Exponential Definition and 1000 Threads

Our universe apparently has a positive cosmological constant so it will look more and more like de Sitter spacetime, expanding at at exponentially increasing rate. So eventually it seems that subatomic spacetime would be affected by this. Eventually even something a Planck distance away would...

I have been working on this integral for a long time ,however i still can't solve it because of the comlicated index of exponential.So if any of you have any idear,please tell me ,thank you so much~~ \int _{0}^{\infty }\!{{\rm e}^{-2\,{{\it m1}}^{2}-2\,{{\it m2}}^{2}}}{ \pi }^{-1}r \left(...

For a Jordan form (which is a direct sum of individual jordan blocks) that has distinct eigenvalues along the diagonal, how would the exponential of the Jordan form be calculated ? As far as I am aware the formula for calculating the exponential of a jordan block can only involve one...

Hey I have some problems understanding my statistics homework. I am given a data set giving the number of calls arriving to different switchboards in three hours as well as the total phone call duration in minutes for each switch board. Something like i y_i t_i -------------- 1...

Homework Statement Ok, so I have an unknown exponential function: y1 = f1(t) By measuring the values of t and yi, a linear connection is generated between Yi (=log (yi)) and t: Yi = Ait + Bi. A1 = -2.12 B1 = 1.96 Problem 1: Describe f1 in the following matter: y1 = f1(t) = Ceλt...

I have a problem that arises in quantum field theory. It involves a problem in combinitorics and about the theory of connected graphs. Essentially, I am trying to prove an identity involving an exponential of an infinite series with the ways to decompose an integer into the sum of integers...

Homework Statement Working on some Laplace transforms, and my lack of knowledge of some properties of exponential functions is coming back to bite me(again). I'm stuck trying to figure out if: e^(-pi*s) - e^(-2pi*s) = e^(-pi*s - (-2pi*s)) Is a true statement or not. I've searched...

Homework Statement This problem is from a first order differential equation i have been playing with but the question does really have anything to do with the problem itself. I can solve it just fine, I just can't resolve the final integral. I will write what I am talking about in section 3...

Homework Statement Given matrix A= [1,1;0,0] and matrix B = [1,-1;0,0] n.b. the semicolon separates the matrix rows find exp(A)exp(B) Homework Equations exp^{A}=\sum\frac{A^{n}}{n!}=I + A + \frac{A^{2}}{2} + \frac{A^{3}}{6} + ... + \frac{A^{n}}{n!} for n= 0 to...

Homework Statement I need to calculate the point of divergence for this exponential function : F(x)= 5.282 * exp ( -0.01726 * x ) may you help me in finding the method to solve such problems ? Homework Equations The Attempt at a Solution

Homework Statement Hello, I'm trying to get my head around the various properties of quaternions that all seem very similar, but I can't quite understand the underlying differences between them. I would like to know the differences between unit quaternions, purely imaginary quaternions...

How do you differentiate lim (2^h - 1)/h ? h --> 0 I would like to know how to do it algebraically instead of picking values of x that approach 0 and plugging it into 2^x.

Homework Statement F_{X}(x)= λe^{-λx} \;for\; x>0 \;\;\;and \;0 \;otherwise After finding the characteristic function for the Exponential Distribution, which is (I could do this without problem); F_{X}(k)=λ(λ-ik)^{-1} Now the question is; Let X_1,X_2,\ldots,X_i be i.i.d. exponential...

f(x)= lnx ; g(x) = ex f{g(x)} = ln ex = x; not an issue g{f(x)}= eln x = ? (answer for this) f(x) and g(x) are inverse of each other. how to solve the problem algebraically.

1. Relevant problem integrate from 0 to infinity of r^2exp^(-r/a0)dr Homework Equations I'm also given; integral from 0 to infinity of x^nexp^-x dx = n! The Attempt at a Solution I'm just wondering if I can split up the exponential to make it look like this form. Eg; integrate from 0 to...

The equation I used for these are: If N=Noekt then DN/Dt=N0kekt so the two problems I have trouble with is A radioactive substance has a decay constant (k) of -.0539 per year. If 371 grams of the material is initially present, what is the instaneous rate of change of the substance at times...

hey~ folks! i'm in trouble with this integral problem. the range of the integral is from -∞ to ∞ and it has x as independent value. and the integrand is a derivative of absolute value in exponential; ∫^{∞}_{-∞} (d/dx e^{-a|x|})dx any idea for the problem??

