darklight03/StackMIAsub huggingface dataset:
How do you find the area of the highlighted subsection of a circle? Linked Below. The circle has a known radius from A-O and a trapezoid that lays inside it. The trapezoids longest edges contact the circle circumference at points D and E. All edge lengths of the trapezoid are known. The shortest distance from the center of the circle to the inner most edge of the trapezoid is also known, O-F. I'm trying to design a lid with these dimensions and need to know the area to get the lids weight. The trapezoid portion with the highlighted area will float on top of a fluid. Unfortunately, I don't remember much from my High School geometry class. Thanks for the help in advance.
I'm curious about pendulums and their behavior during a solar eclipse. I also wonder about gyroscopes and if their behavior during stellar events has been observed. I wonder about the both of them, and of their relationships to each other. I wonder about Mobius loops and gyroscopes; what if a gyroscope was a Mobius loop in rotation, would it precess in a traditional manner? What if you lined the outer rim of a gyroscope with a plurality of strong magnets, all spinning the same way outwards? What would happen next? I wonder endlessly.
Suppose, I have a sample from an unknown distribution. I want to prove/disprove (mathematically!) the following statement: The maximum likelihood (ML) estimator for the (unknown) population mean will always be equal to the sample mean irrespective of the likelihood function. We suppose that, the likelihood function is twice differentiable with respect to its parameters and the mean and variance is finite under the inverse likelihood function (pdf). I believe for symmetric distributions it is straightforward. To maximize the likelihood the center of the mass should be placed at the mean. So, sample mean should be the best estimator to maximize the likelihood of the observed data. But I can not relate to it mathematically.
I have a question about contact force and normal force. whenever two bodies are in contact and one body tries to push another body there will be a normal force acting between them. like when we push or pull a body, when we hit a ball by a bat, when we lift a body from ground, like pushing a wall at horizontally or at an angle etc... these all are contact forces does that mean that all contact forces are normal force?
Basically something that starts with the substitution principles, definition of an equation, of subtraction and division, axiom of opposites, your usual commutative, associative, distributive axioms, and covers all the way up to the end of high school trigonometry. Dolciani's two volume "Algebra: Structure and Method" was good but I need another similar work. Serge Lang's "Basic Mathematics" wasn't good enough. Reading the first few chapter of abstract algebra books wasn't that helpful as they were too broad in scope. Any other suggestions?
Lately I've been approaching problems with conservation of momentum of systems, I was wondering, if I draw the free body diagram, then write the equations and then add them togheter; if momentum is conserved along an axis I will always get that the sum of the forces must be equal to zero in the equations of the dynamic along the axis where momentum is conserved, is that right?
I see that the Oxford dictionary has a plural dice for "a small cube with a different number of spots on each of its sides, used in games of chance". However, there is no plural listed for "a block with a special shape that is used for shaping pieces of metal" (both definitions summarized). Researchgate has a photograph of "Two dies arranged side-by-side". Is dies the correct plural of this meaning of die? Why do the two meanings have different plurals? Which was in use first?
For a new book I am writing with two friends, I like to include three biographies (mine as well as the other two friends) after the preface. Ideally, we like to keep three photos (A.jpg, B.jpg and C.jpg) on the left and our biographies on the right.. The book is in single column format, and I don't know how this biographies page can be done in double column format. Also, the biographies need to be aligned with our photos. We are OK with any format or style in a professional way as long as we can post our biographies along with the photos. Your suggestions are most welcome. Thank you.
I have a pretty strict requirement for a document (I'm currently using memoir), which must: use biber/biblatex in the usual way based on a primary bib file (e.g., main.bib), and sort the resulting list of refs by author then year. at some other point in the text, I want to print out a list of all the refs of type article from a secondary bib file (e.g., extra.bib), sorted by youngest to oldest. Is there some biblatex voodoo that would make this easy-ish?
This particular example comes from a peer-reviewed publication with authors who seem to be native speakers: This trend is both popular and has presented a variety of challenges I wonder if this is grammatical? If this sentence didn't have "both", we would parse it as follows: This trend ((is popular) and (has presented a variety of challenges)) But with "both", what do we have? This trend is both ((popular) and (has presented a variety of challenges)) but this gives us "is has presented", so this parsing is incorrect. Alternatively, we could try This trend ((is both popular) and (has presented a variety of challenges)). but then "both" goes inside the first coordinate. This is different from, say, You and me both where it's at the end.
How or where can I find the Absorption cross-section of Gaseous Ions? I have looked over the internet and can only find it for neutral atoms. Does it increase or decrease for ions? I have found formulas but they include the imaginary part of the refractive index of the specific medium and I can't find how to calculate or get a relative order of magnitude for it even for plasmas. Scattering cross section will do too Please help.
