Relation Definition and 1000 Threads

Hello, I may working through attached paper and really need help with deriving equation in appendix - A4 to give A10. http://iopscience.iop.org/article/10.1088/0004-637X/744/2/182/pdf Any help would be greatly appreciated. thanks, Sinéad

Homework Statement Homework Equations $$\frac{\partial S}{\partial u}\Bigr|_{v} = \frac{1}{T}$$ $$\frac{\partial S}{\partial v}\Bigr|_{u} = \frac{-P}{T}$$[/B] The Attempt at a Solution a.) $$\frac{S}{R} = \frac{UV}{N} - \frac{N^3}{UV}$$ $$\frac{S}{R} = \frac{UV}{N} - \frac{N}{uv}$$ $$...

I need a clear-cut explanation of vacuous truth, as I can't seem to wrap my head around it. I guess this more precisely comes down to why we organize the truth table for the conditional statement the way that we do. Also, in connection to this, I'm wondering why the empty set is a subset of all...

Hi! In school I was thaught that magnet doesn't have anything to do with the motion of electrons, but then when you see the way electromagnetic induction work, it seems like the magnet move the electrons somehow. How is that possible and can we control the movement? Thanks a lot and sorry for my...

I have information about temperature, pressure, normal and shear stresses, viscosity, conductivity, density, heat capacity and adiabatic heating for a particular area of mantle in the form of 2D matrices. I want to show phase relation for this region of mantle. Is there an equation (group of...

My book says that the real numbers are complete in the sense that they satisfy the least upper bound property. So it is the case that completeness and satisfying the l.u.b. property are equivalent by definition, or is it the case that satisfying the l.u.b. property implies completeness, meaning...

Hi, say for example we have a magnetic core with a coil wound around, and if we introduce an airgap (i.e. increasing the reluctance), how is inductance reduced? I read on some forum (see source below) that inductance scale inversely with reluctance. So I do not have the mental picture of why...

It's pretty easy to explain why objects appear small as the distance from them increases, if we use ray theory: as the distance increases, the angle become smaler. But I know the ray theory is far from being a accurate theory of light. My question is then, How can we explain the phenomenon of...

Homework Statement The problem that I am having stems from a problem given in the following way:[/B] "a)Show that for a gas, the mean free path ##\lambda## between collisions is related to the mean distance between nearest neighbors ##r## by the approximate relation ##\lambda \approx...

Homework Statement A 16m long vessel moved passed you at a relative speed of 0.86c. What was the length of the vessel recorded by your measuring device? Homework Equations Speed = distance/time t=to/√1-v2/c2 L=Lo⋅√1-v2/c2 The Attempt at a Solution Ok, so I can just sub the 16m and 0.86c in...

Is there a relation between these concepts? We know that as we move down the number line, the primes become less common. This makes sense: as we get more and more numbers, they could be constituted using all the primes that came before early on and less likely to be constituted by all the recent...

So I learned that voltage/emf is proportional to the negative change in flux so the graph of the voltage is the negative derivative of the flux graph. What is the relation between flux and current. In a motor, a change in flux induces a current that creates an opposing magnetic field, and...

(1) Magnetic force acting on charge moving in magnetic field is given by, F = qvBsinθ...F ∝ v This means that if moving charge particle has more velocity then more magnetic force will act on it. Due to more magnetic force the direction of velocity changes rapidly and it will move on the...

I was looking at the fundamental equation ##dU = Tds - Pdv + \sum_i \ \mu_i \ dN_i## and I was thinking of how many different ways one has for deriving it. I know I have to look through a book on Thermodynamics. I actually have done that some time ago and I will do that again. But the following...

Hi there... I have a question about the tipical mass-radius relation plot for a neutron star, something that looks like this for different equations of state: My question is, what is exactly happening at the ends of the EOS lines? I know that after passing the maximum mass the curve starts...

Hi all, How does matter curve space (what's the mechanism)? Does this Curvature happen instantaneously or does it happen at light speed? Thanks in advance.

Homework Statement A particle of 1kg loves along x acid such that it's position x varies with time t as x =t(t-1)(t-2) m find the force exerted on the particle at t=0,1,2 Homework Equations Just given that position x varies with time t as x=t(t-1)(t-2) The Attempt at a Solution After opening...

I wish to find a closed form relation between ##\theta## and ##d## in the attached figure as a function of ##r##, the radius of the circle and ##s## the distance from the point ##p## to the center. Thank you.

