Domain Definition and 704 Threads

The domain is \(0\leq x < \infty\) and \(0\leq y\leq b\). \begin{align*} \phi(x, 0) &= f(x)\\ \phi(x, b) &= 0 \end{align*} I want to show that \[ \phi(x, y) = \frac{1}{\pi}\int_0^{\infty} \int_{-\infty}^{\infty}f(\xi) \frac{\sinh[u(b - y)]}{\sinh(ub)} \cos[u(\xi - x)]d\xi du \] Why isn't the...

In the case of a function like \sqrt{x}, where the function is only defined for values equal or greater than 0, does the limit exist at 0? I know both the left and right side limits as x approaches a must be equivalent and real for the limit at a to exist, but what if the domain is restricted...

Homework Statement I constructed my own question to try to make sense of the following notation. g(x) = 2√x g : X → Y. What does X and Y equal? Homework Equations For 2√x, x = or > than 0. The Attempt at a Solution g(x) = 2√x g : [0, ∞) → [0, ∞) So X = Y = [0, ∞) The...

Consider the following solution to the steady state heat diffusion problem on an infinite y domain. \[ T(x, y) = \sum_{n = 1}^{\infty}c_n\exp\left(-\frac{\pi n}{\ell} y\right) \sin\left(\frac{\pi...

Can somebody tell me exactly what is 'S' in frequency domain? I know that s=σ+jw where σ is neper frequency and jw is complex frequency but i want the precise information on s you can suggest me a book in which it is clearly explained. Thank you.

Hello, folks, A Sturm-Liouville operator is typically defined not on the whole space of C^2 functions, but rather on some subspace described by boundary conditions. My question is: are those subspaces closed (hence complete, hence Hilbert) in L^2? In case of an affirmative answer, how can...

Homework Statement Can anyone help me to check whether the first two are correct or not? For the third question, i may need some help on it. Evaluate the following if they exist: a) sin(3Logi) b) (1+i)^(1/3-i) (principal value) Determine the largest open set in which the function...

Im trying to combine this domain into something of the form a>b and b<c however I cannot seem to convert this equation :/ Is it possible to convert this domain into a single expression?? The domain is sqrt(x^2+y^2-1)>0 and 1<= x^2+y^2 <= 20 any ideas?? I've encountered this problem many...

Homework Statement Calculate the current in the capacitor shown if the voltage input is a. v1(t) = 10cos(377t - 30°)V b. v2(t) = 12sin(377t + 60°)V Give answers in both time and frequency domain. Homework Equations I = dQ/dt = C * dV/dt The...

Homework Statement Why integral from a to b of f(x) equals "minus (-)" integral from b to a of f(x)? when a<b or a>b Homework Equations The Attempt at a Solution

Hi all, I have an all time doubt here. We know that if r.v z = x + y where x and y are 2 random sequences having corresponding pdfs p(x) and p(y), the pdf of z, p(z) = convolution ( p(x),p(y) ). I have seen the derivation for the continuous case although not thorough how to prove it. I...

Hi, Basically I have circuit with an input Vi (s) across a capacitor C which is in parallel with a resistor R1. And these 2 components are in series with another resistor R2 (please see attached drawing). The question states: Show that the transfer function of the circuit is: Vo/Vi...

Dears, I wish to measure the entropy of visual data such as image and video. I did transform these image and videos into frequency domain such as DCT, then measured the entropy with these pdfs for each AC components of image and videos. However, when I measured the entropy over spatial domain...

Hello. Say I have a given noise spectral density and I want to plot the random noise signal arising from this spectral density in the time domain. How can I generally accomplish this? For white noise, I would just pull numbers from a normal distribution, but I don't know what to do for non-white...

Homework Statement f(x)= √[(2x+1)/x3-3x2+2x] Homework Equations The Attempt at a Solution here For f(x) to exist x3-3x2+2x >0 and 2x+1≥0 by solving this i found that x \in [-\frac{1}{2},-∞]\bigcup[2,∞] but the answer given is (-∞,-1/2]\bigcup(0,1)(2,∞) so please...

Dear Experts If I invented something and took a video explaining it and include the date and time, and upload the video into the internet, what happens to the patentability of this idea or product or invention? Is there any benefit for doing so ? Thank you for reading. Have a nice...

Find the domain of the real valued function: f(x)=x−10−−−−−√x2+9x+8=x−10−−−−−√(x+8)(x+1) Why does the x2+9x+8 become (x+8)(x+1)? Thanks for the help!

