Characteristic Definition and 307 Threads

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...

Homework Statement Solve u_x^2+u_y^2=1 subject to u(x, ax)=1 Homework Equations The Attempt at a Solution I let u_x=p andu_y=q and F=p^2 +q^2 -1=0 Then x'=2p, y'=2q, u'=p.2p+q.2q=2, and p'=0=q'. So p=p_0, q=q_0 are constants. I got x'=2p_0, y'=2q_0 and integrating the...

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...

Constructing a "smooth" characteristic function Suppose I'd like to construct a C^\infty generalization of a characteristic function, f(x): \mathbb R \to \mathbb R, as follows: I want f to be 1 for, say, x\in (a,b), zero for x < a-\delta and b > x + \delta, and I want it to be C^\infty on...

1. Show that, if the velocity field (V) is a fixed (spatially constant) vector, then the characteristic curves will be a family of parallel-straight lines. 2. ut+V1ux+V2uy=f f=S-[dell dotted with V]u characteristic curves: dX/dt=V1(X,Y) & dY/dt=V2(X,Y) 3. really looking for...

Why is frequency response an important characteristic of an amplifier? in this situation we are using a transistor and had to calculate gain using specified frequencies and the resulting voltages through our circuit. My understanding of contemporary electronics is not as strong as i...

For any characteristic polynomial determined from A - eI (where A is a nxn matrix, e is an eigenvalue and I is the identity matrix), is it a rule that the coefficient associated with the char. polynomail term of highest degree must be positive ? My tutor made a theory that if the...

The problem statement: Find the largest interval in which the solution of the following initial value problem is valid: cos(t/3)y'' +(6t^2)y' + ((t-5)^-3)y = 0 Initial conditions: y(1) = 1 y'(1)= 3 I have a few questions concerning this problem. I've converted it to it's...

I want to write an algorithm that gives as output the numbers a_n,\ldots, a_1,a_0, when a matrix A\in\mathbb{R}^{n\times n} is given as input, such that \det (A - \lambda) = a_n\lambda^n + \cdots + a_1\lambda + a_0,\quad\quad\forall\lambda\in\mathbb{C} If n=2, a_2 = 1,\quad a_1 =...

Homework Statement sin(y)\frac{ \partial u}{ \partial x} + \frac{ \partial u}{ \partial y} = (xcos(y)-sin^2(y))u where ln(u(x,\frac{\pi}{2})) = x^2 + x - \frac{\pi}{2} for -1 \leq x \leq 3 determine the characteristic curves in the xy plane and draw 3 of them determine the general...

Homework Statement i)write down the general form of a semi lenear first order pde in the unknown u(x,y) ii)write down the ode satisfied by a characteristic curve in the x-y plane for your pde ii)give a careful derivation of the ode satisfied by u(x,y) along such a charcteristic curve...

I am stuck on solving for the roots of a charactristic equation: y'''- y''+y'-y=0 where I set r^3-r^2+r-1=0 and factored out r to get r*[ r^2-r +1] -1 =0 to get the real root of 1. How can I solve for the compex roots?

Roughly speaking, in cohomology theory, characteristic classes are elements of the cohomology of the base space of a fibre bundle which can tell you something about the nature of the fibre bundle. In "Characteristic Classes" by Milnor, he mentions that characteristic homology classes for the...

Hello, I'm trying to figure out connection between the characteristic polynomials for real matrices [3x3] and their powers. Suppose A is a real matrix [3x3] which's c.p is t^3+t^2+t-3, how can i find the c.p. of A^2. Now suppose p(t)=a_1t^3+a_2t^2+a_3t+a_4 Right away I can know that...

Hello, I have a quick question about Characteristic curves. [PLAIN]http://pokit.org/get/1958a855486487230cd4e3c0a1cc0908.jpg First: Do these curves go to infinity, i mean in theory? If I had a steeper load line, I would hit saturation later. And what about that portion of load line between...

Hello :) I have been giving a mathematical problem. But I find difficulties solving this. Therefore, I will be very grateful if anybody might wanted to help? The problem is "Let K be a compact convex set in R^n and C a closed convex cone in R^n. Show that ccone (K + C) = C." - Julie.

polynomial? i find this but i do not understand;its too complex. http://www.math.sc.edu/~howard/Classes/700/charAB.pdf any simpler way/idea?Thanks!

Hey I'm studying for an exam and one of the things i need to know is this: 4. Given the eigenvalues of a matrix: a) Determine the characteristic polynomial. b) Find vectors than can act as bases for the associated eigenspaces. Part a seems relatively straight forward but for part b I...

Let K be a field of characteristic p. Suppose f(x)=(xk+ck-1xk-1+...+c0)(xp-k+...) in K[x] with 1≤k≤p-1. My question is: 1. since f(x) in K[x], can I conclude g(x)=xk+ck-1xk+...+c0 in K[x] as well? 2. We see that in general if g(x)=xk+ck-1xk-1+...+c0 then ck-1=-(α1+α2+...+αk) where...

Hello, I am trying to find a characteristic function (CF) of a Compound Poisson Process (CPP) and I am stuck :(. I have a CPP defined as X(t) = SIGMA[from j=1 to Nt]{Yj}. Yj's are independent and are Normally distributed. So, in trying to find the CF of X I do the following: (Notation...

