Terms Definition and 1000 Threads

Assume that players A and B play a match where the probability that A will win each point is p, for B its 1-p and a player wins when he reach 11 points by a margin of >= 2The outcome of the match is specified by $$P(y|p, A_{wins})$$ If we know that A wins, his score is specified by B's score; he...

The starting point is the identity $$\left(\frac{\partial u}{\partial T}\right)_n = T\left(\frac{\partial s}{\partial T}\right)_n.$$ I then try to proceed as follows: Integrating both with respect to ##T## after dividing through by ##T##, we find $$ \int_0^T \left(\frac{\partial s}{\partial...

TL;DR Summary: Why were the two terms "visible light interference" and "the non-visible spectrum" omitted from the translation? I am doing a contrastive study of a Chinese sci-fi novel and its English translation. The following is a more faithful translation of the original: The initial...

The mathematical representation of the net external force on a system(obtained from Newton's second law) is ##\vec F_{net} = \frac {d\vec P}{dt}##, which is the rate of change of linear momentum of the system. If we substitute ##\vec P = m\vec v## into the formula for force and differentiate, we...

Hmmmm was a nice one... took me some time to figure out ...seeking alternative ways ... My working; ##x=\dfrac{-2±\sqrt{4+4 \sinh^2 2u}}{2 \sinh 2u}## ##x=\dfrac{-2±2\sqrt{1+ \sinh^2 2u}}{2 \sinh 2u}## ##x=\dfrac{-1±\sqrt{1+ \sinh^2 2u}}{\sinh 2u}## ##x=\dfrac{-1+\sqrt{1+ \sinh^2 2u}}{\sinh...

Where could you find a systematic review of terms specifying the possible sex structures of plant populations? This https://en.wikipedia.org/wiki/Plant_reproductive_morphology has a list of 30 terms, arranged by alphabet not meaning, containing many synonyms... It seems to me that a plant...

This is an Argand diagram showing the first 40,000 terms of the series form of the Riemann Zeta function, for the argument ##\sigma + i t = 1/2 + 62854.13 \thinspace i## The blue lines are the first 100 (or so) terms, and the rest of the terms are in red. The plot shows a kind of approximate...

I feel like this should be pretty straightforward knowing all the equations involved but my brain seems be stalling for some reason.

d) The block of mass m is pushed toward the wall until the spring has been compressed, and so the spring has stored PE, and when the block is released, it follows a projectile motion and strikes the floor ##stored PE\rightarrow K.E ##. By law of conservation of energy, $$ E_i = E_f $$ $$ mgh +...

In Dirac's "General Theory of Relativity", he begins Chap 16, with "Let us consider a static gravitational field and refer it to a static coordinate system. The ##g_{\mu\nu}## are then constant in time, ##g_{\mu\nu,0}=0##. Further, we must have ##g_{m0} = 0, (m=1,2,3)##." It's obvious that...

I have a great difficulty in understanding the current and voltage ratings of the inverter, at the input of the inverter the ratings are different compared to the output side. What are the formulae of those conversions example, If i check the above diagram, power supply is 24V, 1.6APk a. Does...

Is there a way to obtain equation 9.42 (I is current, j is current density, and sigma is conductivity) in the following image (from Modern Electrodynamics by Andrew Zangwill, the part on electromotive force) besides using V=IR and substituting the line integral of j/conductivity for V? The...

non-relativistic physics，classical mechanics and low speed physics I think these three terms are synonyms, but I am not sure whether there is any stylistic difference between them? Is "low speed physics" informal or outdated or non-standardized compared with the other two? Please teach me if you...

In the solution, the term Lcm and Icm is used. Explain the meaning of these terms? I think cm stands for centre of mass. why that is used in the subscript?does the term angular momentum from the centre of mass of the sphere makes sense? Is the term Lcm and Icm stand for angular momentum of the...

Hello. As is known, we can neglect high-order term in expression ##f(x+dx)-f(x)##. For ##y=x^2##: ##dy=2xdx+dx^2##, ##dy=2xdx##. I read that infinitesimals have property: ##dx+dx^2=dx## I tried to neglect high-order terms in integral sum (##dx^2## and ##4dx^2## and so on) and I obtained wrong...

