Characteristic Definition and 287 Threads

Homework Statement In order to determine the characteristic function of a random variable defined by: Z = max(X,0) where X is any continuous rv, i need to prove that: F_{l,v}(g(l))=[ \phi_{X}(u+v)\phi_{X}(v) ] / (iv) where F_{l,v}(g(l)) is the Fourier transform of g(l) and...

Homework Statement Let V:= ℝ_{2}[t] V \in f: v \mapsto f(v) \in V, \forall v \in V (f(v))(t) := v(2-t) a) Check that f \in End(V) b) Calculate the characteristic polynomial of f. Homework Equations The Attempt at a Solution a) Is it sufficient to check that (f+g)(t)=f(t)+g(t) ...

Why does Quantum Mechanics have objective statistical characteristic,but does not have subjective statistical characteristic? QM has two axioms: 1-To each dynamical variable there coresponds a linear operator,and the possible values of the dynamical variable are the eigenvalues of the...

I've been having this small problem with modulo arithmetic that's just irking me and this is the perfect example to get clarifivation find the remainder for 75 congruent to x (mod 21) here's my issue...so I'd set this up to solve and see if I could find this relationship 7\equiv x...

Homework Statement The characteristic function of a set E is given by χe = 1 if x is in E, and χe = 0 if x is not in E. Let N be a natural number, and {an, bn} from n=1 to N, be any real numbers. Use the definition of the integral (Riemann) to show that \int \sum b_{n} X_{ \left\{ a_{n}...

Suppose your characteristic equation for the 2nd order equation has complex roots r+ and r- These are conjuagtes of each other so the general solution is: y = Aer+ + Ber- My book chooses the constants A and B as conjugates of each other for the reason that this constructs a real...

Hello everyone, first time poster, long time reader here! I'm an ex-math major and while I'm no longer pursuing a degree anymore in mathematics, I still continue onwards in my spare time trying to learn as much as I can about it because it's always been something I've enjoyed partaking in and...

Homework Statement 1)The pion is an unstable subatomic particle whose characteristic decay time in its own frame is 26ns. A beam of such particles emerges from a source at point X in the laboratory traveling with speed ##v = \sqrt{3}/2\, c## in the laboratory frame. Determine i) the decay...

Homework Statement Given the initial value problem: \frac{(u)}{(1-e^-(2x))}u_{x}+ \frac{\sqrt{t}}{u}u_{t}=1, with x, t, u > 0 Subject to condition u(x,1)=e^{-x} Homework Equations a) Classify given partial differential equation. b) Write the characteristic equations. By...

A second order system has the following standart form; http://controls-design.com/mathtex/mathtex.cgi?H%28s%29%3DK%5Cfrac%7B%5Comega_n%5E2%7D%7Bs%5E2%2B2%5Czeta%5Comega_n%20s%2B%5Comega_n%5E2%7D%20%5Cmbox%7B%20for%20%7D%200%20%5Cle%20%5Czeta%20%5Cle%201 However, sometimes the system I...

Homework Statement Show that the descriminant of the characteristic polynomial of K is greater than 0. K=\begin{pmatrix}-k_{01}-k_{21} & k_{12}\\ k_{21} & -k_{12} \end{pmatrix} And k_i > 0 Homework Equations b^2-4ac>0 The Attempt at a Solution I have tried the following...

What is the load line equation for I-V Characteristic plots? Why is load line slope negative? According to Ohm's Law: i = V/R; so as voltage increases current increases then slope should be positive, right?

Homework Statement Let X,W,Y be iid with a common geometric density f_x(x)= p(1-p)^x for x nonnegative integer and p is in the interval (0,1) What is the characteristic function of A= X-2W+3Y ? Determine the family of the conditional distribution of X given X+W? Homework Equations...

Homework Statement There are a few problems I have with my HW that involve the characteristic size of an atom in a certain state. For example, the hydrogen atom in the ground state. Homework Equations - The Attempt at a Solution I don't know where to begin to find the characteristic...

Hello guise. I am familiar to a method of diagonalizing an nxn-matrix which fulfills the following condition: the sum of the dimensions of the eigenspaces is equal to n. As to the algorithm itself, it says: 1. Find the characteristic polynomial. 2. Find the roots of the characteristic...