Let ABCD be a convex quadrilateral with AD = BC. Show that AD and BC determine congruent angles with the line passing through the midpoints of sides AB and CD... MY IDEAS MY DRAWING As you can see i noted some points. Okey, so, i thought of similar or congruent triangles. But i don't know where to start. Hope one of you cn help me! Thank you!
There is literature on the lie symmetries of quantum harmonic oscillator differential equation. The generators satisfy certain lie algebra. On the other hand, we have ladder operator method. The relevant operators satisfy some lie algebra. I was interested in knowing if there might be some connection with the two approaches. Is there some relation between the two lie algebras. Cause if there is, it might help me explain ladder operator method better.
In the Einstein field equations, the only tensor that shows up is the Ricci tensor and the metric tensor, together with the Ricci scalar. The Weyl tensor though is a tensor that is a part of the Riemann curvature tensor as well (the off-diagonal part). It represents tidal forces, which are non-local. Why doesn"t the Weyl tensor show itself in the Einstein field equations? Is it because gravity is based on the equivalence principle, which is a first-order equivalence?
I had recently come across "Russian for the Mathematician" by S.H. Gould, and saw it as a wonderfully useful resource. I have very little experience in Russian (only skill is ability to read Cyrillic), but I saw it as a useful introduction to the language, in the sense that I would be able to decipher Russian language math literature without the need to be entirely fluent or understand every word. Reading through a preview, I like how it breaks apart the words piece by piece to I was wondering if there were any resources for other languages in this similar vein, e.g. learning French or German with the main focus of reading scientific or mathematical literature. Downloadable here
I hear this kind of false implications pretty often, e.g.: If you're smart you'd agree with me People who understand the situation would all agree that ... Anyone who says something else must be trying to confused us These often come up in social deduction board games, where the good team is trying to gain information and the evil team is trying to spread misinformation. If someone says one of these lines and I disagree, they can say "see, he disagreed, so he must be on the evil team". Is there a term for this kind of faulty logic trap?
Is it possible to use magnets to lessen the force of a pull that is associated with Cervical Dystonia (spasmodic torticollis) which is causing an involuntary pull of the head over one shoulder. Having the magnets attached to clothing on one side such as a shoulder pad and more on a collar. Would the strength of magnets keep the head from pulling to other side ? As a person with Dystonia I'm trying to find a way of creating some sort of "crutch" to allow the head to look straight :)
Imagine a tank that accelerates towards a relativistic speed. As the caterpillars are at rest with respect to the ground, the caterpillars will show no length contraction there. But the tank body above it will. The upper part of the caterpillars, on the other hand, will show more contraction than the tank body does. What will happen? Will the lower parts of the caterpillars slide along the tank body to "deliver" an extra piece of caterpillar for the upper part which contracts more than the tank body? Will the caterpillars snap? I'm not sure.
This question may have been asked a bunch of times, but I have not found exactly what I was looking for. I say calculus, but mathematical/real analysis works as well as long as it does not have calculus as a prequisite. I have been looking for books that take an inquiry based approach, where the theory and everything else is build by solving problems with minimal explanations from the Author aside from introducing some definitions (Bogart's "Combinatorics Through Guided Discovery" is exactly what I am looking for, but for calculus/analysis). I am aware of jiblm, but I was wondering if there are published books on calculus/analysis using this approach that may be more suitable for independent learners?
According to MathWorld, the probability distribution of the length of lines between randomly selected pairs of points inside a cube has a very complicated form. In particular it is not uniform. This distribution relies on the fact that the pairs are chosen uniformly and independently. My question is - is there a way to do a reverse engineering and enforce uniform line lengths density? Namely, say I want the probability distribution of the length of lines between randomly selected pairs of points inside a cube to be uniform, from what probability distribution should I sample my pairs? In particular, I want this sampling to still be independent, but not uniform.
If I use a transformer the get a high voltage, the power of the transformer remains the same, as the current is reduced proportionally. However, according to ohms law, the current through a resistor connected to that secondary side of the transformer will be the voltage divided by the impedance of the resistor. But that is impossible, because this way both the voltage and the current felt by the resistor will increase, meaning an increase of power, while the power of the transformer remained the same, compared to the first side of it. Please sort out my confusion over it.
Yesterday I heard this: suppose you have a rubber hose, in which you inject helium, which replaces the air which was there before. Now, because there is no helium in air, so the partial pressure is zero there, the helium escapes through the rubber into the surrounding air and creates vacuum in the hose (insofar it is possible in a rubber hose, effectively you'll get substantially lower pressure than before). Is this correct? If so, se can create vacuum using a solid membrane, which permits the gas (that we used to replace the air inside) to escape to the outside world, where its partial pressure was zero/low?
