Discrete Definition and 829 Threads

Homework Statement For every non-negative integer z, z2 - 3z is an even integer. Prove this statement. So far, I have learned about direct proofs and indirect proofs such as contraposition and contradiction. Homework Equations An integer z is odd when there is an integer a so that z = 2a+1...

Homework Statement The system is given by: G(s) = 1/((s+0.1)(s+3)) I need to convert it to G(z), it's discrete form. The sample time T is 0.1 seconds. Homework Equations To convert it they give G(z) = (1-z^(-1))*Z-transform[G(s)/s] The Attempt at a Solution Obviously I...

Homework Statement [PLAIN]http://img833.imageshack.us/img833/6932/metric2.jpg The Attempt at a Solution I've shown d_{X\times Y} is a metric by using the fact that d_X and d_Y are metrics. What is a simpler description of d_N with d_X the discrete metric? Is it just: d_N(x,y) =...

Hi all I was wondering if you could help me with this problem: http://img713.imageshack.us/img713/4306/giflatexl.gif Could someone explain this relationship in plain english for me please? [PLAIN][PLAIN]http://img9.imageshack.us/img9/338/codecogseqno.gif This is what I was...

Homework Statement A gas supply company is trying to set up contracts with two clients, A and B. The company will make a profit of ten million dollars for each contract that is successfully agreed. The probability of agreeing a deal with client A is 1/4 and the probability of agreeing a deal...

Got a DSP problem. I think this is a bit complicated, and may need some DSP gurus to answer it. I've been banging my head on this literally for months now. Thought I had it figured out, but today find I'm still not done. I have some Impedance spectroscopy data from electrodes, sampled at...

Let X be a discrete random variable that can assume the values -1, 0,1,2,3,4 with the probabilities 1/6, 1/12, 1/6, 1/4, 1/12, 1/4. Find the probability densities of the following random variables: a) Z= X^2 + 1 h(y)= f(g^-1(y)) Attempted Solution X= -1 0 1 2 3 4 Z=...

Ok, so I'm having difficulty adapting to subjects like set theory etc. For example this question: L.{A,a} = {A, a, b, ab, ba, aba} Find L Now, I know the answer but it was a battle getting there. It took me 30 mins before giving up and turning on my PC. I got annoyed so much that...

What's the proof that eigenfunctions of discrete eigenvalues are in Hilbert Space?

Homework Statement In 2006, Red Rose tea randomly began placing 1 of 10 English porcelain miniature animals in a 100-bag box of the tea, selecting from 10 "Pet Shop Friends." a) On the average, how many boxes of tea must be purchased by a customer to obtain a complete collection consisting of...

I have a data curve with discrete time points that I imported into MATLAB. The x-axis is an array named t: t = 1.0e+003 * 0.0319 0.0505 0.0851 0.1037 0.1356 0.1648 0.2021 0.2313 0.3616 0.5823 0.8880 1.1778 1.4996...

None of my advanced courses require discrete math as a requisite. In fact, the only course that does explicitly require it is not on my degree plan of operations research. However, is this going to bother me when it comes time for say Real Analysis, Advanced Calc, or Abstract Algebra? I think...

Homework Statement There are 17 street lamps along a straight street. In order to save electricity and not affect the regular use at the same time, we can shut down 5 of these lamps. But we cannot turn off a lamp at either end of the street, and we cannot turn off a lamp adjacent to a lamp...

Homework Statement There are 17 street lamps along a straight street. In order to save electricity and not affect the regular use at the same time, we can shut down 5 of these lamps. But we cannot turn off a lamp at either end of the street, and we cannot turn off a lamp adjacent to a lamp...

Discrete Mathematics -- Symmetric Closure Math help in Numerical Analysis, Systems of I can't seem to find the way to approach this problem. Because it has symbols I don't know how to type here, I have attached an image here instead. Please help me if you can. Any input would be greatly...

Hi, i have studied discrete math and there are topics like linear algebra and analytic geometry and googling i found that there are not in other courses, what are the topics in your discrete math courses?

Homework Statement Determine if the statement is true or false. Prove those that are true and give a counterexample for those that are false. If r is any rational number and if s is any irrational number, then r/s is irrational. Homework Equations A rational number is equal to the...

