Discrete Definition and 897 Threads

I am dealing with (below) and r > 0 $$ N_{*} = \frac{rN_*}{(1 + aN_*)^b} $$ So the steady states are $N_* = 0$ and $N_* = \frac{\sqrt[b]{r} - 1}{a}$. Let $f(x) = \frac{rx}{(1 + ax)^b}$. Then $f'(x) = (ax + 1)^{-b}\left(\frac{br}{ax + 1} + (1 - b)r\right)$. Evaluating the derivative at $N_*$...

The book works out the case with x and y irrational and xy rational. They used the nonconstructive existence proof method with x = sqrt(2) and y = sqrt(2). If that's rational, then you're finished. If it's irrational, then you can simply raise it to the power of sqrt(2) to get 2. I'm not sure...

"For the router to support the new address space it is necessary that the latest software release be installed." I said Q: The latest software released be installed R: The router to support the new address space. I interpreted this as Q is necessary for R, therefore R => Q. The professor has...

Homework Statement Use the equivalence p\rightarrow(r \rightarrow s) \equiv p\wedge r\rightarrow s to rewrite the following problem before the proof. Homework Equations [p\rightarrow (q\rightarrow r)]\wedge (p\rightarrow q) \tautologicallyimplies (p\rightarrow r) The Attempt at a...

The population of a certain species subjected to a specific kind of predation is modeled by the difference equation $$ u_{t+1}=\frac{au_t^2}{b^2+u_t^2}, \quad a>0. $$ Determine the equilibria and show that if $a^2 > 4b^2$ it is possible for the populationto be driven to extinction if it...

So the book is showing an example about discrete steady states but neglected to show how the steady states were found. Here is what it has $u_{t+1}=ru_{t}(1-u_t), \quad r>0$ where we assume $0<r<1$ and we are interested in solutions $u_t>0$ Then it list the steady states $u^*=0, \quad...

Here's the problem. Theorem: If n^2+1 is odd, then n is even. Give indirect proof.

How to solve log10000000 base is 10.

How to solve log100000000, base is 10.

What if: There are only discrete protons in the atomic nucleus combined with electrons (not the orbital ones) being shared,in some random manner, leaving a net positive charge. The two particles only become discrete with the known different characteristics when the atom is "smashed" and a...

Q 1. On a circular island we build n straight dams going from Sea to sea, so the ever two intersect but no three go through the same point. Use Euler’s Formula to determine how many Q 2. Into how many parts do two quadrilaterals divide the plane, If (a) They are convex (b) They are not...

Homework Statement Homework Equations BIBO stability requires, for every input, that the system output y(n) is: |y(n)| ≤ By < ∞ Linear time invariant systems are BIBO stable when: Summation from -∞ to ∞ |h(n)| ≤ Bn < ∞ The Attempt at a Solution For part a, I got the...

I am currently a CS undergrad. my university offers no courses in Abstract algebra or Number theory or Topology or Analysis. recently I have got interested in Number theory in Discrete math course. moreover I was and still am interested in algebra too. but the problem is, can I apply to CS grad...

Hi guys, Long time lurker of this forum, but first time poster. Discrete Math is going to be the end of me; I'm just not understanding how to solve problems and write the proofs. Any help would be greatly appreciated. Thanks in advance. The Problem: Let nεZ≥1. Show that...

Prove that (A n B) - C = (A - C) n (B - C). n = intersect ≠ε = not a member I got the first one by doing: (xεA ^xεB) ^X≠εC ( by identity law and compliment law) where would I go on from now?

Ceiling = "{" & "}" Floor = "[" & "]" f(X) = [ 1/2 - {x/3}] How would I graph this function? Note: If the decimal is floors it will be rounded down , if the decimal is ceiling it will be rounded up. ~Thanks.

Hello Forum, a continuous time, continuous amplitude sinusoid like sin(2pi*f*t) is 2pi periodic: sin(2pi*f*t)=sin(2pi*f*t+m*2pi) where m can be any positive or negative integer. Let's sample the sinusoid at a sampling frequency fs (sample interval is ts=1/fs) and get the discrete signal...

the discrete time system defined by y[n]= x[n] ^ 2 Is it time varying ? I proceeded as follows x[n] → x[n]^2 x[n+a] → x[n+a]^2 so y[n+a] = x[n+a]^2 So according to me it is time invariant Am i right ?

Homework Statement Find all subrings of \mathbb{R} which are discrete subsets Homework Equations For the purpose of our class, a ring is a ring with identity, not necessarily commutative. The Attempt at a Solution First suppose that S\subset \mathbb{R} is a subring of \mathbb{R}...

