Property Definition and 608 Threads

Homework Statement Define the numbers G_n = \prod_{k=1}^n (\prod_{j=1}^{k-1}\frac{k}{j}). (a) Show that G_n is an integer, n>1; (b) Show that for each prime p, there are infinitely many n>1 such that p does not divide G_n. Homework Equations The Attempt at a Solution I can see that the...

Hiya guys, I've just started a project, of which the aim is to develop a thermodynamic property database for hydrcarbon fuels. I've been asked to start by reading up on the maxwell relationships and clapeyron equation etc. so hopefully this will give you an idea of what I am trying to...

Homework Statement I decided to cram these two unrelated question into one post, because they are too small and I don't want to crowd the forum with my many little bitty questions. 1. log(base A) of B= 1/[log(base B) of A] because: if log(base B) of A=C, then B^C=A and so B=A^1/C...

This is similar to the question However, it is slightly different. It's probably more of a philosophy of math topic, however, I posted this on a philosophy forum and can't find many people interested in math there. I hope it hasn't been overly discussed. Thank you for reading even if you don't...

As we know, plastic is non-conductor, iron metal is conductor, does anyone have any suggestions on what kind of property in term of molecule structure allows electricity to get through? Thanks in advance for any suggestions

This isn't really hw. I need someone to explain a certain line in a proof: " b2 \leq \frac{1}{n} for all n in the natural numbers. This implies that b2 \leq 0 (a consequence of the Archimedean property). " I don't see how the Archimedean is applied in this context. This is my understanding...

Homework Statement Use part (a) to prove the Greatest Lower Bound Property. (a): If M is any upper bound for A, then: x\in(-A), -x\inA, and -x\leqM. Therefore x\geq-M, hence -M is a lower bound for -A. By the Least Upper Bound Property, inf(-A) exists. If inf(-A) exists, then...

Homework Statement I tried to work out the FT of a sin function with a time delay using first mathematical manipulation, and then using the time shifting property. However I get two very similar, but for some reason not identical answers. Homework Equations Please open the .jpg to...

Hi There The associative property of convolution is proved in literature for infinite interval. I want to prove the associative property of convolution for finite interval. I have explained the problem in the attached pdf file. Any help is appreciated. Regards Aman

Homework Statement Suppose B_t is a Brownian motion. I want to show that if you fix t_0 \geq 0, then the process W_t = B_{t_0+t} - B_{t_0} is also a Brownian motion.Homework Equations Apparently, a stochastic process X_t is a Brownian motion on \mathbb R^d beginning at x\in \mathbb R^d if it...

Homework Statement The problem is to find sufficient and preferably also necessary conditions on random variable X such that its characteristic function g(x) satisfies the limit property: \lim_{t\to0}\frac{1-g(\lambda t)}{1-g(t)}=\lambda^2 I may assume X is symmetric around 0, so the...

Ok so the ideea of the proble is the following.F:A->B...where A={1...k} and B={1...n}.The problme is divided in 2 parts. The first part of the problem asked me to write in terms of k and n the formulas for the number of functions,number of injective functions,number of increasing...

Dear Friends, I'm would like know classic problems about parity property, in other hand, classic problems that has in your solutions, in any way, issues about parity. I want investigate issues about the use of parity in distributed algorithms. Anybody can help me? Thank's.. Nulll

3^3 = [3^3 - 3^2] +[3^2 - 3^1] + [3^1 - 3^0] + 3^0 Practical Demonstration: 27 = [27-9] + [9-3] + [3-1] + 1 27 = 18 +6+2+1 27 = 27 Is this property discussed in theory of games?

Hi! While studying a text " A First Course in Real Analysis" by protter, I've been asked to prove a property of riemann stieltjes integral. The propery is as follows ; Suppose a<c<b. Assume that not both f and g are discontinuous at c. If \intfdg from a to c and \intfdg ffrom c to b exist...

Homework Statement In an experiment we were given a broken piece of alluminium that was (before broken) 50mm long. Then we measured it and found the elongation. From this it is pretty easy to calculate the strain. What does this actually tell me about the material though?. Actual Question...

I'm not physicist, but a software developer. Please don’t hang up.:smile: I am building massive multiplayer online game server, and I started building it from scratch. I found that some programming issues emerged from it which had striking resemblance to quantum quirkiness, so I just wanted to...