I believe I am doing everything right up until the point where I have to try and find a recurrence relation. I honestly have no idea what to do from there. I've listed my work in getting the powers of n and the indicies to all match. Any help appreciated. Here is the original DE...

How do I re-write $$\displaystyle\sum_{n=1}^\infty \frac{1}{n^x} *(\displaystyle\sum_{k \in S, \mathbb{Z}\S =n})$$ in terms of ##\zeta (x)## ? I want to solve for ##\zeta (x)## and simplifying the above expression in terms of ##\zeta (x)## would avoid repetition.

Let's arrange the rod's axis parallel to the z axis. ##T_{00} = A/\mu## (since it represents the energy density) ##T_{03}=T_{30} = \frac{F\sqrt{\mu / F}}{A}## (It represents the flow of energy across the z direction) ##T_{33} = F/A## (pressure) It seems that ##T_{33}## i have got has the...

Summary: How to express ωₙ in terms of only mass (m) and stiffness (k)? I tried doing it with F=kx but it is out of my ability to simplify it to only m and k. Here is my approach:

Hi, This is a simple question that I just wanted to clarify. I was reading the following paper on label propagation: HERE and I can't understand whether the terms are vectors or scalars in one of the equations - specifically, equation (2.15) shown in the image below. My understanding: - ##f##...

I'm trying to figure out the second order extension of the "trick" used on page 92 (https://www.damtp.cam.ac.uk/user/tong/aqm/solid3.pdf) for the calculation of the effective mass matrix ##m^{\star}_{ij} = \hbar^2 (\partial^2 E/ \partial k_i \partial k_j)^{-1}## on page 94. I think for this one...

|exp(2z+i)| = e2x, where did the imaginary part go? |exp(2z+i)| = exp(2(x+iy)+i) = exp(2x+2iy+i) = exp(2x+i(2y+1)), I understand this but I'm confused how the solution is e2x. Could someone help explain it to me, thank you.

So in my Calculus book, it asked a question in its Transcendental Functions chapter. It wanted me to express ##3^{\sqrt{2}}## in terms of natural logarithms I have no idea how to solve this. All I know is that ##3^{\sqrt{2}} = e^{\sqrt{2}\ln{3}}## but that's not completely in natural logarithm form.

M. Blennow's book has problem 2.18: Show that the contracted Christoffel symbols ##\Gamma_{ab}^b## can be written in terms of a partial derivative of the logarithm of the square root of the metric tensor $$\Gamma_{ab}^b=\partial_a\ln{\sqrt g}$$I think that means square root of the determinant of...

Hi. A electromagnetic wave consists of an electric and a magnetic component. I believe that the electric field strength is measured in volts per meter. The magnetic field I think is measured in Tesla. Let's imagine that I measure the electic field strength of two different radio stations and...

I'm happy I understand why the dq terms cancel out. So, $$E_{average} = U = \frac{\frac{1}{2M} \sum_{\alpha = 1}^{3N} p_{\alpha}^{2} \int_{-\infty}^{\infty} \Pi_{\beta = 1}^{3N} e^{\frac{-p_{\beta}^{2}}{2M k_{b}T} }dp}{\int_{-\infty}^{\infty} \Pi_{\beta = 1}^{3N} e^{\frac{-p_{\beta}^{2}}{2M...

Problem statement : I copy and paste the statement of the problem from the text. (Given ##\boldsymbol{a+b+c=0}##) Attempt : I am afraid I couldn't make any meaningful progress. With ##a = -(b+c)##, I substituted for ##a## in the whole of the L.H.S, both numerators and denominators. I multiplied...

hi guys I am trying to calculate the the potential at any point P due to a charged ring with a radius = a, but my answer didn't match the one on the textbook, I tried by using $$ V = \int\frac{\lambda ad\phi}{|\vec{r}-\vec{r'}|} $$ by evaluating the integral and expanding denominator in terms of...

This is a spring problem From this, it says I need to answer in terms of kinematic friction which to me doesn't make much sense. I also looked at similar questions online to the "in terms of" problems and they don't use all four variables in their derived equation. Do I not need to use all...

Hi. In the context of Bell-like inequalities, the words to use seem to be "realism", "locality", "contextuality", "definiteness" and of course their negations. I have rarely seen those terms in classical physics (except maybe locality) before the Bell context. In classical physics (and...

