darklight03/StackMIAsub huggingface dataset:
The problem I'm working on has a region that's largely accurately modeled by a GP model using a squared exponential kernel. However, there is a large region in the "truth" model that is uniformly zero, with all samples taken from this region being zero as well. However, the GP model in this region oscillates from positive to negative when it's necessary for the problem I'm working on that this region is accurately modeled as uniformly zero, or at least negative when the remainder of the data is positive. Adding a dot product kernel to the squared exponential kernel to create a custom kernel helps somewhat but can't eliminate the spurious oscillations.
this is my first post on Stack Exchange. I need a study guide for linear algebraic expressions. I am good at vector analysis and calculus, but not so good at linear algebra. Image : In the image above, is the part I have colored in blue a linear algebraic expression? I am having trouble searching and learning this. I can't type expressions by math symbols into the Google search bar. I can't find a proper interpretation of the formula and just figure out what it means from the context. I'm not even sure if that's a linear algebraic expression. Is my only option to take my time and study a linear algebra textbook sequentially? I apologize if this question doesn't fit into the Stack Exchange.
If we place a point charge in a grounded metal box and view a slice of the box, the lines of equipotential deform from circular (immediately around the point charge, as we'd expect) to square at around the perimeter of the box where it is grounded. Is there a mathematical relationship we can derive for the morphing of the field lines from circular to square? I am unsure if the change is a linear combination of the two functions.
For some reason, TexShop started autocompleting any ampersand & by adding a period/full stop, which is not a feature that I consider desirable, given that I almost exclusively use the symbol for tabular and align environments. I feel that there is probably a simple way to turn this behavior off in the preferences, but I couldn't see how to do so. How do I change the default behavior?
When we think of functions, we refer to their oscillations or periodic components in terms of frequencies. The Fourier transform allows us to decompose a function into its constituent frequencies, providing a way to analyze the function in the frequency domain. For operators that act on infinite-dimensional function spaces, is there an analog of the frequency concept? Is there a transform or methodology that lets us analyze operators in a similar "frequency-centric" manner? I'm curious about both theoretical constructs and any potential applications such a perspective might offer.
From what I have read and seen online. The explanation of why there is a net reduction in the speed of EM waves through a medium is due to the interference with the oscillating EM fields produced by charged particles caused by the EM wave passing close by. I hope my understanding, if at least a base level, is correct so far. But would there be any reduction in the speed of light passing through matter made up entirely of neutrons? Either a neutron gas or possibly neutron degenerate matter in the cores of neutron stars. Thank you for your time.
I was wondering if there is an easy way to create diagrams like the following: where a, b, c are colors and strings connect like colors. In the paper I am reading, they don't allow crossings, but I would like to allow crossings between different colors. So something like this would be allowed (two colors red and blue) I tried to do this with the braid package, but the problem is that I don't know how to make those semi-circles Thanks in advance!
I'm writing an online game, and I want to tell users what their highscore is since the beginning of the hour. But I don't want to say something wordy like: Your highscore since the beginning of the hour is... At the moment I've got: Your highscore this hour is... I have 'today' and 'this week' for the other timeframes, but it still feels very unnatural. Is there any pithy phrase I'm overlooking? Many thanks!
Is there a ready-made LaTeX package that produces a calendar in a format known as Familienplaner in German speaking countries: Each month is set as a table on one sheet of paper. There is one row per day, and there are additional empty columns to be filled in (between one and five, typically). Sundays are specially marked (e.g., by red colour of the date, or by a grey row instead of a white one). Nice-to-have features: German language support for day-of-week and month names, week numbers, German holidays. P.S. Searching the net for "Familienplaner" results in a lot of free pdf offers for such calendars. P.P.S. The Familienplaner layout is different from the monthly calendar layout of this question: Calendar in LaTeX
I was wondering if the book Contemporary abstract algebra was suitable for self study. I've heard from people that the level is somewhat low and that things such as polynomials in several variables, particularly theorems on symmetric ones. Also,ive heard that applications from abstract algebra to linear algebra are lacking as well. Is this true? if so, which books would you reccomend for abstract algebra self study?
I am currently working on a BSM model for unification where I am adding scalars for unification. I add many scalars, so finding the most general gauge invariant lagrangian is becoming difficult. Is there a tool kit where I can enter the particle content, and under what representation of the gauge group they transform and get out the most general gauge invariant lagrangian? I have heard SARAH can do it, but I am unsuccessful with it. If anyone knows how to implement this in SARAH, that would be helpful, too.
