Properties Definition and 1000 Threads

In textbooks, are words such as 'metallic', 'metal', etc indicating to the person doing the problem that the material in question is a conductor? This one problem said 'metallic' and the answers were as if it were a conductor with the electric field between 2 concentric hollow spheres being 0...

Hi, if I wanted to show ##(Z \otimes Y)^{\dagger} = Z \otimes Y##, then I could simply multiply out the matrices belonging to the operators of quantum gates ##Z## and ##Y##. But my question is whether this is also solvable via the properties of the tensor product and the properties of the...

Hello everyone, Here, we observe that the familiar properties of the real logarithm hold true for the complex logarithm in these examples. So why does a whimsical mathematical use of real logarithm properties yield coherent solutions even in the case of complex logarithm?

I was curious what meta materials can do or be used for? Particularly I was curious if they can mimic the properties of expensive and rare materials like rare earth metals which China has an advantage with.

Position and momentum are the popular pairs of properties with uncertainty we often hear about, for example that we cannot know with precision where an electron is and its momentum at the same time. What are others? Such as an example of an energy and a time that we cannot know both...

I believe at the current time quantum computers can't get as much done as fast as normal computers, but do quantum computers have access to information by its own nature that allows it to run special calculations that normal computers can't? In particular physics or biology simulations using...

What about water makes it such a great substance? I'm aware of properties like a high SHC providing aquatic habitats with stability, being a liquid at room temperature due to Hydrogen bonding and etc but what about water makes it so great why is it such a miracle substance, solely because of the...

TL;DR Summary: I'm interested in constructing an artificial universe and discussing its properties and behaviors. I would like to construct an artificial universe somewhat akin the Conway's Game of Life and discuss its behavior and properties. Is that allowed? Is this the place to do that...

I was wondering if the following is true and if not, why? $$ \begin{split} \hat{f}_1(\vec{k}) \hat{f}_2(\vec{k}) &= \hat{f}_1(\vec{k}) \int_{\mathbb{R}^n} f_2(\vec{x}) e^{-2 \pi i \vec{k} \cdot \vec{x}} d\vec{x} \\ &= \int_{\mathbb{R}^n} \hat{f}_1(\vec{k}) f_2(\vec{x})...

Why isn't the sky violet? Since violet has a shorter wavelength even than blue, why doesn't it dominate then?

Hey all, For my physics major I need to quantify the acoustic effect of sunfields. I'm trying to do this by measuring the sound level before and after a sunfield, and after that by measuring a comparable situation, only without a sunfield. By comparing the results of the two measurements I'll...

I came across this question; i noted that the hyperbolic trigonometry properties are somewhat similar to what i may call cartesian trigonometry properties... My approach on this; ##\tanh x = \sinh y## ...just follows from ##y=\sin^{-1}(\tan x)## ##\tan x = \sin y## Therefore...

Problem Statement : I copy and paste the problem as it appears in the text (Lang, Basic Mathematics, 1971). Attempt : There are several questions in both a) and b) above. I type out the question and my answer each time. a) (i) Show that addition for ##E## and ##I## is associative and...

Hey! :smile: We have a sidebar menu and at browser I clicked Inspect and we have : I want to change the width. So I have to customize the given width of Material UI, right? For that do I have to add a css file with the following? <Drawer defaultValue={260} sx={{ width: 500, color...

Hi Physics folks,I am currently collecting resources for my senior seminar project at my university and would like to ask if anyone has any good references for gold thin films. I am planning on focusing primarily on the electrical and optical properties of gold thin films. I appreciate any...

While not having a professional physics background I was still interested in knowing more about special and general relativity. Therefore I was trying to find out where the space time interval was coming from in relation to the speed of light. Of course this is the first point to start I...

Have these articles been discussed here previously? I could not find it but my search skills suck. Kerr stability for small angular momentum https://arxiv.org/abs/2104.11857 (just 800 pages) Recently (31th May this year) Wave equations estimates and the nonlinear stability of slowly rotating...

Assume I could produce a stream of calcium ions from a 2nm diameter nanotube by pushing them through the nanotube using coulomb repulsion. Assuming these coulomb repulsed ions produce a stream of entangled ions which then create a slowly emitting quasi static electric (near) field. Even if...

