darklight03/StackMIAsub huggingface dataset:
In order for the jars to be sterilized for pickling tomatoes, they need to be boiled. But when one of the inverted jars was standing on the rack in the pot, it started sucking in the water that was boiling there (and sucked out almost all the water). The jars were turned over so that their open side was completely submerged in the water (so that approximately the entire surface of the neck of the jar was in contact with the grid). An approximate drawing of what is happening from the side: I took the jar out, emptied the water out of it, and put it back, but after a while it filled up again. The plastic grate on which the jars stood was uneven, and had holes in it. Why does this happen? Thank you!
According to Kepler's First Law, the orbit of a planet is an ellipse round the sun with the sun at one focus. There's an inherent asymmetry in this. Instead of the sun being in the dead center, its shifted over a little bit. In the hydrogen atom, all the orbitals of the electron are symmetric about the proton at the dead center. Why is there no similar asymmetry? You can convert the function for the position of a classical simple harmonic oscillator with respect to time to a space dependent probability distribution where the probability is higher at the classic turning points where the velocity is at its lowest. The ground state of the quantum harmonic oscillator has a higher probability exactly between the classical turning points. The quantum solutions more closely match the classical probability at higher quantum numbers. I was thinking the classic "lopsidedness" of gravity could be recovered at higher quantum numbers for a Coulomb like potential Schrodinger Equation. But higher principle quantum numbers just enlarge the orbitals, they all remain symmetric about the proton. So that can't give you higher probabilities on an ellipse. The technique to recover classical behavior that works for the harmonic oscillator fails for Coulomb like potentials. Are there circumstances where any asymmetry appears in the probability of the electron, in particular, concentrations of probability along an ellipse?
The Question: Boolean algebra is to classical logic like what is to relevant logic? Context: I guess this is a terminology question, so there's not much I can add, except that I've been interested in paraconsistent logic for a long time. Is the answer de Morgan algebra or is that something else? Meta Question: Is the question well-formed? Perhaps the question ought to be something like, Boolean algebra is to classical logic like what is to paraconsistent logic? I don't know. But: If the answer to the Meta Question (MQ) is yes, then please answer the main question. If the answer to the MQ is no, then please feel free to tell me why and answer what I hope will be a clear intended question. If the answer to the MQ is nonclassical, please explain.
If I launch a ball into the sky it would reach a distance after which it would return into the ground transforming the potential energy into kinetic energy as it hits the ground This is similar to what happens at galactic scales, where material (like gases) from an outflow get expelled from the galaxy, they reach a distance where they turn back, and fall again into the galaxy, increasing their kinetic energy as they are attracted by gravity towards it However, the presence of dark energy at galactic scales, causes outflows to be less bound to their galaxy (and could even reach a distance where the influence of gravity and dark energy are balanced, beyond which, it would be expelled from the galaxy to never return: Is there a distance from a gravitational source where the influence of gravity and dark energy are balanced out?). This then can make these outflows reach a greater distance before turning back into the galaxy. Then, as the material would travel more distance towards the galaxy, and there would be a point in this trip where the influence of dark energy would be negligible (only leaving gravitational attraction), would the infalling material have more kinetic energy in this scenario (than in one without dark energy)?
I finished calculus books like Thomas and currently reading a book on advanced calculus and another one on real analysis. I noticed recently that I don't solve enough "hard problems". I usually just solve the exercises on my books. so I figured that I need problem book(s) on calculus. I want a book(s) that has many exercise on calculus topics like Limits(without l'hopital) ,derivatives, integrals , series and sequence , multiple integrals etc... I also want them to be challenging and interesting problems and not "too hard" I consider myself on an intermediate level as the advanced exercises on Thomas book seems very easy to me, I also don't want "forward substitute questions" which is plugging numbers in formulas or straight forward use of a theorem or equation as I want to increase my problem solving skills. I will appreciate any suggestions ,thank you in advance .
There is much talk of using lasers to bring down drones. That talk is followed by talk of protecting the drones by surfacing them with mirrors. Would that work or does light falling on a mirror impart all its energy to the mirror first before it can get re-emitted? I am aware that lasers themselves use internal mirrors to reflect the light so it would seem that if lasers don't destroy themselves then the energy is not absorbed: or lasers are cooled, I don't know which is the case. There are two questions here really: the Prime question is about the possible efficacy of protecting a drone by mirror surfacing. The more general 'underneath' question regards reflection of light. Is it so that all light falling on a surface must be absorbed by that surface before it can be 'reflected' ? It is my belief that it must. That 'reflection' is in fact re-emission.
