Function Definition and 1000 Threads

Hello everybody! I am working on a code in which I need to study the dependence of ##<p_T>## vs ##p_L## (the average transverse momentum and the longitudinal momentum of a particle). I am looking for references, papers, books, etc. concerning this topic, but I have not been so lucky. My...

f(x)=2xand g(x)=2^x Find the composite function of fg(x) fg(x) =f(g(x)) =f(2^x) =2(2^x) I don’t understand how this in turn equals to 2^(x+1) [Moderator's note: Moved from a technical forum and thus no template.]

I am currently doing some task on a website called Codility (link and bottom of post). The task basically ask for me to create an algorithm to shift an array to the left K times (Full details below). Which seem to work for a non function but I still seem to be shifting it wrong as the output is...

Homework Statement: Solve for x. Homework Equations: sin(3x)= -1/2 sin(3x) = -1/2 3x = sin-1(-1/2) 3x = -π/6 x = -π/18 x = -π/18 + 2π/3 = 11π/18 11π/18 + 2π/3 = 23π/18 11π/18 + (2π(4))/3 = 35π/18 The solutions I obtained were 23π/18 and 35π/18. Are these correct? I'm not entirely sure...

Dear All, Here is my question. The marketing department estimates that if the selling price of the new product is set 40 dollar per unit, sales will be 400 units per week. If the selling price is 20dollar per unit, sales will be 800 units per week. The production dept estimates that variable...

Recently I have come into Special Relativity and specifically Lorentz transformation. Let's assume two frames A and B moving relative with speed ##v##. The position of a particle moving with respect to B is given by ##x′=f(t′)=3t′##. What is the function of position ##x=f(t)## of the particle...

Hi, I understand how any function could be decomposed into even and odd parts assuming the function isn't a purely even or odd to start with. It's just like saying that any vector in x-y plane could be decomposed into its x- and y-component assuming it doesn't lie parallel to x- or y-axis...

Homework Statement: I do know how to solve the resistance network problem in two dimensions. However, in this problem they want it in 3 dimensions and higher and I don't know how to do that Homework Equations: - In the picture you can see the solution to the two dimensional version

I am currently working my way through some w3schools python exercise on tuples and lists etc and one question was to write a program to converted a tuple to a string. Now originally I used the str() function on the tuple and printed the result. I then used the string in a for loop for a...

Heavier bosons like ##W## or ##H## require high energy accelerator to be detected. Yet these bosons fulfill their function in the ambient energy of the universe. Why is it that their detection takes high energy environment but their function is possible in lower ambient energy?

$\textsf{6.2.15 Find the domain of each function.}$ (a) $f(x)=\dfrac{1-e^{x^2}}{1-e^{1-x^2}}$ set the denominator to zero and solve $1-e^{1-x^2}=0$ then $x=1,-1$ from testing the domain is $(-1,1)$(b) $f(x)=\dfrac{1+x}{e^{ \cos x}}$ set $e^{\cos x}=0$...

If we have a function ##f(x+\Delta x)## where ##\Delta x << x##, is it valid to approximate this as: $$f(x + \Delta x) \approx f(x) + f'(x)\Delta x$$ even if ##\Delta x## is not necessarily small? If not, what is the valid expansion to first order?

Basically, I wanted to create a Numpy array with linearly spaced integers between 0 and 3, the increment being 0.01. Yes, I know Numpy offers a linspace function. I used it like this: x = np.linspace(0, 3, num=300) (where np is numpy), and got this: I know that the numbers cannot be exact...

I have a PDE that I want to solve for a stream function ψ(j,l) by discretizing it on a 2D annulus grid in cylindrical coordinates, then solving with guas-seidel methods (or maybe a different method, not the point): (1/s)⋅(∂/∂s)[(s/ρ)(∂ψ/∂s)] + (1/s2)⋅(∂/∂Φ)[(1/ρ)(∂ψ/∂Φ)] Where s and Φ are...

In a simple circuit with battery connected to a resistor or a combination of resistors where is the electric field directed . What do we mean when we say battery creates a potential difference between two points in a conductor? And by the statement that battery moves positive charge from low...

Hi, I was trying to numerically integrate the following inverse Fourier transform integral,, using the code below. The plot is also shown below. The plot looks good which means the result is good as well. By the way, I was getting a warning which I quote below the code. % file name...

