Variables Definition and 1000 Threads

Examine for which u \in \mathbb R the series \sum\limits_{n=1}^\infty \frac {(1+(-1)^n)^n}{n^2} |u|^{\sqrt{n}(\sqrt{n+1})} converges. What I found out so far: (1+(-1)^n) alternates between [0;2], that means that the whole series becomes zero for the even n. The interesting part are the odd n...

Hi, So here's my latest problem as I get to grips with Mathematica. I will give a simpler version of the one I am actually doing. I started with a closed set of differential equations. Consider the following equations a'(t)=P*b(t) b'(t)=P^{2}*a(t) with known initial conditions and P is a...

qq- --->qq- differential cross section and mandelstam variables Homework Statement for the problem statement please look the attachement Homework Equations The problem is asking to express the mandelstam variables in temrs of the scattering angle θ.I would like to ask the quastion...

Okay, so we were doing forces, and my teacher had this question: In an atwood machine, a massless, non stretching string passes over a frictionless peg, one end of the rope is connected to object m1, and the other end to object m2 (heavier). When the system is released from rest, m2 goes...

Here is the question: Consider the experiment of rolling two tetrahedra that are unfair in the sense that each has the following probabilities for each of the four faces: P{1 dot}=1/10 P{2 dots}=2/10 P{3 dots}=3/10 P{4 dots}=4/10 Let X be the total of the outcomes in the two...

Homework Statement All variables are given in the pictures. Homework Equations Nothing more than simple force equations. The Attempt at a Solution I attempted it on my own, but I don't know if the answers are right.

Hi, I have a bunch of closed differential equations that I want to solve. The variables of the DEs are 2x2 matrices. So, I want to enter some 2x2 matrices of variables and then use NDSolve to get the solution. How should I define a 2x2 matrix with four variables inside it? I tried...

Everyday analogy why hidden variables can’t explain entanglement I tried to come up with an everyday “obvious” analogy that explains why a hidden variable theory cannot explain quantum entanglement. Here’s the story: There are two guests and one moderator on a stage. The moderator...

Homework Statement Homework Equations Assume the solution has a form of: The Attempt at a Solution It looks like a sine Fourier series except for the 2c5 term outside of the series, so I'm not sure how to go about solving for the coefficients c5 and c10. Any idea?

Hi, all I am looking into inverse cosine operations. I have a question like follows: Let x and y be two variables of degrees, how to separate equation arccos(x+y) into an equation that contains x and y separately? Such as arccos(x+y) = f1(...x) + f2(...y)? Thank you very much for your...

An interesting question has been posted in... Infinite Series Conditional Converging ... about the following two variables function... $\displaystyle \sigma(x,y)= \sum_{k=1}^{\infty} \frac{1}{(k+x)\ (k+y)}$ (1) ... and in particular it has been requested if the domain of $\sigma(*,*)$ must...

I'm completely lost on this probability problem, Homework Statement A Box contains 5 indiscernible CDs.It is known that among them 2 are for children .So in order to find the first children's CD ,they are tested one after the other (successively ),Denote by X the random variable which...

Given The 1D wave equations p_{x}'' - (1/c_{0}^2)p_{t}'' = 0 u_{x}'' - (1/c_{0}^2)u_{t}'' = 0 ρ_{x}'' - (1/c_{0}^2)ρ_{t}'' = 0 and linearised continuity and momentum equations ρ_{t}' = -ρ_{0}u_{x}', ρ_{0}u_{t}'=-p_{x} how may one derive the following two equations? u=p/ρ_{0}c_{0}...

Homework Statement Derive the Euler Equation of the dynamic programming problem: \[max_{\{ z_t \}^\infty_{t=0}} \sum_{t=0}^{\infty} \delta^t f(x_t, y_t, z_t) \] subject to: x_{t+1} = g_1(x_t, y_t, z_t), \ y_{t+1} = g_2(x_t, y_t, z_t), \ x_0 = x^0, y_0 = y^0 and where \delta <1...

Hello I have the limit lim (x^9 * y) / (x^6 + y^2)^2 (x,y)---> (0,0) when I use polar the final result is limit = lim (r^6 cos^9 (theta) sin (theta) ) / (r^4 cos^6 (theta) + sin^2 (theta)) r--->0 and substituting r = 0 , it will give zero * I tried it on wolfram...

Homework Statement Locate all relative maxima, relative minima ,and saddle points if any. f(x,y)=ysinx fx(x,y)=ycosx fy(x,y)=sinx ycosx=0 sinx=0 y=0 x=0,∏,2∏... up until infinity Critical points at (0,0),(∏,0),(2∏,0)... fxx(x,y)=-ysinx...

