Discrete Definition and 897 Threads

Homework Statement The probabilities of blood types O, A, B and AB are 0.46, 0.39, 0.12, 0.03 respectively. If a clinic is seeking either type O or B from six random individuals, what is the probability that at least 2 people have the desired blood type? Homework Equations The...

Hi all, Now naturally after completing a physics degree I am very familiar with the form and function of the Fourier Transform (FT) but never have grasped it quite conceptually. I understand that given a function f(x) I can express every functional value as a linear combination of complex...

I am simulating an ODE where the differential function is a function of sampled data points and are having trouble obtaining data in between sampled points (for the step computations of RK4). The first thing that I tried was to linearly interpolate the data, but that introduced large...

In a Hilbert-space whose dimensionality is either finite or countably infinite, we have the discrete resolution of identity \sum_n |n\rangle \langle n| = 1 In many cases, for example to obtain the wavefunctions of the discrete states, one employs the continuous form of the resolution...

A problem i made up for some of my friends who need help with discrete distributions tables. Can you do it? Dice Generator Part I: 1. Construct a discrete probability distribution table for a fair six-sided dice. (Round according to example) 2. Calculate the mean, variance, and standard...

I'm trying to do some extra course work to prepare for my final next week but I'm having a lot of trouble with the book problems. They talk about a lot of things we weren't taught. Can someone help me out here? Prove: n\niZ, n= a multiple of gcd(a,b) ⇔ n is a linear combination of a and b This...

Hello, I have a question regarding discrete energy levels of atoms. If electrons must inhabit certain energy levels, when they are excited up to a higher energy level, do they instantaneously jump to that level, or do they exist for some short time 'in between'? Furthermore, if the...

Hi everybody, I am interested to do some DEM(Discrete Element Method) simulation for my miniproject. So far I have seen that the most available opensource codes require large computation resource for parallel calculation. I don't have access to such facility and also my initial problem...

Hi guys, so I'm trying to create this thing that gets accelerometer values and integrate those values at about 25 samples a second. From what I understand if I integrate the values, that means each second I have 25 values I want to integrate. I read this research paper where someone used the...

I have a 3 rad/s sine wave that I am sampling every 2 seconds. The slow sampling has created an alias of -0.14 rad/s. I have plotted this over the top of the original continuous time signal, please see attachment. My problem is that I only want to plot the first period of the discrete signal...

How do you calculate the intersection of discrete data points and an equation? Actually I have two ways already, one is to just take the equation of the discrete points then solve it using a root-finding technique. The other would be substituting the x values of the discretized points to the...

I am currently enrolled in Calculus 1. Will be taking Calculus 2 in summer and Calculus 3 in Fall. I have already registered for these courses. One of the Math electives I have a choice in Fall Semester is either Discrete Math or Linear Algebra. Any suggestions would be greatly appreciated...

1. Given: The DTFT over the interval |ω|≤\pi, X\left ( e^{jω}\right )= cos\left ( \frac{ω}{2}\right ) Find: x(n) 2. Necessary Equations: IDTFT synthesis equation: x(n)=\frac{1}{2\pi}\int\limits_{-\pi}^{\pi}X\left ( e^{jω} \right ) e^{j\omega n}d\omega Euler's Identity...

Hello all, I've breadboarded a simple astable multivibrator to generate 38kHz (identical to http://upload.wikimedia.org/wikipedia/commons/6/6a/Transistor_Multivibrator.svg) using 2N3904s. Upon power up, it's a solid 38Khz. After 60 seconds, it's drifted up to ~44Khz... and stabilizes to...

Homework Statement Hi Everyone, I am trying to show why the given sum is zero. I am pretty sure it is zero. Homework Equations sin[8*\pi*n/5]+sin[12*\pi*n/5] n is an integer. The Attempt at a Solution n----sin[8*\pi*n/5]----sin[12*\pi*n/5] 0 ----...

Hi all I need some assistance 1. Homework Statement with the attempt How many 5-digit briefcase combinations contain 1. Two pairs of distinct digits and 1 other distinct digit. (e.g 12215) I wasn't sure on which approach was correct. 10 * 9 * 8 (because there are three distinct...

