Function Definition and 1000 Threads

I first took out the variation of conductivity along the radius of cylinder.Also we know that J=sigmaE.Therefore i have to find variation of E also.But how will i find that as potential is also not given.Help.

If for a field say ##f=xyz## ,it's value is defined at 10 points in the 3-D Cartesian co-ordinate system...now using these 10 values of f and the corresponding coordinates is it possible to find the value of f at any ##(x,y,z)## of choice??

Let ##f:\mathbb{R}^n\rightarrow\mathbb{R}^n##. Is there any class of function and some type of "growth conditions" such that bounds like below can be established: \begin{equation} ||f(x)||\geq g\left( \text{dist}(x,\mathcal{X})\right), \end{equation} with ##\mathcal{X}:= \{x:f(x)=0\}## (zero...

I have calculated the normalization constant, but I'm struggling with the discontinuities in the derivatives of the wave function. Due to the symmetry, it should suffice to consider the first two cases. The results should be (according to WolframAlpha): \left( \frac{\partial^{2}}{\partial...

Hi. If I have a function f(x) = √(x+1) and I define u=x+1 is it correct to state f(u) = √u ?

If I'm trying to solve the problem of a particle in free space (H = P2/2m ). the eigenfunctions of the Hamiltonian cannot be normalized. now assume I have a legitimate wave function expressed in terms of the eigenfunction of H and I want to measure its energy. what will happen to the...

I'm trying to determine if a certain bicycle tire size will fit my bike, and that determination is based on the inflated diameter (or width) of the tire. As such, I'm trying to come up with a formula that will give me the diameter of a bicycle tire as a function of the tire's carcass width and...

Here is a picture of these plots from a paper: When I try to reproduce the 3rd graph above (yellow line below), I get sharp discontinuities: Those jump discontinuities should not occur, and the function should never rise to the high value of the two other plots. So, what could be the cause...

I understand how to reach $$\int_0^\phi \frac{d\theta}{\sqrt{1-k^{2}sin^{2}\theta}}=\sqrt \frac g l t$$ from physics but from there I don't get how to turn that into this new (for me) sn(u) form.

We know from first law of thermodynamics for a closed system that ##dE##=##\delta Q## -##\delta W## , my question is that for a closed adiabatic system net heat transfer =0 this mean net change in energy = work done , does that mean for an adiabatic system work done is a point function as...

What exactly is this equation telling me? How can I use it to work out the Equations of Motion given an equation of potential energy? Won't I have to solve a PDE? I'm extremely sorry if this question comes off ignorant.

I am reading a text which talks about the WIMP speed distribution in the galactic halo in the frame of the Sun and Earth. The point where I am stuck it is trying to explain the concept of Gravitational Focusing of WIMPs at the location of the Earth due to the gravitational well of the Sun...

Problem Statement: Determine whether f is continuous at c. (see image for piecewise function f) EDIT: Sorry if it is a little blurry that is x^3 in the numerator of the rational function and x^2 in the denominator Relevant Equations: Basic understanding of limits My work: Since the...

I am solving a problem of the boundary condition of Dirichlet type, in order to solve the problem, the functions within the differential equations suppose to be harmonic. I have a function f(x,y,z) (the function attached) which is not harmonic. I must find an equivalent function g(x,y,z) which...

Because the Taylor series centered at 0, it is same as Maclaurin series. My attempts: 1st attempt \begin{align} \frac{1}{1-x} = \sum_{n=0}^\infty x^n\\ \\ \frac{1}{x} = \frac{1}{1-(1-x)} = \sum_{n=0}^\infty (1-x)^n\\ \\ \frac{1}{x^2} = \sum_{n=0}^\infty (1-x^2)^n\\ \\ \frac{1}{(2-x)^2} =...

Hi, I'm reading "Wave Physics" by S. Nettel and in chapter 3 he introduces the Green's function for the 1-dimensional wave equation. Using the separation of variables method he restricts his attention to the spatial component only. Let ##u(x)## be the spatial solution to the wave equation and...

I want to compute the gradient of some smooth function at many points by taking the value of the function at point x(i) subtracted from the value of the function at point x(i+1) and then divide the result by ( x(i+1)-x(i) ). My function has a struct as an argument and within that struct I have...

Red line being the function and blue an approximation of the derivative. Does it look right?

Introducing the spacetime spherical symmetric lattice, I use the following notifications in my program. i - index enumerating the nodes along t-coordinate, j - along the r-coordinate, k - along the theta-coordinate, l - along the phi-coordinate. N_t - the number of nodes along t-coordinate. N_r...