I have found a sentence that goes like this: "Serenity may be the name of the company, but it doesn't describe the company." Someone translated this sentence to my language as if "may be" meant there was a possibility that Serenity was the name of the company (and a possibility that it wasn't), but I feel like the sentence really means "While Serenity is the name of the company, it doesn't describe the company". Is there a specific name (akin to "non-continuous verb" or "inclusive or") for this usage of "may be"? I want to be able to say "This sentence is using a [...], so the correct translation would be...", chere [...] might be something like "comparative may" or "comparative auxiliary".
[A partial groupoid (half-magma) is a set S equipped with a (single-valued) partial binary operation, as in Bruck's Survey of Binary Systems.] This question may be nonsensical, given that the duality between Cayley graphs and groups is deeply related to the mutual complete-ness of each structure. If that is the case, perhaps what I am really asking for is a common diagrammatic representation of partial groupoids. Here is a crappy mock-up of what I'd expect from diagrams of half-magmas in the latter case. If Cayley graphs encode the abstract structure of group, is there a similar type of graphs that encode the abstract structure of a partial groupoid? If there is not, is there some other commonly used diagrammatic representation used for partial groupoids? Thanks!
There is a medical specialty called obstetrics and gynecology. In the UK I have only heard this truncated to something like the first syllables separated by a truncated "and". This could perhaps be written as "obs 'n gy-nee". I have multiple times recently heard this specialty referred to by Americans by spelling out prominent early letters, an initialism. This could perhaps be written as "oh bee gee why en" (as in one spelling out OB GYN). Is this a UK/US difference? Is there a "right" way to abbreviate this specialty? I am particularly interested in how it is said, as opposed to how it is written.
While solving inverse function problems, I got confused in a part, like for any Inverse function to be defined, it must be one-one and onto, then in many questions why the codomain is given more than the Range as if we know that the codomain must needs to be equivalent to the Range for the Inverse function to be valid or defined, then why does they gave us the codomain different from the range? Kindly help me solving this doubt.
So I understand that matter emits EM waves when hot. And that the higher the temperature, the shorter the wavelength, so cooler flames start off orange and the hotter flames reach light blue and white. What I'm wondering is if, hypothetically, you could take that blue-white flame and could make it considerably hotter, would the emitted wavelength reach UV thus making it invisible to the human eye? If so what temperature would need to be reached?
I am interested in modeling the populations of low-lying, long-lived "dark" electronic states after excitation of an atom in the ground state with a laser. Using just a regular rate equation solver, I get nonsensical results. Provided there are no interactions between the low-lying states and the branching ratios to these states are known, is something like an Optical Bloch Equation solver needed to determine their population as the laser irradiates the atom?
I downloaded a nice latex class, but I'm having trouble with one aspect of it - every page's header gets marked with either the chapter name or section name. As you can see, it makes the page look really cluttered. The code for the class is here. I've tried for a really long time to solve this, but I can't. I searched online and found that some commands containing mark have that info, and I've tried commenting out lines containing such commands. Still no luck and could use some help on this - I just want the page numbers to show in the header.
If a block of mass m is attached to one free end of a spring and is performing simple harmonic motion of some amplitude A . Now if a wall is placed at some distance x (x < A ) from its mean position . It collides elastically, how is its amplitude going to change ? [ Will it be different in the side with the wall or uniform throughout? ]
We know that sound travels through a medium through vibrations in the form of longitudinal waves. An example of it is here: We also know that particles of any medium vibrate when we give them more energy in the form of heat which gives them more kinetic energy. From this a logical inference can be drawn: heating the medium might disrupt the propagation of longitudinal sound waves. Consequently, should the disruption occur, would sound production be inhibited altogether?
I am taking the second law of thermodynamics in the 'useful energy minimized' sense, although I am not sure if that is necessarily the most correct. Take the example of two electrons: electron A and electron B. Electron B has a wavefunction. Can we say that electron B's wavefunction will not have high probabilities close to electron A because that would lead to there being more useful energy than otherwise? Otherwise, is there a similar type of 'wasted energy maximized' or 'entropy maximized' for singular wavefunctions rather than groups of particles? Instead of treating entropy as an outcome of different particles, perhaps the wavefunction's different possible positions of particles can do a similar job?
I know that the work done by gravity in going from A to C, and from A to B to C is the same. I also know that the work done by an applied force in going from A to C is the same as negative of the work done by gravity if there is no change in kinetic energy. But what is the work done by an applied force in going from A to B to C if there is no change in kinetic energy?
