Discrete Definition and 897 Threads

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...

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...

Homework Statement Let a system that converts a continuos-time signal to a discrete-time signal. The input x(t) is periodic with period of 0.1 second. The Fourier series coefficients of x(t) are X_k = \displaystyle\left(\frac{1}{2}\right)^{|k|}. The ideal lowpass filter H(\omega) is equal to 0...

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...

Okay, so I'm a college student approaching my (second) senior year and I have the option of either taking CS2 or discrete mathematics. My schedule is completely full. CS2 is "Data structures and algorithmic techniques that are fundamental in programming solutions to complex problems...

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)?

Homework Statement Find the DC Gain and the Frequency Response of the above discrete-time system. The Attempt at a Solution This isn't really a homework problem but something I've been struggling with for my exams. I am given a transfer function in terms of z and am asked to find its...

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?

Hi I have recently been investigating an idea I had based around the phillosophical notion of order and the nature of time. My starting point goes somewhere along the lines of: If there are two particles in space. How does one particle know what the other has done until the light can...

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

We know that every discrete metric space with at least 2 points is totally disconnected. Yet I read this: A MS that is countable with more than 2 pts is disconnected. Is it that I'm misreading this statement. It sounds like if it has 2 or less points it is connected? more means greater than.

Hi guys! I got really stuck with a Discrete Mathematics homework in Integers and Algorithms. I know it is not very clear due to lack of symbols. If anyone didn't understand some part of the exercise I would like to clarify it. The exercise is the following : Homework Statement Define for B...

This is a question i hope someone on the forum can help me answer. Recently In a lab i had this question pop into my head, here goes: If I have a set of data and i am asked to find the derivative, I can plot it using the equation f'(x) ~ (y2-y1)/(x2-x1) if i have sufficently close points. A...

hi, i have trouble in understanding the concepts of the impulse response first of all, let's assume that we have a signal y[n] = x[n] which is time invariant and linear, hence if I understand correctly linear means that if for input a*x1[n] we have an output a*y1[n] b*x2[n] we...

Hi... It is an easy to see fact that, instead of moving along the hypotenuse of a right triangle, one starts from the lower corner and reach the upper corner moving only along the directions of the other two sides, i.e only vertically and horizontally and not diagonally...the distance moved...

Homework Statement Define the relation a I b ( a divides b) between integers a and b and then define the greatest common divisor, gcd ( a,b), and the lowest common multiple, lcm ( a,b) Is there any number for m for which you have n I m ( n divides by m) for every n. I just found this...

Hi All, I've come across a theorem that I'm trying to prove, which states that: The quotient group G/H is a discrete group iff the normal subgroup H is open. In fact I'm only really interested in the direction H open implies G/H discrete.. To a lesser extent I'm also interested in the H...

Homework Statement Let A be the set of all strings of a's and b's of length 4. Define a relation R on A as follows. For all s,t \in A, sRt, s has the same first two characters as t. s=baaa t=abaa Homework Equations The Attempt at a Solution I just want to know if the order of the first two...

Homework Statement How many was can 3 identical prizes be awarded to 98 potential winners? Homework Equations The Attempt at a Solution Well. I know that if the prizes were unique, the first prize would have 98 possible winners, the second prize would have 97 possible winners...