##r,\theta,\phi## are the usual spherical polar coordinate system. ##\int_v\nabla•(\frac{\hat r}{r})dv## over a spherical volume of radius ##R## reduces to ##\int_s(\frac{\hat r}{r})•\vec ds=4\pi R## Now ##r## runs from 0 to ##R,\theta## from 0 to ##\pi## and ##\phi## from 0 to ##2\pi##. In...

The singularities occur at ##z = \pm i\lambda##. As ##\frac{d}{dz}(z^2+\lambda^2)^2|_{z=\pm i\lambda}=0##, these singularities aren't first order and the residues cannot be calculated with differentiating the denominator and evaluating it at the singularities. What is the general method to...

I set the location of the particle (x,y,z); therefore, → the force F_1 is (z^2/root(x^2+y^2) * x/root(x^2+y^2) , z^2/root(x^2+y^2) * y/root(x^2+y^2), 0), since cosΘ is x/root(x^2+y^2). →...

This is the form of the function above: I started by equating (1) to 1/2: $$T(\varphi)=\frac{r^{2}+\tau^{2}-2\tau\cos\varphi}{1+\tau^{2}r^{2}-2\tau r\cos\varphi} = \frac{1}{2},$$ which can be rearranged to: $$2r^{2}+2\tau^{2}-1-\tau^{2}r^{2}=2\tau\left[2-r\right]\cos\varphi$$ using...

Hi colleagues This is a very very simple question I can show when $f$ is integrable and is even i.e. $f(-x)=f(x)$ then $\int_{-a}^{a} \,f(x)\,dx=2\int_{0}^{a} \,f(x)\,dx$ what about improper integrals of even functions, like the function ${x}^{2}\ln\left| x...

WHAT HAPPENS IS That I need to model the example of A Protein G example, using a function f in Matlab, but when I execute the script, the graphics I get do not correspond to those of the example. The problem is that I can not understand what the model seeks to represent, besides that I do not...

Hi PF! Do you know what a strictly convex function is? I understand this notion in the concept of norms, where in the plane I've sketched the ##L_1,L_2,L_\infty## norms, where clearly ##L_1,L_\infty## are not strictly convex and ##L_2## is. Intuitively it would make sense that any...

The question before asked to find the net force as a function of time which I got: F = 4.83×10¹⁰ (1.65×10⁻⁸ t − 7.41×10⁻⁶) N I just have no idea how to do it with the y directed force since I only have a horizontal acceleration equation. Thanks so much to anyone that helps, I appreciate it!

Hello, I have the force defined as a function of time, where F=A-Bt and A=100N, B=100Ns-1. I have to determine, how long it will take for object to stop, if t0=0s and v0=0,2ms-1 and mass of the object is m=10kg. Can somebody please help me with this, because I'm having hard time with this task.

Section ##3.8## talks about the gradient and smooth surfaces, defining when the directional derivative ##(\partial f/\partial\mathbf{u})(\mathbf{p})## takes maximum value and that when it equals ##0##, then ##\mathbf{u}## is a unit vector orthogonal to ##(grad\ f)(\mathbf{p})##.It also says that...

Well doesn't ##u(x) = 0.4 x## work? Seems too easy, but the phrasing at the end "for all ##x\in I##" makes me think since ##0.4x = x## only at ##x=0##, and not all of ##I##, that this is okay. But am I wrong?

All I've done so far is think about F_net. Since F=ma, and a is a vector, I was thinking that I should find the x and y components of a and then try to calculate F_net that way, but I'm confused as to where I should use x(t) and y(t). Or instead, thinking about it as the change in momentum over...

Hello All, I have a question regarding the simple function in MATLAB. My textbook talks about it and it looks very useful, it will show you a bunch of steps of how to simplify an expression or equation. I am using MATLAB R2018b and it looks like the function is gone. I am wondering if something...

I recently had to find what f(7) equals if f(x) = \frac{x^2-11x+28}{x-7}. I first tried \frac{x^2-11x+28}{x-7} \cdot \frac{x+7}{x+7}, and it seemed like a perfect fit since I eventually got to \frac{x^2(x-4)-49(x+4)}{x^2-49}=(x-4)(x+4), but that gave me f(7)=33, instead of the right answer...

Hi,everyone. Recently, I am studying green's function in many body physics and suffer from trouble.Following are my problems. (1) What is the origin of the definition of green's function in many body physics? (2) What is the physical meaning of self energy ? It seems like it is the correction...