I am reviewing for the mathematics GRE subject exam, and I have this review book, and in the book when they speak of the characteristic of a ring they give the following def "Let R be a ring. The smallest positive integer n such that na = 0 for every a in R is called the characteristic of the...

Characteristic function and preimage? Homework Statement Let S be a nonempty subset of ℝ. Define χs= { 1 if x is in S and 0 if x is not in S Determine χs-1(Q) [where Q=set of all rational numbers] and χs-1((0,∞)) We haven't really dealt much with this function, and I really...

Homework Statement I must find the characteristic function of the Gaussian distribution f_X(x)=\frac{1}{\sqrt{2\pi}\sigma} e^{-\frac{1}{2} \left [ \frac{(x- \langle x \rangle )^2}{\sigma ^2} \right ]}. If you cannot see well the latex, it's the function P(x) in...

Homework Statement I must calculate the characteristic function as well as the first moments and cumulants of the continuous random variable f_X (x)=\frac{1}{\pi } \frac{c}{x^2+c^2} which is basically a kind of Lorentzian.Homework Equations The characteristic function is simply a Fourier...

Homework Statement Hey guys, I'm self studying some probability theory and I'm stuck with the basics. I must find the characteristic function (also the moments and the cumulants) of the binomial "variable" with parameters n and p. I checked out wikipedia's article...

Regarding the term "Spin"... I've see a number of different descriptions. In the book I'm currently reading it says it is "loosely" the measure of the strength of rotational motion, and "technically" the measure of the quantity called angular momentum. It also states we consider the spin...

Homework Statement Show that for any square matrices of the same size, A, B, that AB and BA have the same characteristic polynomial. Homework Equations The Attempt at a Solution I understand how to do this if either A or B is invertible, since they would be similar then. I saw a...

In this thread Antiphon had written that When I first encountered that, I thought there's something wrong with that, but could not figure it out. In order to create a current the electron must flow from one place to another. But in EM radiation although the electron oscillates or jiggles, it...

I was looking back at a proof I did a while ago. Suppose na=0 with n≠0 and a≠0. Then n is a multiple of the characteristic. I supposed p < n is our characteristic, then I simply used the divison algorithm (I divided n by p) and the distributive property which lead to the remainder being 0. From...

Homework Statement Transmission line is designed so it has selfinductance, L = 7.0x10^-7 Hm^-1 & signal speed 70% of c Find characteristic impedance Homework Equations Z = √L0/C0 Ω also v = 1/ √L0C0 The Attempt at a Solution So L = 7.0x10^-7 Hm^-1 v = 0.7c (c = 3x10^8...

Hi Guys, Attached is a problem from an old exam for a Process Control and Instrumentation unit. I have tried everything I know (which isn't much, it's not the main assessable portion of the unit). Other questions similar involve giving us either the characteristic closed loop equation...

Homework Statement Prove that the characteristic function \chi_A: X\rightarrow R, \chi_A(x)=1,x\in A; \chi_A(x)=0, x\notin A, where A is a measurable set of the measurable space (X,\psi) , is measurable. Homework Equations a function f: X->R is measurable if for any usual measurable set...

How to compute \chi(\mathbb{C}\mathrm{P}^2)? This problem is from a class on differential topology, so we have defined the Euler characteristic as the sum of the indices of isolated zeros on a non-vanishing vector field. Off the top of my head, I cannot think of any theorems which really help...

"Given operators σ,τ on a finite-dimensional space V, show that στ=i, and that σ=p(τ) for some polynomial p in F[x]." The first part was no problem. As for the second, I have a strong suspicion that p is the characteristic polynomial, mostly because I believe I heard of that fact before (that...

If K is a field of characteristic p, and there exists an element a \in K which is not a pth power (i.e. the Frobenius endomorphism is not surjective), then I am told we can show x^p - a is an irreducible polynomial (and since it is not separable our field is imperfect). I see that x^p - a...

So I know that the characteristic equation for a 2x2 matrix can be given by t^2 - traceA + |A| So how would this be generalised for a 4x4 or higher matrix ?

Any ideas? Thanks so much!

So we are told in our class that the characteristic impedance of a coaxial cable is impractical to be at a value like 500Ohms. Why is that? The assumption is that the transmission line is lossless and that the dielectic constant (Er) is 1

let's say you are given the following matrix T: T11 T12 . . . T1n T21 T22 . . . T2n . . . . . . . ...