Let n belongs to N, let p be a prime number and let $$Z/p^n Z$$denote the ring of integers modulo $$p^n$$ under addition and multiplication modulo $$p^n$$ .Consider two polynomials $$f(x) = a_0 + a_1 x + a_2 x^2 +...a_n x^n$$ and $$g(x)=b_0 + b_1 x + b_2 x^2 +...b_m x^m$$,given the coefficients...

I'm an MTech fresher in electronics domain, have been looking for job since 3 months.. its getting almost an year since i finished my exams. I don't even remember the names of companies where I'm applying and almost nil response. I did my BE from an average college and in mass recruitments i...

please anyone can help me to get the answer?I have idea about aliasing which is basically in frequency domain caused by lower sampling rate which does not satisfy the Nyquist criteria. Frequency aliasing refers to higher frequency getting the image of lower frequency.But what is time domain...

Let \mathbb{Q}_\mathbb{Z}[x] denote the set of polynomials with rational coefficients and integer constant terms. Prove that the only two units in \mathbb{Q}_\mathbb{Z}[x] are 1 and -1. Help with this exercise would be appreciated. My initial thoughts on this exercise are as follows: 1 and...

Homework Statement A triangle is defined by the 3 points P=(1,0,0), Q=(0,2,0) and R=(0,0,2). Set up the double integral over its area. The Attempt at a Solution The triangle can be described as a plane 2x+y+z+2=0, with xE [0,1], yE [0,2], zE [0,2]. I parametrized it into r(u,v)...

Homework Statement Let C be the boundary of the domain enclosed between y = x^2 and y = x. Assuming C is oriented counterclockwise. Evaluate the integral ∫c (6xy+e^(-x^2))dx Homework Equations I was thinking of using Green's Theorem. Would be the approach be correct? The Attempt at a...

Suppose you have a function y = f(x) such that the domain of f(x) is 1 ≤ x ≤ 6 and the range of f(x) is −3 ≤ y ≤ 5. a) Find constants B and C so that the domain of f(B(x − C)) is 8 ≤ x ≤ 9 B= C= b) Find constants A and D so that the range of Af(x) + D is 0 ≤ y ≤ 1 A= D= I'm working on...

Homework Statement We have f(x) = \frac{x^{2}+x-2}{x-1}+cos(x) , x\in\mathbb{R}\setminus \{1\} and wish to prove that it is continuous on its domain. Homework Equations The delta-epsilon definition of the continuity of a function. The Attempt at a Solution I've managed to reduce |f(x) -...

Homework Statement determine thevenin equivalent of circuit at terminals (a,b): Homework Equations Z(L)=jwL Z(C)=-j/wC V(th)=V(oc) R(th)=V(ex)/I(ex) The Attempt at a Solution actually 1st i need help with finding V(th). i do know that V(th) would be the voltage across the 2ohm resistor, so...

Homework Statement obtain a thevenin equivalent circuit given that iS(t)=3cos(4x10^4)t A. to that end: a) transform the circuit to the phasor domain. b) apply source-transformation technique to obtain the thevenin equivalent circuit at terminals (a,b). c) transform the phasor-domain thevenin...

Homework Statement Find the domain of 1/(sqrt(2x)-1)2 Note: the minus one is not included under the square root Homework Equations Title The Attempt at a Solution So the denominator cannot be zero so that means that sqrt(2x) cannot equal 1 x cannot be 1/2 letting the...

So I made a program that, so far, converts a password to a string of the binary representation of its successive ASII characters. Here's some output for an example: [FONT="Courier New"]"gs0dpsrln2" --------> 01100111011100110011000001100100011100000111001101110010011011000110111000110010...

Homework Statement F(x)=√x G(x)= 2/(x-4) Find g(f(x)) and its domain Homework Equations The Attempt at a Solution I am having trouble finding the domain for this composition. I know that g(f(x))= 2/(√x)-4 I believe that for the domain you combine the domain of the input (f(x)) and the...

Homework Statement Let ##R## be a PID and let ##\pi\in{R}## be an irreducible element. If ##B\in{R}## and ##\pi\not{|}B##, prove ##\pi## and ##B## are relatively prime. Homework Equations ##\pi## being irreducible means for any ##a,b\in{R}## such that ##ab=\pi##, one of #a# and #b# must be a...

Homework Statement Evaluate the triple integral for the function \int\int\int y dV over that part of the cube 0 \leq x,y,z \leq 1 lying above the plane y +z = 1 and below the plane x+y+z = 2 Homework Equations The Attempt at a Solution This is the first attempt at a triple...

Homework Statement Find the limit (if it exists) and domain of the following function. (I do not need to use epsilon delta proof, just results on different curves to prove this) \stackrel{lim}{_{(x,y)→(−1,0)}} [SIZE="4"] \frac {x(x+1)y^2}{(x+1)^2+y^2} Homework Equations The Attempt at a...

