darklight03/StackMIAsub huggingface dataset:
Is the word multiperspectively (sometimes polyperspectively) only used to describe literature, as in narrative perspectives? Could I use it to describe a personal trait? For example: In debates people despise that I multiperspectively argue.... I did see a post asking what the word was for "seeing from multiple points of view" and this word didn't come up. Also, I understand this is a serious English site, my question is not for any scholarly reason. I am trying to write to a person and I got stuck while trying to find an adverb that means this.
I have a Kalman filter that uses location as part of its internal state. This location is expressed as x, y coordinates in meters north and west from a fixed point (the home location). Part of my measurements for the filter are GPS coordinates. Can I translate the measurements back to the state space using the H matrix? The range of movement for the tracked object is small enough that I can use a fixed multiplier to scale the longitude to meters. But how do I add the transpose to the matrix, so that the GPS coordinates use the home location as the origin?
I am self studying algebraic topology, the fundamental groups and covering spaces and homologous groups. I have read the topological properties of classical matrix groups like connectedness, path connectedness and compactness. Now I want to study the algebraic topological properties of these groups. In particular what are the fundmental groups of patnconnected components of the matrix groups? Does there exists any relation among the matrix groups via covering spaces? If anyone provide some referances regarding these questions that will be very much helpful. Thanks in advance.
When an electromagnetic wave interacts with a free electron the electron starts to oscillate in the direction perpendicular to the propagation of the wave meanwhile when a photon interacts with a free electron what will the electron do? Will it oscillate in the direction perpendicular to the momentum of the photon? or will it travel in the direction of the momentum of photon? How can someone describe this interaction in photons form so that the electrons oscillates?
In present tense or past tense, subject and verb can be omitted after conjunction. For example People tend to laugh when (they are) imagining pleasant things When (I was) going home, I met my father Then could it be possible to omit subject and verb in case of the past perfect tense as well? For example, As it had been written in a hurry, the report showed many errors. As written in a hurry, the report showed many errors. Or, because this case is of the past perfect tense is changing this way only correct? (Having been) written in a hurry (without conjunction 'as'), the report showed many errors.
I live in this region and is studying to retake the national test and I need a big amount of tough exercises to practice but I can't find good documents/ textbooks over here. Any appropriate textbooks help me greatly. The topics are: calculus, algebra (especially logarithm), complex numbers, Oxyz algebra(?) (I really don't know what to call this one. It includes the equations of lines, planes, spheres, etc. And vector formulas. No matrices.). Thanks for your help.
From the perspective of an electron in the double slit experiment, does the "rest of the universe" that it is disconnected from behave in the same manner as the electron does in our view? As in, is the world around it, from the electrons point of view, as a closed, separate system to be interpreted the way we see the electron? Is the effect relative? From the electrons perspective, could it be in a "collapsed"-state and consider only the universe around it to be in a superposition? I hope the question makes any sense, because I am really curious and a little confused about the whole thing. Thanks in advance!
I was reading Lazarsfeld's Positivity in Algebraic Geometry, and I realize that Cartier divisor can have torsion elements, but I can't find such an example. I know for the Noetherian scheme that is locally factorial, the Cartier divisor is isomorphic to Weil Divisor and we know Weil Divisor group is free therefore it's torsion-free. So this can only happen when the Weil Divisor do not isomorphic to Cartier divisor is there any example that the Cartier divisor has a torsion element.
Okay, apart from the American slang term, or the reference to a male chicken, what is the meaning of the syllable "cock"? For example, shuttlecock ... in badminton. Or, as I'm doing housework and learning about plumbing, a "ballcock" valve in a toilet, or a "sillcock" valve in pipes? Does it refer to a specific shape, or a mechanism or something? Which might make sense for the valves, but then what about the shuttlecock?
I can't decide what I prefer - having empty space at the end of a page or a split box. For example: Should I be aiming to make sure the page is full with no need to break boxes? Like, I can add more text I probably don't need further up the page so that the last box starts on a new page, is this something people do for aesthetics? Or should I be happy enough with a break like this? Or the empty space?
Consider the small weight is attached to a big diameter wheel and the big weight is attached to a smaller diameter cilinder. I've read that if you ignore friction and all the forces are balanced perfectly, you could consider the possibility of this machine lowering the lighter weight through the distance of one wheel circumference at uniform speed while the heavier weight is raised by the smaller distance of one circumference of the cylinder. In this situation, what would be the forces that balance out the differences in the gravitational forces that act on each mass?