All analitic function can be express how: f(x) = \frac{1}{0!} \frac{d^0f}{dx^0}(x_0) (x - x_0)^0 + \frac{1}{1!} \frac{d^1 f}{dx^1}(x_0) (x - x_0)^1 + \frac{1}{2!} \frac{d^2f}{dx^2}(x_0) (x - x_0)^2 + \frac{1}{3!} \frac{d^3f}{dx^3}(x_0) (x - x_0)^3 + ... that is the taylor series of the function...

I am a math major and I need to take Methods of Discrete Mathematics. What is methods of discrete mathematics? Should I take it after My calculus series( including linear/ diff. equations)? Is it easy enough to take with Calculus 2? Thanks

Hello, I have a question I am trying to figure out how it works and I am so confused I need a break down of what is exactly going on with this problem the Question. "Concern three persons who each randomly choose a locker among 12 consecutive lockers" What is the probability that no two...

Homework Statement \sum_{x} x^k for k ∈ Q Homework Equations \sum_{x} x=\frac{1}{2}x^2-\frac{1}{2}x\sum_{x} x^2=\frac{1}{3}x^3-\frac{1}{2}x^2+\frac{1}{6}x\sum_{x} x^{-1}=\Psi (x) The Attempt at a Solution I don't know. There isn't way to compute the antiderivative of any function and I...

Homework Statement Suppose A={ø,1,2,{1,2},{3}}. Determine if each statement is true or false. Give a brief justification for your answers. (I finished the majority of them except for the last two) g) A-ø=A h) A-ø={1,2,{1,2},{3}} Homework Equations The definition of difference between...

Does anything connect the discrete wave functions? I thought they were suppose to be connected.

How to have better discrete math "insight" Greetings: I came a cross a textbook example in a discrete math book that I have been reading on my own, and I thought this example in the book was a good example of what I want to be good at: Given integers from 0-9 arranged in a circle, is...

Hello I am trying to solve this problem: A coin is given with probability 1/3 for head (H) and 2/3 for tail (T). The coin is being drawn N times, where N is a Poisson random variable with E(N)=1. The drawing of the coin and N are independent. Let X be the number of heads (H) in the N draws...

Why parity is discrete transformation? ##Px=-x## ##P\psi(x)=\psi(-x)## when ##x## is continual variable. Could you explain me difference between discrete and continual transformation?

I'm trying to prove that the discrete form of the Fourier transform is a unitary transformation So I used the equation for the discrete Fourier transform: ##y_k=\frac{1}{\sqrt{N}}\sum^{N-1}_{j=0}{x_je^{i2\pi\frac{jk}{N}}}## and I put the Fourier transform into a N-1 by N-1 matrix form...

Homework Statement is it possible to have a topological space that is neither the indiscrete nor the discrete, and very set in the topology is clopen? Homework Equations The Attempt at a Solution let ##X## = {(0,1),(2,3)} with the ordinary topology on R. (0,1) is open, but...

Hello Everyone! Homework Statement There exists a very large (discrete) system of N coupled masses, each of mass "m", where every pair is connected via a spring of constant "K". Assuming all motion is horizontal, find the amplitude of the oscillations of an nth mass in the system, under the...

I just want to make sure I understand the normal modes of a vibrating system of particles with discrete spacing. I have tried to drawn what I understand as the lowest and highest frequency mode of the standing waves. Is the drawing correct? Edit: actually I have drawn the maximum frequency where...

Hello! I was told, that there are no mainstream physics theories, in which time is discrete. My question is this: At any present or any given future scenario, there will always exist the smallest amount of time, that a machine is able to measure. How come this variable, is not a main...

Homework Statement There are a set number of marbles in a bag; the marbles consist of two colors. We are given the mean number of marbles of color 1 in the bag, as well as color 1's standard deviation. We are then asked to find the mean and standard deviation of color 2.Homework Equations How...

If two fair dice are rolled 10 times, what is the probability of at least one 6 (on either die) in exactly five of these 10 rolls? So this problem is hard to wrap my head around. I'm probably wrong on many counts, here's what I'm doing: Two fair dice are rolled 10 times but this question only...

Hi guys, I'm trying to solve the S.E. For a potential that's time dependent but the time variable is not continuous. Essentially the potential is a finite square well and it shifts over time but not continuously. I.e. At time 0<t<t' it's a finite square well centered about some x' At...

Consider a triangulated discrete manifold (a polyhedron) with known vertices (i.e. each vertex is given in terms of its $$(x,y,z)$$ coordinates ). Assign scalar values (some kind of potentials) to each vertex (i.e. at each vertex, a $$k_t(\mathbf{v})$$ is known through its value, no...