Let T:V to V be a linear operator on an n-dimensional vector space V. Let T have n distinct eigenvalues. Prove that the minimal polynomial and the characteristic polynomial are identical up to a factor of +/- 1 I'm probably over thinking this, but it seems that if you have n distinct...

Homework Statement Given the matrix 3 2 1 0 0 2 0 2 0 Find the characteristic equation and the eigenvalues. Homework Equations |\lambdaI-A| The Attempt at a Solution If the characteristic polynomial is (\lambda-3) 2 1 0 (\lambda-0) 2 0...

Find the characteristic lines for the equation: 2 du/dx + 8x du/dt = 16x Here's my attempt a = 2 b = 8x c = 16x Using dt/dx = b/a = 8x/2 = 4x t = 2x2 + C C = t1 -2x12 Hence the characteristic is: t = 2x2 + t1 - 2x12

Hi All, I am using PC1D (is the most commonly used of the commercially available solar cell modelling programs) when I tried to simulate PV silicon to see I-V characteristic curve the curve flip as you can see attached file. My question how can I make short_circuit Ib positive value...

Homework Statement Let A be an nxn matrix with real number entries, in which all entries are 1. Find the characteristic polynomial of A. Homework Equations characteristic polynomial: f(t)=det(A-tI), I is identity matrix The Attempt at a Solution I've tried to do this by various...

http://img847.imageshack.us/img847/1922/capturevq.jpg I need help starting this. So far I am getting Voh = +10V from the zener diode, and Vol = -10V, the upper and lower saturation limits based on the zener diodes Then for threshold values I am getting an upper threshold Vth = -R1/R2 * Vol =...

Hi i wonder if the diode I-V characteristics will be as usual at it is operated at high frequency? Some one told me that it will be not the same. There will be a some kind of hysteresis loop will appear in the curve. Can anyone ensure me about that or give me a useful link about that topics?

I want to confirm this, for any position vector. 1) They are radial vector that start from the origin to a point in space. 2) If A is a position vector: \nabla X \vec A \;=\; 0 \;\hbox { and }\; \nabla \cdot \vec A \;\hbox { not equal to zero. } 3) Any position vector in spherical...

Homework Statement If the characteristic polynomial of an operator T is (-1)^n*t^n, is T nilpotent? Homework Equations The Attempt at a Solution My first instinct for this question is that the answer is yes, because the matrix form of T must have 0's on the diagonal and must...

If the characteristic polynomial of an operator T is (-1)^n*t^n, is T nilpotent? My first instinct for this question is that the answer is yes, because the matrix form of T must have 0's on the diagonal and must be either upper triangular or lower triangular. This is what I found when I tried...

Hey guys, I really need some help please! I would really appreciate it if anyone can help out, if we have F16 = F2/(x^4+x+1). can anyone explain to me how can I compute the minimal polynomials and the characteristic polynomils over F2 of elements of F16 and to point out the primitive ones...

Show that if R is an integral domain with characteristic p>0, then for all a,b in R, we must have (a+b)^p=a^p+b^p. Show by induction that we must also have (a+b)^p^n=a^p^n+b^p^n for all positive integers n. R is an integral domain, so ab=0 implies a=0 or b=0. The smallest positive integer...

1. If \phi is a characteristic function, than is e^{\phi-1} also a characteristic function? I know some general rules like that a product or weighted sum of characteristic functions are also characteristic functions, also a pointwise limit of characteristic functions is one if it's continuous...

Hello, I considered a Binomial distribution B(n,p), and a discrete random variable X=\frac{1}{n}B(n,p). I tried to compute the characteristic function of X and got the following: \phi_X(\theta)=E[e^{i\frac{\theta}{n}X}]=(1-p+pe^{i\theta/n})^n I tried to compute the limit for n\to +\infty...

Homework Statement find the characteristic equation of a binomial variable with pmf p(x) =\frac{n!}{(n-k)!k!}*p^{k}*(1-p)^{n-k}Homework Equations characteristic equation I(t) = \sump(x)*e^{tk}The Attempt at a Solution I(t) = \sum\frac{n!}{(n-k)!k!}*(p^{k}*(1-p)^{-k}*e^{tk})*(1-p)^{n} i am...

When working over a field of characteristic not 2, or otherwise with modules over a ring where 2 is invertible, there is no ambiguity in what one means by symmetric or anti-symmetric rank 2 tensors. All of definitions of the anti-symmetric tensors The module of anti-symmetric tensors is the...

Homework Statement Let J be the nxn matrix all of whose entries are equal to 1. Find the minimal polynomial and characteristic polynomial of J and the eigenvalues. Well, I figure the way I'm trying to do it is more involved then other methods but this is the easiest method for me to...

Homework Statement Where A is an n x n matrix and I is the n x n identity In the expansion of det(x*I-A), show that the coefficient of x is equal to the sum from i = 1 to n of the determinant of the Aii minor. (where Aii = the submatrix of A formed by deleting row i and column i)...

What exactly is a "joint characteristic function"? I want the characteristic function of the joint distribution of two (non-independent) probability distributions. I'll state the problem below for clarity. So my two distributions are the normal distribution with mean 0 and variance n, and the...

Homework Statement Come up with the frequency directly from the solutions of the characteristic equation. {{z=0.-5.71839 i},{z=0.+5.71839 i}} Homework Equations characteristic equation = z^2+b z+c=0 The Attempt at a Solution Not sure where to start. Any help would be greatly...