Discrete Definition and 897 Threads

Hello all. I am working on a problem and I am getting a bit confused. Suppose we have a poisson equation that we wish to solve subject to certain boundary conditions. Let's say we are in 1D (we can later extrapolate to more dimensions). Is it possible to impose Dirichlet boundary...

I have these problems I need help with. Can anyone take a look at them? https://www.dropbox.com/s/vq8rk6z5ea5gpwd/Problems.docx

Having a hard time with this problem. Can anyone guide me in the correct direction? Random graphs are a fascinating subject of applied and theoretical research. These can be generated with a fixed vertex set V and edges added to the edge set E based on some probability model, such as a coin...

Use a truth table to determine that "division into cases" rule of inference is valid.

How many comparisons are performed to find 13 in the following list by using Binary Search? 7, 12, 5, 22, 13, 32 Is it true that there are 10 comparisons performed to find 13 in the following list by using Binary Search? If this isn't right, then can somebody please help explain this to me?

How many vcomparisons did you actually need?

I have just started working with discrete time signals, more specifically various system properties. I am wondering if their is a discrete time system that is homogeneous but not additive? This is basically testing the linearity of a signal with the additive and homogeneous criteria.

Link to theorem: http://en.wikipedia.org/wiki/Law_of_the_unconscious_statistician Suppose Y is a discrete random variable related to X, a continuous random variable by some function r (so Y = r(X) ). Let A be the following set: A_y = {x ∈ R ; r(x) = y}. Since Y is discrete, f_Y (y) = P(Y = y)...

Consider a discrete set of ##k## points. First, is it a manifold? I know that a manifold is a topological space that contains a neighborhood homeomorphic to Euclidean space for each point. Can we just consider each point's neighborhood to be a set containing only that point? Second, would the...

Hello everyone: I have some question using the FFT in MATLAB for data interpolating. I don't know what the relation between the normal Fourier series and the real, image number. For example, given a set of measurement data, I can use the curve fitting toolbox to fit a curve. The general...

Testing for chaos in data I have data for 3 variables ,each with respect to the discrete time values. How do I check for the existence of chaos for this discrete 3D system?(I don't have the analytic eqs.,just the data.) MY IDEAS ON CHECKING FOR CHAOS FROM DATA:(which of these are feasible...

Homework Statement Hi, this is not a homework question per se, but something I'm wondering. Let C be a circulant n x n matrix, let x, b, be vectors such that C x = b. We would like to find a solution x. One way is to use the DFT: According to section 5, In Linear Equations, in the wikipedia...

Hi all, I'm a complete novice when it comes to describing images in frequency space and i understand that it is a way of representing images as being composed of a series of sinusoids. So a horizontal striped pattern with a single spatial frequency would have a magnitude image in frequency...

Homework Statement I have am doing a two dimensional discrete Fourier transform on an image (using MATLAB). What are the units associated with each pixel of the image in the frequency domain? Homework Equations The Attempt at a Solution I thought that the frequency should be...

Hi, I'm interested in building a breadboard version of the simplest comparator using transistors and resistors. Ultimately I'd like to understand the LM393 but looking at the datasheet schematic, it seems quite complicated. I was hoping there was a simpler comparator I could mimic to start out...

Wikipedia says it deals with distinct objects and is differentiated from continuous math, which has objects that "vary smoothly." For a layman, can someone explain what this means? And is all math discrete or continuous? No other options?

Hi, Homework Statement How may I find to what number Ʃ(m=1 to ∞) m/2m-1 converges? Further, suppose I know it converges to 4, why would then E(Y), given that P(Y) = 1/2m-1, be equal to 2 (thus asserted the answer) and not 4? Homework Equations The Attempt at a Solution I am...

Homework Statement Hi, for a project for school, I need to implement the Discrete Haar Wavelet Transform to compress an audio signal. This would be fine and dandy, but I do not really understand how to use the the DHWT. Could anyone direct me towards some resources that would be very helpful...

Homework Statement Homework Equations The Attempt at a Solution I'm not really sure if this belongs here or in the precalculus mathematics section. I had to take calculus before taking this class so I'm putting it here. I'm confused about part (b). I don't really...

