Properties Definition and 1000 Threads

For arbitrary Fermionic self energy, \Sigma(i wn) with wn=(2n+1)pi T, its real part is always an even function of wn while its imaginary part is always an odd function of wn.

In a dipole, p = qd is the dipole moment. q is the magnitude of either charge, while d is the distance of separation. I was just wondering what differences in properties would be evident if both charges in the dipole were not the exact negatives of each other. For example, if you have a positive...

I have a few waves questions I would really like to have addressed. I'll post my logic/solution for each question and any feedback is welcome. Q. 10: This one seems pretty straight forward but shouldn't the units be 3.0 rad/m? Since x is in meters and we're not changing the order of...

I am having a hard time understanding the concepts of a universal property :\ What are they used for? Do they abstract the notion of constructing mathematical objects? Can the concept of a group be described by a universal property or is this not how it works?

Use the properties of Logarithms to write the expression as a sum, difference, and/or constant multiple of logarithms:

Do such materials exist? If they do, are there materials that go from very high to very low thermal conductivity depending on electrical input?

Wave function and its first derivative must be continuous becaus wave function is solution of Schroedinger equation: Let's examine one dimensional case. ## \frac{d^2 \psi(x)}{dx^2}+V(x)\psi(x)=E\psi(x) ## David J. Griffiths gives a problem in his quantum mechanics book...

Let me start off by stating that I have no formal education in Astrophysics, or any other education beyond high school, so if my question is stupid, just say so! Dark Energy, from my understanding Dark Energy is used to explain the expansion of the universe, because when we look at distant...

If a red light drops on a red object, we know that all of the red light is reflected, and none is absorbed. But what happens if a red light drops on a white surface, is all of the red light reflected, will the intensity of the reflected light be the same? Or will the reflected light be of a...

Homework Statement Which of the following phases is capable of permanently withstanding a force perpendicular to its surface? A. Gas B. Liquid C. Solid D. All of the above Homework Equations The Attempt at a Solution I understand that the answer is D. However, what does...

Homework Statement I am solving a problem and I arrived near the end, and can't figure out what to do here: (1/(2m)) [P^2,X]+[P^2,X] m - mass P - Momentum operator X - Position operator Homework Equations P = -iħ(∂/∂x) [A,B]=AB-BA [AB,C]=A[B,C]+B[A,C] where A, B...

I am learning Chemistry from one book and I have bumped onto a following image with given tasks: What is the balanced reaction? What is the RMM of thiazole? What is the fuel-air mass ratio? What is the oxygen depletion? What is the yield of CO2? What is the...

Homework Statement Construct a function f:C \rightarrow C such that f(x+y)=f(x)+f(y) and f(xy)=f(x)f(y) (aside from the identity function) Hint: i^2=-1 what are the possible values of f(i). The Attempt at a Solution All I've been able to do so far is come up with some (hopefully correct)...

Hey! :) I have to show that if $f:[a,b] \to \mathbb{R}$ is integrable,then $f^2$ is also integrable. Knowing that $f:[a,b] \to \mathbb{R}$ is integrable,does this mean that $f$ is bounded??

Parody math paper - defining "properties" And no, I don't mean properties in the mathematical sense, but rather in the "everyday" sense. In a parody mathematics paper I'm writing, I'm trying to define the "properties" of an object as a stepping stone to defining similarity. If we let P(o) be...

I've been thinking about some common properties of mathematical objects and I've been wondering if they are redundant. Like: Aren't all associative operations also closed under a set? Doesn't the existence of inverses imply the existence of an identity element? So that stating associativity...

Homework Statement . A space ##(X,\Sigma, \mu)## is a complete measure space if given ## Z \in \Sigma## such that ##\mu(Z)=0##, for every ##Y \subset Z##, we have ##Y \in \Sigma##. In this case, prove that a) If ##Z_1 \in \Sigma##, ##Z_1ΔZ_2 \in \Sigma## and ##\mu(Z_1ΔZ_2)=0##, then ##Z_2...

Homework Statement The demand for good A is unit elastic. This means that a 5 percent increase in price will ______ A) result in an infinite increase in the quantity of A demanded. B) result in a 1 percent decrease in the quantity of A demanded. C) result in 5 percent increase in quantity...

