples, like compact surfaces (orientable or not), wedge product of many circles, and a combination of those. Are these any slightly more complicated but special examples which shows important facts about the truth/falsity of some interesting statements? I find that I need to know more examples, but I do not know where to start. Some reference would be helpful. To be more focused, I am mostly interested in just singular homology and spaces with "low dimensions". To give an example of something which is more specific, for instance, examples of spaces with homology different from the examples above would be interesting.
Arrow orbit around point C like graph show. Is motion of arrow, rotation or curvelinear translation according to physics definition? What is definition and types of translation and rotation? I find this: "When the paths of motion for any two points on the body are parallel lines, the motion is called rectilinear translation. If the paths of motion are along curved lines which are equidistant, the motion is called curvilinear translation"
Can anyone suggest a reasonably generalisable way to generate these marginal drop caps? The key features are that the drop cap may be more than one glyph long its width is scaled to fill the margin (minus a bit of white space for legibility) its height is scaled to a user-specified whole number of lines (nb. the first example spans five lines and the second four).
Our pre calculus teacher told us to start our mathematical investigation and he gave us three topics to explore to formulate a problem, a title and a our own formula that is novel or cannot be found in the google. Our group decided to focus on the third topic that was given which is algebra. So I would like to ask for help if you could give me ideas on what to research and come up with a problem/situation involving algebra. Thankyou
I made a guess two years ago. I have a strong feeling that there is a proof using the fixed point theorem with geometric visualization, but I couldn't do the proof. If you have a simple closed convex curve, thr line Perpendicular to the tangent on the curve at both ends must be present If this feature is already known, please point to a reference that mentions it If you can prove it would be appreciated, thanks
Bases for vector spaces are non-unique. Also, new bases can be generated from other bases very easily and formulaically. Is there some "prototype" basis, which we could find for every vector space, that defines a specific relationship between the elements in and across the different vectors for every possible basis for the vector space? In the same vein, how generally can we specify what a basis looks like for some vector space?
My sense is that it never means an actual physical defect as in, "The quarterback's knees were shot -- he could still throw, but he knew that to management he was damaged goods." Or can it be used in the case of concrete damage to a person's body as the above example? It seems like for a simple medical issue, the term is too nebulous and indeed would be used when the extent or classification of the problem is not so clearcut, like some psychiatric problem that most people do not fully understand.
I cannot simply know where to use "port" and "interface", because these two words translate into one same word in my native language. So, I wanna figure out the difference between "port" and "interface", and when and where to use which. In my understanding (please correct me if I were wrong), the physical things, such as the holes on the side of laptop into which you plug the power cable are called "ports", whereas the visual holes inside the laptop, such as the signals transmission connection are called "interface"?
I'm Finding it hard to visualize how higher pressure makes the boiling point higher. I understand how pressure increases then temperature increases such that say air molecules compressed gives it energy and then the molecules move fast and average kinetic energy increases hence temperature increases. But When we can say pressure increasing the bonds between molecules can easily be broken with the external force , but it somehow takes more temperature to disassociate bonds such that it transfers into a gas?
Let assume a metal tube open on one side having alpha emitter material on the other blocked side. Since alpha particles are blocked by the metal they will be emitted only through the open side and make thrust by the momentum of the alpha particles. Very small one, but continually accelerate the satellite. Partially depends on other question - how alpha particles are emitted from in depth of a chunk of material, aren't they blocked by the outer layer of this chunk?
It seems like 'my sister and her' are both subjects so it should be 'my sister and she'... And it would be if they worked on something specific together (the obvious object). Eg: My sister and she work on this project. But the "together" at the end changes everything right? Unbundling the sentence it is clear that it is actually saying "my sister works with her", making 'her' the object. In this case should it be my sister and her work together? Does the together really change the object?
I am given: Five points on the ellipse, The sharing center of the ellipse and the circle, And the circle. One of those five points is one of the intersections of a circle and an ellipse. Can we construct the three intersections of an ellipse and a circle that is not given? Blue ones are given, and greens are the points I want to find.
For a conductor in an external field, I would like to know whether the electron clouds of each atom, just shift slightly (resulting in positive charges just on one edge, and negative charges just on the other with all internal area remaining neutral). Or, whether the electrons fully dissociate, leaving positive ions throughout the conductor volume but with all electrons on one side. If this second case, then how would the electric field work out as zero inside?
Question: When we only listen to the sound of that machine (TV), not watching its screen, which is appropriate to say "listen to the TV" or "listen to TV"? Background: When we watch that machine, we say "watch TV"; and when we put it work, we say "turn on the TV." I think these usage indicate that we use "the" when the object is material thing not function. But we say "listen to the radio" or "listen to the music", so I wonder about the question stated above.