Hello all, If R is a partial order relation, is it true to say that \[R\cup R^{-1}\] \[R^{2}\] \[R\cap R^{-1}\] Are equivalence relations ? Regarding the first one, I think that the answer is yes. If \[xRx\] then it remains after the union. Asymmetry means that \[xRy\] without \[yRx\]...

Hi all, Recently I am reading some online material about Tully-Fisher relation and Faber-Jackson relation which is describing the dynamical constrain on the mass of spiral/elliptical galaxies. In spiral galaxy, TF relation suggest Luminsoty ≈ (some const) (Vmax)^4 while in elliptical galaxy...

Hello all, I have another question about partial order relations, again, a few statements which are either true or false. R is a partial order relation on a set A which is not necessarily finite. 1) With this order, A has at least one maximal and one minimal elements. 2) If with this order...

Hello, I have a question which includes several statements, which I need to decide if they are true or false. I am not sure how to do it, if you could give me hints or "leads", it will mostly appreciated. R is a partial order relation on A, a set of functions from [0,1] to [0,infinity) such...

Here is a link to a derivation of classical intrinsic angular momentum: https://www.scribd.com/document/349675642/Potential-energy-Prop-to-SL In 2.1 in the image above they define: ##m=2\mu S## and say that ##\mu## is the bohr magneton. By using the defintion of the bohr magneton I get...

Hi, How can I relate the beam energy of an electron beam produced by an electron gun to the accelerating potential? I realize that accelerating potential, initial energy (before acceleation), and losses by synchrotron radiation, etc, will play a part. I searched online and can't find much. Thanks

Hi. This is the problem 5.1-1 from the second edition of Callen's Thermodynamics. It says Formulate a proof that the energy minimum principle implies the entropy maximum principle. That is, show that if the entropy were not maximum at constant energy then the enrgy could not be minimum at...

The sound intensity formula is given by: dE/dT*dS. So the variables are energy, related to the amplitude of the wave, area, related to wavefronts distribution on space, and time. So many times I don't see any reference about the relation between frequency and sound intensity, but if time is a...

Homework Statement definition of εijk εijk=+1 if ijk = (123, 231, 312) εijk = −1if ijk = (213, 321, 132) , (1.1.1) εijk= 0,otherwise . That is,εijk is nonzero only when all three indices are different. From the definition in Eq. (1.1.1), show that...

The Nonlinear Schrodinger Equation (NSE) is presented as: $$i\frac{∂A}{∂z} = \frac{1}{2}β_2\frac{∂^2A}{∂t^2}-\gamma|A^2|A$$ The steady state solution $$A(z)$$ Can be derived as an Ansatz given by: $$ A(z) = \rho(z)e^{i\phi(z)}$$ By substituting and solving the ODE, the steady state...

Isn't, if we have xRy and yRx then xRx will also make transitive? Because if I am right {(x,x),(y,y)} on set {x,y} is symmetric and transitive. Isn't the above similar to, if xRy and yRz then xRz is transitive relation? Thanks.

I am reading a proof of why \left[ \hat{L}_x, \hat{L}_y \right ] = i \hbar \hat{L}_z Given a wavefunction \psi, \hat{L}_x, \hat{L}_y \psi = \left( -i\hbar \right)^2 \left( y \frac{\partial}{\partial z} - z \frac {\partial}{\partial y} \right ) \left (z \frac{\partial \psi}{\partial x} -...

When I tried to derive this relation I got the wrong sign. Please check the pic and tell me my mistakes.

Homework Statement Show how the given physical magnetic field is consistent with a monochromatic plane wave solution to Maxwell equation Homework Equations [/B] Physical: > Bphys(t) = B0 sin (2πft) ex Maxwells: > B = iB0 exp[i(kz − ωt)] ex.The Attempt at a Solution I know that field is the...

Relations between vectors in cylindrical and Cartesian coordinate systems are given by \vec{e}_{\rho}=\cos \varphi \vec{e}_x+\sin \varphi \vec{e}_y \vec{e}_{\varphi}=-\sin \varphi \vec{e}_x+\cos \varphi \vec{e}_y \vec{e}_z=\vec{e}_z We can write this in form \begin{bmatrix}...

Source: Çengel/Cimbala. Above part is confusing for me from some points. First of it what can a closed system refer to? I just understand a piston/cylinder arrangement with an ideal gas in it. But this concept must be more comprehensive than I have it in my mind. Second, does "closed system...

