Property Definition and 635 Threads

Mean Value property (harmonic functions) with a source?? Homework Statement I understand that the heat equation may yield ∂u/∂t=0 on the LHS and on the RHS we may still have Uxx+Q where Uxx is partial with respect to x twice and Q is a heat source. U in our case may be the temperature...

Homework Statement Suppose that f is holomorphic in an open disc U and that Re(f) is constant in U. I have to show that f must be constant in U. Also what is the essential property of the disc U that it used here? Give an example of an open set U for which the conclusion fails.Homework...

Homework Statement proof if f(n) = O(g(n)) then g(n) = O(f(n)) = stands for element of c is some constant Homework Equations if f(n) <= c*g(n) then f(n) = O(g(n)) if g(n) <= c*f(n) then g(n) = O(f(n)) The Attempt at a Solution I tried to go from the left-hand-side(LHS) to the...

My book defines the covariant derivative of a tangent vector field as the directional derivative of each component, and then we subtract out the normal component to the surface. I am a little confused about proving some properties. One of them states: If x(u, v) is an orthogonal patch, x_u...

I'm wondering if there's a term for the property of spheres that makes gravity pull equally on all aspects of the sphere's mass. The wording for what I'm asking is tricky, so I'll give an example of a shape that wouldn't have this property, a long prism. If you drop a long prism on an angle...

Homework Statement Hi, We meet again PF, this time I am little stumped on the following question(link posted down). Homework Equations Link to the question "Question" The Attempt at a SolutionI think I get the gist of it for part (i) my calculated value for equlibirum separation is about...

Homework Statement G=\{x\in R|0\leq x<1\} and for some x,y\in G define x*y=\{x+y\}=x+y-\lfloor x+y \rfloor Homework Equations The Attempt at a Solution I want to proof Associative property: x*(y*z)=(x*y)*z \Leftrightarrow x*(y+z-\lfloor y+z \rfloor)=(x+y-\lfloor x+y \rfloor)*z \Leftrightarrow...

Does anyone know what the physical property measured in seismic surveys is? Seismic surveys used in searching for hydrocarbons to be more specific. I was thinking it would be the rocks density but I'm not sure, can anyone help please? :)

Edit: I answered my own question, I guess this thread serves no purpose so mods, you can delete this. y = x^2 ln y = ln x^2 ln y = 2 ln x Can we do the same thing with: y = x^{2/x} ln y = ln x^{2/x} ln y = \frac{2}{x} x Would that be correct? I just want to make sure because I used this...

Hi. I just saw on wikipedia that natural logarithm has such a property: [x/(1+x)] < ln (1 + x) < x (http://en.wikipedia.org/wiki/Natural_logarithm) Can anyone pls tell me how to prove this? Proving [x/(1+x)] and ln (1 + x) less than 'x' is easy.. But how abt [x/(1+x)] < ln (1 + x)...

Hi, If we have two commuting operators A and B, is true that any function of A will commute with any function of B? I have a result which takes [L_{z},r^{2}]=0 and claims that [L_{z},r]=0. How can this be proved? Thank you

1. The problem I have a problem grasping what the point of the sifting property of the Dirac function is. It isolates the value at a point in a function, right? Doesn't just substituting that point into the function do exactly the same thing? Homework Equations Sifting poperty: if f(t)...

I have a question. I understand that one of the main problems with a theory of everything is the unification of gravity with the other three forces. Could this be due to the fact gravity may not be a force at all but a property of space? If Einstein essentially defined gravity as such, then why...

Homework Statement F-1 is the quantile function of a general random variable X and has the following property that is analogous to the property of the c.d.f. Prove: Let x0 = limp→0,p>0 F-1(p) and x1 = limp→1,p<1 F-1(p). Then x0 equals the greatest lower bound on the set of numbers c such that...

Hi, this is my first post, and I'm not an expert of any kind or do not believe I am. I have always been fascinated by science, but I some time ask myself some questions, here's one I don't seam to find much info. I found a lot of treads that mentioned the subject but nothing that actually...

Homework Statement N refers to the set of all natural numbers. Part 2: From the previous problem, we have σn : N → N for all n ε N. Show that for any n ε N, σ(n+1)(N) is a subset of σn(N), where we have used n + 1 for σ(n) as we defined in class. 2. The attempt at a solution For Part 2, I...

Homework Statement Working on some Laplace transforms, and my lack of knowledge of some properties of exponential functions is coming back to bite me(again). I'm stuck trying to figure out if: e^(-pi*s) - e^(-2pi*s) = e^(-pi*s - (-2pi*s)) Is a true statement or not. I've searched...

Why is it that a metric space (X,d) always has two clopen subsets; namely {0}, and X itself? Rudin calls it trivial, and so do about 15 other resources I've perused. What confuses me is that if we define some metric space to be the circle in ℝ2: x2+y2 ≤ r2, then points on the boundary of...

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...

Is discreteness a topological property? Hey guys. I'm currently in an advanced calculus course (not topology), and the only mention of topological property in my text is that it's a property that is conserved under continuity. This section is just a brief primer on compact sets and...

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...