I had the following problem with the index: The alphabet order of the words in English: I have the order of capital letters come first then the order of small letters come next. I need the order to come according to the letters regardless of being capital or small. For example: Abed Dep Ced amid bned I need those words to be like: Abed amid bned Dep Ced The next issue is: I have one gap in the index as shown in the below picture
I only recently thought about this, and I can't come to any conclusion. An explanation for ferromagnets is perhaps explainable, and my teacher said Quantum Mechanics complicates things since the magnetic behavior is distorted, given for ferromagnets their origin is the spin of the electrons. But what about materials that are magnets but are not ferromagnets, for whom the origin of magnetism is not spin? Any of my reasonings is too vague for any explanation. If anyone can lead me to a source where I can read about this, I would be very grateful.
In my notes the axiom of extensionality is that 'two equal sets contain the same elements', this language suggests to me that there are two different sets that happen to be equal, which suggests there is an infinite number of sets with the same elements. I see this definition given many places and it causes me some confusion. This seems to defeat the point of equality, which usually defines the 'same value', the above seems incorrect then, is it just a choice of language and clearly there exists only one set with a certain group of elements, or can we have two seperate sets with the same elements?
From school we know examples of energy conversions: from electromagnetic to electric, from electric to heat, from heat to electromagnetic, etc. However, obviously this almost has nothing to do with conversion, because as heat, as electricity, as friction, and so on are electromagnetic field energy. But what if there is some electrically charged and massive particle moving at constant velocity and being accelerated by gravitational field, and not electrical. Will it emit (scatter) gravitational wave (quants) instead of electromagnetic, or both? Also in opposite situation, same particle, accelerated by em field radiates photon, only because of electromagnetic interaction, or it emits photon (and gravitational waves) independently on the type of interaction?
I recently learned that we always break components of force along and perp to direction of net acceleration (for simplification) So in problems involving circular motion.... We resolve forces along centripetal acc So in problems involving vertical circular motion...we break mg along centrifugal force(ofc working from non inertial frame) But in problems involving banking of road w friction....we break centrifugal force along and perp to mg ...Why so?? We should have broken Normal and friction along centrifugal force
Huygens principle. can we accordingly define refraction to be diffraction from an infinitesimal length slit? According to Huygens principle, sticking to classical physics terms. as long as slit length is at most a wavelength, spherical form of waves is maintained. If we look at propagation inside a homogeneous medium the shape of waveforms is maintained and we can claim "mono-refraction". So is diffraction actually a mono-refraction through an infinitesimal length of slit? As a thought experiment...
In PowerPoint, there are often nice three key point diagrams like (source: https://www.slideteam.net/performance-mapping-ppt-powerpoint-presentation-portfolio-graphics-pictures-cpb.html) or (source: https://www.slidegeeks.com/business/product/three-levels-relationship-marketing-examples-ppt-powerpoint-presentation-ideas-display) My question is, how do I best generate such diagrams in LaTeX for usage in beamer? I assume this will likely involve TikZ? Ideally, some guidance, if possible even a MWE could be given to create a similar nice diagram. That way, also LaTeX users can make use of such styles. One central node on the left, like in the first example Three (or even better, a flexible amount) of child nodes arranged around the central node (to the right of it) Text entries next to child nodes like in the second example Color style like in the second example
From the following image, why do we still call it isotropic? if the density at A and B differ, I don't think it's enough to call it isotropic. In my opinion, material is only isotropic if when we choose some point, around it in all directions, properties are the same throughout the end of the material from that point, but image taken from here, still says material is isotropic.
I know about the conditional sentences that go as following: "If I were he, I would have forgotten the whole lesson." In the sentence above, "he" is preferable to "him," but can it also be preferred in the following case? Whom can I trust, if not ___. a) he b) him I pardon, if this is related to conditional sentences. Quora has similar question but with very short answers, as in: Edit: I don't think my example sentence is concerned with relative clause, rather the first part of the sentence looks independent: "Whom can I trust, if not he" contains comma between them. And how does following sentence is related to the above sentence: If I can't rebuke him, whom should I rebuke. (Does 'him' makes sense here?)
the xelatex compile output will automatic write some output in content folder, when compile in the root of project, there contains a content folder and it works fine. Now I tweak my command and add the -output-directory parameter like this: xelatex -output-directory=/Users/xiaoqiangjiang/Downloads/cquthesis/out/ main.tex the out folder did not contains the sub-folder content make the compile failed. the error looks like: ! I can't write on file `content/introduction.aux'. Is it possible to make the xelatex compile command auto create the content folder in the output new out folder? because all the compile process was automatcially running by robot. I can not created the content folder by hand one by one.
