Discrete Definition and 829 Threads

I've been looking over quantum gravity threads here for a year or so. One thing keeps puzzling me. It appears to me that difficulty coming up with a viable quantum gravity theory is melding the continuous nature of the general relativity equations with the discrete (i.e. quantized) nature of...

Homework Statement Let their be a set A, and let B be the set: {A, {A}} (the set containing the elements A and the set that contains element A) As you know, A is an element of B and {A} is also an element of B. Also, {A} is a subset of B and {{A}} is also a subset of B. However...

Which one is a better course to take? I feel like MATLab is simple enough I can learn on my own if I ever need it. How useful is discrete math in physics? Should I take that now or stick to MATLab?

Calculate value(s) of the root(s) of the charateristic equation of a discrete system that correspond(s) to a time constant of 0.03 seconds when the sample period is 0.02 seconds. I'm not sure if I should use a first order or 2nd order equation. Either/or, why is it? Any ideas on how I should...

Homework Statement A random variable X takes values 1,2,...,n with equal probabilities. Determine the expectation, R for X and show that the variance, Q^2 is given by 12Q^2=n^2-1. Hence, find P(|X-R|>Q) in the case n=100 Homework Equations The Attempt at a Solution I can show...

I don't quite understand the treatment of discrete symmetries, for example, in Peskin's QFT book: Because by definition time reversal symmetry should flip the spin and momentum, so he defined an operation to flip the spin state of a two-component spinor, i.e. \xi^{-s} \equiv...

Hello! I'm not quite sure where to put this. I'm programming, but my question should be strictly mathematical. However, just for your information, I'm programming with Mathematica. I have a function that will give me points. If I give it inputs, I can get a value out of it. I can take a...

What determines whether an operator has discrete or continuous eigenvalues? Energy and momentum sometimes have discrete eigenvalues, sometimes continuous. Position is always continuous (isnt it?) Spin is always discrete (isn't it?) Why?

I have a frequency response diagram(frequency vs head) of discrete values. I have to perform Fourier analysis on these discrete values. The resultant frequency and head should be in FREQUENCY DOMAIN. how I can do this... by using FFT or any other ... using Nyquist frequency... please tell me...

I have a single parameter discrete probability distribution defined over the domain of non-negative integers with pmf in k of: Pr(k;L) = \frac{L^{k}}{k! * k! * I_{0}(2*\sqrt{L})} Where I_{0}() is the modified Bessel function of the first kind with order 0. I do know that E(k^{2}) = L...

As it says in the title, will anyone please give me the equation (in pre-algebraic terms) for discrete choice probability? I can see that the equation is P = Prob( Person n chooses Alternative i ) = G(xni, xnj(forall j inequal to i), sn, β), where xni is a vector of attributes of...

One the things which always bugged me about the definition of the integral is that limit of a Reimann sums consists of a countably infinite number of terms, yet it is supposed to be giving the under area under a curve which varies in a continuous manner. Has anyone else thought seriously about...

1. Explain how to find a shortest path between any given pair of vertices, given the length of edges connecting the vertices and the shortest distance between vertices (after doing the shortest-path calculation) So I am given a two matrices, as said one with length of edges connecting and the...

Hi Everyone, I am looking for some assistance on a problem that I have been working on for the last few weeks. I would like to optimise the performance of an accounts receivable department. In this dept there are several tools available to obtain a commitment to pay such as letters...

Homework Statement Hi Say I have a 5x5 lattice, where each entry (or we can call it site) contains the number 1. Now, on the lattice we have a function g(R), which is equal to the number on the site. In this case g(R)=1 for all sites (here R is a vector from the point (3,3), which denotes the...

Hi community, I have a linear systems of equations (8x8), but the matriz's components are discrete. In this moment, I make values' all of components and I write them in 64 files of 150x6000. My question is How do you solve a linear systems of equations discrete?, I mean, How do I work with...

I think I've screwed up my future. I am in my third year, double major in physics and math (math major more to supplement my understanding of physics), and this semester was just horrid. I made the mistake of moving off campus, working two jobs, and in the time I had to study, could not focus...