Definition: A subset $D$ of $\mathbb R$ is said to be discrete if for every $x\in D$ there exists $\epsilon>0$ such that $(x-\epsilon,x+\epsilon)\cap D=\{x\}$. Question: Does there exist a discrete subset $D$ of $\mathbb R$ such that the set of limit points of $D$ is an uncountable set. ___...

Corollary from book: if d= gcd(a,b), then there exists integers x and y such that ax + by = d. This is not an obvious statement to me. Are there any direct proofs to prove this statement? The book proves this by induction. My proof: Suppose d = gcd(a,b) and a and b are positive integers. a...

Hello. I am reading an introduction to induction example, and I am having the hardest time trying to determine what exactly happened in the proof. Can somebody please help? How can ##3^{k-1}## + ##3^{k-2}## + ##3^{k-3}## all of a sudden become ##3^{k-1}##+##3^{k-1}##+##3^{k-1}## and how can be...

Quantum Phys Homework: I am given a function: $$f(x)=\frac{1}{10}(10-x)^2\,;\,0\leq{x}\leq{10}$$ and $$f(x)=0$$ for all other \(x\). I need to find the average value of \(x\) where $$\bar{x}=\frac{\int_{-\infty}^{\infty}x\,f(x)\,dx}{\int_{-\infty}^{\infty}f(x)\,dx}$$ I am not really even sure...

Homework Statement Consider a discrete time birth and death process in which the maximal population size is N = 6. Birth rates and death rates are directly proportional to the current size Xt of the population at time t (t = 0; 1; 2; : : :). If the maximal population size is reached, no more...

Stuck on the induction step,please help

1. The problem statement, all variables and givenknown data We have a system of three atoms arranged in a circular arrangements. They each have a valence electron that can tunnel to the nearest neighbor. For a tunneling rate -A/\hbar we have the Hamiltonian (shifted by an energy E_a on the...

How would I go about solving this? We are starting to learn about venn diagrams so would creating a venn diagram be helpful? This is what I tried so far, I created a set C consisting of all people who have taken calculus and a set D consisting of all people who have taken discrete math...

Homework Statement Are these system specifications consistent? "Whenever the system software is being upgraded, users cannot access the file system. If users can access the file system, then they can have new files, then the system software is not being upgraded." Homework Equations p...

Homework Statement . Prove that a metric space X is discrete if and only if every function from X to an arbitrary metric space is continuous. The attempt at a solution. I didn't have problems to prove the implication discrete metric implies continuity. Let f:(X,δ)→(Y,d) where (Y,d) is...

The N real numbers x0, ..., xN-1 are transformed into the N real numbers X0, ..., XN-1 according to one of the formula by DCT. I would ask what is the benefit and why should we do that?

Homework Statement Using the rules of inference, prove that if ∀x(P(x) ∨ Q(x)) and ∀x((￢P(x) ∧ Q(x)) → R(x)) are true, then ∀x(￢R(x) → P(x)) is true as well. Homework Equations The Attempt at a Solution The problem arises step 5. I feel this is correct but the...

To give you a sense of strong induction and the relationship between mathematical induction and recursion (next session), let's do the pile splitting problem: Take a bunch of beads, rocks, coins, or any kind of chips. Ten is a good number. Split the pile into 2 smaller piles and multiply their...

I took f(t) = SIN(10*t) +SIN(5*t) and got this f(0) = 0 f(1) = -1.5 f(2) = 0.4 f(3) = -0.3 now I tried to do the DFT Fs = 4Hz N = 4 samples 3 f[r] = Ʃ x[k]ε^(-j(2πkr/4) k=0 f[r] = 0 -1.5ε^(-j(2πr/4) + 0.4ε^(-j(2π(2)r/4) -0.3ε^(-j(2π(3)r/4) f[0] = 0 - 1.5 +...

Homework Statement Determine the finite dimensionality of the following system: y[n] = nx[n] Homework Equations y[n]= f(y[n−1], y[n−2],..., y[n−N],x[n],x[n−1],..., x[n−M],n) Where N is how many dimensions the system has. The Attempt at a Solution I understand that the following system...

h is a constant in Planck's equation but I have not seen anything written saying that the frequency cannot be arbitrarily small, thus making E arbitrarily small. Is it that v is only allowed to be integral (after all, when we're measuring a frequency we're essentially counting how many times...