Gaussian Definition and 706 Threads

Homework Statement Using Gaussian Elimination: 3x - 2 y = 5 6x-4y =7The Attempt at a Solution [ 3 -2 5] [6 -4 7] * top row by 1/3 [1 -2/3 5/3] * Top row by -6, add to bottom row: [0 0 -3] So I get this: [1 -2/3 5/3] [0 0 -3] How can 0y equal -3?

Would just like a hand with this question If X and Y are independent standard Gaussian random variables (that is, independent N(0, 1) 's ) do the following: (a) Write down the joint probability density function fXX,Y (x, y) of X and Y . I know what the gaussian density function looks...

So I'm pretty sure I have the right answer I just want to make sure I am getting the idea. There is a large solid copper cube. At the center of the cube there is a hollow sphere of radius a. At the center of the hollow sphere there is a charge Q. What is the total charge induced on the...

Homework Statement It can be shown that the position probability density for the one-dimensional, free-particle Gaussian wave packet can be expressed as shown below, where m is the mass of the particle and L is the position uncertainty at time t=0, vgr = hbar *k0/m, k0 is the average wave...

Homework Statement 3. A laser scientist tells you that her He-Ne laser can be focused to a spot size of 5.00 microns. When pressed for details, she tells you that she got this number by measuring the Full Width Half Maximum (FWHM) of the intensity profile of the laser waist. a) What is...

Gaussian surfaces...need help...can someone help walk me through this problem?? A solid insulating sphere of radius 5 cm carries a net positive charge of 2 μC, uniformly distributed throughout its volume. Concentric with this sphere is a conducting spherical shell with inner radius 10 cm and...

This is probably an easy question, but my math is not good enough to answer it. For Gaussian integrals: \frac{\int \Pi_i [dx_i] x_k x_l e^{-\frac{x_i A_{ij} x_j}{2}}} {\int \Pi_i [dx_i] e^{-\frac{x_i A_{ij} x_j}{2}}}=A^{-1}_{kl} As far as I understand it, in QFT, Aij is a local operator. So...

Hello, I was wondering if anyone could tell me where the documentation exists for the output of Gaussian 09 runs. The .out file is plain text and human readable, but I can only decipher parts and units are not always clear. I would have thought the Gaussian website would have an explicit...

Homework Statement http://img189.imageshack.us/i/50468910.png/ Homework Equations The Attempt at a Solution I'm wondering how I do this? I don't really know. Supposed to be 17 rows. How many columns and how many each row? No clue! And how do I get the numbers for the matrix here?

The following data represent a frequency distribution of 200 variables drawn from a parent Gaussian population with mean=26.00 and standard deviation=5.00. the bins are 2 units wide and the lower edge of the first bin is at x=14. 4;8;11;20;26;31;29;22;26;13;5;2;3 a. plot a histogram of these...

\mathrm{prob} \propto \mathrm{e}^{-\frac{(a -x_1)^2}{2 \sigma^2}} \mathrm{e}^{-\frac{(x_1 -x_2)^2}{2 \sigma^2}} \mathrm{e}^{-\frac{(x_2 -x_3)^2}{2 \sigma^2}} \mathrm{e}^{-\frac{(x_3 -b)^2}{2 \sigma^2}} a and b are known real constants. Is there a way to generate x_1, x_2, x_3 independently...

I am trying to use Gaussian elimination to solve the 2D poisson equation. I've done this for the 1D problem without problems, but for some reason my solution for the 2D problem is incorrect; it looks something like the correct solution but it's as if the resulting field were cut in half, so...

Hi, I would like to ask a question please. Assume we have a random vector X that is distributed under the Gaussian model and take the inner product of this vector and another constant vector d. Will the source distribution (Gaussian) remain the same? My intuition (although I might be...

How do you do a gaussian integral when it contains a heaviside function!? Very few textbooks cover gaussian integrals effectively. This isn't a big deal as they are easy to locate in integral tables, but something I cannot find anywhere is how to handle a gaussian with a heaviside heaviside...

Homework Statement At t=0 the particle is localized around x=x_0 that is: \langle x\rangle (0)=x_0, and the impulse is: \langle p\rangle (0)=\hbar k_0, we can describe the particle with the wave function: \psi(x,0)=Ae^{-\frac{(x-x_0)^2}{2\sigma^2}+ik_0(x-x_0)} Now, my question is: If I...