It is assumed that a valid QFT, must have states/observables in a Hilbert space, transform according to the projective unitary representations of the Poincare group. I can understand why the observables must transform according to unitary representations of the Poincare group, but don't see any compelling reason for that symmetries must be projective as well. Some have explained it, as it is required for dealing with the phase factor redundancy in the wavefunction,but I guess this redundancy is dealt by the unitary representation itself, as the phase factors cancels out. I don't see why a phase factor redundancy demands the symmetry be projective.
Exactly the question above. I've recently posted a question, and the more I look at it, the more it seems like a bug to me. The upstream code base on GitHub seems pretty inactive too (for about two years), having many open issues. I'm missing some experts who could help me or even the maintainer. Do you know whether there are good alternatives for PGFPlots which I can integrate easily into LaTeX and are quick to learn?
Imagine spreading double-sticky tape all over the surface of a car or a plane. Would there more significantly more aerodynamic drag as a result of the adhesive 'sticking' to air molecules and slowing down? This would certainly cause more resistance in solid mediums but would this cause more resistance in air or water? If an adhesive surface can drastically increase friction with solid surfaces, could one also increase friction with the air?
In finding this article, I questioned my understanding of the word 'gadget'. My current understanding is the word is (and please let me know in your answer if I'm right or wrong on this one) synonymous with 'accessory'. The only difference really being that accessory somewhat precedes the technological age. Hence, 'gadget' carries a sort of electronic/technological connotation (but not necessarily?). The article enumerates a 'backpack' as a gadget. Is that correct?
A lever and a fulcrum is able to to multiply the input force to the output force and trade moving distance for increased force. The same happens in automobile transmissions, taking advantage of high motor RPMs. What exactly is the physical mechanism behind this? I am very aware you can mathematically prove it, for instance via an energy approach where energy in roughly equals energy out. Still, is it possible to explain the phenomena down to atomic level? That is, how is it in qualitative terms, that the force on the other side of the lever is amplified?
I will have to teach a first course in differential equations. A good motivator might be to promulgate modelling with differential equations but I have seen some teachers have made polemic against modelling. Are there any really good resources on modelling with differential equations? I want something which will have an impact and motivate the learner. I am not really looking for artificial engineering examples but some bona fide real applications. Also, would like to bring in some history of differential equations to motivate the learner.
What are local laws? I was reading this line in a book... Newtons second law is a local law. This means that it applies to a particle at a particular instant without taking into consideration any history of the particle or it's motion. What does this mean in simpler terms? Are their non local laws as well? Please explain with an example. I'm a high school student.
It might well be that universal constants, say the speed of light, are only constant as far as we can tell in our chunk of the universe - in the same way that the Earth looks flat in the area you live. Are there any ways to tell that the speed of light is actually the same not just in our "neighbourhood" but in all the observable universe?
Take a deck of cards, cut it in three, and rearrange the three packs in any order (for instance, the middle goes on top, the top in the middle, and the bottom stays). Repeat as many times as you want with different (and possibly uneven) cuts. What permutations can you generate? Motivation: given a set of symmetric matrices, the trace of their product does not change if they are subject to a permutation generated in the way above.
I may be misunderstanding the general idea and the following specific example, but I was told that Dirac predicted the existence of the positron based on a formula for the motion of the electron(?) and then feeding in a negative value or imaginary value and somehow this suggested antimatter being a real thing. Sure enough the particle was soon discovered; perhaps the discoverers were guided by Dirac's work. But just why would anyone expect this? Could it not be that an equation works in many cases but not all? Was Dirac surprised by the discovery of the positron or would not finding such a particle have been more of a surprise?
If we consider the addition of orbital sngular momentum L and spin angular momentum S to produce the total angular momentum vector J, then J is a member of the vector space that is constructed by taking the tensor product of the vector spaces associated with L and S. Why don't we take direct sum of the vector spaces of L and S instead to construct the J-space? Why are we particularly using tensor product to combine the spaces?
From my textbook, A noun phrase is headed by a noun. Modifiers include articles, adjectives and demonstratives. Qualifiers include prepositional phrases and relative/adjectival clauses. Given the following: Your bag is in your locker What is the grammatical name? I know that its grammatical/syntactic function is the complement of the preposition . The problem is that I suspect it is a noun clause because "your" is neither an article, adjective nor a demonstrative. It is a determiner. Also, a noun clause can be perform every function that a noun phrase can, or so I think.
Recently I learned about Markov chains. Consider a simple two-state Markov chain: This looks like a categorical diagram, with states as objects, transition probabilities as morphisms/arrows, and of course, identities as the same state transition probabilities. Although I don't know much, I also came across connections between two separate Markov chains, implying a functor equivalence. I wonder if there is such treatment in literature. Is there any benefit in approaching it this way?