Can anyone help me answer this question? " Every exponential function is a geometric progression but not every geometric progression is an exponential function. Explain."

1. Hello there, I have a few questions on the derivative homework that I did but not sure if it's right or not. These are difficult and my teacher doesn't go over all of them so I don't know if it is right or not. Please help me so I can understand the concepts before the upcoming test. 1...

hey, I have a question about the taylor series.I open cosθ function, I forward while making this solution but I can not write as the definition of exponential function. How Can I write this expression as an exponential function. Maybe I can not see something in it.. Do you have any idea...

I posted a related thread, in the same forum regarding matlab, but I want to discuss this here separately. Few minutes ago I became very confused baffled and surprised at the same time. consider function 2^{x}. Now consider the sum of this function for n iterations.(from 0 to n)...

Homework Statement City has 500 000 citizens. One citizen knows a gossip. After 10 minutes, he tells that gossip to another 2 citizens. Those 2 citizens tell that gossip to another 2 citizens(both of them tell 2 citizens). After what time whole city will know the gossip? Homework Equations...

Hey, I'm not too sure if this is pre-calc or not because it's in a different course but I think I remember doing this in pre-calc a long time ago... 1. Determine cartesian(z = x + jy) and exponential(\rhoe^{j\theta}) forms of the following complex numbers: z = 3 + 5j 2. I have no...

Hey everyone! I was recently scribbling on paper, and after a series of ideas, I got stuck with a problem. That is, can I find out if there exists some integers A and B such that C=2^{A}3^{B} For some integer C? For an arbitrary C, how do I know whether some A, B \in \textbf{Z}...

Homework Statement \int|e-k|x-a||2dx This integral is from -inf to +inf Homework Equations A table of integrals would seem to be needed. The Attempt at a Solution \int|e-k|x-a||2dx =\int|e-2k|x-a||dx from here it would seem to simplify down to a variation on the theme of \int|e-ax|dx...

Homework Statement Hi. I actually understand most of this question, but not the parts in red. Question. http://img703.imageshack.us/img703/7237/2008testhphysf.jpg If above doesn't load, please go to [PLAIN]http://img703.imageshack.us/img703/7237/2008testhphysf.jpg Homework...

Help! exponential function Please look at the attachment for the question! Thank you for your help

Homework Statement Give the inverse of this function N=f(L)=1816-8L The answer has to be filled in in Maple Homework Equations The Attempt at a Solution N=1816-8L 16-8L=ln(N)/ln(18) -8L=(ln(N)/ln(18))-16 L=-ln(N)/(8*ln(18))+2 Is this correct? When i fill...

I want to show that e^x e^x = e^{2x} using a power series expansion. So I start with \sum_{n=0}^\infty \frac{x^n}{n!} \sum_{m=0}^\infty \frac{x^m}{m!} \sum_{n=0}^\infty \sum_{m=0}^\infty \frac{x^n}{n!} \frac{x^m}{m!} \sum_{n=0}^\infty \sum_{m=0}^\infty \frac{x^{m+n}}{m!n!} I am...

Hi, this is not really a homework problem, but something that came up during my research, upon trying to integrate some empirical function. This function consists of many terms, but specifically, there is a term containing double exponential functions which is giving me some trouble. If...

Homework Statement Give a formula for the exponential function illustrated. The two points marked on the graph are A=(−1−17) and B=(1−2). The red horizontal line is given by y=−1, and is a horizontal asymptote of the function The Graph: http://tinyurl.com/3oywz8l

Homework Statement Consider the system X'(t)=AX+B(t) where: A = [0 0 -1] [1 0 -3] [0 1 -3] and B(t)= [e-3t] [et] [3 ] Find X(t) by frist determining P such that P-1AP=J is in Jordan form and then solving the three simple equations directly. Homework Equations...

Homework Statement is e^x^2 = 4 equivalent to e^x = 2 Homework Equations As above The Attempt at a Solution This is just an exercise, but I'm quite stuck as how to show this is true (or false for that matter). I thought to take the log of both sides and use the log identity to get...