I'm an undergraduate studying math taking intermediate proof-writing courses, and there are certain basic identities of set theory and functions that still confuse me - i.e., I have to reprove them or think about them carefully every time. Examples: (A\times B)\cap (C\times D)=(A\cap C)\times...

Hi guys and girls, Just had a question I have been thinking about for a while. Suppose you have a sound maker than makes a pure tone at a particular frequency. You play this tone for an instant directed directly at a flat wall (not absorbent at all). If you could measure the reflected tone...

Does light intensity and brightness depend on amplitude?

I am working through an explanation of the wave function of the Hydrogen atom. I have got as far as deriving the version of Schrodinger's equation for the one-dimensional problem in which only the radial coordinate can vary: ##[-\frac{\hbar^2}{2m}\frac{\partial^2}{\partial^2...

If the abs(a+b) = abs(a) + abs(b), so the abs(z) = abs(x+iy) = abs(x) + abs(iy) = abs(x) + i abs(y). However, the correct wouldn't be abs(z) = √[x²+y²] ? √[x²+y²] ≠ abs(x) + i abs(y) => abs(z) ≠ abs(z) It's no make sense. What there is of wrong with those definions?

Homework Statement ##D_{ijk}## is an array with ##3^3## elements, which is not known to represent a tensor. If for every symmetric tensor represented by ##a_{jk}## $$b_i = D_{ijk}a_{jk},$$ represents a vector, what can be said about the transformation properties under rotations of the...

I find it strange that Aluminum is high on the activity series but does not react with evolution of hydrogen with many strong acids. I actually tried this when I was a kid. I had access to any acid or salt I wanted. I tried dissolving Al in H2SO4, HNO3, and HCl with no H2 bubbles. Aqua regia...

I understand that the centring of the Fermi energy at the Dirac point is a highly sought after property in Topological Insulators but I'm unsure as to exactly why? I see that the state at the conical intercept will be unique but I'm not sure of what is theorized to happen to the electrons...

Hi, Recently in class, my professor went over a relationship that exists between trigonometric functions, T(x), and their complementary functions. That is: ∫ T(x)dx = W(x) + C ∫ coT(x)dx = -co[W(x)] + C Without really providing a proof, we were told this relationship. I've plugged in numbers...

I read a textbook about limits. I saw several properties about the limits. lim f(bx)= b*lim f(x) as x approach cThank you Cbarker1

Apologies for the break from format, but I'm not sure how to make this fit! I'm designing an experiment to compare the insulation properties of several materials. I would like to find the Thermal Conductivity (K) or the U (or R) values of these materials. However essentially all I am after...

http://www.cell.com/abstract/S0092-8674(13)01479-7

Hello sir, I am new to this forum i am looking for thermophysical properties of heavy water for my computer simulation. following properties i found in the wed. can anyone suggest me that these considered properties are correct (ref temp 40 C and 6.549 kPa) density = 1099.99 Kg/m3 specific...

Dear members, I'd like to collect those properties of "spin" that makes it different to a normal (classical) angular momentum or magnetic moment. Please help me, correct, reword my sentences one by one. I'd like to create a short but still understandable and correct list. 1. Spin quantum...

I know I am jumping ahead, as I am still working through part 1 of Spivak's Calculus, and am absolutely not properly equipped to prove his properties (if they are indeed provable). However, as I am trying to work on my proofing skills, my interpretation thus far has been, that these 12...

Is there any material,when made a hollow ball out of it & filled with lighter gas than air,will rise in air according to archimedes principle? But upon removal of that gas,it should not contract itself in volume like any balloon does...it should be able to retain its volume as it is even if...

Hello, I was given the attached 3 degree of freedom spring system with the purpose of analyzing it. I came up with the following equation of motion and then I ran Matlab to calculate the corresponding natural frequencies and mode shapes using eigenvalues and eigenvectors; I was asked to...

Homework Statement A deuteron is the nucleus of a hydrogen isotope and consists of one proton and one neutron. The plasma of deuterons in a nuclear fusion reactor must be heated to about 300 million K. (a) What is the RMS speed of the deuterons? Is this a significant fraction of the speed of...