I know the restatable environment from the packages thm-restate combined with thmtools, which allows to formulate theorems that can be restated later in the document. Now I am wondering, if there is a similar solution for equations like equation, align, etc.. I have already tried to just reuse that restatable environment for equations, but as expected I got an error. I have already found "solutions" that suggestion to copy the content and tag the reference number. However, this seems to be a stopgap.
I would really like to create these pictures to help with fractions. I know how to begin using tikz package. I am not sure how to go about setting it up so that I do not have to draw it separately each time. I would love to show something that I have started with but have no idea. And what if I wanted to make the rectangle horizontal and not vertical? Thank you so much for any responses!
Suppose that I have two electrons in a box that were originally spread by a infinite potential wall. The two electrons are in their ground state wave function (sine function). Now I removed the barrier for the two electrons to interact. How is the Pauli antisymmetrical pair formed? Do I have to impose them to become the antisymmetrical pair in the beginning, or can I derive the antisymmetrical form from the original sine functions?
If I were to have asked this question about local systems, it would be extremely easy to give examples from physics/biology, etc. I can give example if people want, but this should be easy to Google. Question: What examples of perverse sheaves naturally show up in nature? More specifically, I mean examples which are not local systems, and the example only applies to perverse sheaves (or constructible complexes of sheaves) and not sheaves of vector spaces in general.
I am not sure why the following configuration can not be a configuration of a electromagnetic wave. I mean, i am sure it can not be the configuration of the fields in a plane perpendicular to a wave, but i can't explain the reason in a satisfactory way. Look, it seems there are souces propagating with it, since these configurations are the configurations of a point electri ccharge and a infinite line with current. But i would like i better way to explain why we can't have it.
At a weight m, a plane is acceleration upwards at rate of a. We also remember the value of g. From my understanding, we have two opposite forces that we care about. The force due the gravitational acceleration, which points in the negative y-direction, The force of the upwards acceleration, which points in the positive y-direction. The first force must be equal to m times g, while the second would be equal to m times a. However, that is not the case with the upwards acceleration. My physics book gives this reasoning for calculating the upwards force: I don't understand why we would add g, since it points in the opposite direction?
The question is simple. Could analog computers (for example, electrical analog computers) in effect avoid traditional numerical instability problems that come from solving a set of PDEs over a discretized domain? Progress on significant physical problems (the computational aspects at least) are often substantially delayed because of time spent figuring out how to avoiding numerical instabilities, and often the solution ultimately utilized is just to hit the problem with lots of artificial diffusion, which seems unrigorous at best. Also, since many physical theories are often significant approximations themselves, maybe some accuracy could be sacrificed (in moving to analog computers) for the greater benefit of avoiding numerical instabilities.
To my understanding, normal reaction is a force that pushes in the opposite direction of gravity, in order to keep the object from falling, or phasing through the surface. Though, what happens when we enter a circular rail? In this case, the guide book is saying that the normal reaction is pushing alongside gravity. Then, shouldn't it fall down? I thought the normal reaction was supposed to be pushing upwards in this case. If not, then is the normal reaction always bound to the center of the circle? I can provide the exercise with the answers, in case there's not much details in there.
A grad school problem has been haunting me for years and I have never been able to find it on the google machine nor was the professor who assigned the problem able to describe how to actually solve the problem... How do you find the surface area of an ellipse projected onto a sphere? The real world application is what is the footprint area of a satellite transmission signal so you know how long a ground station will be in contact with the satellite?
Say a spaceship is traveling at a certain velocity v (>>c) and it emits light from the nose of my spaceship in the direction of travel. The speed of light is finite and hence there should be a change of wavelength of light. How does the speed affect the momentum transfer does my light have lower momentum thanks to the direction in which it has been emitted?
My math professor told us that the upper and lower bounds theorem of polynomials (pictured) applies not only to rational roots, but also to the modulus of complex zeroes. They were unable to come up with an explanation for why this works, and I do not grasp this concept at all. Why/how does the bounds theorem apply just as well to to complex zeroes as it does to rational zeroes? How does the modulus come into play at all for that matter? Bounds Theorem
I heard that if Universal Expansion continues at some point galaxies will be so separated that a future civilization would have no way to know there are other galaxies, for them the Galaxy they live in is alone in the universe. (I'm planning to write a sci-fi story about it). Thus more or less in what time frame would that expansion would cause that effect? Thank you in advance.
I am new to it, so please help. As I know, AC current is back and forth motion of electrons, which radiates electromagnetic waves, so there is energy radiation from power line to our home. But in case of DC, if the magnetic field and electric field are static then how does energy radiate. I have searched that drift velocity of electron is slow, so DC flows at the same speed as of AC which is C. So, how does this happen if there is no radiation of DC? Please answer.
