darklight03/StackMIAsub huggingface dataset:
I have been looking up at available database that had dielectric constants for metals since I need them for my research and wanted to get an idea of what the values were before I focus on actually calculating them numerically if ever it is needed for my research. Thankfully I was able to find this website https://refractiveindex.info/?shelf=main&book=Ti&page=Johnson However I noticed that there are two values for the relative permittivity when it came to metals and I was wondering why this is the case. From what I know so far, metals should have a negative permittivity, so I was confused as to why it shows that Titanium also has a positive permittivity. Can someone enlighten me as to why this is the case for the permittivities that I found on the website. Apologies as well for the question since I dont know a lot yet about the properties of materials when it comes to permittivity and permeability.
If a quantum particle is described by a certain wave function and we express it as superposition of for example its possibles energy states, after we measure it the wave function collapses and we observe the quantum particle as having a certain energy. I have a couple questions. No matter what happens to that particle or what I do with it everytime that I observe it again it's going to be in that same energy state? If after measuring energy I now try to measure something else like position could the energy state change when I measure it again? In general I'm trying to understand what it means that the wave function collapses because by what I've studied it sounds like it's undoable but that doesn't make much sense to me. So far I thought that when we observe a particle's energy for example we measure a certain energy but then if we measure it again right after we could measure any of the other possible energy states but I'm told this is wrong. How does it actually work then?
Reading Harris' Modern Physics, specifically the classic example of Anna holding two lightbulbs on a moving train. I find myself confused about this passage: Before moving on, we emphasize a vital point: The preceding arguments had nothing at all to do with Bob's specific location in his frame or the time it takes light to reach his eyes. The issue here is not which beam reaches Bob first, which does depend on where he stands, but rather which begins first, which has nothing to do with where he stands. Attempting to blame the effect on optical illusions is the comfortable yet incorrect way out of accepting a counterintuitive notion. The truth is more challenging. Bob could be standing right next to one flashbulb when it flashes and have an assistant, Bob Jr., standing next to the other flashbulb when it flashes. Each records the time of his flash and neither has to wait for the light to reach his eyes. They record different times. Anna, in her frame, causes the bulbs to flash simultaneously, but Bob and Bob Jr., from their frame, determine that she causes the bulbs to flash at different times. I guess my understanding of the relativity of simultaneity was dependent on thinking about the path that light took to travel to Bob. If Bob/Bob Jr can be right next to the lightbulb, I am failing to see how that's any different then them being on the train with Anna.
Context: I would like to talk about how a book questions the reader's traditional, conservative values about family structures. I want to say we are introduced to a shared household wherein there isn't a typical nuclear family structure, the children are not trained in table manners and everything is loud, lively and disorganised. This contrasts the presumed reader (at the time)'s traditional beliefs that a house should have a nuclear family, children should be taught table manners, etc. The sentence I want to say is, "The reader is positioned to feel [insert word], as their beliefs are subverted and challenged." Words I've tried so far: Unsettled Uneasy Disturbed These are the closest words I could find but I feel like they have a more negative association, and creates a malaise in the reader. I feel that the effect of the book is more subtle and just lightly 'shocks' the reader, positioning them to just take notice of their preconceived beliefs, rather than evoke a negative reaction. Destabilise Bewildered These words suggest that the representation of these households are completely weird and confusing, however, that is not the case. It's not so weird that a reader wouldn't comprehend it, these households are just different to the mainstream households. Source for definitions: Google dictionary
Background: I tile lidar and photogrammetry products as part of my job. Project areas are typically single polygons outlining an area, and can be quite irregular in shape. Overall there is a lot of data and I am required to achieve a maximum file size per tile by creating square tiles that cover the project area. I know from experience what this tile size is but it differs by product. Although tiles are square, they are allowed to hang over the edge of the polygon. I'd like an algorithm to take a polygon and a square tile and return the tiling which has the fewest number of tiles that completely cover the polygon. The square tiles must not be off-grid or rotated, they must be orthogonal. If possible I'd like actual code, preferably in python and utilizing arcpy, however I'm willing to accept any answer that provides the algorithm I'm after. Bonus - multiple polygons representing disjoint areas need to be tiled using one tiling scheme. Tiles that don't cover any project area aren't needed, but all tiles must be on the same grid.
