Characteristic Definition and 287 Threads

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...

Homework Statement 1)Prove that the characteristic roots of a hermitian matrix are real. 2)prove that the characteristic roots of a skew hermitian matrix are either pure imaginary or equal to zero. Homework Equations The Attempt at a Solution

Homework Statement Given characteristic functions f and g on the intervals [1,4] and [2,5] respectively. The derivatives of f and g exist almost everywhere. The integration by parts formula says \intf(x)g'(x)dx=f(3)g(3)-f(0)g(0)-\intf'(x)g(x)dx. Both integrals are 0 but f(3)g(3)-f(0)g(0) is...

I am trying to compute the inverse Fourier transform numerically (using a DFT) for some complicated characteristic functions in order to compute their corresponding probability distribution functions. As a test case I thought I would invert the characteristic function for the simple exponential...

Homework Statement B = |a 1 -5 | |-2 b -8 | |2 3 c | Find the characteristic polynomial of the following matrix. Homework Equations None The Attempt at a Solution So basically I have to find the det(B-λI). No matter what I do to the matrix I can't make the...

Hi: There are 3 invariants. The first one is a trace. The third one is a determinant. So they are invariants. The strange thing is the 2nd one. It is a hybrid term. Why is it also an invariant?

Let V =Mn(k),n>1 and T:V→V defined by T(M)=Mt (transpose of M). i) Find the minimal polynomial of T. Is T diagonalisable when k = R,C,F2? ii) Suppose k = R. Find the characteristic polynomial chT . I know that T2=T(Mt))=M and that has got to help me find the minimal polynomial

Hello physics forum, I'm running an experiment where characteristic x-ray are produced from an Iron sample, and I was just wondering if these x-rays are emitted in any random direction, or is there a "favored" direction they can be emitted in? Thank you in advance. Neville.

According to the Brønsted-Lowry definition, a base is a compound that can -keyword- accept H+, and an acid anything that can give H+.

Homework Statement Let f(x,y) be the soloution of xu_x +yu_y = u^4 that is defined in the whole plane. Prove that f = 0 . Hint: Think of the characteristic curves of this PDE. HOPE You'll be able to help me Thanks in advance! Homework Equations The Attempt at a Solution...

I have been thinking about this for quite some time now. When I look at the function that descibes the fat cantor set namely: f(x) = 1 for x\inF and f(x) = 0 otherwise, where F is the fat cantor set. I wonder, how do I prove that this is non-riemann integrable? I have considered...

Is there an example of a real vector bundle over a compact smooth manifold with all zero characteristic classes (Euler class,Stiefel-Whitney classes and Pontryagin classes) that is non-trivial?

hii... you all know about IV Characteristic PIN diode.. I fabricate PIN diode and want to analysis my result.. what is the forward voltage drop for PIN diode? are the voltage fix o variable.. ??

Hi there, Recently I have come across a proof with application of characteristic function. After some steps in the proof, it concluded that there is a neighborhood of 0 such that the characteristic function is constant at 1, then it said the characteristic function is constant at 1...