darklight03/StackMIAsub huggingface dataset:
The matrix is not necessarily symmetric. The highest eigenvalue is positive and real (per Frobenius). Assume there is another eigenvalue with real part less than or equal to highest eigenvalue, real part positive, and higher than any other real part of any other eigenvalues. By "semidefinite" eigenvector I mean that the signs of the real part of all non-zero components are equal, since an eigenvector is invariant upon multiplication by a scalar.
"Export settings" disambiguation and meaning. The aforementioned quotation is ambiguous. As I see it, it could mean either of the following: Export (verb) settings ---> Action of exporting the settings Export (adjectival noun) settings ---> Settings of export Is there a way to disambiguate "export settings" or is the English language, in such cases, inherently ambiguous and the actual meaning has to be inferred from context?
The sentence: This essay will analyse this topic from both points of view and express my opinion. I think might be grammatically incorrect because it combines two separate actions while the coordination sounds ambiguous to me. Alternatively, are these the more correction versions? This essay will analyze this topic from both points of view and then express my opinion. This essay will analyze this topic from both points of view, offering an analysis, and conclude with my opinion.
In the case of a particle system the wave function or state vector is in a superposition of possibilities before measurement. But does this rule apply in the case of vacuum state? Is it in a superposition of (energy) possibilities before measurement? We might say that nothing is there to measure in the vacuum. In particular virtual particles in the vacuum are non observable by definition. But with gravity, the effect of vacuum on curvature, can be measured and we can get information about it. Does "before measurement" make sense here at all?
In the book: Logical Foundations of Proof Complexity (S.Cook), we have a proof for the Derivational Soundness and Completeness of LK assuming that the underlying vocabulary does not contain =. In this proof is said that the soundness direction holds also when he underlying vocabulary contains =. Theorem in the mentioned book My question is, why the soundness holds with = and completeness does not?
Is there a single word to describe all the elements in a list, except the last item? The head of a list refers to the first item in the list and the tail refers to the last item. In mathematics and computer science, the tail can also refer to all the elements after the first; I'm not sure if that carries over into other domains. (chatGPT suggested "penultimates", which made me chuckle)
I Would like to know a place (book, paper) that discuss thorougly the problem of degenerate elements in singular homology. I know that they are not a problem with simplices but you need to explicity deal with them in cubic homology (Massey for instance) I have read an terse old paper by Tucker (degenerate cycles bound) that address the problem in simplicial homology but I would like further details. In fact I am puzzled because all the standard texts tiptoe this matter (Hatcher, Munkres, Rotman, Vick). Thank you very much. To further clarify Is there any result that allows to forget degeneracy at once or should we check that is not a problem in any theorem (Hurewicz for instance
Considering, the phenomenon of surface tension, is the interface of the liquid more dense than the bulk phase? Considering, if it were more dense, the phenomenon of surface tension would be explained, more dense, would result in greater strength at the surface. However, i've found various answers that state the interface is of higher density, while answers that state the interface is of lower density. Which one is the definite correct one?
So imagine this situation. An object is experiencing two forces, one due to gravity in downward direction and other applied by us in upward direction such that our force is less than gravitational force. So the object will accelerate downward and its potential energy will decrease. Will the change in potential energy equals to negative of the work done by gravity? And If so then how, isn't it should be less than that because of our force, but then the change in potential energy will be negative of the work done by resultant force. Thanks if you answer it.
When using Set heading in the margin to the left of text this method to place paragraph headings in the margin, this works for single-column documents. But when the twocolumn option of geometry is used (in report class), the second column's heading overlaps into the first column's text. Is there a way to have the left column's headings in the left margin, and right column's headings in the right margin?
Is there a Hilbert curve for every space? as I understanding it in layman terms, it's a way to order a space sequentially which visits every place once. Does it work with continuous spaces, or just discrete? Are there certain limitations of dimensionality that you cannot use a Hilbert curve to explore? I guess I'm asking if everything can be serialized? What must I understand to understand the boundary of the Hilbert Curve concept?
Why after Big Bang it is not going to Heat Death in the easiest path, actually the energy can get distributed uniformly to all directions. Instead we see the energy in Big Bang is being converted to atoms, then the stars, galaxy etc. are formed. Isn't these formations making the path to Heat Death more distant? Any natural law explain these formation of concentrated energy structures like atoms, stars, galaxy etc.
As we know, a star that is too massive to become a white dwarf becomes either a neutron star or if it is even more massive, a black hole: neutron stars form with great gravity that comes with great mass, the gravity pushing down on its core, merging protons and electrons into neutrons making the core consist only of neutrons. Take this into consideration, is it possible that the same thing happens to stars that become black holes, since their mass (and thus gravity) is so large that even light can't escape?