Homework Statement Show that det(eA)=etr(A) for A\inCnxn Homework Equations The Attempt at a Solution I am sooo bad at proofs. And I am still trying to wrap my brain around the concept of matrix exponentials. Can someone please get me started ...

Homework Statement Given the matrix A= [0 1] [1 0] Find eA Homework Equations The Attempt at a Solution I have no idea how to approach this. I know the expansion for an exponential matrix, I was able to apply this for a nilpotent matrix. Could someone please explain to me...

why is it that the largest value of n^( (((n-k)*(k-1)/(2k)) + (k-1))/(n-1) ) always seems to be when k=36?

Homework Statement Compute the Fourier transform of \phi(t)=(e^(-at))H(t) where H(t) is the Heaviside step function Homework Equations The Attempt at a Solution I am stuck in an attempt at the solution, I am confused at how the heaviside step function factors in and think...

Hi, I am explaining the function of each parameter in my model: a*bcx Are these correct? I said that as a changes the graph is stretched parallel to the y axis. The movement takes place when we change b and c but I said the growth is exponential... Is that the correct term...

Hi, I have a problem which I believe could be solved using a fairly simple Trig equation, if someone can provide a solution to this I would be very greatfull.. I have an RC plane and a computer radio which allows servo travel to be adjusted exponentially by percentage. If you imagine the...

Hi guys, I need to model a curve and I am trying to come up with an exponential equation. I have several points I can work with and this is what I tried so far. (I want to know if this is the correct method or if there is a more precise way to go about this) I am working on something of the...

Hi all: I have one confused question. one continuous exponential decay function f=exp(-lamda*t) start from t=0 to infinity. I sample 1024 data points from the decay function. time variable (t) ranges from 0 to 1 second. the tail data of this exponential function is zero. I apply discret FFT on...

I'm attaching the problem as a png. The top half is the question whereas the second half is the solution. I understand everything about the question until the ultimate answer the final answer is: (r (constant) x0(constant) / k (constant)) * (1 - e^-60t) as shown. However I don't...

Homework Statement This is from Peskin & Schroeder p. 14 in case anybody's interested. The function is U(t)=\frac{1}{(2\pi)^3}\int d^3p\, e^{-it \sqrt{p^2+m^2}}e^{i\vec p\cdot(\vec x-\vec x_0)} Homework Equations The Attempt at a Solution Essentially you write out the dot product as p\cdot...

Homework Statement I was following a derivation of some laws and I didn't get how they approximate some portion of the expression. That portion/part is exp[gbH/(2kT)]. The book says gbH/2 <<1 and therefore exp[gbH/(2kT)] = 1+gbH/(2kT). Homework Equations The Attempt at a Solution I agree with...

Hi, I'm being asked to test whether a function is of exponential order, i.e. whether abs( f(x) ) <= M*exp(a * t), for all t >= T (which is finite). The function is x * ln( x ). Now, I have the solution right here, so I know how to solve it. However, I did it a different way and wanted to ask...

What is the function that I get when I take a large sample from an exponential distribution (many values from the same distribution) and sort the sample points. I'm a bit surprised it's not really exponential. The shape seems to fit some data I have nicely, but I don't know the function to fit...

Hello! I was wondering if they're any identities between exponential and logarithmic functions? Maybe identities isn't the right word, but what I'm talking about is something like euler's formula. Other than than {e^x} and {ln(x)} are inverses, if that counts. Any help is very much appreciative!

[B][B], Dear Fellows I need to find the solution of cubic equation in exponential form which is written in a research article If EQUATION is (k^6-A k^4+B k^2+E)Y(z)=0 and solution given is as, Y(z)=M exp(-k_1z) where M is a constant and k_1 is solution of the above equation...

I can't seem to understand the procedure, can anyone post any links to a useful tutorial? I took it this year and it was the only thing I didn't understand, 3 questions about it came in my maths final and I got an 82 (I got everything else right but I made a small calculation mistake in a...

What is the PDF of the exponential of a Gaussian random variable? i.e. suppose W is a random variable drawn from a Gaussian distribution, then what is the random distribution of exp(W)? Thank you!