Relation Definition and 1000 Threads

Hoping someone can help me here, I'm only a student so I'm sorry if my question is badly worded. I'm doing my maths dissertation on a binary eclipsing star and I'm trying to work out the mass of one of my stars. I know the B-V value and effective temperature, and I believe the equation I need...

I am trying to numerically solve the recurrence relation for: $$ T[n]=\frac{sm}{2\hbar^2i k_n}(T[n-1]+T[n+1]) \\ k_n=(\frac{2m(E-\hbar \omega n)}{\hbar^2})^{1/2}$$ My code is: RecurrenceTable[{Tn[ n] == (s* m/(2*\[HBar]^2* I*(2*m*(En -...

This came up in a discussion in another forum - the context was the gravity of a photon... for which we need quantum gravity. But imagining a pulse of monochromatic light, it was asserted that it's gravity could be well approximated by replacing one of the mass terms in Newton's Law by E/c^2. I...

Homework Statement Help. If w = ∫F dx where w is work, f is force and x is displacement, and also F = k1v2 where force is a quadratic function of velocity v times a constant k1, what would be work with regards to velocity? Homework Equations More info if needed. v = ∫a dt a = k2 - k1v2/m k2...

Homework Statement Hi,I have got a question as follow: Compute the commutation relations of the position operator R and the angular momentum L.Deduce the commutation relations of R^2 with the angular momentum L Homework EquationsThe Attempt at a Solution In fact I have got the solutions to...

Hi folks, When you study Mendelian laws you learn about dominant alleles of a gene, A, or recessive alleles of a gene. My question is, What is its relation to DNA? -So in terms of bases we have A, T, C and G. And I know a gene may be in a chromosome and it may contain several million of...

Homework Statement Show that regular homotopy of regular curves γ : I → Rn is an equivalence relation, that is: i) γ ∼ γ (where the symbol ∼ stands for “regularly homotopic”); ii) γ ∼ γ˜ implies ˜γ ∼ γ; iii) γ ∼ γ˜ and ˜γ ∼ γˆ implies γ ∼ γˆ (here you have to use a smoothing function)...

Homework Statement This is a system of n coupled harmonic oscillators in 1 dimension. [/B] Since the distance between neighboring oscillators is ## \Delta x ## one can characterize the oscillators equally well by ## q(x,t) ## instead of ## q_j(t) ##. Then ## q_{j \pm 1} ## should be replaced...

Hello! I am a bit confused by the formula ##dU = TdS - PdV##. If I want to compute for example ##\frac{\partial U}{\partial V}## I obtain ##-P##, but how should I proceed to obtain, for example ##\frac{\partial U}{\partial P}## or ##\frac{\partial P}{\partial T}## which are not obvious from the...

Let U be a universal set, and let C be any subset of U. Let R be the relation on P(U) defined by A R B if $A \cap C = B \cap C$. Determine whether the relation is reflexive, symmetric, and/or transitive. Prove you answer.

Hi all, I've been able to find the answers to most of my questions in these forums, but this time I was not able to. So here goes my first post: I've been learning about thin film interference, and it all makes sense to me except for the correlation between destructive interference caused by...

Hi I have some questions about operator and experimental action 1, For each experimental action(no matter how trivial or complex), can they ALWAYS be described by some corresponded operator? how to proof? For example, adding some energy to excit a particle can be described in operator language...

Are there fundamental limits on the accuracy for measuring both position ##q## at time ##t## and momentum ##p## at time ##t+\Delta t##, with tiny ##\Delta t##? If yes, why? If no, why can't one then measure (in principle) both ##q## and ##p## arbitrarily well at the same time ##p## (which is...

My professor informally defined a n-ary relation as a "function" that assigns to an n-tuple from arbitrary sets ##X_1, X_2, ... X_n## a well-formed statement that either holds or does not hold. I know that this definition is somewhat informal, but how can the professor use the word function if...

Hi all, I read in Cheng and Li's book "Gauge theory of elementary particle physics" Ch 11, specifically : Eq. (11.46) that the hypercharge commutes with the SU(2) generators, i.e., ##[Q-T_3,T_i]=0##, I'd like to understand what that mean and how this could be proved ?

$\tiny{{s4}.{13}.{5}.{41}}$ $\textsf{find if planes are $\parallel, \perp$ or $\angle$ of intersection }\\$ \begin{align} \displaystyle {P_1}&={x+z=1}\\ \therefore n_1&=\langle 1,0,1 \rangle\\ \\ {P_2}&={y+z=1}\\ \therefore n_2&=\langle 0,1,1 \rangle\\ \\ \cos(\theta)&= \frac{n_1\cdot...