Recently, I watched small dominoes toppling over, until they push over a massive one. However, I am slightly confused why this doesn't violate conservation of energy. Consider supplying some amount of energy to a small domino, eventually when it topples over the large domino, that large domino can do significantly more work, and should have more energy. This clearly cannot violate the laws of physics. So what is wrong with my logic?
Googling and Wikipedia, gives only the following construction A golden rectangle can be constructed with only a straightedge and compass in four simple steps: Draw a square. Draw a line from the midpoint of one side of the square to an opposite corner. Use that line as the radius to draw an arc that defines the height of the rectangle. Complete the golden rectangle. Question: What are the other known methods of constructing a golden rectangle with a ruler and compass?
I saw this solution to a problem on twitter, and the solution seems to of used the direct comparison test for the improper integral. I asked my professor about it, but they replied with "yes, just make sure to follow the given conditions." However, they didn't mention what conditions we would need to follow. If we can use Series Tests for Improper Integrals, how would we go about using them?enter image description here
I want to make a commutative diagram in the tikz (or tikz-cd) environment to demonstrate the universal property of the pullback. To be precise, I want to make the following diagram in LaTeX (the arrows on top need NOT be curved): I am not sure how to draw this. I know how to make general commutative diagrams, and there are answers to making pushouts with universal property diagrams (How to do the pushout with universal property?) but I can't figure out how to make the above pullback diagram. Any help will be appreciated.
I came across this question while studying for the SAT. After World War I, Percy Spencer was hired to work in the research _____ later known as Raytheon Manufacturing. A) lab of American Applicance Company: (a colon) B) lab of American Appliance Company-- (em dash) Though the answer choice states that B) is the correct answer, it does not specify the reason why A) is not preferable over B). I wonder if the usage of the colon in this sentence is correct. (As it sounds, to me, a little awkward to place a phrase like 'later known as --' after a colon.) I'd appreciate it if you could enlighten me. Thank you.
As in the picture, we have a room with vents at the bottom to let cold air in and at the top to let hot air out. Normally the air flow is limited by the temperature gradient (correct me if I'm wrong). If we place a hot object in the vent on top, won't that create a faster draft? That way we could get very high "wind" speed indoors to replace fans. Is this possible, and if yes, what's the limit for air flow per second?
Consider the following sentence Your time is limited, so don't waste it living someone else's. When I put it into a few grammar checkers like Grammarly, I get no errors. But I feel that there should be an error - like a word following "else's" (e.g., "Your time is limited, so don't waste it living someone else's life.", a quote due to Steve Jobs) Is there some sort of grammar error here, and if so what is it called?
Is Aristotelian categorical syllogism (as in Copi's Introduction to Logic) a special case of the first-order logic? (This is my thought after making efforts.) Is it exactly the specialization of the first-order logic without any function symbol (but only predicate symbols)? (This is my thought after making efforts.) If it is still a specialization of the above specialization, what kind of specialization is it exactly? How would you define it as a formal logic system? Thanks.
When a nucleus decays it is finding a more stable configuration, as all nature is. But is there a way of finding whether a specific configuration will decay? I know that there is a specific proton-to-neutron ratio range, of which outside nucleus decay. This can also be seen on the nuclides chart. I have also looked into concepts like nuclear binding energy and gluons. However, I never found a definitive answer to my question. My question: Is there a way, given the number of protons and neutrons (and electrons if need be), to find if the nucleus in this configuration will decay? (Please don't hesitate to use math to explain the concepts. In fact, I'd prefer it if I ended up with a formula.)
Today I was explaining to my friend about opposite categories, and how the definition of monomorphism leads to defintion of epimorphism in opposite category. He asked me quite an interesting question. If we have a morphism in a category, how does that relate to the morphism in the opposite category? For example, let's consider that category Top, and a homomorphism between two topological spaces. What would be exact expression for arrow in the opposite category? I think it'd be something like the inverse function but I am not sure.
This might be a very simple question, but the answer is not entirely obvious to me and I've been unable to find it stated anywhere. Consider two sets of generators (vectors), which are reduced in the sense that no two generators are parallel to each other (if one starts with two parallel generators, reduce that set by adding them together to make a single one). Then, if these two sets are not identical, can they possibly represent the same zonotope? I believe the answer is no. Am I wrong? A proof one way or the other would be appreciated.
Outlook is questioning "equipment register" and asking me to double check if I am using singular or plural (error underline on the word register). This has me really confused and I can't find any information about what could be wrong with this phrase. For context, the phrase is part of a list of other items and I am using it to mean a register of equipment, like you would have a register of users, or a register of stock...etc. I get no grammar errors if I replace "equipment" with other words (although obviously I haven't exhausted all possible words!) If I write "An equipment register" the error remains. If I write "One equipment register" it goes away. Thanks!