Homework Statement Prove by contradiction. Your proof should be based only on properties of the integers, simple algebra, and the definition of rational and irrational. If a and b are rational numbers, b does not equal 0, and r is an irrational number, then a+br is irrational. Homework...

[SIZE="6"]Name 5 signals and the systems that process them. – Draw the block diagrams to show how the signal gets transformed. • Choose both Continuous and Discrete signal • Include some examples from Bio Medical Engineering.

I'm struggling in an application of Fourier transform.here is my problem: a series of points from experimental data plotted as a cruve. I'm planning to do a Fourier transform to see how smooth the curve is? my question is: is it possible/useful to calculate the Fourier coefficients? if yes, how...

Commutators on a discrete QM lattice = ? Please let me know if any of the following is unclear: I was thinking about how you could go about doing QM not in a continuous space but instead on a lattice, take 1D for simplicity. Let's use a finite (not countably infinite) number of positions say...

Why does an atom emit discrete frequencies of light? Solving the Schrodinger wave function for the hydrogen atom (that is a single particle representing an electron bound by a spherical potential) we find that it has discrete energy levels. Plotting every possible value of f in E'-E = \hbar f...

Discrete Mathematics - (A∪B)-(A∩B)=(A-B)∪(B-A) - prove by cases?? Hi, I'm new to these forums so please redirect me if I've posted this in the wrong place. I'm trying to graduate and this is my last class, but as I'm not a math major, I'm really struggling with this particular problem. I've...

I'm not a mathematician, but I want to understand how a mathematician would view this issue. I'm working primarily with degree distributions for finite graphs, and when I make a log log plot of the frequency distribution the data points form a nice straight line (at least for low degree...

couple of questions a) the operators not commuting would also be true of position and momentum operators in classical mechanics (x d/dx -d/dx x) f(x) so the non-commutation does not inherently constitute a proof for the uncertainty principle, or do you just not care about the uncertainty at...

Hi all, I am having trouble with the concept of joint pdf's. For example - a set Z1,Z2,...ZN are each gaussian rv. Let Z1~N(0,1), let X be +1 or -1 each with probability 0.5. Z2=Z1X1, so Z2 is ~N(0,1). (I assume this to be As Z2 is just Z1 multiplied by a simple factor, an instance...

I'm having trouble understanding the results of a discrete convolution. I have two functions: 1) High resolution spectra 2) Gaussian curve The point of this operation for me is put the high resolution data in terms of the lower resolution represented by the guassian curve (filter) I...

Hi guys, I'm a bit embarassed that my first post here is in this section, but I'm taking a Elec. Eng. course abroad, which is out of my confort zone (i'm majoring in automotive eng.) and I'm trying to solve a few model problems. This one in particular deals with the DFT. Anyway:Homework...

I have a feeling this question has a very simple answer, yet I cannot find it anywhere online. Let's say that I have a data set that represents and evenly-spaced sample of a function, taken uniformly over the interval (a,b) \qquad a,b \in \mathbb{Z} I perform a discrete Fourier transform to...

Homework Statement Let A be the set of all integers x such that x is = k2 for some integer k Let B be the set of all integers x such that the square root of x, SQRT(x), is an integer Give a formal proof that A = B. Remember you must prove two things: (1) if x is in A, then x is in B, AND...

What are the conditions for which it can be concluded that a system has discrete energy levels? For example a system in one dimension with the potential V(x)=b|x| has only a discrete spectrum. How I can prove it? My book says moreover that the energy eigenvalues have to satisfy the...

I have a discrete set of data. I'd like to visualize it probabilistically. Unfortunately, I focused in Num Methods in grad school and am very weak in Probability. Where is a good place to start to visualize this data set using a discrete pdf? I know a histagram is good to show # of...

Homework Statement Let F(x)=\begin{cases} .25e^{x} & -\infty<x<0\\ .5 & 0\leq x\leq1\\ 1-e^{-x} & 1<x<\infty\end{cases}$. Find a CDF of discrete type, F_d(x) and of continuous type, F_c(x) and a number 0<a<1 such that F(x)=aF_d(x)+(1-a)F_c(x) Homework Equations The Attempt at a...