Homework Statement Let X,W,Y be iid with a common geometric density f_x(x)= p(1-p)^x for x nonnegative integer and p is in the interval (0,1) What is the characteristic function of A= X-2W+3Y ? Determine the family of the conditional distribution of X given X+W? Homework Equations...

Homework Statement f(x,y)= (4/5)(x+3y)exp(-x-2y) for x,y, >0 Find E[Y|X] Homework Equations E[Y|X] =integral y *f_xy (x,y)/ f_x (x) dy The Attempt at a Solution f_x (x) = integral [o,∞] [4/5](x+3y)exp(-x-2y) dx = (2x+3)/(5exp(x)) When taking the integral of y[(4/5)(x+3y)exp(-x-2y)] /...

Homework Statement let y_1 and y_2 be iid bin(5,1/4) random variables let v=y_1+2*y_2 and u = 3*y_1 -2y_2 find f_uv (u,v) and the cov(u,v) Homework Equations f_y (y) = (5 choose y) (1/4)^y (3/4)^5-x for x=0,1,2,3,4,5 covariance=E(uv)-E(u)E(v) The Attempt at a Solution...

Homework Statement Show that f(x) = x1x2 is a convex function on [a,ma]T where a \geq 0 and m \geq 1. Homework Equations By definition f is convex iff \forall x,y\in \Re \quad \wedge \quad \forall \lambda :\quad 0\le \lambda \le 1\quad \Rightarrow \quad f\left( \lambda x+(1-\lambda...

Hi, I have 3 correlated variables that I wish to model with a copula function. 2 of the variables are continuous and 1 is discrete. My question is, generally speaking can you model continuous and discrete variables within the same copula? Yes/No? Thanks

Hi, another thread talking sbout QM interpertations sparked my interest on the subject. Now let's assume that we have electrons in a box, it could be anywhere inside. And let us assume that the electrons do indeed have unique positions instead, that each electron has a set of three continuos...

Given $$ u(\xi,\eta) = F(\xi) + G(\eta) $$ and $$ \xi = x+ct\qquad\qquad \eta = x -ct. $$ How do we get to $u(x,t) = F(x+ct) + G(x-ct)$? I see that we can make the sub $$ u(x+ct,x-ct) = F(x+ct) + G(x-ct) $$ but how do I then get simply $u(x,t)$?

I had a question about about the integration measure for the path integral after a unitary change of variables. First they consider a 4D spacetime lattice with volume L^4. The measure is \mathcal{D}\phi = \prod_i d\phi(x_i) They expand the field variables in a Fourier series...

In the last question in this link: http://pages.uoregon.edu/csinclai/teaching/Fall2009/files/hw8.pdf 1) I did not understand how they got the region for y1, y2, and y3... 2) How would the solution be different (or not possible) if X1, X2, and X3 were not iid? Thanks in advance

Homework Statement I'm solving a problem where a conducting pipe with a square cross section is being analyzed to find the potential everywhere in space. The pipe lays along the z-axis, so we're really concerned with the x-y plane. My issue isn't so much the general solution via separation...

We have two independent random variables X and Y whose pdfs are given as f(x) and f(y). Now when you multiply X and Y you get a random variable say Z. Now what is the resulting pdf f(z)? I mean how is that related to the pdf of f(x) and f(y)? From what I read it looks like f(z)=f(x) *...

Homework Statement Find the third degree Taylor polynomial about the origin of f(x,y) = \frac{\cos(x)}{1+xy} Homework Equations The Attempt at a Solution From my ventures on the Internet, this is my attempt: I see that \cos(x) = 1 - \frac{1}{2}x^2 + \frac{1}{4!}x^4 - \cdots...

Homework Statement I have a question. How in general would one differentiate a composite function like F(x,y,z)=2x^2-yz+xz^2 where x=2sint , y=t^2-t+1 , and z = 3e^-1 ? I want to find the value of dF/dt evaluated at t=0 and I don't know how. Can someone please walk me through this?Homework...

Homework Statement Show (using the epsilon-delta method) that the ##\lim_{\substack{x\rightarrow a\\y\rightarrow b}} y = b ## Homework Equations Epsilon-Delta Definition ##\lim_{\substack{x\rightarrow a\\y\rightarrow b}} f(x,y) = L ## means that for every ##\epsilon## > 0, there...

Homework Statement I have a program which will sort out three inputted variables into order from lowest to highest. I now must get the program to work out if these 3 values could be the sides of a right angled triangle. Homework Equations I am going to use a^2+b^2=c^2 to solve...

Homework Statement V_o varies as V(t) = 2000e^(-100t) volts for t > 0 i1(0) = -6A i2(0) = 1A thus i0(0) = 5A Find i0(t) for t > 0. I found Leq = 4H V(t) = L di/dt I separated variables and integrated, got 5e^(-100t) but the software is telling me it's wrong... supposedly the answer is...

