Discrete Definition and 829 Threads

Hi, I am a neophyte in Discrete Fourier Transform and I am procticing with discrete Sine-transform. Specifically I want to calculate $$ \mathcal{F}_s \lbrace x \cdot e^{-x^2} \rbrace = \int\limits_{0}^{\infty } x \cdot e^{-x^2} \cdot \sin\left(x\right)\, \mathrm{d}x = \frac{1}{2} \pi^2 \omega...

In the classical electromagnetic field theory, the field density of energy is given by: $$u = (\epsilon/2)E^2 + (\mu/2)H^2$$ One of the differences between the classical electromagnetic theory and the real world is that in classical EM all charge and current density, (ρ(r), J(r)), is...

I've read several articles discussing how Max Planck decided to assume that the energy radiated by oscillators in a black-body came only in discrete increments of En = nhf, where n is an integer. Using this concept, he determined that the average energy of an oscillator was given by...

Hi, this thread is an extension of this one: https://www.physicsforums.com/posts/5829265/ As I've realized that the problem is that I don't know how to properly use FFTW, from http://www.fftw.org. I am trying to calculate a derivative using FFTW. I have ##u(x)=e^{\sin(x)}##, so...

Hi. I was checking the library for the discrete Fourier transform, fftw. So, I was using a functition ##f(x)=sin(kx)##, which when transformed must give a delta function in k. When I transform, and then transform back, I effectively recover the function, so I think I am doing something right...

Hi, I am currently an undergraduate student and I plan on taking advanced math courses such as Abstract Algebra, Real Analysis, Complex Analysis, etc. There are two courses which I think could help me prepare for the courses above as they are proof intensive: discrete math and bridge to advance...

Consider the Gaussian position measurement operators $$\hat{A}_y = \int_{-\infty}^{\infty}ae^{\frac{-(x-y)^2}{2c^2}}|x \rangle \langle x|dx$$ where ##|x \rangle## are position eigenstates. I can show that this satisfies the required property of measurement operators...

Homework Statement [/B] I am trying to match each of the following 28-point discrete-time signals with its DFT: Set #1: Set #2: Homework EquationsThe Attempt at a Solution Set #1 We have already established (here) that: ##Signal 1 \leftrightarrow DFT3## ##Signal 4 \leftrightarrow...

Homework Statement Discrete time causal LTI system has impulse response h(n) = (-1/2)^n, n≥0. a)Find transfer function of given system. b)Find frequency characteristics of system. c) Find response for u(n) = μ(n)-μ(n-4) The Attempt at a Solution a) Either from definition, or from table...

Homework Statement Match each discrete-time signal with its DFT: Homework EquationsThe Attempt at a Solution I am mainly confused about Signal 7 and Signal 8. Signal 1 is the discrete equivalent to a constant function, therefore its DFT is an impulse (Dirac ##\delta##), so it corresponds...

If we assume that there is a fixed charged particle and another charged particle is spiraling down towards it, it emits electromagnetic waves as it is accelerated motion. We get a continuous spectrum. Now, if I allow the emitted photons to fall on a very photosensitive material, whose efficiency...

I'm considering taking the upper-level probability course at my school over the elementary course offered because of time constraints. The latter is not a prerequisite for the former. Do you think I will be alright taking the more advanced probability course over the elementary course? Any input...

Say you have two energy eigenstates ##\phi_1## and ##\phi_2##, corresponding to energies ##E_1## and ##E_2##. The particle has a 50% chance of having each energy. The wavefunction would thus be ##\psi=\frac{\phi_1}{\sqrt{2}}+\frac{\phi_2}{\sqrt{2}}## Even though the coefficients are normalized...

Homework Statement Prove by Strong Mathematical Induction[/B] Homework Equations N/A The Attempt at a Solution The steps to solving this problem are shown below. I understand all steps of the problem until the part where it says 44/49 becomes 49/49 since 44 < 49. Can someone please explain...

Hey everyone, Pardon the novel of a post. Short story: Got an 'A' in Discrete 1 (proof methods) using Epp's book at community college with an easier professor (the only offering for that course), and I'm understanding nothing to very little amount of information in Discrete 2 (computational...