I don't have any idea to answer these questions. I am working on it by searching the reference books where similar questions have been solved by authors. Meanwhile, any member of Physics Forums may help me in answering these questions.

I don't have any idea to answer this question. So, any math help will be accepted. I know ##\nabla fg = f\nabla g + g\nabla f \rightarrow (1) ## But I don't understand to how to use (1) here?

In [this post][1] user William Ryman asked what would happen if we try to build "complex numbers" with shapes other than circle or hyperbola in the role of a "unit circle". [Here][2] I proposed three shapes that could work. The common principle behind them being that if the unit curve is...

I am considering tunnel effect with a potential barrier of a certain height that is ##\neq 0## only for ##0 \le x \le a## . I write the Hamiltonian eigenfunctions outside the barrier as:## \psi_E(x)=\begin{cases} e^{ikx}+Ae^{-ikx} \quad \quad x \le0 \\ Ce^{ikx} \quad \quad x\ge a \\...

From what I've gather the primary benefits to worm wheels are: - their ability to provide high reduction ratios - self-locking which can be useful for hoisting and lifting applications. - Operates silently and smoothly, which reduces vibrations Feel free to add any important ones I might've...

I have read about doppler effect in acoustics so i searched for the relation ship between wavelength of wave produced by linear movement of body and its momentum along with other dependent variables such as density of fluid (leaving acoustics for a second) and temperature but souldn't find a...

1. A is a matrix of order 2x2 whose main diagonal's entries' sum is zero. Prove that A^2 is a scalar matrix. 2. Given: A and B are two matrices of order 2x2. Prove that the sum of the entries of the main diagonal of AB-BA is zero. 3. A, B and C are three matrices of order 2x2. Given: A^2 is a...

Ok for ##1##, we also have, ##a⋅0=a⋅(0+0)=a⋅0 + a⋅0 ## We know that ##a⋅0=0 ## by additive cancellation. For ##2.11##, Number ##2##; We first show and prove that ##-b=-1⋅b## adding ##b## on both sides, ##-b+b=0## for the lhs ##-1⋅b +1⋅b=b(-1+1)=b(0)=0## for the rhs therefore...

I did only the the first three prop. And on a means we have, on pose or posons means let there be , propriétés means properties, alors meand then. I apologize i am a french native speaker and i am busy so i cannot rewrite this in entirely english

Hey all, I want to buy Ipad Air 5th Gen Tablet. Currently My computer has this specs: CPU(s): 4 On-line CPU(s) list: 0-3 Vendor ID: GenuineIntel Model name: Intel(R) Core(TM) i5-7200U CPU @ 2.50GHz CPU family: 6 Model...

I am reading J. J. Duistermaat and J. A. C. Kolk: Multidimensional Analysis Vol.II Chapter 6: Integration ... I need help with the proof of Theorem 6.2.8 Part (iii) ...The Definition of Riemann integrable functions with compact support and Theorem 6.2.8 and a brief indication of its proof...

Hi. This semester I have chosen "Properties of Matter" as my Physics Elective. The university syllabus generically prescribes texts by Newman & Searle to be studied in this regard but tbh I find them somewhat outdated. Below I have attached a small snippet of my course syllabus. I shall be...

Hello my friends. I would like to know if you guys are aware of some site or paper that provides informations about gas. That is, i would like to know the energy band in which the ionization of a gas is high, and also the energy in which multiple scatter is high. The gas need to be Argon of Neon.

Hi, Would any member of Math Help Board explain me the highlighted area in the following paragraphs? Generating Random Distributions Now the only missing thing in previous cases is how would one generate a Uniform random, Normal random distributions. We therefore look to cover algorithms to...

Let us assume magically that elements 77 to 79 do not exist on Earth, and we ignore any other consequences for the purposes of this query. Without actually making gold to see, is our understanding of QED sufficient to be able to look at Hg as a silvery metallic liquid and work out all the unique...

I am in the need of airtight materials. Naturally, metal came to my mind. Metal is used in jar tops to create “airtight” seals. However, as I contemplated how the tops must expand slightly as they are screwed down towards the glass part of the jars, I wondered if this expansion compromises...

We have Galois extension ## K \subset L ## and element ##\alpha \in L## and define polynomial $$f = \prod_{\sigma \in Gal(L/K)} (x - \sigma(\alpha))$$ Now we want to show that ## f \in K[x] ## which is relatively easy to see because we can take ##\phi(f)## for any ## \phi \in Gal(L/K) ## then...