Hi everybody, I'm newbie and I would like to have your opinion on the following issue (I've search in past topics but could not find anything relevant): I am very close to finish my PhD and as major outcome I've developed some IT tools which can be quite appealing for industry. I am...

Homework Statement Does [0,1] \times [0,1] in the dictionary order have the least upper bound property?Homework Equations Dictionary Order. (on \mathbb{R}^2) Let x , y \in \mathbb{R}^2 such that x=(x_1 , x_2) and y = (y_1 , y_2). We say that x < y if x_1 < y_1, or if x_1 = y_1 and x_2 < y_2...

I do not understand the proof of Proposition 0.16 in Allen Hatcher's book Algebraic Topology. If someone has the book, could you please clarify the part of the proof when he says "If we perform the deformation retraction of X^n\times I onto X^n\times\{0\}\cup (X^{n-1}\cup A^n)\times I during...

Is the following system stable. If so how. y(t)= \frac{d}{dt} x(t)I have tried the following proof but i think it is wrong. PROOF: The System is LINEAR The system is time invariant So on applying the stability criterion for LTI systems ie . \int^{\infty}_{-\infty} h(t) dt < \infty...

Hi all According to the textbook Signal and Systems by Oppenheim (2nd edition) pages 685 and 686, if the Laplace transform of x(t) is X(s) with ROC (region of convergence) R, then the Laplace transform of x(at) is (1/|a|)X(s/a) with ROC R/a. Consequently, for a>1, there is a compression...

Homework Statement Prove that \displaystyle \int_{-\infty}^{\infty} \delta (at - t_0) \ dt = \frac{1}{ | a |} \int_{-\infty}^{\infty} \delta (t - \frac{t_0}{a}) \ dt For some constant a. The Attempt at a Solution Edit: Looking at this again, I really don't understand where this is coming...

I don't know how to construct formal proofs but there is the obvious geometric approach for 2 and 3 factors. However, how do you prove the commutative property holds up for 4+ factors? You end up with a lot of different orders in which you can multiply the factors and you can't just construct a...

Hello everyone, :smile: The creator of C++ is Bjarne Stroustrup. It is his invention. Who really owns C++? Is it its inventor? It should be its inventor because he invented it so he should make money out of it like Microsoft does out of its Windows. Tell me please. Many thanks for every help...

Homework Statement Prove the statement http://www.mathhelpforum.com/math-help/vlatex/pics/60_32c8daf48ffa5f233ecc2ac3660e517e.png The Attempt at a Solution I am clueless as to how I would go about doing this, I know the basic properties. I think it has to do with using epsilon...

Homework Statement Consider the ellipse r(t) = <acost, bsint>, for t between 0 and 2PI, where a and b are real numbers. Let Θ be the angle between the position vector and the x-axis. a) Recall that the area bounded by the polar curve r = f(Θ) on the interval [0,Θ] is A(Θ) = (1/2) ∫...

Homework Statement \int_{0}^{1} \int_{0}^{1} (xy) dx dy = [\int_{0}^{1} (x) dx] [\int_{0}^{1} (y) dy] Its use to prove the convolution formula.. Homework Equations The Attempt at a Solution

I was walking through my house the other day and noticed a circle of light on the wall. I traced it back to a nearby window, but noticed that the opening was square. When I put my hand close to the opening, the light made a square, but as I walked backwards and kept my hand in the path of the...

Hello, this might be a silly question for many of you. How would you prove that: (a^{x})^y = a^{x\cdot y} when a,x,y are reals and a>0. The case for x,y integers is easy to prove, but how would you extend the proof to real numbers?

Dear Colleagues, I would like to submit to your court the article in which we attempt a physical analysis of living matter. Biology is a very difficult field for physics as a result errors are very likely. We would appreciate guidance on possible errors. Prokhorenko DV and Matveev VV. The...

This is not a homework problem. I came across this in an analysis book: In a complete ordered field (not specifically R) a member that is not zero is positive ⇔ this member is a square. WHY? How can we prove it? Is this similar to Hilbert's 17th problem?