It is well-known the notion of weak limit in category theory. To obtain it, just take the notion of a limit and drop out the uniqueness property in the universal property. Now, as the universal property is crucial when proving the uniqueness (up to isomorphisms) of a limit, I expect the non-uniqueness of weak limits, in general. Well, it is possible to find an explicit example of category that admits weak pullbacks, where a cospan diagram admits two non-isomorphic weak pullbacks?
While starting out on Lang's Algebra I have encountered the term "exact" sequence of homomorphisms. And I understand its definition and all the demonstrated examples but I would like to know more on this, like what are the things we get to know out of an exact sequence and does it aid in any kind of constructions or whatsoever. Is it possible to generalize them and how does that look like ?. For my background, I have only been introduced to Groups, Rings and Fields in my introductory algebra course but I would be delighted in seeing a bigger picture on these structures.
I understand the fact that if there was no metallic ball in it, then when the ice melts, the level of water would neither rise nor fall. Now let us consider the case where there is a metallic ball in it. When the ice melts, the volume of water added to the vessel would be less than the volume displaced by the ice structure when it was floating. This should mean that the water level will fall if i am not mistaken, further which the metallic ball would sink. When that happens, it is displacing the same amount of volume as it did when it was within the ice. So shouldn't it mean that the water level would fall ?
My intuition: In a system without air resistance, I would expect an arrow shot at an angle with its head pointing upwards to follow a ballistic trajectory without rotating around the horizon - because gravity can't induce torque on the body. So the arrow will impact the ground on its tail - not its head. Is this correct? If yes, what causes the same arrow to impact the ground on its head when there is air resistance?
I don't think I understand correctly what it means for a Boolean formula to be reversible. By my current understanding, if a Boolean formula is satisfiable, then there exists a setting of variables such that the formula evaluates to true. If you were to reverse said formula, simply flipping each variable in the setting would also satisfy the reverse formula. You can similarly show that the reverse formula is satisfiable if the original formula. Overall, the reversible formula is satisfiable if and only if the original Boolean expression is. Since the author claims that determining reversibility is NP-complete, I think I'm missing something here. This is from the paper: On the Complexity of Polyhedral Separability
Working on a thesis, I was wondering how to correctly hyphenate (if at all) the term "high data rate" in the following sentence: High data rate ECUs are connected directly to the backbone. The term "data rate" as such is not hyphenated. But compounds with "high" are hyphenated, e.g. as in "high-income", "high-stress". However, writing "high-data rate" doesn't seem right to me. What would be the correct hyphenation in this case?
I've been reading a bit about how it is necessary to consider anharmonic effects in crystals if one wants to properly understand things like thermal expansion etc. So for example here: So the cubic term is said to represent 'asymmetry of mutual repulsion' and the fourth-order one 'large amplitude weakening' of vibrations. How could one come to understand these intuitively? How does one look at a cubic etc. term and come up with this explanation?
I heard a while ago that the negation of the axiom of choice leads to the existence of a partition of the real numbers, into more partitions then there are real numbers. I found this post which says You don't want non-measurable sets? This means that you can partition the real numbers into strictly more parts than real numbers, but no part is empty. Yes, let that sink for a moment: you can partition the reals into more parts than numbers! I looked for a proof of this online, but could only find the result mentioned. A couple referenced this link, but it's locked behind a paywall. So, why does the axiom of choice lead to this counterintuitive result?
So I was searching online for methods to approximate Pi and found this continued fraction that supposedly approximates to Pi when continued infinitely. I've tried searching all over the internet for how this was derived or why this works but could only find something similar but not close enough. I've got some basic knowledge of continued fractions but do not have experience with numbers that change throughout, how would one derive this equation? Thanks
To compile my document (even a little one), my computer needs to load a lot of packages. During compilation (with pdflatex) I can see in the terminal that most of the compiling time is used to load the packages. It would save me lot of time (and ressources) if it was possible to keep the loaded packages in memory and resume compiling operations after that step when I don't modify the preamble. Is this feasible?
Suppose one measures the position, then momentum, then position of a particle, and that all these measurements are done in quick succession of one another (ie. arbitrarily close to zero-time as possible). After the momentum measurement, the particles position is very uncertain. Therefore, the second measurement of the particles position can be quite different from the first. But does this not violate causality, since the particle can move a great distance in practically no time?