Why can't the general state, in the presence of coupling, take the form $$\psi_-(r)\chi_++\psi_+(r)\chi_-$$ where ##\psi_+(r)## and ##\psi_-(r)## are respectively the symmetric and anti-symmetric part of the wave function, and ##\chi_+## and ##\chi_-## are respectively the spinors representing...

Let $f(x)=(2x+1)^3$ and let g be the inverse of $f$. Given that $f(0)=1$, what is the value of $g'(1)?$$(A)\, \dfrac{2}{27} \quad (B)\, \dfrac{1}{54} \quad (C)\, \dfrac{1}{27} \quad (D)\, \dfrac{1}{6} \quad (E)\, 6$ok not sure what the best steps on this would be but assume we first find...

This thread is to look at the notion of wave function collapse and relativity of simultaneity. The other thread I started on QFT has helped to clarify a lot, so hopefully this one can do the same. I may have this all wrong, but I will outline my question and hopefully someone can point out...

Instinct tells me to just plug in the number, say the limit is zero, and be done with it. But at the same time, while reading the statement from the "Relevant equations" section of this post, I cannot feel but feel some doubt as to whether or not this is the right approach. I mean, only the...

Recently in college, we have started learning python. I found that the print statement can accept multiple variables. For example, if I have variables x1, x2 and x3, I can write print(x1, x2, x3) in python. Something similar exists in Matlab as well. I have learned Java for nearly four years...

Fermions such as the electron and proton can be described by wave function in momentum and in position, and it is possible to get the momentum wavefunction from space wave function and vice versa by Fourier Transform. what about photons? can photons be described by position wave function? If...

217 $f(x)=\begin{cases} \dfrac{(2x+1)(x-2)}{x-2}, &\text{for } x\ne 2 \\[3pt] k, &\text{for } x=2 \\ \end{cases}$$(A)\,0\quad(B)\,1\quad(C)\,2\quad(D)\,3\quad(E)\,5\quad$

Probability density function plays fundamental role in qunatum mechanics. I wanted to ask if there is any analogous density function in classical mechanics. Obviously if we solve Hamilton equations we get fully deterministic trajectory. But it should be possible to find function which shows...

Summary: In the past, physicists talked of the phenomenon of "wave function collapse" very freely, whereas now there seems to be some reservation about it. Why? In reading older popular physics literature, physicists used to talk about "wave function collapse" freely and more often...

I am experimenting with using a radiometer as an approximate indicator of pressure in my homemade high vacuum system, running a small turbo pump. I am interested in the relationship between pressure and vane rotation speed, with light intensity being constant. I have only been able to find...

There are meaningful ways to assign values to things like 1 - 1 + 1 + ... or 1 - 2 + 3 - 4 + ... In a similar spirit, is it possible to assign a value to the integral of a function like this: ##f(x)=x*sin(x)## or this one: ##g(x)=Re(x^{1+5i})## (Integrals from some value, say zero, up...

## u_x = 3x^2 -3y^2 ## and ## v_y = -3y^2-3x^2 ## ## u_y = -6xy## and ## v_x = -6xy## To be analytic a function must satisfy ##u_x = v_y## and ##u_y = -v_x## Both these conditions are met by x=0 and y taking any value so I think the functions is analytic anywhere on the line x=0 However...

I have been playing around with Taylor expansion to see if I can get anything out but nothing is jumping out at me. So any hints, suggestions and preferably explanations would be greatly appreciated as I’ve spent so so long messing around with it and I need to move on... But as always, thank you

Hello everyone. I am currently using the pca function from MATLAB on a gaussian process. Matlab's pca offers three results. Coeff, Score and Latent. Latent are the eigenvalues of the covariance matrix, Coeff are the eigenvectors of said matrix and Score are the representation of the original...

Hello, From wikipedia, this is the partition function for a "classical continuous system": This is the pillar of classical statistical physics, but it can be seen as a mere kind of "mathematical transform" . It can be used even without thinking to statistics or temperature. If we focus only...

I am not able to understand what the question asks of me in Q75, part a)

I am reading Zettili’s “Quantum Mechanics: Concepts and Applications” and I am in the section on functions of operators. It starts with how ##F(\hat A)## can be Taylor expanded and gives the particular and familiar example: $$e^{a \hat A} = \sum_{n=0}^\infty \frac{a^n}{n!} \hat A^n...

In Peskin book they calculate the QED Vertex Function named Gamma which depend on two scalar functions called form factors F1(q^2), F2(q^2). they are calculating F1(q^2) and they do not really finish calculating for what I understand. They are just showing the Infrared divergent is canceled by...