I am wondering, when solving rigid body exercises, how can I express the relationship between linear and angular acceleration for a general case? E.g. what would be the linear acceleration in function of the angular one of a 1m rod that is rotating through a fixed point 0.6 m away from its mass...

Two questions regarding the completeness relation: First: I understand that the completeness relation holds for basis vectors such that ## \sum_{j=1}^{m} | n_{j} \rangle \langle n_{j} | =\mathbb{I}##. Does it also hold for unit-normalized sets of state vectors as well, where ## | \phi_{j}...

Okay...I read that the decomposition of water is a reversible reaction (because the constituents can react to form water and water can decompose to form constituents)...This lead me to another thought that almost all compounds can be decomposed (although it is true that their conditions for...

Homework Statement (I have dropped the hats on the ##\alpha_{n}^{u}## operators and ##L_{m}##) ##[\alpha_{n}^u, \alpha_m^v]=n\delta_{n+m}\eta^{uv}## ##L_m=\frac{1}{2}\sum\limits_{n=-\infty}^{\infty} : \alpha_{m-n}^u\alpha_{n}^v: \eta_{uv}-\delta_{m,0}## where : denotes normal-ordered. Show...

i'm trying to understand the solution to this problem: http://physweb.bgu.ac.il/COURSES/StatMechCohen/ExercisesPool/EXERCISES/ex_2065_sol_Y13.pdf (link to the problem and the solution of it) All my questions come from the partition function: 1) From where the term (2*pi)^d comes from?, I...

Is it true for all material that if young's modulus is high then melting point will be high and coeff of thermal expansion will be lower? Any example that doesn't follow the above statement. Many Thanks

Homework Statement A set ##P=\left\{ \ p1,p2,p3,p4 \right\}## is given. Determine the number of antisimmetric relations of this set so that ##p1## is in relation with ##p3##, ##p2## is in relation with ##p4## but ##p2## is not in relation with ##p1##. Homework Equations 3. The Attempt at a...

Hi. I must prove that, in general, the following relation is valid for the elements of a density matrix \rho_{ii}\rho_{jj} \geq |\rho_{ij}|^{2}. I did it for a 2x2 matrix. The density matrix is given by \rho = \left[ \begin{array}{cc} \rho_{11} & \rho_{12} \\ \rho^{\ast}_{12} & \rho_{22}...

Homework Statement Calculate the radius of a 1.3 Msun white dwarf using the mass-radius relation for white dwarfs. Give the answer in solar radius. Homework Equations Mass-radius relation: $$R \propto M^{-\frac{1}{3}}$$ The Attempt at a Solution So I've tried the following: $$R_{D} \propto...

Hello everyone Im new on the forum and I just discovered what are sync machines... I have really basic question what I still cannot figure out.. I did some experiments with motor for different field currents and torques. In the result I measured armature currents and did V curves. But next...

Dear Forum: I have a question about atmospheric photodissociation. I use methane as an example, but any atmospheric gas molecule would suffice. Methane, CH4, has a photodissociation energy of 439 kJ/mole at 298oK, meaning that CH4 + hv --> CH3 + H , hv<274nm. It also has an “absorption cross...

hi, I do not know much about PDEs and programs like wolfram alpha and maple don't give me a solution. it is possible to calculate the function through PDE?. I would appreciate any help $$\frac{\partial }{\partial a}f(a,b,n)+\frac{\partial }{\partial b}f(a,b,n)=-n f(a,b,n+1)$$...

Homework Statement Question: If the attenuation between Earth and satellite is 190dB, with reference to attenuation explain why there should be a difference between uplink and downlink? (I am a senior high school student so I haven't learned in too much depth) The Attempt at a Solution My...

A friend has severe sleep apnea and uses a Cpap machine to manage it. He also has a testosterone level of 5. He has been as low as 3. He has some testosterone replacement left but is running out so went to his GP to get some more. He refused to give him any until they find the cause of the low...

Homework Statement Suppose R1 and R2 are relations on A and R1 ⊆ R2. Let S1 and S2 be the transitive closures of R1 and R2 respectively. Prove that S1 ⊆ S2. Please check my proof and please explain my mistakes. thank you for taking the time to help. Homework Equations N/A The Attempt at a...

$y=x^3-ax^2-bx---(1)$ $y=ax+b---(2)$ $a,b\in R$ $x$ is a negative integer, $y$ positive integer (1) find the relative equation between $a$ and $b$ (2)pair(s) of $(x,y)$