Homework Statement Hi, As part of the proof that : the set of periods ##\Omega_f ## of periods of a meromorphic ##f: U \to \hat{C} ##, ##U## an open set and ##\hat{C}=C \cup \infty ##, ##C## the complex plane, form a discrete set of ##C## when ##f## is a non-constant a step taken in the...

Hello, Just a really quick question on definition of discrete subgroup. This is for an elliptic functions course, I have not done any courses on topology nor is it needed, and most of the stuff I can see online refer to topology alot, so I thought I'd ask here. I need it in the complex plane...

I am currently taking a course in discrete mathematics. The literature used is "Discrete Mathematics And Its Applications by Kenneth H. Rosen" 6th ed., or 7th ed. I have encountered most of the topics from that book. I.e. Logic, naive set theory, &c. What I have encountered also is the...

Homework Statement Let ##p## and let ##\nu : \mathbb{Q}^\times \rightarrow \mathbb{Z}## be defined by ##\nu (\frac{a}{b}) = \alpha##, where ##\frac{a}{b} = p^\alpha \frac{c}{d}##, where ##p## divides neither ##c## nor ##d##. Prove that the corresponding valuation ring ##R := \{x \in...

Homework Statement I watched two videos on KhanAcademy, one was about light interference with 2 slits and the other was with 4 slits. The video with 2 slits got a continuous spectrum whereas the one with 4 slits got a discrete spectrum. So my question is: how many slits does it take to get a...

Homework Statement 1. Why is the statement: " Vicky is not clever" Not a mathematical proposition? Provide examples please 2. Why is the statement: "a^2+b^2=c^2 an indeterminate proposition?" 3. Why is the negation of " If a triangle has two equal angles it is isosceles" = "Not all triangles...

I am looking for a way to think about this type of problem and this is not a coursework problem 1. Homework Statement How many cards from a 52 card deck of ordinary playing cards would you have to draw to have either a flush or 4 of a kind If you have a 30 6 sided dice, how many dice rolls...

Hi, I was wondering which course will be more beneficial to take first for a first year student majoring in computer science? Note: I tend to dislike proofs and theories. Discrete Structures - An introduction to the basic concepts of statistical analysis with special emphasis on engineering...

I was reading this article which talks about the theoretical model behind blackbody spectra: http://www.cv.nrao.edu/course/astr534/BlackBodyRad.html At the start, it mentions standing waves in a cavity. Standing waves in this model consist of an integer number of wavelengths. The standing waves...

Is there any way to convert a continuous, aperiodic spectrum, to a discrete spectrum, in a signal? If so, would part of he energy of this signal be lost, I am this process of conversion, or would it be " distributed" amomg the various frequencies?

Is Discrete Mathematics hard? Is it pure or applied math?

Theorem: Let ##A_1, A_2, ..., A_k## be finite, disjunct sets. Then ##|A_1 \cup A_2 \cup \dots \cup A_k| = |A_1| + |A_2| + \dots + |A_k|## I will give the proof my book provides, I don't understand several parts of it. Proof: We have bijections ##f_i: [n_i] \rightarrow A_i## for ##i \in [k]##...

Homework Statement We have JUST started writing proofs recently, and I am a little bit doubtful in my abilities in doing this, so I just want to verify that my proof actually works. I was expecting this one to be a lot longer since the previous 2 were. I don't see any glaring flaws in it, but...

Does anyone have recommendations for reading/resources on Discrete Exterior Calculus and/or Finite Element Exterior Calculus? In particular, I want to learn the topics to use in a project for a course and so would like to learn how to implement these methods (specifically geared toward...

Homework Statement The (computing) task at hand is to take a function f(x) defined at 2N discrete points, and use the Discrete Fourier Transform (DFT) to produce F(u), a plot of the amplitudes of the frequencies required to produce f(x). I have an array for each function holding the value of...

Hi All applications of discrete mathematics I know of seem to be in computer science. I want to know if there is somewhere discrete mathematics are applied outside of software. What can I work as if I like discrete mathematics but do not want to program? (outside of academia, of course)

Homework Statement [/B] This is a computing coursework problem. (There is a reasonably long theory preamble). Create a single slit centred on the origin (the centre of your array) width 10 and height 1. The array containing the imaginary parts will be zero and the array containing the real...