Levitated pits were introduced after after solid pits. In this design the tamper is separated from the fissile with an airgap. From the Nuclear Weapon Archive: The original Fat Man pit design used a Christy solid plutonium core, surrounded by a close fitting natural uranium tamper. The Sandstone devices all replaced the contiguous tamper-core approach with a "levitated core" in which the core was suspended within a larger hollow space within the tamper so that a gap existed between them. The collision between the tamper and core would create more efficient compression of the core than the explosive-driven shock in the wartime design. Other vague descriptions I found: The first improvement on the Fat Man design was to put an air space between the tamper and the pit to create a hammer-on-nail impact. Efficiency of the implosion can be increased by leaving an empty space between the tamper and the pit, causing a rapid acceleration of the shock wave before it impacts the pit. I recently started studying shockwaves and I don't understand this. How does leaving an empty space increase schokwave acceleration? If I remove the airgap, the mass of the core won't change but now I can use the extra volume for more explosive. Inside the pit, compression of the fissile is the result of work performed by the explosive charge, so how is it possible that I can increase compression by reducing explosive volume ??
In table tennis it is often desirable to produce as much spin on the ball as possible using a glancing contact. (The rubber covering of a table tennis bat is typically highly elastic and has a high coefficient of friction.) Anecdotally, the view is sometimes expressed that acceleration at the point of contact is more important than speed. I take this to mean that when the ball is hit with the bat at the same angle and travelling in the same direction, it is possible for a bat at a lower velocity but with some acceleration to impart more spin on the ball than a bat travelling at a constant higher velocity (higher than the maximum speed of the accelerating bat) without acceleration. Is this true? If so, why, and how can the optimal contact (in terms of speed and acceleration) to produce maximum spin be determined?
One English rule is to hyphenate two or more words when they come before a noun they modify and act as a single idea, called a compound adjective. This is the most common use of the hyphen I've seen. For example: A non-cloud platform Some cloud-based platforms What happens when there are three adjectives before a noun? Should I hyphenate all three? This example looks awful, but maybe that's because it's joining two compound adjectives that we usually see by themselves: Non-cloud-based platform That compound adjective would look better without the two hyphens. For most groups of three or more hyphenated words, they tend to form expressions that behave like compound adjectives, e.g. up-to-date, hit-or-miss, trial-and-error, etc. but they would also look alright as phrases by themselves. The three-word compound adjective in my example doesn't fall into that category.
I heard that Lagrange mechanics can be derived from Newtonian mechanics, and Newtonian mechanics can be derived from Lagrange mechanics. I've heard many times that they have equal explanatory power. But I encountered that there is a tricky point in deriving the law of conservation of angular momentum in Newtonian mechanics. On the other hand, theories that use the principle of least (or stationary) action derive each conservation law from the Noether's theorem by assuming each symmetry. So, is my understanding appropriate? That is, while Newtonian mechanics itself derives conservation of linear momentum without any additional assumptions, and requires some manipulation to derive conservation of angular momentum, but Lagrangian mechanics cannot derive both without the assumption of symmetry, or derive both if the assumption is made. Then, it seems that it can be explained by Lagrangian mechanics, but there is something that is not correct in Newtonian mechanics, or it seems that more assumptions are made in Newtonian mechanics than in Lagrange mechanics. Which of the two makes sense? I'd also like to ask if Newton's third law conflicts with Lagrange mechanics, and if it's possible to find a set of Newtonian laws that have the same explanatory power as Lagrange mechanics. However, I want to know (even short) to just the above two questions.
I have problems in understanding the terminology used in Sylvester's Criterion about the "sign" of a matrix. I got the "positive-definite", the "negative-definite", the "indefinite" and "non-definite" (the last one is when the determinant is zero, whilst the penultimate refers to two eigenvalues with different signs). What it's really unclear are those two: positive semi-definite: "all its eigenvalues are non negative" positive semi-definite but non positive definite: "there is one zero eigenvalue and the rest are non negative". I would really understand why one has to complicate the terminology in such a horrible way. Why shall we use "non negative"? Just say "Positive". Also, what's the difference between "all its eigenvalues are non negative" and "there is one zero eigenvalue and the rest are non negative"? I don't get this. If zero is counted as "neither negative nor positive" then wouldn't positive semi-definite mean positive definite? It's all so messy.