The textbook I'm using to study integral calculus usually assumes for it's proofs that the function takes on only positive values. The author says that if we divide the x-axis into intervals, and pick the point in each interval for which the value of the function at that point is a minimum at the interval, then we can approximate the area under the curve using inscribed rectangles. Specifically, the author says, this would be the lower sum. The upper sum is achieved by picking the point at each interval for which the value at that point is the maximum of the interval. I was thinking: wouldn't this be the opposite for negative functions. Because the upper sum would be achieved by taking the minimum at each interval, at the lower by taking the maximum at each interval. If I were to prove the same theorem for negative functions as well, is this the only difference that it makes? Or is this not the case? Because if the upper sum is always the greater numerically, and the lower sum is always the less numerically. And if "negative area" is a thing, then the lower sum would still be the one that is formed by taking the minimum at each point, and the upper by taking the maximum. So I am confused with the exact definitions right now and would enjoy guidance. Thank you in advance.
If we spectroscopically observe a cloud of hot gas, which is on the whole not very absorbent, and which is not illuminated by a source behind it, we observe emission lines. How does this type of spectrum form? I had thought that those lines are those in which there are transitions of atoms is true, but I don't think that's enough. Why should all the material as a whole emit like that. Why are there these electronic transitions? And then: if there is a light source behind the material, one observes a spectrum that is in a way the negative of the one I put, i.e. the lines become absorption lines. I had thought that something different must be happening in the two cases, although I don't know what. And then again: if we knew nothing about electronic transitions and only wanted to consider the macroscopic properties of the gas (which could be composed of complicated molecules, in which there are not only electronic transitions but also other phenomena), could we still justify the fact that the emission and absorption spectra are the negative of each other? Thank you for any input; complex, articulate and in-depth answers are also welcome.
Saw this on reddit: A: I'm a gun owner and I think any sort of gun sticker on a vehicle is cringe. -> B: Ditto any sort of camo, esp. grey/urban camo prints, sure go ahead and tell the world you're itching for an excuse to defend yourself with a gun while you wait for your latte -> -> C: But the hunting community uses camo! Do you think hunters are looking to kill people? Etc, where C continued to belabor the edge case. Now, to me, C misunderstood what B was saying and just continued to argue when it was clear that B didn't think that hunters were included in the group that they were talking about. It feels like C went out of their way to think that B was saying something about ALL people who wear camo -- but to me unless someone says "ALL ___" they just mean "in general the people who ____". Is there a term for "deliberately misunderstanding what someone said so that you can argue about it"? I see it all the time in forums/reddit/insta. Strawmanning doesn't seem adequate -- that's more about mischaracterizing someone's point so you can dismiss it. My best attempt at this is "reaching for outrage" but I've never heard any say that.
In a recent Introductory course on logic, we were introduced to first order and propositional logic. The purpose of these concepts is portrayed as being a way for us to formalise the reasoning we use when we compose proofs in other branches of mathematics, but something about this bothers me, namely that in defining these theories, we extensively used set theory, and the axioms that it grants us, however one needs first order logic to actually describe the axioms of set theory, and so neither of these theories can truly "precede" the other. I read around a bit, and to some other question on this site, someone commented that this is fine, since for example we use the English language to describe the grammar rules of the English language, and we are satisfied with that, so w should be satisfied with this. But there's a reason language and mathematics are different fields of study, and I find this answer unsatisfactory. Is there some way to avoid this circular dependency in a meaningful way? Edit: from my understanding of the answers given to the purposed duplicates, the consensus is "no we cannot". Can we do one better and in fact prove that a sufficient formalisation without this property is not possible?
I am studying the solubility of gases in liquids (flowing then into the study of oscillations of gas bubbles out of the liquid phase). The task at the moment is to familiarize myself with the laws of solubility of gases in liquids, gather material, etc. However, the only law I've discovered is Henry's Law. So far I'm only studying the simple case like water as a solvent and air as a gas. (no electrolytes in the liquid, no chemical reactions or anything). But for such a simple case, apart from Henry's Law, I have found nothing. Also I could not find any literature that could help in studying this question. I am wondering if there are other laws or equations of gas-liquid solubility for the simple air-water case, or is there nothing else besides Henry's law?
I have been reading recently about tension. I don't exactly understand how it works. Here are my major doubts: Here, Tension is said to be acting in the opposite direction of mg. I will assume tension is not the net force across the rope because net force is zero due to newton's third law. Thus, tension must simply be the force exerted on an object by another one through a rope/chain/rod, etc.In this case, since in all cases of an object exerting force on another object, since the other object exerts an equal and opposite force, the tension here is really the reaction force to the force of gravity. However, if pulling a box along the ground with a force F, tension along the rope is said to be in the same direction as F, but can't it be said that it exists in both directions as both the pulling body and the mass exert equal forces on each other? What decides which direction is assigned to tension?