Hi I was working on a physics problem and it was almost solved. Only the part that is mostly mathematical remains, and no matter how hard I tried, I could not solve it. I hope you can help me. This is the equation I came up with and I wanted to prove it: $$\lim_{n \rightarrow+ \infty} {...

Hi all, I am hoping someone can help me understand a PDE. I am reading a paper and am trying to follow the math. My experience with PDEs is limited though and I am not sure I am understanding it all correctly. I have 3 coupled PDEs, for $n$, $f$ and $c$, that are written in general form, and I...

According to this link here https://en.wikipedia.org/wiki/Relativistic_mechanics#Force , we can inverse the relation of force in terms of velocity and acceleration: $$ \mathbf{F} = \frac{m\gamma^3}{c^2}(\mathbf{v} \cdot \mathbf{a})\mathbf{v} + m\gamma\mathbf{a} $$ to get: $$ \mathbf{a} =...

Hello. I'm not sure how the generalisation comes about (where I circle). I assume that r means the the rth derivative of f(x). If that's the case, as I plug 3 = r into this generalisation, the third derivative term should equal to (-1)^3x^7 /7!, but the third derivative term is -1x^3/3...

The coherent state can be written in terms of e^(αb†+α∗b)|0>. But how the even coherent state i.e. |α>+|-α> can be written in terms of displacement operator?

You are given the dollar value of a product in 2016 and the rate at which the value of the product is expected to change during the next 5 years. Use this information to write a linear equation that gives the dollar value V of the product in terms of the year t. (Let t = 16 represent 2016.)1...

Let's say I want to study subalgebras of the indefinite orthogonal algebra ##\mathfrak{o}(m,n)## (corresponding to the group ##O(m,n)##, with ##m## and ##n## being some positive integers), and am told that it can be decomposed into the direct sum $$\mathfrak{o}(m,n) = \mathfrak{o}(m-x,n-x)...

Hello: I'm not sure if there's an accepted canonical form for a quadratic equation in two (or more) variables: $$ax^2+by^2+cxy+dx+ey+f=0$$ Is it the following form? (using the orthogonal matrix Q that diagonalizes the quadratic part): $$ w^TDw+[d \ \ e]w+f=0$$ $$w^TDw+Lw+f=0$$ where $$...

Given a list [ a,b,c,..., z] in Python, write a program to determine if the terms are monotonic or not. I can do either , and combine theminto a long, clunky program, but trying to see if I can find a succint way of doing both. I have heard that using ' Nums' may do it,but it seems too...

According to the equation, the answer is B. Since the lecture didn't cover much about it, can someone explain this formula in a less physics way? Thanks.

The way I tried to solve it is by using following reasoning. The inclined part of the string will each have a speed of U m/s. So the point P just above mass M where the inclined strings meet is being moved up by each inclined string at ##U \cos {\theta} ##. Therefore, the speed of the point P...

Hello, I'm trying to understand the counter-rotating terms of the Rabi Hamiltonian : ##a^\dagger \sigma_+## and ##a \sigma_-##. I find these terms rather strange, in the sense that naively I would interpret them as describing an electron that gets excited by emitting a photon (and vice...

How many different arithmetic sequences have the sum of the first n terms n^2? solution an= 2n-1.Does that mean there is only one arithmetic sequence?

So in figure 4.8 the path difference between the two waves is d*sin(theta), then is the phase difference just (d*sin(theta)*2*pi)/lambda?

First a disclaimer: I am neither an electrical engineer nor a mathematician. I am a programmer. As part of a simulator project, I've been asked to solve a particular problem -- and I'm in over my head. Given an unbalanced 3-phase AC circuit, I have learned that I can solve for the...

good day I want to study the convergence of this serie and want to check my approch I want to procede by asymptotic comparison artgln n ≈pi/2 n+n ln^2 n ≈n ln^2 n and we know that 1/(n ln^2 n ) converge so the initial serie converge many thanks in advance!

I have some dimensionless numbers commonly used in fluid mechanics and I want to express a certain expression in terms of these dimensionless numbes If I, after defining my dimensionless numbers, enter the command : simplify(*expression*) where the expression is a function of variables that...

I enjoy explaining spacetime curvature to people with a rank-beginner understanding of GR. But someone asked about that favorite concept in pop-sci, spaghettification. I'm having a hard time with it. If you fell into a black hole, there's no reference frame within which you could describe...