The interaction (of an electron with an external electromagnetic field) is because of the electron's charge, but charge causes an electric field, so, by Syllogism one can say the interaction is because of the electron's electric field. Now we can say that, by linearity, the external field and the field of the electron sums together. So how does a force arise from this summing process?
We know for a fact that if an electron absorbs a photon with enough energy it gets excited to a higher energy level, which increases that electron's total energy and we know that energy can present itself either with rest mass energy, kinetic energy and potential energy. And we know from Bohr equations that the higher the r(radius) is lower the linear velocity is, so its kinetic energy should decrease and be converted into potential energy? If so , if it is just a matter of energy conversion between kinetic and potential energies how does the total energy of an excited electron increase? How does the photon energy that excites an electron to a higher energy level shared between the potential and kinetic energy of that electron?
"Inclusion" means for something to be part of a group "Exclusion" means for something to not be part of a group Whether something is in the group or out of the group is obviously modified be the "in" or "ex" prefix, so the root word should be "Clusion" to mean "part of a group?", but I can't find any references to the word "Clusion" and im trying to come up with something that isn't super esoteric.
Say you want to wear a shirt: it would be odd to say, "I'm going topful". Is the reason due to topless being more out of the norm, and thus requiring a term? Maybe in places where not wearing a shirt is more normal, topful may be a more likely word to exist. Or maybe topful sounds like it would be totally covered, so the term isn't used. Or maybe the suffix 'less' often isn't paired with a converse version with 'ful'. Or maybe it's a combination of these things. In any case, any ideas why topful is not said? Topful is indeed a word, but that doesn't seem to apply here: Full to the top, or brim; brimfull. (Webster)
I want to understand what are the techniques one can explore to debug linear programming related optimization problem which is turning out to be infeasible. It turns out infeasible saying so and so equations lead to infeasibility but the problem is that the equation is formed using multiple inputs and has a logic behind it. How do I know which exact input caused the resultant equation to be such that it leads to infeasibility
A Device independent test is a procedure used to characterise quantum resources with the minimal level of trust. If one wants to test correlations like entanglement in a device-independent way, we get non-local correlations. Then my question is: given that Quantum Discord is considered as a form of quantum correlation that has no classical analogous, is it possible to test in a device-independent way? Has anybody addressed this question in the past years? If the answer is no, then a second question comes: is quantum discord really a notion about "correlations", if it can not be tested in a device-independent experiment?
I'm writing some text, with a float at some point. I don't mind where my float is placed exactly, but - I do mind if it breaks up individual paragraphs into two pieces, before and after the float. I just read this: How to protect text from being split by a float? where the (single and accepted) answer suggests some measure of clearing floats, or postponing the presentation of any floats (using placeins or flafter). But - that's not what I want; I'm ok with floats either appearing or not-appearing after or earlier than this point - I just want paragraphs to remain intact. What should I use instead?
I need advice on the statistical method, and I've included some preliminary findings from my dataset, which includes mean, standard deviation, and variance. To distinguish between artifact-related and non-artifact-related data, I would like to receive the results from the mean, standard deviation, and variance formulation. Can someone provide me with a statistical formula that will enable me to distinguish between artifact-free findings and those that are not?
At the moment I am trying to simulate charged droplets and their berakup in an homogeneous electrical field in vacuum. I am using a VoF-Method, but as the droplets get smaller and smaller I would need a finer mesh and smaller timestep. So I was thinking of using an Eulerian-Lagrangian approach by identifying droplets below a certain size and turn them into Lagrangian particles. The question then becomes how will I handle breakups for the Lagrangian particles. From what I gatthered there exist droplet breakup models between fluids like KH-RT, TAB, or PilchErdmann. Is there something similar for just electrostatic breakup?
Say we want to inscribe a cicle with a regular polygon: The circumradius is is the distance to the vertices of the regular n-ngon. We can see on the image, this circumradius of a regular n-gon is greater at lower n. And as n goes to infinity, the circumradius should approach the radius of the inscribed circle. But what is the equation of the radius? I've tried calculating it and google it, and the condition must be, the apothem of the regular n-ngon should equal the radius of the inscribed circle. I would love your help on this.
If the eigenvalues of two matrices are known is there any (generalized) way to tell the eigenvalues of the sum of the two matrices? I have come to hear that no such theorem exists that can handle the general case. I want to ask if it is possible to find and prove such a theorem. If yes, what background in linear algebra is required for it?