Homework Statement This is not so much a homework problem but a part of a project I'm working on. So in just a few words; what I have (at time t=0) is a discrete state (half simple harmonic oscillator) connected to a wire with continuous states. These states are coupled by a complex...

Homework Statement A 8-point data set is transformed with a DFT and the resulting array has values 1,2,3,4,5,6,7,8 was the data set real or complex? why? Homework Equations The Attempt at a Solution kind of confused with this question all i know is the discrete Fourier...

The energy and the power contents of a signal x(t), denoted by E_x and P_x, respectively, are defined as (1) E_x = \int ^{\infty}_{-\infty} |x(t)|^2 dt (2) P_x = lim_{T\rightarrow \infty} \frac{1}{T} \int ^{T/2}_{-T/2} |x(t)|^2 dt Let us use the discrete time (sampled) signal, with sampling...

Homework Statement How many positive divisors does each of the following have? 2^n where n is a positive integer. and 30 The Attempt at a Solution for 30 i get 2 , 5 , 3 , 10 but my book says 2 ,3 ,5 I don't understand why 10 isn't a divisor. and for 2^n I am trying...

Homework Statement δ = dirac delta x[n] = δ[n] + 2δ[n-1] - δ[n-3] h[n] = 2δ[n+1] + 2δ[n-1] y[n] = x[n]*h[n] Homework Equations y[n] = x[n]h[n] = \sumh[k]x[n-k] The Attempt at a Solution I have graphed the x[-k] and h[n], the solution saids y[n] = h[-1]*x[n+1] +...

If the universe is http://en.wikipedia.org/wiki/Digital_physics#Wheeler.27s_.22it_from_bit.22", then would force fields be quantized (not extend to infinity)? Must force fields extend infinitely for conservation of energy (transmission of em waves)?

1. For any integer n, prove that 3 divides n^3 -n The Attempt at a Solution I'm stuck. I understand that means that n^3 -n mod 3 =0. or I can n^3 -n can be expressed as 3x. But I don't know how to prove it. Where do i go from here. Thanks

hey I was just wondering if anyone can teach me how to graph a signal like this x[n] = { 1 for 0<=n<=4 { 0 elsewhere im not sure how to do this, what I have tried is x = [1 1 1 1] but this is not a function of 'n'.

Homework Statement 10 face cards are face down in a row on a table. Exactly one of them is an ace. You turn the cards over one at a time, moving from left to right. Let X be the random variable for the number of cards turned before the ace is turned over. What is the probability function...

Hi all, I am going to be taking Discrete Mathematics in August and my last Math course was about 5 years ago. I am a little intimidated to just 'jump' back into Math especially a course like this one. Can anyone who was successful give me a few pointers? I ordered the Textbook and will...

"Continuous eigenstates" vs "discrete eigenstates" There's this thing that's bothering me: if I have an Hamiltonian with a discrete and continuous spectrum, every book I read on quantum mechanics says that eigenvectors of discrete eigenvalues are orthogonal in the "Kronecker sense" (their...

Homework Statement Two charged objects Q1 = +4Q and Q2 = -Q are located on the x-axis. Q1 is at the origin and Q2 is at the x = +S m position. You also have a test charge +qo Homework Equations F = kQq/d2 The Attempt at a Solution So you find that qo is past Q2 on the x-axis...

Whats the difference between a discrete time impulse and a continuous time impulse signal ?

Hey guys, I was imagining that I have a sine function: y = sin(x) where x represents a distance in meters for instance. Now let us say that I sample the function at x = 0,1,2,3...,10 (meters) producing a list of values: {sin(1), sin(2), sin(3),...,sin(10)} = {0.000, 0.841, 0.909, 0.141...

I recently heard of this theory: Discrete Scale Relativity which can be found here: http://www.science20.com/discrete_scale_relativity/blog/discrete_scale_relativity-78208 and http://www3.amherst.edu/~rloldershaw/ What are the issues with this theory and why has it not picked up more...

What is the corresponding discrete version to the first, second, and higher order derivatives of function?

Homework Statement Homework Equations I need to prove this by using induction. I need help with the induction step. The Attempt at a Solution. Basis step: let n=0; 2^0 = 2^(0+1) - 1 -----> 1=1