So a and b were pretty straightforward. Got stuck on part c. The question says they approximated Van der Waals in first order in a and b. So I started with that by rewriting Van der Waals eqn as ## p = \frac { N \tau } { V - Nb } - \frac {N^2a} {V^2} ## and I then Taylor approximated ## \frac...

How can a quantum object interact with its environment before it has any definite properties? It seems like a ‘chicken and egg’ scenario to me. I can’t see how anything could interact with a quantum object which has only potential properties (what is there to interact with?), yet if I’ve...

Ok, the last time I did something with physics, save for simple in-game simulation of gravity, was many moons ago in high school. I certainly did not learn to do this in high school, although two subjects I had there at a basic level, are touched: Waves and Classical mechanics. I have no idea...

I want to know if a right triangle can only have one leg that is a perfect power of a number. Another words is it impossible for a right triangle to have two legs that are numbers that are raised to the same perfect power? Can somebody answer this question and show me the proof?

Hi everyone, recently I was working out an elasto-plastic model to make some residual stress predictions: see it here. Recently I got some real tensile tests results from a lab, therefore I would like to extract a better stress-strain curve to plug into my elasto-plastic model using the...

Hello, I have problems with this exercise Let $(X,\mathcal{B} , \mu)$ a measurement space, consider $\bar{\mathcal{B}} = \{ A \subseteq{X} \; : \; A\cap{B} \in \mathcal{B}$ for all that satisfies $\mu(B) < \infty \}$, and for $A \in \bar{\mathcal{B}}$ define $\bar{\mu}(A) = \left \{...

See attachment for question and math work.

Use the properties of limits to find the limit. lim [x(x − 1)(x + 10)] x→−1 lim [x(x^2 + 9x - 10)] x→−1 lim [x^3 + 9x^2 - 10x] x→−1 lim (x^3) + lim (9x^2) - (10x) x→−1 x→−1 x→−1. (-1)^3 + 9(-1)^2 - 10(-1) -1 + 9 -(-10) -1 + 9 + 10 -1 + 19 = 18 The limit is 18. You...

Use properties of limits to find the limit. lim (-3x + 1)^2 x→0 [lim (-3x + 1) as x→0 ]^2 [-3•lim(x) as x→0 + lim (1) as x→0]^2 [-3•0 + 1]^2 [0 + 1]^2 [1]^2 = 1 The limit is 1.

Basically the thread title. For some background, I'm trying to model laser-material interactions, where I'm assuming that the laser is interacting with a free electron gas (copper). To model the interaction, I need to determine the properties of the electron gas, such as the heat capacity...

Hey! :giggle: Let $U\subset \mathbb{R}^n$ be an open set and $f:U\rightarrow \mathbb{R}$ is a $k$-times continusouly differentiable function. Let $x_0\in U$ be fixed. The $k$-th Taylor polynomial of $f$ in $x_0$ is $$T_k(x_1,\ldots ,x_n)=\sum_{m=0}^k\frac{1}{m!}\sum_{i_1=1}^n \ldots...

Hi All the expressions for calculating the properties are given in terms of ##S##, ##V## and ##N##. Should I find the energetic representation and then apply the formulas, or is there another way? Then, for finding the energetic representation, I know that ##A=U–TS–\mu N## But I want all these...

In the double slit experiment, are there articles that study different slit properties (e.g. charges, magnetic fields, current, etc.)? Curious if a wave is the property of the measurement, changing the properties of the experiment may alter the output measurement.

For instance if we are given only a PDF in the form of ##p(x)##, how can one calculate the characteristic function, the mean, and the variance of these PDF's ? Any site or explanation will be enough for me

===(1)=== Let ##n\in \mathbb{N}##. Express ##A_n## and ##A_{n+1}## as: ##A_n=\sup\{a_n,a_{n+1},\ldots\}## ##A_{n+1}=\sup\{a_{n+1},\ldots\}## Suppose for some ##m\geq {n+1}##, ##a_m=A_{n+1}##. By definition, ##a_m\geq a_k## for ##k\geq {n+1}##. If ##a_n<a_m##, then ##a_m\geq a_k## for ##k\geq...