It puzzles me. In Einstein's paper on the photoelectric effect he proposed that photons with E = nhf were the explanation. Wouldn't a more elegant explanation be that the tangent of the electromagentic wave must take on discrete values because of the boundary conditions between the emitter...

Hello I have a problem. im looking at discrete event arrivals of items. the x-array represents the time of arrival and if one number occurs more than once it obviousely means that more than one item arrives at the exact same time. for instance: x=[0 0 0 0 3 3 3 3 6 6 6]; this means...

Hi all I have a function F, which depends on a discrete variable x, and I need to Fourier Transform it. I have put all the values of F in a table. Then I have used the command "Fourier" on the table, which - according to http://reference.wolfram.com/mathematica/ref/Fourier.html - results...

Homework Statement "The electrical charge exists in discrete quantities, which are integral multipuls of the electronic charge, 1.6022 e -19 C" What does "discrete quantities" mean? and Why is electrical charge an integral multipul of the electronic charge instead of just a multipul of...

Hello, I have a function in discrete domain f:\mathbb{Z}\rightarrow \mathbb{R}, and I assume that f is an approximation of another differentiable function g:\mathbb{R}\rightarrow \mathbb{R}. In other words f(n)=g(n), n\in \mathbb{Z}. When one wants to approximate the first derivative of g...

So, I'm taking an EE class and my teacher is terribly handwavy. She couldn't really explain this to me (not homework, lecture). I detect a fundamental problem in the math, coming from a science background, but it could just be my ignorance: Here's her lecture: physical setup: a...

Homework Statement X1 and X2 represent the values of two honest dice throws (independent of each other). Find the joint probability function of U and V when: a) U = min{X1,X2}, V = X1 + X2 The Attempt at a Solution This is what I thought: P(U = u,V = v) = P(\min \left\{...

Hello, If we are given a gaussian function which is continuous in x we know that: \int_{-\infty}^{+\infty}e^{-x^2}dx=\sqrt{\pi} What if the gaussian function is discrete in x? What is the result of \sum_{x=-\infty}^{+\infty}e^{-x^2} = \\? where x\in \mathbb{Z}

Homework Statement Suppose A, B, C are sets and http://latex.codecogs.com/gif.latex?f:A\to%20B,%20\text{%20and,%20}%20g:B\to%20C If f and g are one-to-one so is http://latex.codecogs.com/gif.latex?g\circ%20f .[/URL] If f and g are onto, so is...

Discrete space has been proposed at Planck length. But has any other distance been proposed(studied), like near proton width.

Discrete math -- links to biology? Hey, I'm in a math and biology program in college and I've recently become more and more into the discrete side of math. I was wondering if anybody knew of any areas of research that integrate discrete mathematics and biology, as there doesn't seem to be...

Homework Statement Ten cards are face down in a row on a table. Exactly one of them is an ace. You turn the cards over oen 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 for...

Homework Statement One sixth of the male freshman entering a large state school are out of state students. If the students are assigned at random to the formitories, 180 to a building. 1) What approximately is the probability that in a given dormitory at least one fifth of the students are...

Homework Statement Prove that H1 +H2 +...+Hn = (n +1)(Hn-n)? Homework Equations Hn denotes the nth harmonic number. The nth harmonic number is the sum of 1+1/2+...1/n, which is n / n +1. I'm not really sure if Hn = (1/ n) . Prove by Mathematical Induction Hn denotes the...

Hi everybody, I'm in the process of writing a discrete Fourier transform program using the algorithm on the DFT wikipedia page. When I throw in functions that I know the frequency domain signal of it gives the predicted shape but I have absolutely know idea how to generate a frequency axis...

First, I'm not an engineer, so I don't know this topic very well. Anyway, we were covering Fourier Transforms in one of my analytical methods class (chem major; NMR was the topic) and the phrase "discrete signal processing" came up. In our particular case, we collect individual points on...