Hi I was working on a problem concerning euclidean topology. I was doing the following exercise : The first statement seemed not to be true because for (i) to be the basis some topology the intersection of any most belong to the basis. As the intersection of any two open squares parallel to the axes is not necessarily a square, possible a rectangle. I assumed it wasn't the basis for any topology. This however didn't make sense when I looked at (ii) as far as I know the collection of all open discs is a basis for the euclidean topology. But the intersection of two disc is not always a disc. Which would mean it isn't the basis for any topology which left me confused. Does anyone know where I could be wrong? Thanks in advance.
Original question: If continuity is the only requirement, here is the solution: Dimension of space of continuous functions But the proofs use trigonometric functions and polynomial functions, which are not monotonic. A further question is, what if I would like to impose additional features on the functions, say, concavity? It seems that one has to search for new bases if using constructive proof because the bases in the original proof may not satisfy the additional feature. I was wondering whether there is a generic way of proof to circumvent this problem (My guess is that no matter what the feature is [as long as the set is a linear space], the set of functions with this feature on an interval is infinite-dimensional). Edit: Thanks for pointing out it is not a vector space. So I changed my question (I thought this new question is equivalent to the original question but it turned out they are not). Edit again [revoked]: I think maybe I should add another constraint that the functions are bounded, or even more stringent: the codomain is an interval...Otherwise, the answer seems to be obviously "No".
I'm currently starting to self study probability and statistic, a friend recommend me to use a book he has but his book does not go deep in the theorem and formula, instead it just state the equation and when to use it along with some properties but not the proof for the equation (for example: the chapter about the Poisson random variable just tells you how to use it and when, but lacks the proof of how mathematicians arrive at that complex equation ). I would like a book that is rigorous and proof-based for every problem in it ( like Tom M. Apostol's calculus books for example), im a colleague student and has good calculus and linear algebra background so an more advance than regular books is ok with me. Do you have any recommendation ?
I'm new to Kalman filters. I have a use case similar to the one-dimensional train example. But I have railroad track with switches and mergers. So it's a non-trivial topology. I would like to model the system as a graph with N nodes and E directed edges. Each edge has length (weight) L. So the system state (e, x, v) consists of the current edge e, the distance x along the edge and velocity v. The edge e is a discrete (categorical) variable, which does not fit the standard Kalman Gaussian methods. Can the Kalman filter be extended to this? Measurements: I do have measurements of (e, x) and related position error err_x. There is no error related to the measured edge e. Prediction model: We can assume a constant speed model with zero-mean acceleration as in the Wikipedia example. In case of a prediction through a node with multiple outgoing edges (rail switch) I'm not sure if I should return a multi-modal distribution. I don't have a requirement that this should run in real-time, so it is possible to look ahead in the data and see which edge is taken. Or to use some kind of backwards smoothing is also ok. The graph is in priciple cyclic, but in practice length of the edges are way larger than the measurement errors.
According to general relativity, if an object keeps moving and warping space and then gets lost by entering a black hole, do all of the distortions in the space caused by that object get lost? Or do the distortions get back to where they began? There is an answer by "Navid" that says it is possible for the distortions that happened in space by the object to disappear. Well, first of all, my imagination says that space will keep warping if an object keeps moving. Meaning that the peak of the distortion keeps increasing; now if there is a case where the distortions will disappear, then wouldn't this come to mind that a new black hole would happen because there is a loss of space? By new black hole, I mean the disappeared or lost space between the destination black hole and the beginning position of the object. My other imagination is that when objects move in space, they carry the space with themselves and don't keep stretching or warping the space.
This question could be really out of the blue and might receive lots of downvotes, but bugging me quite a time and would appreciate your thoughts easily explained. We know that when we do work against nature force, we increase the potential energy of an object. Lifting a ball and putting it on the table increases potential energy of it as my putting work into it is transferred to the ball's potential energy. So as a sum up, for something to gain potential energy, some work must be done externally in opposite of nature. The same happens with charges. Taking away negative charge from positive increases potential energy of negative charge. It's all clear till this point, but if we imagine that worm by default appeared on a mountain, how would it have potential energy? As I understand, some external work must be done so the work is transfered/converted into its potential energy. What energy is transfered into worm's potential energy? I don't believe that gravitation itself gives potential energy to the worm.