Solve for x: 4x=6(mod 5) Here is my solution: From the definition of modulus, we can write the above as \frac{4x−6}{5}=k, where k is the remainder resulting from 4x~mod~5=6~mod~5=k. Solving for x, x=\frac{5k+6}{4}⟹x(k)=\frac{5k+6}{4} Now, my teacher said that is incorrect, and that...

For the first question it deals with onto functions I was able to do a-e which deals with actal numbers. Then questions E stumped me. I have no idea what to do or even how to start. It reads: Let C (n,m) be the number of onto functions from a set of m elements to a set of n elements, where m >...

The discrete-time spectrum of a sampled continuous-time signal x(t) is shown in the figure above, where (A = 9.8exp(-j0.06π), B = 0.51π, C = -0.27π, and D = 1.9exp(-j0.41π) ). If the sampling frequency is 4928, which of the following continous-time signals is a possible solution for x(t)...

Find the DTFT of: h[n]=(-1)^{n}\frac{sin(\frac{\pi}{2}n}{sin(\pi n} useful properties: x[n]y[n] --> X[Ω]*Y[Ω] \frac{sin(\frac{\pi}{2}n}{sin(\pi n} --> rect[\frac{2Ω}{\pi} I have no clue how to deal with the (-1)[itex]^{n}[\itex] the DTFT of that doesn't converge. . . any help...

Given that GCD(na,nb) = n * GCD(a,b) for a,b,n ∈ Z+ a) Prove that, if GCD(a,b) = 1 then GCD(a+b, a-b) = 1 or GCD(a+b,a-b) = 2 Hint: Let D = GCD(a+b, a-b), show that D | 2a and D | 2b thus D | GCD(2a,2b) then use the given b) Prove that, if GCD(a,B) = 1, then GCD(2a+b, a+2b) = 1 or GCD(2a+b...

Hello guys, I will be taking Linear Algebra (Intro.) and Discrete Math in the Fall. I heard that these two courses are different from the Calculus sequence. I am afraid since I am not good with proofs. Will I be able to do well as long as I put in the time? Can you guys give me an advice so I...

Say I have a model, y = f(x), and ten discrete data points to compare to this model, (x1, y1)...(x10,y10). The normal way would then be to take the residuals and square them to get a quality of fit, ie. average residuals squared = {[f(x1) - y1]^2 + ... + [f(x10) - y10]^2}/10 I also remember...

I can't seem to wrap my head around the types of sums used in probability theory, and here is a classic example. Section 6.1 of this article: http://en.wikipedia.org/wiki/Expected_value#Discrete_distribution_taking_only_non-negative_integer_values The first line of the proof, what is going...

Is there a way to know one way or another? If smallest possible scale is Planck scale, does it mean that space-time is discrete where smallest possible step is Planck's length (PL) and smallest possible time is Planck's time (PT)? If I move my hand from point A to point B, say 1m exactly in...

Hi, I am learning Fourier transformation by my own. I am reading a book "Fourier Transformation" by R. Bracewell. In chapter 11, in examples of discrete Fourier transforms, it gives for N =2, {1 0} transforms to 1/2{1 1}. I can do this in MATLAB but I can't figure it out how to do it by hand...

Evaluate the following discrete-time convolution: y[n] = cos(\frac{1}{2}\pin)*2^{n}u[-n+2] Here is my sloppy attempt: y[n] = \sumcos(\frac{1}{2}\pik)2^{n-k}u[-n-k+2] from k = -∞ to ∞ = \sumcos(\frac{1}{2}\pik)2^{n-k} from k = -∞ to 2 We can re-write the cos as...

Well I was reading this " A Mathematical Theory of Communication" paper by Claude Shannon. He says that the capacity of a discrete channel is given by [ tex ] C= \ \lim_{T \to +\infty} \ \frac{\log ( N(T) )} {T} [ \tex ] Here N(T) is the number of possible sequences in a duration of T...

Hey guys, I'm taking Discrete Mathematics and am having a bit of trouble with one of my proofs. If any of you has any experience with that and could tell me where I'm going wrong, I'd appreciate it! Ok, here it is: Prove each statement in 8–23 by mathematical induction: 27. A...

Consider an unbounded self-adjoint operator defined in a hilbert space(its domain isn't the entire hilbert space,of course).Can its spectrum have discrete and continuous parts simultaneity?Does it have eigenvectors with finite norm? Thanks

Hello, I'm working with a 2 x 3D arrays of fluid velocity values (east-west -> u and north-south -> v) and would like to properly calculate vertical velocities (w) from them (n.b. this is not homework). This ultimately needs to go into a processing algorithm, so while symbolic math is...