Hi all! Can anyone confirm (or point me to literature) that the dispersion relation for the attractive Kronig-Penney potential is correctly given on Wikipedia (https://en.wikipedia.org/wiki/Particle_in_a_one-dimensional_lattice): $$cos(ka) = cos(\beta b)cos(\alpha (a-b))-\frac{\alpha ^2 +...

can anyone help me ? i have a homework and i did't find any answer for it the question is find the Domain , Range , matrix and the digraph for the relation R a ) A = { 1,2,3,4,8 } = B , aRb if and only if a=b b) A = { 1,2,3,4,6 } =B , aRb if and only if a multiple of b

Homework Statement At first I needed to calculate the angular resolution of a telescope (diameter 1m, for visible light) so I used θ=1.22λ/D and got 4.88x10^-7 rad. Now I am asked: "If we wished to use this telescope to image the moon, what is the closest distance two objects can be to be...

This question was originally posted by ElConquistador, but in my haste I mistakenly deleted it as a duplicate. My apologies... For part (a) we can define two cyclic subgroups of order $2$, both normal, $\langle J\rangle$ and $\langle K\rangle$ such that $V=\langle J\rangle \langle K\rangle$...

I have a really simple question that I can't figure it out. I have a process X that took 905 seconds to finish. Process Y took 950 seconds to finish. I want to know a) how much in % process X is faster than Y, and b) how much in % process Y is slower than X? I think that the answer is the...

Hamiltonian of tight binding model in second quantization is given as H = -t \sum_{<i,j>} a_i^{\dagger} a_j After changing basis it is H = \sum_{\vec{k}} E_{\vec{k}} a_{\vec{k}}^{\dagger} a_{\vec{k}} where E_{\vec{k}} = -t \sum_{\vec{b}} e^{i \vec{k} \cdot \vec{b}} where \vec{b} is a nearest...

Homework Statement Which cannot be the structure of two acoustic branches, nor three acoustic branches? Simple cubic, FCC, BCC, diamond cubic, NaCl lattice Homework Equations N/A http://solid.fizica.unibuc.ro/cursuri/solid_en/curs_solid_EN.pdf#page=61...

Below is a snipet from http://file:///C:/Users/Christian.Hollersen/Downloads/Britto_2011_2%20(1).pdf of Britto. Similar explanation can be found in the QFT books of Zee, Schwarz or the Scattering Amplitude text of Huang. Or any other text that covers BCFW recursion. My dumb question: how and...

Homework Statement Find a recurrence relation for the number of ternary strings of length n that contain two consecutive 0s. Homework EquationsThe Attempt at a Solution Let ##a_n## count the number of ternary stings of length n that contain two consecutive 0s. Then, we can split the total...

Homework Statement If ##a_n## counts the number of ways to climb a flight of n stairs if one can take 1, 2, or 3 steps at a time, then ##a_n = a_{n-1} + a_{n-2} + a_{n-3}##. What are the three initial conditions? Homework EquationsThe Attempt at a Solution I would say that ##a_0 = 1## since...

Homework Statement Homework Equations I don't think there are any in this case The Attempt at a Solution I know that in order to prove R is an equivalence relation, I'd have to show that it is Reflexive, Symmetric, and Transitive. I'm not sure why, but I'm finding this a bit difficult in...

I am a little confused about how we prove that a solution for a recurrence relation is correct. For example, say that I have the recurrence relation ##H_n = 2H_{n-1} +1##. Using an iterative process, we guess that the solution is ##2^n - 1##. Now, to prove that this is correct, it seems that it...

Hi there, Suppose we had a car going in a circle. We know that the turning angle(angle between the movement direction and the wheel axis) and the friction are connected, because friction determines the centripetal force and it determines the radius of the circle that we make with our car. I need...

Homework Statement Deduece the commutation relations of position operator (squared) \hat R^2 with angular momentum \hat L Homework Equations [xi,xj]=0, Lj= εijkxjPk, [xi, Pl]=ih, [xi,Lj]=iℏϵijkxk The Attempt at a Solution The previous question related R and L and the result was [\hat R,\hat...

Homework Statement Suppose you are given the following relation among the entropy S, volume V , internal energy U, and number of particles N of a thermodynamic system, where A is a constant.: $$ S = A(NVU)^{\frac 1 3} $$ Find the chemical potential μ(T,P) Homework Equations $$ \frac μ T =...

I've just started with statistical mechanics and arrived at the part where they relate entropy to the number of microstates for a given system. The derivation starts of by adding an amount of heat ##\delta Q## to a system and observing the resulting change in internal energy : $$\delta U =...