I've been asked to write a function (.m file) in Matlab to calculate the discrete Fourier transform coefficient for an arbitrary function x. So far this is what I've done: function a = mydft(x,N) %MYDFT Calculates the discrete Fourier transform %usage: %[a]=mydft(x) %x=[ x[0] x[1] ... x[N-1] ]...

Can anyone help me out with this one? I need to find an explicit formula for: n 2 ∑ i i=1 I was already asked to find the explicit polynomial formula for the above equation which is n·(n + 1)·(2·n + 1) _________________ 6 I'm not sure on what the difference...

Homework Statement Prove that 3 divides n3 + 2n whenever n is a positive integer. Homework Equations The Attempt at a Solution Basis Step : P(1) : [13 + 2(1) ] /3 [1+2] /3 [3]/3 1 Since 3/3 =1, P(1) is true Inductive Step: [ k3 + 2k...

How to compare the topology on R generated by the subbasis S={[x,y)|x,y are rational}U{(x,y]|x,y rational} to the discrete topology on R?

Apparently everyone uses either Discrete Mathematics and Its Applications by Kenneth H. Rosen or Discrete Mathematics with Applications by Susanna S. Epp. Are these really the best ones? Both are very long texts which make me think they're not rigorous and they're descriptive like Stewart’s...

Another one of my homework asks is this true or false and prove it: For all sets A, B, and C if A U C is a subset of B U C then A is a subset of B Please help!

One of my homework problems says is this true or false and prove your answer: For all sets A, B, C if A n C is a subset of B n C then A is a subset of B. I believe the answer is true but i have no idea please help!

Homework Statement [SIZE="5"]x(n)=u(n); h(n)=(0.5)^n; y(n)=x(n)*h(n); find y(n) Homework Equations The Attempt at a Solution thank you

Homework Statement Find a formula for when m \sum k=0 the flooring function of[k1/3 ] ,m is a positive integer. Homework Equations n\prod j=m aj The Attempt at a Solution the flooring function of[k1/3] = K the summation of K is \frac{m(m+1)}{2} There's a table of...

Here is convolution: c[k]= (0.5)^k * delta(k-1) What do I do about delta(k-1)? I know if it is c[k]= (0.5)^k * delta(k), then it just equal (0.5)^k But what do I do with delta(k-1)?

I'm completely stumped on how to begin a discrete math proof, and I'm looking for a little advice on what might be a good way to approach this. In a previous problem I did a proof by contradiction to show that at least one of the real numbers a1, a2, ... an is greater than or equal to the...

Homework Statement Airlines sometimes overbook flights. Suppose that for a plane with 50 seats, 55 passengers have tickets. Define the random variable Y as the number of ticketed passengers who actually show up for the flight. The probability mass function of Y appears in the accompanying...

A point particle that has a charge of 15.0 µC is located at x = 0, y = 0 (we'll call it q0 and a point particle that has a charge q is located at x = 12.0 cm, y = 0 (we'll call it q1. The electric force on a point particle that has a charge of 6.0 µC at x = 24.0 cm, y = 0 is -(19.7) N \hat{i}...

I need to show that P<->Q is logically equivalent to ( P ^ Q ) v ( ~P ^ ~Q) So far I have P <-> Q is equivalent to ( ~P v Q ) ^ ( ~Q v P ) by a example I have no idea where to go from here

Discrete Math "Proper Subsets" Hey everyone, I am confused on part of this. Any input would be much appreciated! X has ten members. How many members does ~P(X) have? (~P is the set of all subsets) How many proper subsets does X have? Well the number of members of ~P is 2^10 or 1024...

Hi, I'm currently taking a seminar course , it's like a "small group" course (like a lecture as a tutorial) in mathematics. It's open for anybody, most people there actually aren't math students. It's basically a discrete math/combinatorial/"problem solving" driven course but the thing is, I...

I'm in a bit of a hairy situation right now. Spring 2010 will be my last semester at my current school studying Forensic Science, and in the fall I'll be transferring to a physics program at another school. I'm trying to get some classes in that will help me in th fall before I leave but there's...