My current level of maths does not allow me to understand any of the proofs I was able to find online for the Fundamental Theorem of Algebra. I find it very unsettling having to continue learning about polynomials without being able to grasp such a fundamental property of them that is there exists a complex root for any polynomial with complex coefficients. My question is, is there a way I can reach the same conclusion of the Fundamental Theorem of Algebra for polynomials with real coefficients instead of complex coefficients. In other words, to prove that at least one complex root exists for a polynomial with real coefficients. Does restricting the coefficients to be real instead of complex make things any easier? If the answer to my question above is no, then I would appreciate it if you could provide any sources that I could've missed, that explain the Theorem by using the least amount of mathematical notation and advanced concepts as possible. If I cannot figure this out, I am going to have to accept the existence of a root as an axiom going further, which is something I really don't want to do.
I've been thinking about the critical point of water, which has three distinct and specific properties: critical temperature, critical pressure, and specific critical volume. However, when I draw a PV and TV graph I can't seem to think of any way in which to bring the water to its critical point because in order to get one property to its final state you have to change one of the others. For instance, if you already have the water at its critical temperature and pressure, you would have to decrease or increase one of those values to get it to its critical volume. To this end, I'm wondering whether it's even possible to bring water to its critical point - because once you achieve two of the three intended properties, it seems impossible to me to get the third property to the correct state without changing one of the other two.
I am reading up on Christol's theoreom and an important part is that k-uniform transducers (where k is somehow related to prime numbers) preserve the algebricity of a formal power series (taking the coefficients as a sequence). So basically, we start with a formal power series that has roots (my friend told me that algebraic means there are roots or zero crossings), run the coefficients through a k-uniform transducer and, when we use the values that come out as coefficients for a power series, that power series is again algebraic. There is a lot I still need to understand here clearly (like, what is a "formal" power series vs a "business casual" power series...), but I'd like to start by understanding what is so special about a power series having roots. Just for context, I have nearly no formal background in mathematics but came across Christol's theorem and thought it was very cool and maybe related to my area of work (computer science, temporal logics, and automata). Any help is appreciated!
Is there a conceptual problem in formulating of Liouville's theorem and the BBGKY Hierarchy for classical field theories? I always see treatments of Lioville's theorem only in the context of classical mechanics. I also know that most references treat linear response theory only for classical mechanics and do not touch upon linear response theory aspects of classical field theories such as Kubo formula. One can definitely take the continuum limit of a classical mechanical system and obtain some sort of Lioville's theorem or BBGKY hierarchy for the continuum field theory. I would like see if this is discussed in some rigorous way in any reference. In particular, I'm looking for references which discuss aspects such as the phase space for classical field theories, BBGKY and Green-Kubo Formula. I'm not a mathematician so a good systematic treatment I'm comfortable with for classical mechanics is David Tong's lecture notes and the text by Evans and Moriss. I'm looking for similar treatments for classical field theories.
When we calculate the excess pressure on the concave side of the meniscus of the liquid surface formed in a capillary tube, we balance the force by the atmospheric pressure, force by the pressure on the the side of the fluid , and the force due to surface tension, to derive the expression for the excess pressure on the concave side of the meniscus, but, my question is, when we balance the forces acting on a body, we balance the net external forces on a body for it to be in equilibrium, but here the surface tension force is an internal force on the surface, applied by the surface molecules themselves, then why do we include it in the equation for balancing the net external force on the meniscus?
I'd like to get some clarity about how nice the problem of decomposing semigroups using the wreath product is compared to the problem of decomposing groups, and where this apparent difference in niceness comes from. Looking at the Krohn-Rhodes theorem for finite semigroups, one can decompose a finite semigroup as a wreath product of finite simple groups and really basic "reset automata" semigroups. If I understand the Krohn-Rhodes theorem correctly, if one applies it to a finite group, you don't get any "reset automata" semigroups, so it gives us a decomposition of our group as the wreath product of simple groups. Is this correct? On the other hand, Meaning of factorization of groups and looking into the extension problem for finite groups leads me to doubt that the case for finite groups is that simple. So is it not as simple as "there's some kind of wreath product-like construction that allows us to reconstruct a group from its factors"? I'd greatly appreciate some clarity about this.
I have been trying to define the notion of a product of second-order classes using (finitary) second-order and if needed third-order logic. It seems to be possible to define the product of finitely many classes, because I can just express this using a finite second-order sentence. The problem is that, when I try to define an infinite product, I seem to need to be able to refer to an indexed family of classes. More specifically, so that I can use an infinite index class. But something tells me this should not be possible to do in higher-order logic, because intuitively, it seems to involve some circularity. Do you know if it is possible? Also, someone suggested me that type theory should help me with this problem, and if so, do you know why?