I have a body on a horizontal surface with friction. My thermodynamics system is only the body and I want to describe this with the first law of Thermodynamics. Suppose the body has a start kinetic energy and for the friction in the final state it has no more kinetic energy. For this problem there isn't a heat exchange but only a work exchange caused from the friction. How can i write the fist law with this system?
I have Two parallel lines, I want to create from one line to another using a cubic Bezier curve (S shaped basically), I'm free to pick any start point and end point. But the constraint is this path should be optimally shortest, also another constraint is I don't want the curves with too much curvature, I just want to switch to the other parallel line smoothly without creating too much curvy path. My question is how to pick start and end point? for having such a curve? I'm considering Bezier curve would be best for this with my very little research Thanks :)
I was thinking about the definition of reversibility but there is something that I cannot understand. In real life the surrounding of a system (anything else in the universe) is always changing making impossible a reversible process even if the process is slow enough to guaranteed the lack of friction heat loss and this surrounding are not in thermodynamic equilibrium so I cannot understand how people calculated entropy under such conditions, am I wrong in the assumption of choosing the surrounding as everything outside the system or it is enough to choose the immediate surrounding that is in thermodynamic equilibrium?
My question is whether there are some books on chess mathematics with theorems and their proofs concerning winning strategies for classes of initial positions. Despite there being a lot of books on chess theory and surveys on the use of AI in chess, it seems there is no purely mathematic chess theory that may use the results of game or group theory. If this is the case, then someone has to start it (despite obvious combinatorial difficulties).
What is the best way (as in most efficient) way of writing pseudocode like below? In particular I like that it is well-structured but gives enough freedom in writing (in reality it it is just standard inline text aligned in a specific way). If a library was used I would be grateful if anyone can spot if. In case there isn't such library, how can I achieve the result?
The following graph is a sensor measurement. Scatter plot The data points are also available in this excel file. I want to do some offset correction/scaling to make the measured points match the actual points. What is the simplest algorithm to do computationally by programming language like Python or MATLAB. These data are acquired in MATLAB continuously point by point, and I have to apply these offset to each point. Will something like finding a linear fit for all possible points and multiplying it with a polynomial work? or if there are any better methods, please suggest.
I am wondering if a vertex can lie on an edge in a planar graph- I am not sure if an edge of this vertex is regarded as crossing the edge on which the vertex lies. I have two questions here: Is the actual edge from the vertex tangent to the edge on which the vertex lies? Even if it only is tangent, does it still fit the definition of a planar graph that edges don't cross- as crossing would mean it would have to go through the edge and out of the edge, rather than just touching it at a single point? Is a vertex simply a point and an edge a line segment in the sense in which these terms are defined in plane geometry?
I'm not scientifically adept, so bear with me. Would it be feasible to retain enough fuel on new satellites/space stations, etc., that we could dispose of them when obsolete by sending them to the sun where they would likely incinerate before they came close to the "surface." How would we ensure burn up rather orbiting the sun? Already in earth orbit, how much speed would be needed to "hit" the sun? Impractical because of fuel needs? We could use the space station as an example. It would seem to me that eventually the gravity of the Sun would pull it lessening the need for fuel, it's getting way from the rest of solar system's gravities that would require fuel.
according to my book the perpendicular component of reaction force is called normal force when there is contact between two bodies. I can not understand that how for example when we jump we pushes the ground downward(action) and the ground pushes us upward(reaction) how this reaction is normal force? or for example if someone jumps to the shore from a boat, the boat moves in the opposite direction we push boat in backward direction and boat pushes us in forward direction(reaction) is this also normal force or friction force plz someone explain i dont understand.
Countable atomic structures are homogeneous, i.e., all finite tuple of the same first-order type are conjugate under automorphisms. While this is classical, I can't think of an example of a countable structure whose homogeneity is best proved via atomicity. Competing proof strategies include construction of that structure as a Fraisse limit possibly in an expanded language. Is there a countable structure whose homogeneity is proved via atomicity in a manner at least as good (whatever that means) as via Fraisse theory?