Let ##\varepsilon > 0## be arbitrary. Now define ##\delta = \text{min}\{\frac{a}{2}, \varepsilon \sqrt{a}\}##. Now since ##a>0##, we can deduce that ##\delta > 0##. Now assume the following $$ 0< |x-a| < \delta $$ From this, it follows that ##0 < |x-a| < \frac{a}{2} ## and ##0 < |x-a| <...

First, let me introduce the notation; given a Hamiltonian ##H## and a momentum operator ##\vec{P}##, and writing ##P=(H,\vec{P})##. Let ##|\Omega\rangle## be the ground state of ##H##, ##|\lambda_\vec{0}\rangle## an eigenstate of ##H## with momentum 0, i.e. ##\vec{P}|\lambda_\vec{0}\rangle=0##...

There are no restrictions for ##a,b,f_1,f_2##. One solution is the first order Taylor series expansion of course with ##f_1(a)=a,f_2(b)=b##, but are there any other solutions? I tried the Bhaskara formula but I couldn't express it in this form.

I mean the first question has derivative form and the second is linear form so what the difference here in steps of converting both to transfer function... please need some ellaboration to make sure i am solving correctly or not... is it correct to apply the same rule on both: Transfer function=...

My questions are now... Do the steps of converting this space to transfer function include any laplace ? or just we do get [SI-A]-1 and then transfer function is = C* [SI-A]-1 * B As [1 0] * [s-1/det -0.5/det ; 0.5/det s-0.5/det] * [0; 1] = -0.5/s^2+s+0.5 I mean do we need any laplace after that...

I have this function, and I want to take the derivative. It includes a unit step function where the input changes with time. I am having a hard time taking the derivative because the derivative of the unit step is infinity. Can anyone help me? ##S(t) = \sum_{j=1}^N I(R_j(t)) a_j\\ I(R_j) =...

We always think in terms of isolated particles. It's better to analyze it with solids. If wave functions were just calculational tools. Molecules like the following still interact by wave functions, right? So how can it be calculational tool? And if it is, then what model do you use to...

I tried to apply the chain rule $$X_{ik} = \frac {\partial U}{\partial \xi_{ik}} = \frac {\partial U}{\partial x_{i}} \frac {\partial x_i}{\partial \xi_{ik}} = \frac {\partial U}{\partial x_{i}} $$ and I got the force x-component of the force acting on ##P_i## I guess. but I do not know what...

Greetings everyone. I have generated a gaussian random process composed of 500 realizations and 501 observations. The used random variables are gaussian normal. I have then applied the pca analysis to that process (Mathwork's help). However, if I plot the histograms of the coeffs I don't find...

I came across an example of a solution to finding the potential of a charged layer using the Green function (here, pdf). The standard algorithm for finding the Green function by boundary conditions for many problems is understandable: \begin{align*} G_\mathrm{Left} = Ax+ B \\ G_\mathrm{Right} =...

In interpretations where the wave function represents something real, like Many worlds, Copenhagen with objective wave function and spontaneous objective collapses. I'd like to understand which of them has true non-locality. First. Is Many Worlds not having true non-locality due to the...

I am studying a beginner's book on QFT. In a chapter on electromagnetic form factors, the authors have written, using normalized states, $$\begin{eqnarray} \langle \vec{p'}, s'| j_\mu (x) |\vec{p}, s \rangle \ = \ \exp(-i \ q \cdot x) \langle \vec{p'}, s'| j_\mu (0) |\vec{p}, s \rangle...

We have a periodic function ##f: \mathbb{R} \rightarrow \mathbb{R}## with period ##T, f(x+T)=f(x)## The statement is the following: $$\frac{1}{T}\int_0^T f(x)dx =0 \implies \frac{1}{T}\int_0^T\frac{d}{dx} f(x)dx =0$$ Can you give me a hint on how to prove/disprove it? The examples I tried all...

Hello! I am facing a difficulty into developing a multivariable function of a dependent variable "x". Let's assume that "x" is a function of 6 independent variables a,b,c,d,e,f,g. From experimental data i have developed 6 functions, each representing how "x" changes by each of the paremeters...

So I'm having trouble understanding the physics behind evaporative cooling. This is what I know: I want to cool some water so I nebulize it and I let an air flow (coming from the outside) pass through this mist of water. Now some water has to evaporate. Here I am stuck because I don't understand...