Dear PF Forum, Perhaps it's not a question, just a light discussion. Time From this, we get the standard time https://en.wikipedia.org/wiki/Caesium_standard, it's 9,192,631,770 ticks per second. I think this number should be discreet. No need to tune it to some figures after decimal point. Is...

The title more accurately should have been "How do you cancel floors and ceilings in discrete functions" For instance, ##\frac{log{\frac{3x}{-6(z)}}}{8t} < 1## If I wanted to get rid of the log, I'd just raise the expression by base 10. ##\frac{(\frac{3x}{-6(z)})}{10^{8t}} < 10^1## But what...

Hi, My classes don't start until next week and I am trying to get a head start in my linear algebra, discrete math and calc 3 class! I am using Discrete Math by Epp 4th edition. 1) I know 4 =/ {4} but why? 4 is a symbol representing the number 4, and {4} is a set with only one element which...

how to solve exercise (34) in discrete Math Adv Counting Techniques - see picture===> how apply the formula?

speed? This question emerged in my mind while studying a discrete and continuous mathematical model of a falling slinky. In the discrete model, we suppose an instantaneous interaction between mass points at a distance, so the action propagates through the chain of mass points with infinite...

Hi Physics Forums Is there a specific technique to measure how smooth a discrete function is? By smooth I mean that if you change the input by a minimum amount then you know that the objective function result will not have a big jump. For example The Closest String Problem is completely...

Homework Statement Suppose A⊂B⊂C. What is A/B, A/C, and A∪B Homework EquationsThe Attempt at a Solution This isn't really a homework question, I am just trying to get some exposure to discrete math before I take it in the fall. The set differences A/B and A/C are both empty sets and the 'or'...

Homework Statement Calculating the open loop output Impedance at 1kHz and the open loop differential gain The Attempt at a Solution Here is the approach. INPUT STAGE: Q111 and Q112 Av1 = Rtot/2re, where Rtot is the total resistance of R117 and the input resistance of Q78 which is Rin. So...

I just switched my major from chemistry to physics because I wasn't happy with the amount of math I was encountering as a physical chemist. So now I am going into a new major program and I am afraid of some of the courses I am about to take. Next semester I will be taking a math methods course...

I have been studying discrete mathematics for fun and I am kind of stuck on this bijection problem. 1. Homework Statement I wanted to apologize in advance if i put this homework question in the wrong part of the forums. Discrete Math and much logic math is a computer science type math of...

Hello, I'm about elaborating a discrete mass-spring model to describe the vibration of a thin isotropic plate. For the flexion i choose a kind of spiral spring in the two directions X and Y: so the momentums will be Mx= Cbx.(Delta Thêta) ; My = Cby.(Dela Psi). and the energies: Eb =...

Homework Statement In this exercise, we are given a discrete Lagrangian which looks like this: http://imgur.com/TL0P61r. We have to minimize the discrete S with fixed point r_i and r_f and find the the discrete equations of motions. In the second part we should derive a discrete trajectory for...

Hello, as a non-physicist enthusiast, but with decent math background, I tried to learn a bit about origins of quantum theory and very soon raised some questions, which I hope this community will answer. So, Planck tried to model the blackbody radiation on where Raighley and Jeans have failed...

This question is driving me crazy. According to the textbook, the answer is 7/15, but I get 2/5. If anyone can tell me where I am going wrong I would be much obliged Here is the question Six fuses, of which two are defective and four are good, are to be tested one after another in random...

Given a continuous random vector (X,Y) with a joint density function In order to check whether it is indeed a joint density ƒ(x,y) the method is to check if ∫∫ƒ(x,y)dxdy=1 where the integrals limits follow the bounds of x and y. However, is it the case that if given an arbitrary discrete random...

Homework Statement So I want to prove that the expression 20Cr×0.1r 0.9(20-r) reaches maximum value for r=(0.1)×20=2 Homework EquationsThe Attempt at a Solution I can prove it by trial and error but can't differentiate the expression because nCr isn't continuous.

Apologies if this question has been asked already. I've been given resources to help me understand, but it's been hard for me to wrap my head around the answer and, for that matter, it is difficult to understand a text when you have to look up every other word (an exaggeration, but you know ...

There is a table tennis tournament consisted of 8 participants that is guided by the following rules: 1. Each player plays with every other player for exactly one party 2. If in the i-round there was a party between A and B and a party between C and D, and A and C play In i+1, then in i+1...