Very often, the term "Green's function" is used more than "correlations" in QFT. For example, the notation: $$<\Omega|T\{...\}|\Omega> =: <...>$$ appears in Schwartz's QFT book. And it seems very natural, basically because the path integral definition of those terms "looks like" the...

If I have a Lagrangian of the form \mathcal{L}=-\frac{1}{2} (\partial \phi)^2 - \frac{1}{2} m^2 \phi^2 - \frac{\lambda}{3!} \phi^6, in 3 dimensions, what is the one-loop correction to the 4-point function? Am I correct in thinking that the following Feynman diagram is the representation of the...

I just went over analysis of a data set that was analzed using Linear Regression (OLS, I believe) and I saw Newton's method was used. Just curious, how is it used? I assume to minimize the cost function, but this function was not made explicit. Anyone know? Thanks.

I'm stuck on a proof involving the Bolzano-Weierstrass theorem. Consider the following statement: $$f'(x)>0 \ \text{on} \ [a,b] \implies \forall x_1,x_2\in[a,b], \ f(x_1)<f(x_2) \ \text{for} \ x_1<x_2 $$ i.e. a positive derivative over an interval implies that the function is growing over the...

If the derivative of a function f is given by $$f'(x)=\frac{1}{5}(x^2-4)^5-x^2$$ how many points of inflection will the graph of the function have?solution find $f"(x)$ $$f''(x)=2x((x^2-4)^4-1)$$ at $f''(x)=0$ we have factored $$2 x (x^2 - 5) (x^2 - 3) (x^4 - 8 x^2 + 17) = 0$$ then...

The Feynman propagator: $$D_{F}(x,y) = <0|T\{\phi_{0}(x) \phi_{0}(y)\}|0> $$ is the Green's function of the operator (except maybe for a constant): $$ (\Box + m^2)$$ In other words: $$ (\Box + m^2) D_{F}(x,y) = - i \hbar \delta^{4}(x-y)$$ My question is: Which is the operator that...

I was able to find the maximum value for this function by differentiating and equating it to zero and find the time t and substitute it back to the original expression to get the max amplitude. tm = -0.001012 s v(tm) = 56.6 Another method that was presented in my book was can you explain how...

It is obvious that the function f is not injective. From the given equation, we get f(f(2))=6.And since,there is an inequality given in the problem, I think we can use that to find f(6).But I have got stuck here and can't move.Do I have to find what is f(x) first?Then how?

205.8.9 Find the derivative of the function $y=\cos(\tan(5t-4))\\$ chain rule $u=\tan(5t-4)$ $\frac{d}{du}\cos{(u)} \frac{d}{dt}\tan{\left(5t-4\right)}\\$ then $-\sin{\left (u \right )}\cdot 5 \sec^{2}{\left (5 t - 4 \right )}\\$ replacing u with $\tan(5t-4)$ $-\sin{(\tan(5t-4))}\cdot 5...

My attempt : Given ##f(x)## and ##g(x)## for ## -1.6 < x < 1.6## we get ##0\leq f(x)<1.6## Thus, for ##f(g(x))## we get ## -3 \leq g(f(x)) < -1.4## Thus the required set should be the interval ##[-3, -1.4)##? My Questions : 1. What have I missed since my answer does not match the given...

Quantum fields have wave functions that determine a particle position in space. It solves non-locality, double-slit paradox, tunnel effect, etc. What if the wave function is also in time? Won't it solve the breaking of causality at quantum level? (Delayed Choice/Quantum Eraser/Time) Not much...

Show that the value of ##\int_0^1\sqrt(1-cosx)dx## is less than or equal to ##\sqrt2## ##1\ge cos x\ge-1## The problem is a worked one but I am just confused by a simple thing. We integrate the function f ##\int_0^1\sqrt(1-cosx)dx in the interval [0,1] but I don't understand that what stands...

To check if it is injective : ##h'(x) = 3(x^2-1)## ##\implies h'(x) \geq 0## for ##x \in (-\infty, -1]## Thus, ##f(x)## is increasing over the given domain and thus is one-one. To check if it is surjective : Range of ##f(x) = (0, e^4]## but co-domain is ##(0, e^5]## thus the function is into...

Say I have a function `func` that does a certain task, returning some expression `exp`. Can I use this expression in another function without having to call `func` again, which I suppose will redo all the steps needed to derive `exp` in the first place? E.g double func() {...