Specifically, this is for the context of hydrodynamic levitation. Below is what I believe the forces acting on the ball are: What equation would be used to calculate R, the force from the Coanda effect? My logic above, by the way, is that since the ball exerts a force on the water that causes it to go to the right and downward, the water must be exerting an equal and opposite reaction force that causes the ball to be pushed upward and toward the left.
From my understanding, but please correct me if I am wrong, this equation is implicit (See the attached screenshot). However, the goal is to create an identical (or similar) shape that is defined using "parametric equations". Is there any good way to do that please? Thank you for the help. In addition, if it is possible to configure this shape to be in the direct "center" of the graph (instead of being on the side), that would be even better. In summary: Define this shape (does not have to be identical, just needs to be similar) using parametric equations Plot the equation/shape to be in the center of the graph (symmetrical by the y-axis) Thank you for any advice or help. A bean-shaped equation modelled in Desmos
The Coulomb's law is an expertimental law which calcuates the electrostatic force between distinct two electrically charged point particles (point charge) at rest. And Point particle doesn't take up space. However, there is following sentence in Content 'Limitation' in an the article in wikipedia: There are three conditions to be fulfilled for the validity of Coulomb's inverse square law: The charges must have a spherically symmetric distribution (e.g. be point charges, or a charged metal sphere). In here, i can't understand this sentence. Why charges must have a spherically symmetric distribution?
What happens to the temperature of a body (not in the body frame) as it approaches the speed of light? My thinking is that the molecules will necessarily 'prefer' (as a natural consequence of the basic effects of SR - yes, I am handwaving at the moment and not giving detail just to avoid extra text) a direction of movement, rendering the conventional notion of temperature less adequate.
I found this sentence in Oxford Dictionary in an entry for "draw up": Sarah drew herself up, full of indignation that he should presume to judge her. Also this one in the entry for "sully": They were outraged that anyone should sully their good name. My guess here is that "should" in the first example really means "should not", i.e, he should not judge her but I am not sure maybe some extreme meaning or pun is being used here beyond my pay grade in English grammar?
I have found a similar question here. However, my reputation is too low to append comment for requiring more information. As a result, I have to post a question. I read Pandas documentation and I encountered the following sentence: The axis labeling information in Pandas objects serves many purposes. I could catch the general idea of this sentence, except the "axis labeling information" part. If I was the writer, I would write as "the information of axis label ...". So, I have mainly two points to ask about: Is it OK to write "the information of axis label"? Why use "labeling" not "label"?
I am a computer science PhD student, and I need statistical manifolds theory for my work. I am currently reading Differential Geometry of Curves and Surface by Kristopher Tapp and Carmo. I plan to study Lee's smooth Manifold next. (My supervisor's recommendations.) Unfortunately I do not have the topology background to the depth I would like to have to; I studied Topology without Tears in my second year (not completely) but I do not remember all of what I read either. But I am keeping it alongside. Can anyone suggest a self-readable set of books to get to Stat. Manifold? I might end up needing quite a bit of Discrete Differential Geometry as well. Other suggestions about alternate study plans are also welcome.
I am currently conducting complex simulation involving deformation of a solid object ( which is a surface, or a shell using the vocabulary of structural mechanics) and some fluid discretized using a particle method ( namely SPH). I am used to look at theoritical results to understand a bit a behavior of the solutions ( existence, unicity, rate of convergence, potential numerical issues, ...) but for this case I could not find anything. Is anyone aware of some literature on the topic ? Thanks, Quentin
I have found answers to similar, much simpler questions on this site before (such as here How do you calculate probability of rolling all faces of a die after n number of rolls?), but can't find anything that deals with this exact generalization. After thinking about it some, this seems headache-inducingly more complicated to solve than these simpler variants, because the combinatorics are more nested and interfere with the simpler approaches used to solve those simpler problems (e.g. the fact that you want to roll each number b times instead of just once as in the linked question means that you can't use such a simple expression for not rolling that number in c rolls).
I can't seem to prove this but I also cannot find a counter example. I am dealing with the idea of a function that is constant on the imaginary axis and is defined through an unbound domain. Is it a constant function?If so, why? And if it isn't, can you show me such function? I would like to note that this is not a function with ImF being constant, but F is constant when fed imaginary numbers. Thank aplenty.
I know that in metric spaces sequentially compact is equivalent to compact. I also know that compact and sequentially compact for general topologies there is no relation between them. But I wanted to know if there is the same implication for Hausdorff I-countable spaces. The only thing I have found is that for Hausdorff spaces with the B-W property implies countably compact. Any books where I can research more on the subject?