Say that there is a random variable X ~ U(a,b) where U is the discrete uniform distribution on integers on the interval [a,b]. Sample n such variables with the same (unknown) parameters a and b. Using those samples it's possible to estimate the mean either by taking the sample mean (sum the...

Hi, Suppose we have these two functions and their z-transforms are P(r,z)=\sum_{t=0}^{\infty}P(r,t)z^t and F(r,z)=\sum_{t=0}^{\infty}F(r,t)z^t. Now we are going to transform the following convolution of P and F: \sum_{t'\le{t}}F(r,t')P(0,t-t'). The result is said to be F(r,z)P(0,z). But I don't...

I want to do a discrete Fourier transform of the solution I have found using NDSolve, however, because the NDSolve creates Interpolating functions rather than numbers I can't do this. Any help is appreciated. I've attatched the file I'm working with. Catrin

String field from Loop SpinfoamQG:how to build SM matter on discrete quantum geometry note: EPRL is the current standard spinfoam formulation of Loop Quantum Gravity. http://arxiv.org/abs/1201.0525 String Field Theory from Quantum Gravity Louis Crane (Submitted on 2 Jan 2012) Recent work...

Hi, I need help in proving the equation in the attachment. Thanks darkfeffy

Hi all, I am currently doing my Final Year Project on the topic of Optimal Placement of Suicide Bomber Detectors. Given 2 dependent bomb detectors, I am trying to prove that the probability of detection in the intersected area will be larger than the individually covered areas, by working...

Hi, I’m looking for a way to combine two discrete random variables (which I have as probability distributions). The combination should be the product (or other operation) of the two variables. This would be easy if they were independent, but they’re not. There is a known correlation between...

Can someone the following steps of this solution for me? http://imageshack.us/photo/my-images/828/80685231.jpg/ Mainly how they got their initial conditions? The 7.30 equation is just h[n-m] = bm which doesn't help me much. For our problem, I know that n=3 and m =1 since the LHS...

Homework Statement Let the DTFT (Discrete time Fourier transform) of a signal beY(f)= {1 0≤lfl< \frac{fs}{8} {0 OtherwiseCalc y(k) Homework Equations y(k)=\frac{1}{f_{s}}\int Y(f) e^{jk2\pi fT}df lkl≥0 The Attempt at a Solution So what I understand from this is that my Y(f) is basically 1...

Did this as a homework problem, got it wrong obviously. Not too sure how to solve it otherwise Homework Statement Let f be a function from A to A. Prove that for all m,n ε N, f^m*f^n = f^(m+N) Homework Equations The Attempt at a Solution f^(m+1) f^(n+1) = f(f^m) * f(f^n) =...

Hi. I wanted to know in what way the group of translations on a real line with discrete topology (let's call it Td) will be different from the group of translations on a real line with the usual topology (lets call it Tu)? Is Td a Lie Group? Will it have the same generator as Tu?

Homework Statement Figure out a self-referential formula for the number of handshakes required for a group of n aliens to introduce themselves by hand-calculating a few small values and coming up with a solution. Homework Equations We are given: Let H(n) be the number of handshakes...

I know that an atom "absorbs" a particular frequency of energy depending on which element and which electron in this element. The question is (for example) if we take one known emission frequency from a particular element, and use that exclusively to bombard another element for a lower...

Homework Statement Question 1: a) Suppose you have brought four pens of different colours to the exam. For each of the ten question on the exam, you choose one pen. In how many ways can this be done? b) In how many ways can you distribute six bananas and five oranges between three children...

Homework Statement Using contradiction, prove that for every four positive real numbers c, d, e and f, at least one of c, d, e, f is greater than or equal to the average of c, d, e, f. Homework Equations I don't believe that there are any relevant equations for this problem. I do know that...

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 If a signal f1[n] begins in a moment N1 and ends in moment N2, and signal f2[n] begins in the moment M1, and ends in the moment M2, derive the formula which states in which moment begins and ends the signal f1[n]*f2[n] Homework Equations The Attempt at a Solution 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...

From a pdf textbook: Example (infinite sets having the same cardinality). Let f : (0, 1) → (1,∞) be defined by f(x) = 1/x. Then f is a 1-1 correspondence. (Exercise: prove it.) Therefore, |(0, 1)| = |(1,∞)|. Exercise. Show that |(0,∞)| = |(1,∞)| = |(0, 1)|. Use this result and the fact that (0,∞)...

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...

Homework Statement X is a random variable with moments, E[X], E[X^2], E[X^3], and so forth. Prove the following is true for i) X is discrete, ii) X is continuous Homework Equations E[X-mu]^4 = E(X^4) - 4[E(X)][E(X^3)] + 6[E(X)]^2[E(X^2)] - 3[E(X)]^4 where mu=E(X) The Attempt at a...

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...