The energy that an electromagnetic field can deliver to a system is proportional to the square of the field. However, we use the terminology watts per meter square to represent the amount of energy going past to represent the intensity of EM waves. How do you give a physical meaning to the 'amount of energy that the field carries past us per second' if you are only given the amount of energy that an EM field can deliver to a system? Why is it necessary to adopt watts per meter square for intensity, whereas I believe the energy that can be delivered to a system is perfectly fine for defining intensity
In the case of a direct bandgap semiconductor, the recombination of an electron and a hole generates a photon that has energy equal to the bandgap of the semiconductor, accounting for energy conservation. But in this case, as the electron and hole have the same momentum, 'K' there is no difference. But the generated photon does have a momentum. So how is the momentum conserved in the radiative recombination in the case of direct band gap semiconductors?
There is a Spanish joke, Ella es mi amiga vieja, disculpe, mi vieja amiga. The joke basically says, "She is my friend that is old, excuse me, my old friend", making fun of the person's age. Would there be a way to translate this into English? Of course, saying something like "She is my friend old..." doesn't work in English, though the joke does also work in languages like French. The translation I wrote may be considered to work, but I was looking for something smoother. Edit: my attempt: She is my old af friend, I mean my extremely old friend, I mean my old pal.
I would like to be able to understand what the fission process is like (ideally, from total ignorance). What references could I read? Would it be more convenient to read chemistry books than physics books? From what I understand, the fission process involves "breaking" the nucleus of an atom. Regarding this: Is any atom fissile? Is there some non-fissile atom? Can this process be understood mathematically? Thank you so much.
I couldn't find any similar topics and was curious if anyone had thoughts on the following: Could a magnet (ceramic and/or neodymium etc.) have an adverse affect on a Police Taser, if held to the Taser or held in proximity to the Taser. If yes, is there a material that the magnet could be covered in, to insulate those effects? (i.e. by effect, meaning unintentional discharge of the Taser, or causing the electronics on board to malfunction.) Thanks for any color you may have on this, much appreciated.
What I was wondering is this. If I had a tube with water in it, with one end open and the other with a piston-like device attached to it, I can imagine that if I was to give the water a pulse, this would transmit down the tube as a mechanical wave as particles collide with each other - something like sound. But if we picture a scenario where instead of a pulse, I begin moving the piston down the tube at a constant velocity, what would the motion of the particles look like? Also what would this look like with air?
I think I understand Ampere's law in the way it was taught to me by my instructor. But as the idea was given that how Gauss's Law in Electrostatics relates to electric field lines produced by charges inside the gaussian surface under consideration. We weren't given any idea that how magnetic field lines even relate to Ampere's law. I have already searched for it on the internet including the posts present here but found nothing. All I ask for is idea that how Ampere's law relates to Magnetic field lines?. Thank you
I imagine that people will instinctively say, "There is no masculine or feminine speech in English," but I am not so sure. For instance, the stereotype is that men speak roughly and women speak softly. Then there is the usage of tag questions, fillers, and raising one's voice pitch so that the sentence sounds like a question. Then again, it may be a question of assertiveness. I hope someone knows what I am talking about!
Suppose we have a causal curve and we can cover the causal curve by convex normal neighborhoods. We also know that, in convex normal neighborhood there will exist a unique geodesic inside the neighborhood, connecting any two points in the neighborhood. So, my question is: Are we making the curve piecewise geodesic? If a curve is piecewise geodesic, can we say that the whole curve is a geodesic?
I have been trying to prove the stability of a queuing system (stochastic), and the state-space I have obtained is uncountable. I am aware of the Foster-Laypunov criterion, but as far as I know, it applies to systems with a countable state-space. I want to enquire of stability conditions for the case with an uncountable state-space, and also if Foster's criterion can be extended to this case. Please let me know! Thank you.
I recently stumbled upon the word biggety, meaning conceited or vain, and when I went to look it up, it seems the word is regional, which might explain why I'd never heard of it, except for one region it's supposedly used (Southern US) in is the region I've lived for over four decades. So, how common is it in the Southern US? How common is it in Midland US?
According to https://en.wikipedia.org/wiki/Closed_manifold "In mathematics, a closed manifold is a manifold without boundary that is compact. In comparison, an open manifold is a manifold without boundary that has only non-compact components." Closed manifold is a compact manifold without boundary. Open manifold is a manifold without boundary that has only non-compact components. Questions: Is open manifold opposite or antonym of closed manifold? (It seems not, but why not?) How do we call "compact manifold with boundary"? What are the differences between open manifold and non-compact manifold? How is the concept "open" in open manifold compared with the "open" in open set in set theory with topology, and open cover in topology? These open seem to mean different things.
Godel's incompleteness theorem says that in mathematics there will be always true statements that cannot be proved and that adding that statement as a axiom generates other unprovable true statements. So, mathematics clearly has logical inconsistencies. I was wondering if it it is possible to find a language that doesn't satisfy Godel's incompleteness theorem or, to put it more simply, such that all its true statements are provable?