Can somebody give me an example of a definite integral satisfying this property? :

dear friends, i've noticed that the main feature of my inner experience is the sense that something exists, and that the main feature of my outer experience is the sense that something is solid, and I've wondered if these two experiences might be two views of the same thing: solid existence...

Homework Statement Show that the operation of taking the gradient of a function has the given property. Assume that u and v are differentiable functions of x and y and that a, b are constants. Homework Equations Δ = gradient vector 1) Δ(u/v) = vΔu - uΔv / v^2 2) Δu^n = nu^(n-1)Δu...

Homework Statement \int_{0}^{\infty } e^-^x dx = -\frac{1}{e^x} \Biggr|_0^\infty = 0 + 1 = 1 Notice that I abused \frac{1}{\infty} = 0. My question is, when we compute integrals, why do we ignore the fact that \frac{1}{\infty} = 0 is not a limit?

Homework Statement prove that 2√2 <= ∫(from 0 to 1) (√x+8) dx <= 3 Homework Equations The Attempt at a Solution well...my only idea on how to solve this would be to evaluate the middle term, but my prof says it's not allowed. Do I just assign functions to the left and right...

Homework Statement Prove that Hausdorff is a topological property. Homework Equations The Attempt at a Solution For showing that a quality transfers to another space given a homeomorphism, we must show that given a Hausdorff space (X,T) and a topological space (Y,U), that (Y,U)...

Homework Statement I recently saw a youtube video in which someone filled a cup with water and created a vacuum with a piece of cardboard. Then, he transfers it to a table and removes the cup using a twisting motion. The end result is the water retaining the form of a cup. Is this actually...

A light source emits light in all directions, and the light travels at light speed, yet when we shut off this light source, all the light rays immediately disappear. I just thought about this and it just seems so strange. When we think of a sound source, we can shut off the sound source but the...

Homework Statement Prove that if A: V - >V is a linear map, dim V = n, and h1,...,hk (where 1,...,k are subscripts) are pairwise different eigenvalues of A such that their geometric multiplicities sum to n, then A does not have any other eigenvalues. Homework Equations Note sure if this is...

Does the Archimedean property work for unbounded sets? My book does a proof of the Archimedean property relying on the existence of sup which relies on the existence of a bound.

Homework Statement I was wondering how I could prove the following property of 2 antisymmetric tensors F_{1\mu \nu} and F_{2\mu \nu} or at least show that it is correct. Homework Equations \frac{1}{2}\epsilon^{\mu \nu \rho \sigma} F_{1\rho \sigma}F_{2\nu \lambda} + \frac{1}{2}\epsilon^{\mu...

Suppose the functions f(t) and g(t) are periodic with periods P and Q, respectively. If the ratio P/Q of their periods is a rational number, show that the sum f(t)+g(t) is a period function. How to prove this?

how do you prove the sign-preserving property? it says here that. If f is continuous at a, and f(a) < 0, then there is an open interval I containing a such that f(x) < 0 for every x in I. For a proof, simply take the open interval (2f(a),0) for the challenge interval "J" in the...

"Antimatter": Property Or Label? I am interested in learning whether a particle’s status as "matter" or "antimatter" is an independent property of that particle, a constellation of other properties or a (somewhat nonspecific) designation. Opinions are welcome if a definitive answer has not...

Say I have a molecule with two metal centers and some bridging ligands binding the two metal centers, how do I know whether the molecule is ferromagnetic or antiferromagnetic (or neither)? What exactly dictate whether this molecule would be ferromagnetic or antiferromagnetic?

1. The function f(x) is not defined for x = 0. It has the property that for all nonzero real numbers x, f(x) + 2f(1/x) = 3x. Find all values of a such that f(a) = f(-a) 2. The function f is defined by f(x) = (ax+b)/(cx+d), where a, b, c, and d are nonzero real numbers, and has the properties...

I came across of an equality which I have difficulty to understand. If f_n is a rational algebraic homogeneous function of degree n in the differential operators and if g_n is a regular non-differential homogeneous function of the same degree n, following equality takes place [Hobson: The theory...

Hello. I need some help to prove the first property of the density matrix for a pure state. According to this property, the density matrix is definite positive (or semi-definite positive). I've been trying to prove it mathematically, but I can't. I need to prove that |a|^2 x |c|^2 +...