I have learned that a blackbody object only absorbs light and thus does not reflect any light. The blackbody object will, however, emit light, and none of this light is due to reflection. Where does this light/energy come from? I assume, given an atom, that the light emitted is due to excitation and decay of electron states. Is this correctly understood, and can there be other methods of emission?
When capacitors are connected in series in a DC circuit, the voltage drop across individual capacitors at and immediately after the initial charging period is inversely proportional to the individual capacitance of each capacitor. But afterwards, this began to change due to leakage current. How does this affect individual voltages across each capacitor? Will this process eventually result in the capacitor with the lowest leakage current gaining a voltage drop nearly equal to the voltage drop across all of the capacitors in series?
I am trying to translate a book from English and am confused about the meaning of the word "block" as it is used in this context. We attempted to block for local spatial variation in the landscape immediately adjacent to stands (landscape patches) that were sampled by comparing the abundances of small mammals in the stands to a single type of habitat that is immediately adjacent to the target stand. [Landscape Ecology of Small Mammals] What is the intended meaning?
I am looking at GKP and cat states. Wigner plots are newish to me, and I'm trying to get an intuitive feel for the imformation they impart. Just by looking at a Wigner plot, can one discern whether the state shown would make a good qubit? What does one look for? Are certain, say, symmetries, important? E.g., I know the grid-like pattern of a GKP state means some error-correction is inherent. (Asking here too as well as on the quantum computing stack)
Suppose the left lead, right lead and the scattering region are all the same metallic system; such as iron. Why is the charge transimission coefficient must be a positive integer number at any fermi energy level? How is the charge transimission coefficient related to the number of corssing points between the fermi energy level and the eigen state in the band structure? Would anyone please give me some suggestions? Thank you in advance.
I am told many time that nothing can escape black-hole because black-holes escape velocity is more than speed of light. But we know object don't necessarily have to exceed speed of light to escape a gravitational body. Rockets can escape earth with lower than escape velocity if constantly thrusted. In the same way would it be possible to make an object cross event horizon from inside by constantly pushing?
I have some questions about the motion of the simple pulley system illustrated in the book Machinae novae. Are the following conclusion about the system correct? Since the length of the rope is constant, the carriage will move to right by the same amount, passenger is pulling the rope to the left, irrespective of the mass of carriage? The carriage will never toppel, irrespective of the amount of pulling force or location of the carriage along the path. Basically, only the angle of the pulling rope will change but the angle of rope supporting the carriage will always be perpendicular. The mass of the carriage will be limited by the breaking strength of the rope?
While we understand the universe to have had a beginning in the big bang theory, if gravity is quantum in nature yet still has an infinite range then surely once the distance between galaxies becomes great enough, pair production will begin in between those galaxies as a result of the gravitational potential energy being converted to stable particles? This is assuming that the expansion of the universe eventually reaches a steady rate and that dark energy is infinite. Am I missing something here? If so, what? I propose such a fate to the universe be named the "steady-state fate" if it is worthy of serious consideration.
I want to know when a vehicle is drifting, assuming it's rear wheel drive and has enough torque to give it some good grip but also has a fairly high steering angle, so the rear tires only slip or do they also roll? Does this change by the radius of the turn? I'm doing an analysis on differential stresses that's why I need to know if I should consider tire and ground friction a force in calculating the differential output or not.
I am a native English speaker but have never found a comfortable approach to requesting help. Would you please is more commanding/ authoritative in tone than I am looking for typically. Can you [please] is not actually grammatically correct: it literally is asking "Do you have the capacity to do X - as opposed to the actual intent of requesting their assistance (and not doubting their actual skills to perform). What might be other way(s) to lightly/tactfully/carefully request assistance?
In the lyrics of song Sorry by Halsey there's this line: I've missed your calls for months it seems Don't realise how mean I can be 'Cause I can sometimes treat the people that I love like jewelry Jewelry is a good and prestigious thing. Why does someone say I am a mean person for treating loved people like jewelry? My thought is that since jewelry makes the wearer more beautiful the wearer loves it for srlfish reasons. So I think the same applies here. It means they love people for selfish reasons, not for the sake of those people. Am I right or I'm missing something here?
When we have a set, is it correct to refer to another set as 'itself' when this other set is merely equal to it? More formally, I am asking whether or not two sets with the same elements can be considered to be two separate mathematical objects. I am a programmer so I am used to the "same object" being a distinct notion to "the object to which this object is equal". Therefore, this has led me to consider whether or not this concept is true within mathematics.