How would you go about convolving two discrete distributions that look something like this: Number: 0, 1, 2 Probability: 0.1, 0.3, 0.6 Number: 0, 1, 2, 3, 4 Probability: 0.1, 0.3, 0.2, 0.1, 0.3

Homework Statement If A is a subspace of X and A has discrete topology does X have discrete topolgy?Also if X has discrete topology then does it imply that A must have discrete topology? The Attempt at a Solution My understanding of discrete topology suggests to me that if A is discrete it...

Homework Statement An eletron is moving along one axis between x=0 and x=L. It's mass is given by m. We want to know the energy and wave function of its possible states given by the quantic number n. Show that the solution to the above equation is En=n^2*h^2/(8*m*L^2)...

Homework Statement A certain manufacture advertises batteries that will run under a 75 amp discharge test for an average of 100 minutes, with standard deviation of 5 minutes. a. find an interval that must contain at least 90% of the performance periods fr batteries of this type. b...

...outside integrated circuits? Can OpAmp's replace them?

Homework Statement There are 8 beads: 4 black, 3 white, and 1 red. How many ways can these be arranged on necklace? Homework Equations Just combinations nCm = (n-m)!/(m!). The Attempt at a Solution 8C4 = 70, 4C3 = 24, and 1C1 = 1, so the total number of combinations is 95? Or...

Hello, I am trying to quantify the difference between two discrete distributions. I have been reading online and there seems to be a few different ways such as a Kolmogorov-Smirnov test and a chi squared test. My first question is which of these is the correct method for comparing the...

Homework Statement 9. This is a simplified inventory problem.Suppose that it costs c dollars to stock an item and that the item sells for s dollars. Suppose that the number of items that will be asked for by customers is a random variable with the frequency function p(k). Find a rule for...

Homework Statement Homework Equations a. I know that x*a mod y should be the same as y*b mod x but I don't understand why b. I know that an inverse can be constructed because x and y are mutually prime and gcd(x,y) = 1 , but I have no clue at what pair x and m is possible c. I have no idea...

Hi all, I'm reading the following PDF about the DFT: http://www.analog.com/static/imported-files/tech_docs/dsp_book_Ch8.pdf Please see pages 152-153. So the inverse DFT (frequency to space, x[i] = ...) is given on page 152. Then it is claimed that the amplitudes for the space-domain...

Discrete signal x[n] is shown in the first picture. Sketch x[2n] Answer Can anyone ecplain why x[2n] is like that. I can understand how to plot it if i have a continuous time signal

See attachment for the question. ---------------- ∀x ∈ D, if P(x) then Q(x). this means ∀x P(x) -> Q(x). all you have to do is find a value for x ∀x this means for ALL x right so you can choose ANY element but for the E its only things in the domain so all you have to do is choose an x...

Homework Statement The textbook exercise asks for a Hausdorff topology on \{a,b,c,d,e\} which is not the discrete topology (the power set). It is from "Introduction to Topology, Pure and Applied", by Adams and Franzosa. Homework Equations Let X be a set. Definition of topology...

Hi members of the forum, Please consider the following: Given $\displaystyle a_{n}=\frac{n^2+1}{\sqrt{n^2+4}}$ where $\displaystyle n\in\mathbb{N}$ and $\displaystyle b_n=\prod_{k=1}^n(a_k)$ prove that $\displaystyle \frac{b_{n}}{\sqrt{2}}=\frac{\sqrt{n^2+1}}{\sqrt{n^2+2n+2}}$. Therefore...

In the page that I attached, it says "...while at the continuity points x of F_x (i.e., x \not= 0), lim F_{X_n}(x) = F_X(x)." But we know that the graph of F_X(x) is a straight line y=0, with only x=0 at y=1, right? But then all the points to the right of zero should not be equal to the limit of...

The DCT of an even function is comprised of just cosine coefficients, correct? I'm playing around in MATLAB and I came up with a simple even function 1.0000 0.7500 0.5000 0.2500 0 0.2500 0.5000 0.7500 1.0000 0.7500 0.5000 0.2500 0 0 0 0...