Homework Statement Let A = \begin{pmatrix}1 & 1 & 0 & 0\\-1 & -1 & 0 & 0\\-2 & -2 & 2 & 1\\ 1 & 1 & -1 & 0 \end{pmatrix} The characteristic polynomial is f(x)=x^2(x-1)^2. Show that f(x) is also the minimal polynomial of A. Method 1: Find v having degree 4. Method 2: Find a vector v of...

Hey, I'm working on a proof for a research-related assignment. I posted it under homework, but it's a little abstract and I was hoping someone on this forum might have some advice: Homework Statement Suppose T:V \rightarrow V has characteristic polynomial p_{T}(t) = (-1)^{n}t^n. (a) Are...

Homework Statement I'm trying to solve an example in Boas's book (Mathematical methods in the physical science page 423) but by using Goldstein's (Classical mechanics) method. The mechanical system consists of 3 springs (with constants k) and 2 masses (with mass m) this way: |----m----m----|...

Hello all, We utilized a differential attenuator to display the i-v characteristic of a 1n4005 diode. However, I was a bit confused as to how I could determine what the y-axis was calibrated as. I know that the vertical axis is actually current, but is there some sort of tactic for determining...

This is inspired by Kardar's Statistical Physics of Particles, page 45, and uses similar notation. Homework Statement Find the characteristic function, \widetilde{p}(\overrightarrow{k}) for the joint gaussian distribution: p(\overrightarrow{x})=\frac{1}{\sqrt{(2\pi)^{N}det...

<< Deletion by Moderator >> My question concerns resistance-current characteristic. The investigation was aimed at measuring current at different potential differences, before the filament lamp started to shine and when it was shining so as to observe both ohmic and non-ohmic behaviour...

Changing voltage - independent variable current flowing - independent variable The investigation was aimed at measuring current at different potential differences, before the filament lamp started to shine and when it was shining so as to observe both ohmic and non-ohmic behaviour. Also after...

i have a coax cable that will be used in data transmission. i have measured the open and short impedance and then characteristic impedance(Zo) for the cable. Eventually I will have a transmitter with Z_source in one end of the cable and receiver with Z_load at the other end of the cable. Is it...

I need some help. Is there a good way to do this type of question? Homework Statement Let X and Y be independent random Variables with exponential densities fX(x) = Ωe-Ωx, if X≥0 0, otherwise fY(y) = βe-βy, if y≥0 0, otherwise...

Homework Statement Solve the following PDE's: \frac{\partial u }{\partial t }+c \frac{\partial u }{\partial x} with u(x,0)=h(x). (1) \frac{\partial u }{\partial t }+u \frac{\partial u }{\partial x} with u(x,0)=h(x). (2) Hints: Specify the characteristic field of directions associated to each...

Hi, I've got some questions about angular momentum. I hope they aren't too stupid, but I can't see the wood for the trees. Is angular momentum something that is characteristic for a particle? I know that spin is characteristic (for example, the spin of a pi- is always 0) if I'm correct...

Just heard someone make that claim...seems a little bit, well, stupid. Do all organisms possesses the ability to learn new things? I would argue that moss on a rock, any plant (note: naturally responding to environmental change is not learning) etc. do not learn..

I know this may be a very stupid question, but I would really like to know. Is the determinant and the characteristic polynomial of an equation unique? I did several textbook questions and when I look at the solutions, they end up with completely different answers. Sometimes I am wrong and see...

Hello. first, sorry for my poor English. Derive characteristic wavelength from radiation powerThis is radiated power from bending magnet (synchrotron storage ring accelerating electron to get x-ray) and these are wave distribution from storage ring and what I have to derive is as follows...

Homework Statement The Kalpha x-ray is emitted when an electron undergoes a transition from the L shell (n = 2) to the K shell (n = 1). Use the following equations to calculate the wavelength of the Kalpha x-ray from a iron target (Z = 26), where E0 is the ground-state energy. The problem...

Homework Statement Let V be a finite dimensional complex vector space and T be the linear operator of V. Prove that the following are equivalent a V has a basis consisting of eigenvectors of T. b T can be represented by a diagonal matrix. c all the eigenvalues of T have multiplicity...