Find all vectors in R^4 that are perpendicular to the three coloumn vectors [1 1 1 1], [1 2 3 4], [1 9 9 7] sorry i don't know how to make them verticle guassian elimination or Ax=b I know that the dot product must equal 0 but I am not sure how to solve it

My numerical analysis book doesn't explain it. It just tells you to use precomputed tables, and directs you to an out of print book from the 80's that I can't find anywhere. After searching, I found http://en.wikipedia.org/wiki/Gaussian_quadrature#Computation_of_Gaussian_quadrature_rules" in...

Hi, I am wondering what happens to a Gaussian distribution when its mean tends to infinity. By looking at the equation of a Gaussian one might infer that the limit will go to zero; but does this imply that it reduces to a Dirac-Delta function? More precisely, if we integrate this limit we...

Hi all, I need your help with a question. Here goes, Homework Statement There is a hollow conducting sphere with a uniform surface charge density of +\sigma. A charge -q, is placed inside the cavity of the hollow sphere. What is the electric flux through a spherical surface just inside...

Hey there, just had a question about Gauss' law, should be relativity simple however the explanation we were given was quite poor and only seems to apply well to the examples we were given. (This isn't homework). I (think I ) know the equation for Gauss' Law and what it means, that basically...

I am looking at a problem, part of which deals with expressing delta dirac as a limiting case of gaussian function. I am aware of the standard ways of doing it. In addition, I would also like to know if the following are correct - \delta(x-a) = \lim_{\sigma \rightarrow{0}} \int_{a -...

Homework Statement Calculate \Psi(x, t) for the gaussian wave packet according to the amplitude distribution function a(k)=C*\alpha*e^{-\alpha^2k^2}/ \sqrt{\pi}and describe its evolution.Homework Equations \Psi(x, t)=\int_{-\infty}^{\infty} a(k)e^{i\{kx-w(k)t\}}dkThe Attempt at a Solution know...

I am currently facing a problem of integrating exp(-ax^2)*erf(bx+c)*erf(dx+f) with the integral boundaries 0 and infinity. I have gone through some handbooks but what I could locate is the integration of exp(-ax^2)*erf(bx)*erf(cx) from 0 to infinity which yields...

If given a set of data points, how do I find a,b,c to input into a gaussian model? y = a exp (-(x-c) / b)2 I know it's centered at x=c Intersects at (0,a), but if the data doesn't have a "0", how do you find it? Also, a controls the height, but in what way? and b controls the spread, but in...

I'm curious to know why chemists like to use Gaussian basis set in case of an ab-initio (ex.DFT) calculation. I understand that the molecules that are of interest to chemists are non-periodic and hence plane wave basis is not useful, but can't they use other real space basis like a grid? What...

Statistical "Error" of Centroid of Gaussian Distribution If I have L data samples, distributed randomly (3D real Gaussian distibution, unity variance) about the origin in 3D real space, how can I derive an expression for the "origin estimation error" (i.e. the distance between the true origin...

Hi, I know that you can determine that the Gaussian curvature of a cone tends to infinity at the vertex, but seeing as the curvature anywhere else on the cone is zero, how is this possible?

Hi, I currently have a Gaussian distribution (Normalized Frequency on the y-axis and a value we can just call x on the x-axis). So for the sake of simplicity, let's say that I ignore any values below 0 and any values above 1 on the x-axis. Then what I will do is take 10 equal segments...

I have been told that the following integral can be expressed analytically as a combination of error functions of t. And that the solution can be obtained from then by numerically integrating over t. \int^a_b sin(k_1x)sin(k_2x')\int_0^\infty \frac{1}{\sqrt{t}}e^{-t(x-x')^2}dtdx dx' While...

Hi all, why does Gaussian Integration in one dimension with n points integrate exactly with a polynomial of order 2n-1 ? thanks

I am completely new to this so bare with me. I have co-ordinates and I want to create a Gaussian function. I already know the function which is y=0.01235140544*e^(-(x-36.28663863)^2/(-135.1643617)) But I need to know how to get a,b,c The Coordinates are {35,.01} {28,0.03} {20,.1} {15,.3}...