Im reading make: electronics, and I have investigated a little bit about displacement current and how a change in electric flux can create a magnetic field in a vacuum. A can understand that, however there is one effect which I don't comprehend the physics behind it. The effect that I'm talking about can be resumed in the next quote from the book: "A sudden change in voltage on one plate in a capacitor induces an equal change in voltage on the other plate, as if is reacting in sympathy". An image from the book showing the voltages in both plates of the capacitor in respect to time. My theory: So my theory is that since there is a current displacement there is also a change in magnetic flux, and this change in magnetic flux can generate a similar voltage on the other plate, since the plate has thickness and thus inside the plate there is an area that is perpendicular to the direction of the magnetic field, which will lead to a magnetic flux, and if you change the magnetic flux a voltage is created (according to Lens and Faraday). However, I don't know if this is right, and at the same time trying to find information on the internet about it is impossible. If anybody has an answer I will be delighted.
I am seeking answers from experts in mathematical logic about the amount (if any) of university mathematics I need to know in order to understand mathematical logic and later hopefully do meaningful (independent) research on the subject in general and Godel's Theorems in particular. I am proficient in high school math and have a bachelor's degree in Physics. I have also recently taught myself some calculus, linear algebra, and parts of real analysis as I assumed you must need at least undergrad math to eventually get proficient in a certain math discipline. Earlier I had decided to learn up to grad level math but after I glanced through some logic books it appears they make close to zero use of even undergrad math. Also, I have come to know that philosophers too do research in mathematical logic, and as far as I know, they don't study any university math. So, my question is should I first teach myself undergrad (and grad math) or just dive into mathematical logic as I don't want to later find myself in a position where I have to study all that university math before I can make further progress in logic? If that is the case I would consider enrolling myself in a math program first and doing the research later in the conventional way.
My understanding is that the word means a rephrasing of something the person has said in expressing the same sentiment or idea. But I think people use the word to mean essentially, say something in a similar way to mean something else. A simple example: Marge is talking to a bullied Bart: "If they beat you up, I do not think they are your friends." Someone who wants to borrow this sort of phrasing to apply to the situation where someone has more extremely pushed an acquaintance off a roof and this is reported in the news as "Woman's friend pushed her from roof" and says, "To paraphrase Marge Simpson, 'If someone pushes you from the roof, I don't think she is your friend.'" In the above, is "paraphrase" being misused and if so, what is a better word for such borrowing/reuse with modification of a phrase?
I'm currently working as a (undergrad) TA for a mutlivariable calculus class and while covering the topic of multivariable differentiability, one of our students suggested that it'd be nice to have some actual functions we could use as examples to navigate how the theorems can be used to both establish differentiability and to flip them back around to deduce things about the partial derivatives if they're not differentiable. In particular, we were discussing a sufficient condition for differentiability which, roughly, states that if all of the partial derivatives of a scalar field are continuous at a given point, then the field is also differentiable at that point. But more specifically I was warning them about how the contraposition of this statement does not forbid a function from being differentiable while having discontinous partial derivatives, as this beautiful example shows. The previous example has all of its partial derivatives be discontinuous, but then a student asked if I knew any scalar fields which only had one or two discontinuous, while the rest remained continuous at the given point. Here's where I ask for your help :) I have looked around in some of the literature but haven't been able to find good enough example of this, although in principle this should be possible (from what I understand). Also, if you have other interesting examples that show how differentiability can be wrinkly or deceiving I'd really appreciate it (and our students would too)!
I have read this question (no answer, just comments): Light, including pulses of light, consists of many photons. A very short pulse has a wide range of frequencies. See The more general uncertainty principle, regarding Fourier transformsA single photon can also have a long or short duration, and a narrow or wide range of frequencies. I have never heard of single photons with a wide rage of frequencies. Each photon is always supposed to have a single quantified energy/frequency, otherwise the quantum effects would not occur. Can you refer to studies that show single photons with a range of frequencies? Relation between attosecond light pulses and photons? And this: This is very fast for a pulse of light, and it is actually so fast that the pulse of light is no longer a periodic electric-field oscillation, and instead it lasts only for a few cycles. But it is still not fast enough. What is an "attosecond pulse", and what can you use it for? Now we have had single photon emitters for a while and the photon is the smallest amount (quantum) of EM energy. But then the question remains, why are attosecond pulses better (for example to track electron orbitals) then single photon emissions? Very naively thinking, if you shoot single photons at the electron (atom), you are using the smallest quantum of energy to do so. Then why is attosecond pulse generation superior to single-photon emitters? Question: How can an attosecond pulse be shorter than a single photon (quantum) emission?