Industrial printing is based on autotypical colour mixing, the simultaneous effect of subtractive and additive colour mixing. This makes it possible to render a large set of colours using only four standardized colours (CMYK): I do understand additive and subtractive colour mixing but I struggle to understand how two dots next to each other, i.e. with no overlapping, additively mix to another colour. This is illustrated in the lower part of the following diagram, e.g. a red dot and a green dot are perceived as a blue dot (provided they are small/far enough): I guess the answer revolves around the size of the dots, the amplitude of the resulting light wave and some properties of the human eye but I could not find any detailed physical/mathematical relation between them so far.
Assertion:Energy changes the kinetic only, and changes in potential require an intermediate change in kinetic. Reasoning: eg:when I throw a ball upward I do work/transfer energy,At the topmost point, there's a changed potential which is an effect of changing its position through its ke. eg:when I lift a weight at constant ke,Im transferring energy to increase the kinetic as I'm doing work against gravity , I can't change the potential without changing the kinetic. I did some research but the only answer I could find is an input of energy can increase both kinetic and potential but I don't see how it changes the potential without changing the kinetic. this seems to make sense for a lot of situations and i need to realize where im going wrong with this My question is: Is this valid and if it is does it hold for all fields in physics? Can energy only change the kinetic and require an intermediate change in kinetic to alter the potential?
This is my current understanding of convolution after having read through this blog post The convolution operator can be thought of as an operation of linear superposition. If we have the response of a linear system to a unit impulse, the overall response to an arbitrary input signal may be constructed by taking a linear superposition of the unit impulse responses accordingly translated and scaled. This can be done through the convolution integral. On the other hand, the convolution theorem allows us to perform the equivalent convolution operation by first taking the pointwise product of their Fourier transforms, then taking the inverse transform. In other words, the convolution operation is diagonalized in Fourier space, and acts on each Fourier component of the input signal by multiplying it by its eigenvalue, the corresponding Fourier coefficient from the unit impulse response. While I follow the logic leading up to either approach, my difficulty is in finding the connection between the two - how does it intuitivly make sense that superimposing unit impuse functions accordingly to the input signal has the equivalent effect to multiplying the Fourier spectra of the two functions?
There are two different senses in which we use the word "attribute"; for example, I can describe someone as "blond", which is a hair color. We say "blond" is a characteristic or attribute, but it is clearly the characteristic or attribute with regards to the characteristic or attribute "hair color" - "blond" is not how they smell or how tall they are, it's one of a set of attributes that fall under the attribute "hair color". I have called both "blond" and "hair color" with the same word, "attribute", here, and, as far as I know, all the popular synonyms of "attribute" really are synonyms - "characteristic", "trait", "property", etc. Is there any way or term or expression to verbalize the difference between an attribute in the sense of what it is - in this case, a person really being blond - and an attribute in the sense of what "category" that attribute belongs to - in this case, blond being a hair color? To put it another way, for the sentence "For the attribute "hair color", he has the attribute "blond".", I would like to find a different word for one or both of the uses of "attribute" here, so that the words used unambiguously convey that one is the actual attribute (blond), and the other is the "category of attributes" (hair color).
When conic sections are taught in high school, the concept of a focus is introduced from the geometric prespective. Well, at least if your teacher is any good. Later, once the algebraic equation of the conic is established, we find that this special geometric point can be in some way derived from the coefficients of the expressions in the algebraic equation for the conic. This is typically derived in school by moving back and forth between arguments involving that of geometric observation and that of algebraic manipulation. From an algebraic prespective, it seems quite unintuitive to me that there is a special point outside the curve which is so critical to understanding the curves' geometric properties. In a way, I see it as more of a meaningful quantity than a root. Now, my question is: Using advanced mathematics, what is the algebraic intuition behind the focus? Can we generalize this intuition to talk about foci of higher degree curves? And, are there analogoues to points like focus for higher degree algebraic curves?
The classical analogy for understanding gravity in Einsteinian physics is picturing a sort of fabric that sinks when an object rests on it. Thus, due to this curvature, objects will move towards each other because of the inherent structure of the fabric-object relationship. However, in this analogy, the objects move towards each other because gravity acts on them. In other words, the curvature itself is not enough to explain this phenomenon. Thus, howcome gravity be defined as the curvature of space-time if curvature itself is not enough to have an effect on two masses? I feel like this analogy tries to explain one concept (gravity) as the unison of two concepts (curvature and a force akin to gravity (redundant)). I mean, try doing this experiment in space. Set a fabric, add two masses and curvature but for some reason the masses don't move towards each other; because gravity doesn't act on them! (I know technically it does but for the sakes of the mental experiment it doesn't).