Homework Statement Determine domain on which the following function is continuous f(x,y)= \left\{\begin{array}{cc} \frac{x(x+1)y^{2}}{(x+1)^{2}+y^{2}} & (x,y)\neq(-1,0)\\ 1 & (x,y)=(-1,0) \end{array}\right. Homework Equations The Attempt at a Solution Because the numerator...

Hi, so the problem is this: I am trying to solve (analytically) the wave equation with c=1: u_{xx}=u_{tt} on x,t>0 given the initial conditions u(x,0)=u_{t}(x,0)=0, u(0,t)=sin(wt) I know how to solve on semi-infinite domains for quite a few cases using Green's Functions, Fourier Transforms...

Good day everyone. I'm confused about how I SHOULD set up the domain of my function that models the word problem. Suppose I have a word problem that goes like this: A square box with no top is to be made by cutting congruent squares from the four corners of a square metal sheet and then...

Homework Statement What is the domain and range of the function y = \frac{2}{x^2-4} The Attempt at a Solution I'm lost, and I noticed it seems like a difference of squares so what I did is y = \frac{2}{(x-2)(x+2)}. So the x value of vertex is 0. And i subbed this into the equation...

Here is the question: Here is a link to the question: Find the range and domain of function of 2 varibles:? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Prove that in a prinicpal ideal domain, two ideals (a) and (b) are comaximal if and only if a greatest common divisor of a and b (in which case (a) and (b) are said to be coprine or realtively prime) Note: (1) Two ideals A and B of the ring R are said to be comaximal if A + B = R...

Homework Statement Prove Z[x]/pZ[x] is an integral domain where p is a prime natural number. Homework Equations I've seen in notes that this quotient ring can be isomorphic to (z/p)[x] and this is an integral domain but I don't know how to prove there is an isomorphism between them and...

When I plot y = 3x^{\frac{4}{3}}-\frac{3}{32}x^{\frac{2}{3}}, I get: https://dl.dropbox.com/u/5653705/pfgraph1.png but I don't see any reason for the domain to be restricted to x > 0 . There is only a cubic root, which is well defined for negative numbers ... I've tried on a few...

Hi, I'm studying Calculus 2 now, and I am a litle bit confused in this question. 1- Determine and plot the domain of the function of two variables a) f(x,y)=\sqrt[]{1+x^{2}+y^{2}} x^{2}+y^{2}\geq -1 doing x^{2}+y^{2}= -1 i guess this is the graph of Hyperbole, but my teacher said is a...

what's negative frequency? can we say s=-3 in example bode plot ! or we can say it's unstable at w=-3 rad/s that's I mean is there negative frequency??

Is something wrong in my assertions below? Suppose we have two quantum systems N and X. Let N is described by discrete observable \hat{n} (bounded s.a. operator with discrete infinite spectrum) with eigenvectors |n\rangle. Let X is described by continuous observable \hat{x} (unbounded s.a...

Homework Statement x is square free (not divisible by a perfect square) on Z Homework Equations Z meaning all integers. The Attempt at a Solution I did a similar problem earlier that asked for the expression for prime numbers on the Natural numbers domain. For that problem the...

Suppose that we have rigged Gilbert space Ω\subsetH\subsetΩ\times (H is infinite-dimensional and separable). Is the Ω a separable space? Is the Ω\times a separable space? Consider the complete set of commuting observables (CSCO) which contain both bounded and unbounded operators...

What is the domain of sqrt(2x-x^3) I thought this would be pretty straight forward but I am completely stumped. So obviously square root is not defined for (-inf, 0), therefore I said: 2x-x^3 >= 0 Working this out you get x <= sqrt(2) as the domain. That is partially correct but I can't for...

I am going through a past paper for an upcoming exam and I want to check that I am approaching this question correctly. H(s) = 1/(s2 + 8485.28s + 36x10-6) Calculate and plot frequency response for 0 rad/s, 500 rad/s, 1000 rad/s and 10000 rad/s. I am under the impression that the 's'...

On one side one can define second-order variables as ranging over all elements of Pk(M) for all natural numbers k (P=power set of M, M is the universe of the model, superscript being iteration). On the other side it is sometimes defined as ranging over all first-order relations and predicates...

Homework Statement If we have R = \{ \frac{1}{2}(a+b\sqrt{2}) \}. Homework Equations The Attempt at a Solution For the identity, we have a=2 and b=0. So the identity is not equal to zero. Also, there can't be any zero divisors, because...