Homework Statement If A is a 2x2 matrix, then det (2A * adj(A)^-1) = ? Homework Equations Adj(A)A = det(A)I The Attempt at a Solution First, I separated them so it became det(2A) * det (1/ adj(A)) Then taking the 2 out, and it becomes 2^2, so 4 det(A) * det(1/ adj(A)) adj(A) =...

Homework Statement For what values of k is (scalar product of vectors a and b) = a_{1}b_{1}-a_{1}b_{2}-a_{2}b_{1}+ka_{2}b_{2} a valid scalar product? The vectors a and b are defined as: a = a_{1}e_{1} + a_{2}e_{2} b = b_{1}e_{1} + b_{2}e_{2} where e_{1} and e_{2} are unit vectors...

Let $(\Omega,\mathcal F,P)$ be a space of probabilities and $(A_n)_n\subseteq \mathcal F.$ Show that a) if the sequence satisfies $\inf\{P(A_n)_n:n\ge1\}=\alpha,$ with $\alpha\ge0,$ then $P\left( \bigcap\limits_{n=1}^{\infty }{\bigcup\limits_{k=n}^{\infty }{{{A}_{k}}}} \right)\ge \alpha .$ b)...

Homework Statement Finding the Fourier Transform using Transform Pair and Properties x(t) = 2[u(t+1)- t^{3}e^{6t}u(t)] Homework Equations The Attempt at a Solution For the first problem, I got u(t) \leftrightarrow ∏δ(ω)+\frac{1}{jω} F(at-t_{0}) \leftrightarrow...

Do you know why it's important for rubber to be resilient? and does anybody have an example of an object that is made out of rubber which must be resilient? and does anybody know why it's important why tires and children's play grounds are made from resilient materials? Many thanks,

Hi, I'm doing one of my physics HL coursework's (IB) on the behaviour of electric putty when conducting electricity. My teacher can't explain to me what electric putty actually is and I can't find it on the internet, so could anyone tell me if the conducting properties of electric putty are...

I am reading Dummit and Foote Ch 15, Commutative Rings and Algebraic Geometry. In Section 15.1 Noetherian Rings and Affine Algebraic Sets, the set \mathcal{I} (A) is defined in the following text on page 660: (see attachment)...

Homework Statement Hey everyone, So I've got to prove a couple of equations to do with the Levi-Civita tensor. So we've been given: \epsilon_{ijk}=-\epsilon_{jik}=-\epsilon_{ikj} We need to prove the following: (1) \epsilon_{ijk}=-\epsilon_{kji} (2)...

Homework Statement A Wiener Process W(t) is a stochastic process with: W(0) = 0 Trajectories almost surely continuous Independent increases, that means, for all t1 ≤ t2 ≤ t3 ≤ t4, we have (W(t2) - W(t1)) is independent of (W(t4) - W(t3)) For t ≤ s, (W(s) - W(t)) follows a normal centered...

I know what is lattice constant but it has been given that nano particles have reduced lattice constant due to huge fraction of atoms being in surface. How come the lattice constant of nano particles reduced due to high number of atoms present in surface? Why do the surface area, hardness...

Homework Statement Let S ⊆ R be such that (i) a, b ∈ S ⇒ ab, a + b ∈ S (ii) for all x ∈ R exactly one of the following holds x ∈ S, x = 0, −x ∈ S. Show that S = {x ∈ R ; x > 0} (the set of positive numbers P) 2. Relevant theorems (T1) a² > 0 ∀ a ∈ R. (So a²∈P) (T2) All positive...

Homework Statement You and a friend each have one rope. You tie the two ropes together and stand as far apart as possible, each holding one end of the new longer rope and pulling to put it under tension. You then begin moving your arm in such a way as to produce a harmonic wave with a...

What do physicists think about water as an example of something with emergent properties? I wonder if the concept of emergent properties has become main stream in modern physics. If so, what happened to reductionism? Does this go for water?

Homework Statement 1. Let ##p(x) = a_{0} x^{n} + a_{1} x^{n−1} + ... + a_{n} , a_{0} \neq 0 ##be an univariate polynomial of degree n. Let r be its root, i.e. p(r) = 0. Prove that ## |r| \leq max(1, \Sigma_{1 \leq i \leq n} | \dfrac{a_{i} }{ a_{0} } | )## Is it always true that? ## |r| \leq...