here is a vague question: I recognized that adjoints of operators and commutants of non-degenerate self-adjoint algebras share similar features, e.g. the double adjoint of a closable, densely defined operator is the closure of this operator. The double commutant of an non-degenerate self-adjoint algebra is the strong/weak closure of it (double commutant theorem). It seems to me, that this property of double(something) implies closure is a recurring feature and I was wondering whether they are somehow related in a maybe category-theory kind of sense? Thanks
When is a category of sets and spans just a category of sets and kleisli morphisms? There is a link between spans and kleisli morphisms, but I feel like they are the same things. I guess I am assuming that the base category for the monad is Set. Is this only true for the multiset monad? To see how we can have a category of sets and spans, just see the nlab article here:
We know that a pair of scissors is hard to use at maximum opening angle, because the force from the blades pushes the object away from the scissors and the actual cutting force is reduced. If we would design a pair of (simple, two-piece, with one point of rotation) scissors whose blades have a limited maximum incident angle, or even better, a constant incident angle, then what shape does it look like? Does it have a mathematical form? image source amazon.com
If the large space voids between galaxies had uniformly-distributed "negative" gravitational lensing, would its presence be obvious from photos in the same way that the presence of Einstein crosses and Einstein rings make clear the existence of positive gravitational lensing? Or would it only cause subtle distortions, such as reducing the angular diameters of distant galaxies as a function of their distance from us or by distorting how light transitions into and out of a positive gravitational lens? If it would only cause the subtle effects (not obvious ones involving the inversion of images), is it possible for this effect to exist given what Hubble, Planck, etc. has received?
I have a question about article usage. I have two sentences and I'm struggling with the articles in the second sentence: There may be invoices on each table. When (?) invoices lying on (?) table disappear, it's a problem. I would guess the invoices and a table. My reasoning is that I'm not talking about specific table so it should be indefinite article. But definite article for invoices because we talk about specific invoices on that table.
If we get magnetic field lines on a piece of cardboard, shouldn't it form a gradient of metal pieces across the board (thick layer of metal pieces near the magnet and thin layer of metal away from magnet) rather than forming lines of metal pieces leaving crevices between them. Like in the red areas it is somewhat evenly distributed on board. But in the blue area they forms pattern of lines. Why do they forms lines? Why don't they form a gradient of metal pieces? According to me there are infinite field lines, and only the magnitude of magnetic field decreases as we go away from the magnet.
Lately I've encountered a few situations in discussions where I feel like there may be a word that is either more succinct and/or perhaps more wry than just 'ethically convenient'. An example sentence would be: You can only say you wont be involved in unethical thing because it so happens that you cant be because reasons unrelated to your ethics. You are being/You are _______. Basically something just fell on your lap with no personal effort, but you then take advantage of that to further your moral standing. Often it is done willingly, but it could be done with less awareness, perhaps through a form of delusion. 'Casuistic' from the answer here is interesting, but not quite right.
A dude has the power to split a nucleus. But this nucleus doesn't hit anything, it just explodes, and that's that. He explodes the atom. He can let the nucleus explode, or he can absorb it. I was making this character thinking he could just split an nucleus, and it would make a nuke-level explosion, and then he could absorb the power of a nuke. But is ONE SINGULAR nucleus splitting, with NO help whatsoever, would that ONE singular nucleus explode with the force of a nuke?
What bugs me the most is that since there is net charge, i dont know two things, how would that charge distribute across the surface (even though my intuition says that one of the sides will have more charge than the other) and how would one calculate the dipole moment since the distribution wouldn't be symmetrical about the X-axis (in this problem the equator of the sphere), i've found the potential around it via legendre polynomials which i guess could help, but i just... dont really have a good idea of what to do neither the confidence
To clarify with a made-up example: When you address the nation state ... Above, 'state' could be taken as either a part of an open compound noun ('nation state', see footnote), or a verb ('to state'). As a non-native speaker I notice that such ambiguous interpretations do briefly hinder my reading flow, as I have to retract a bit. Also, similar ambiguous cases don't seem that rare. Hence, must, or at least may, one use a comma to disambiguate such cases? In the running example, is this allowed (or even required)? When you address the nation, state ....
In piezoelectricity, the piezoelectric tensor is of rank three and its a reason why piezoelectricity is not present in all materials whereas for electrostriction, it is present for all crystal symmetries because the electrostriction tensor is of rank four. So, I think the presence of the electromechanical phenomenon is related to the rank of the related tensor because the rank is related to the crystal structure ?
I've always curious about one interesting fact. I will explain it with example. Currently, I'm watching an example which shows the following picture and says that box at the left is the speaker and it produces a sound wave. I wonder why it's being drawn like the above. since it's a longitudinal wave, which actually doesn't have the shape like that. Since particles move in the same direction as wave, their motion is right and left back-and-forth. On the graph though, I get why they end up drawing sin/cos functions, but in the real motion, they don't have the shape as on the above picture. Transverse waves do though which I get why. Thoughts?
I am learning multivariate regression, with matrix equations and heavy use of: Transposes Inverses Identity, idempotent matrices Can anyone refer some books where I can learn the properties of matrix equations. Practice problems would be a great help. (I looked up some standard books on Linear Algebra - for example, Anton - but the topics are different from what I need. For example, Anton has Vector spaces, subspaces, eigenvectors, which is not really what I need).