Hello forum, I am trying to solve a differential equation for the last four hours and I can't figure out how... here it is \frac{d^2x(t)}{dt^2} + \frac{dx(t)}{dt} + c x(t) = d e^{-a t^2} actually my problem is how to handle the Gaussian term... if anyone can help please...

Got it

I am fitting a detector response using Matlab. I have been asked to fit the spectrum using a Exponentially Modified Gaussian. This is as follows. [ tex ] a^x_n [ /tex ] h(t) = [ tex ] \frac{A}{\sqrt{2 \pi} \sigma} e^{-\frac{(t-t_{R})^{2}}{2\sigma^{2}} [ /tex ] f(t) = [ tex ]...

I'm trying to figure out how to enter this into my calculator and get a graph, but I think it may be underpowered. I have a Casio fx-9860gii, to be clear. The problem is: y=0.0034e^-(x-515)/26,912 200 greater than/equal to x smaller than/equal to 800 Thanks for any assistance. :-)

i would really appreciate if someone could help me out with this one. i m preparing for an exam and this question is a question from papers of previous years and its bugging me because it seems very specific in that i can't seem to find anything like it in textbooks. what i m mainly stuck on...

i would really appreciate if someone could help me out with this one. i m preparing for an exam and this question is a question from papers of previous years and its bugging me because it seems very specific in that i can't seem to find anything like it in textbooks. what i m mainly stuck on...

I'm not sure if this is the right place to post this. Let me say, this is not for any homework. I've been asking all over the internet with help for this, and no one seems to be able to know. I am applying this function to a Program I am writing in Delphi. I have no trouble applying it how it...

Is it correct that the Gaussian elimination procedure is used in computer software to solve systems of linear equations?

First I try to find a way of finding area under Gaussian peak by using simple means. Questions at bottom of post. This concerns peaks with Gaussian distribution, eg. peaks in a chromatogram in some chemical analysis. The Gaussian distribution is f(x) = \frac{1}{\sigma...

Hello, I want to do the convolution of a gaussian function and a hole. If I want to use Fourier transform which functions should I use? Can I use rms? I want to calculate the spot size of a gaussian signal after a circular aperture. Thanks!

Please explain to me in detail why a gaussian surface within a conductor has an electric field of zero? thanks.

Homework Statement Hi all, I'm writing a program to solve a system of linear algebraic equations using the method of Gaussian elimination. The only thing I can't figure out is how to perform the actual pivot. In the %Forward elimination nest, I can't figure out how I am supposed to find the...

I'm sorry this is not really a school question i was just intrigued and did not now where else to ask about it. I have seen videos of these Gaussian guns and they appear to generate energy from nowhere, obviously impossibly. So what is the physics behind how they work?

Hi, Im learning about gaussian integration right now but i can't really find anything about the error approximation other than that it goes proportional to the 2nth derivative of the function at some point in the interval I am trying to integration the function over. But that doesn't really...

Hello all, new here. In the past few weeks, I have been trying to gain a basic understanding of classical electricity and magnetism through the fantastic lectures at http://ocw.mit.edu, specifically the physics course...

Hi I am currently reading: http://www.cs.cornell.edu/~asaxena/learningdepth/saxena_ijcv07_learningdepth.pdf which deals with reconstructing depth from a single still image. A gaussian multiscale markov random field is trained in a supervised context where the model is shown below...

Can tell me the exact relationship between the intensity and the amplitude for a gaussian beam ? I know that I is proportional to |A|2 .. but i want the value of this proportianality constant

Homework Statement A 655nm gaussian laser beam has a waist of 15mm located at a lens with focal length of 12 cm. What is the minimum beam waist and where is it located? Homework Equations Beam radius w = w0*sqrt(1-(z/zr)^2) w0 = min beam waist; z = distance, zr = Rayleigh range The...

Homework Statement Consider the random process X(t)=A+N(t), where A is a constant and N(t) is a white Gaussian noise with spectral density equal to 1. The process X(t) is filtered with a system with impulse response h(t)=u(t)exp(‐t/T). Compute the probability that X(t), once filtered, is...