Homework Statement A gas obeys the equation of statez=1/(1-b(molar density)) What is the molar entropy change of expanding this gas from a volume of 1 dm3 to 2 dm3 at a temperature of 300 K, given b = 0.2 dm3? Calculate your answer to three significant figures and select one answer from the...

Hey! :o Let $f(x)=x^3-3x-1\in \mathbb{Q}[x]$. Then $f(x+1)=(x+1)^3-3(x+1)-1=x^3+3x^2+3x+1-3x-3-1=x^3+3x^2-3$. The prime $p=3$ divides all the coefficients except of the one of the term of the highest degree and $p^2$ doesn't divide the constant term. So, from Eisenstein's criterion we...

can dark matter explain Tully-Fisher relation, or is modified MONDlike gravity a better explanation for this? new paper The Radial Acceleration Relation in Rotationally Supported Galaxies Stacy McGaugh, Federico Lelli, Jim Schombert (Submitted on 19 Sep 2016) We report a correlation between...

Homework Statement I have the following circuit What is the relation between $$I_{eq}~~and~~ i_1, i_2, i_3$$? Homework Equations Kirchhoff Laws The Attempt at a Solution See the image above

Hello all. I have a question about a reflexive relation. Consider ##1_V : V \rightarrow V## with ##V## a vector space. Obviously, this is an isomorphism. My book uses this example to show that V is isomorphic with V (reflexive relationship). However, suppose I have a function ##f: V\rightarrow...

Recently, I was thinking about the nature of reciprocity in some cases of natural phenomenon, for example, Newtons Thrid Law of Motion, or, Faraday's Law of Induction. Considering that spacetime distortion, due to a gravity field, leads to a change in the light path, or, a change in light...

Here's a thought from other thread A reply So what's the relation between gravity and the laws of thermodynamic, or should it be conservation of energy?

We know that Poincare matrix which is 0 Kx Ky Kz ( -Kx 0 Jz -Jy ) describes the boost and rotation is very similar to -Ky -Jz 0 Jx...

With a modest understanding of 'spooky action at a distance', I've been informed that using entangled particles as a form of quantum bit system would not work for vast distances. It wouldn't be a viable option to communicate instantly with points like our moon, satellites orbiting Jupiter, or...

Suppose you are given a first order system whose transfer function is HP(s) = KP/(TP*s + 1). Now, you want to control this system using a standard P (proportional) controller whose transfer function is HR(s) = KR (a proportionality coefficient). There is also disturbance that acts upon this...

Homework Statement I want to prove this relation ##J_{n-1}(x) + J_{n+1}(x)=\frac{2n}{x}J_{n}(x))## from the generating function. The same question was asked in this page with solution. http://www.edaboard.com/thread47250.html My problem is the part with comparing the coefficient. I don't...

Dear all, in a lot of undergraduate textbooks you find the claim that antiparticles can be motivated by Einstein's energy-momentum relation ## E^2 = p^2 + m^2 ##, which has both 'negative' and 'positive energy' solutions. In the context of a single wave function this is problematic. In the...

The definition from the current Wikipedia article is a good start: My technical question is whether "each further term" is a function of only the values of the preceeding terms, or is it also a function of the index of the "further term"? For example, if we are given that the values of two...

Homework Statement Homework EquationsThe Attempt at a Solution If I consider a specific case of adiabatic process , then ##dQ = 0 ## and ##dU = -PdV ## If we differentiate with respect to T on both sides , ##\frac{dU}{dT} = -P\frac{dV}{dT}## . Now , the closest I see is option B) , but...

KE is proportional to v^2. In a gravitational field KE=1/2 m*v^2. It's easy to find mathematically Work=Fd=mad=m(v/t)(v*t)=m*v^2. But how to visualize it or get an intuitively "feel" for this v^2 relationship?

So I see them in the books labelled as accoustic and optical phonons but I don't seem to find a comprehensive treatment of the matter for a beginner who doesn't know a thing about the dispersion curves. I'd prefer not to dwell too much into the mechanical treatment if possible since I just need...

I have a hard time understanding the variation of mass with velocity, more precisely the proof. In almost every material I've found, the author analyses 2 bodies colliding. The idea of looking at the collision is not hard to grasp and by considering one of the velocities equal zero, you get a...

You can model the probability for radioactive decay as a Poisson distribution. This is the probability for radioactive decay within a specific time interval. (I probably got some of it wrong here). P(k,μ)=λ^k⋅exp(-μ)/k! Is there a way to use this formula to derive the other formula for...