Homework Statement Find the maximum and minimum values of the function f(x,y,z,t)=x+y+z+t subject to the constraint x^2+y^2+z^2+t^2=400. Homework Equations I think the Lagrange multiplers can be used ∇f=λ∇g The Attempt at a Solution So I found ∇f=<1,1,1,1> and ∇g=<2x,2y,2z,2t> and...

Hi, I need your help, Say we have two random variables with some joint pdf f(x,y). How would I go about finding the pdf of their sum?

Derivative with "constant" variables Hi, I need some help figuring out this one situation that's got me thrown for a loop... not the first time, since my grasp of calculus is slippery at best. Homework Statement a and b are both positive constants Drag(D) = av^2+b/v^2 I'm trying to find the...

Hello Let's say we have some continuous i.i.d random variables X_1, \ldots X_n from a known distribution with some parameter \theta We then place them in ascending order X_{(1)}, \ldots X_{(n)} such that X_{(i)}, < X_{(i+1)}. We call this operation T(\mathbf{X}) where \mathbf{X} is our...

In the Equation E=hλ Could the variables be subsituted for other similar energy problems like E=mc2? Would then the energy of something be written as E=hm or E=λc2?

Solve for $x$: $$4x^2 +4xy - 6y - 9 = 9 $$

Homework Statement Given that f(x,y) = g(r,\theta), where x = r\cos\theta and y = r\sin\theta, find formulae for \frac{∂f}{∂x} and \frac{∂f}{∂y} expressed entirely in terms of r, \theta, \frac{∂g}{∂r} , \frac{∂g}{∂\theta} . The Attempt at a Solution I said \frac{∂f}{∂x} =...

Hi, it's me again, as you may know I've always have had a very hard time with circuit analysis. How can you possibly know which states variables are you suppoused to use in second or third order circuits?. Let's say you have to do the following exercise: If you want to obtain a...

Homework Statement Ok I have this function: f(x,y)=\sqrt{4xy-3y^2} And then I have to find the limit:\lim_{h\rightarrow +0}{\frac{f(h,rh)}{h}} Where r \in [0;\frac43] Homework Equations The Attempt at a Solution Well I must admit that I do not really understand the notation of this limit...

Homework Statement I have this function of two variables: f(x,y)=\sqrt{4xy-3y^2} Where I have to declare the domain of the function. Homework Equations Since you cannot take the square root of something negative, when dealing with real numbers. The square root has to be zero or...

Homework Statement ∫∫∫V 9z2 dxdydz, where V is the solid defined by: -1≤x+y+3z≤1, 1≤2y-z≤7, -1≤x+y≤1 Homework Equations The Attempt at a Solution I did this using the bounds, 1/3(-x-y-1)<=z<=(1/3)(-x-y+1), -x-1<=y<=1-x, -3/2<=x<=1/2 but I think the answer is wrong is there a better way to do...

Homework Statement ∫∫Se2x+3ydydx where S is the region |2x|+|3y|≤ 1 Homework Equations The Attempt at a Solution So I've done this two ways and gotten two different answers and I'm not sure which is right. I used change of variables where where u=3y+2x and v=3y-2x and I got an...

Homework Statement Given the function Study its continuity Homework Equations The Attempt at a Solution I don't know how to solve this function. Normally I'd try to prove the limit doesn't exist by getting different results trough different ways. However, in this function...

I'm trying to make up an automatic spreadsheet for my Physics students so they can enter the data and see everything calculated for them, but I ran into a snag. I have two random variables, h and t with uncertainties Δh, and Δt, respectively. The uncertainty in h is simply estimated, based...

Homework Statement I have a parallel plate capacitor of area A, width d, potential difference V between the plates, and it is disconnected from the source of emf. A wire of resistance R is placed between the plates to allow a current to flow. Draw a sketch to show how the voltage, current and...

I just encountered a limit-problem [1] which is supposed to lack a limit: x*y*e^(-(x+y)^2) as x^2+y^2 approaches infinity and e is the base of the natural logarithm. My approach was to express x and y in terms of polar coordinates, where x = r*cos(t) and y= r*sin(t). I got the following...

Hi, The question is the following: Another student proposes that c is proportional to d0.5 State a suitable graph that can be plotted to test this proposal. I suggested plotting log c = 0.5 log d. One of the answers the markscheme accepts is log c = log d Can anyone tell me why my...

Homework Statement Find the gradient of the function at the given point. Then sketch the gradient together with the level curve that passes through the point. g(x,y) = x2/2 - y2/2; (√2, 1)Homework Equations ∇f = (∂f/∂x)i + (∂f/∂y)jThe Attempt at a Solution ∇g = <x, -y> ∇g(√2, 1) = <√2, -1>...