Is this grammatically defective? The rides were fast and long, as well as exciting, despite my apathy. Context: I often find myself writing sentences that I don't want to reorder but may contain an error, and am ignorant of grammar, if not absolutely naive; I have confused chat-gpt, asking it this. Background: I understand, I think, that it would be: You can either do "The mayor, as well as his brothers, is going to prison" or "The mayor as well as his brothers are going to prison." but am reluctant to admit defeat yet.
I am a student in robotic assocciation and I designed working spectrometer for UV-Vis emission spectrum. The issue is evoking emission spectrum. The spectrometer is designed to be working on board of martian rover. Can I evoke the emission by shining the rock samples with UV lamp or X-ray lamp? We can't use laser beams or burn the sample due to onboard safety. Are there any other methods of obtaining one?
I had a sentence like this in my manuscript: [describing some limitation] .... Some studies worked it around by combining the results of two models ... in the sense that those studies made a workaround for the limitation. The native speaker changed the bold term to "worked around it", but I am almost sure I know the original form (from the IT world, where workarounds are a very common topic :)), and also can find it on the Internet. But I can find his version too, I just like the original one better. Are both acceptable? The result is supposed to be in US English, if it makes a difference. (Note that this paper is not in the IT area, but the statistical modelling methods in ecology).
Suppose a straight current carring wire of finite length if kept in a external magnetic field (perpendicular to its length say dot). I know initially it would experience a magnetic force of magnitude ILB due to drift velocity of charges inside wire but now the wire would gain velocity , but if I use lorentz law to find magnetic force again what way the wire be doing motion.
It is often recommended to the particular symbol from MnSymbol that you require instead of importing the package entirely such as the answer by @egreg. What is the general process of doing this? What if I need several symbols? Is there a difference, say, if I need an arrow vs. delimiters? Not really a question, just a complaint: seems crazy to me that I need to do this just to get a few symbols from a package that offers them.
Wikipedia claims for the proof of Arrow's Impossibility Theorem that when Every voter in segment one ranks B above C and C above A. Pivotal voter ranks B above A and A above C. Every voter in segment two ranks A above B and B above C. (B and C may switch for segments one and two but not pivot) by IIA the societal outcome must rank A above C, as in the previous case Why is this true?
In the light clocks, time ticks via the motion of light and since speed of light is constant therefore when the clock is in motion ,the photon has to cover a greater distance by the perspective of an object at rest . So in the perspective of object in rest time ticks at slow rate but in other clocks such as mechanical clocks .time ticks via the motion of different objects not light. and the speed of the objects are not constant.so from the perspective of an object at rest time ticks at the same rate. How can be this possible as time dilation affects all clocks?
So this was a test question, I answered that both cars have the same acceleration. Since the graphs for A and B both are straight lines, therefore, the acceleration of both must be zero. But the answer given to us was that both are moving with same velocity. These graphs are not always to scale, so I thought that the d option would be more appropriate than c. The beginning of the test says to mark the most appropriate answer.
In the solution to this question, they have first taken the component of downwards-acting gravity(g) along the incline which is the sin component then again they have taken the component of the gsin along the x-axis and y-axis. Now my question is how are we supposed to take the component of a component and why not just g in the downwards direction used for calculation of centre of mass?
Say we have a plate full of soup, why to cool it down we move the spoon around in the plate? Is it to facilitate the thermal interchange between the air and the soup? Also why is the edge of the plate always cooler than the center of the plate? It may be because of how close it is to the plate so it exchanges heat with the plate?
are modus ponens and tollens axioms if not how can they be derived or proved? if I am good at math then I am good at logic, I am good at math, therofe I am good at logic this seems evident but is there any proof for them? looking at the truth table for implication we see p->q is true when P is true and Q is true
I'm trying to name categories on my online shop, I have a category for whimsical items, kids, etc. I'm trying to name a category for items that have actual day to day functionalities. For example, a suction cup used to fix car dents. Thus: Manual lint remover Manual fruit juicers Car back seat bag with pockets Scratch removal device for cars... These products, _____s, are mainly cool looking items, all with special functionalities.
This question about how to choose a singular or plural verb for sentences with number as the subject has been asked a few times here. Nonetheless, will ask again for the following sentence: The number of each type of fruit (apples, oranges, and bananas) is chosen based on the published price. This answer The number of students is larger and this answer A number of questions have been asked describe that the definite article "the" indicates that a single number is chosen. In this case, three numbers are being chosen: one number for each type of fruit.