Separation Definition and 448 Threads

Homework Statement if \nabla^2u = 0 in 0 \leq x \leq \pi, 0\leq y \leq \pi, boundary conditions u(0,y)=0, u(\pi,y)=cos^2y, u_y(x,0) = u_y(x,\pi)=0 Homework Equations I am required to show that u(x,y) = \frac{x}{2\pi} + \frac{cos2ysinh2x}{2sinh2\pi} The Attempt at a...

Can I separate water from Carbon tetrachloride by the method of fractional distillation? (I agree separating funnel is a better method)

For conventional PDEs like diffusion, waves, it seems the standard way to solving them is in two steps. 1. Use separation of variables method to make them into ODEs 2. Use eigenvalues and eigenfunctions theory on ODEs to construct the final solution consisting of an infinite number of...

If two objects move away from each other in opposite colinear directions at the speed of light. How long will it take for the light from one of the objects to reach the other? I think the answer is never, but not sure.

"Use separation of variables to find particular solutions of u_t-u_{xx}-2u_x=0, 1<x<2, 0<t, u(1,t)=u(2,t)=0 hint: change coordinates" I can't find the solution. The equation seems already separated, so all I need to do is to find a change of variables, I think. But I can't find one that...

Let be the integral equation: g(s)g(p)g(u)= \int_{0}^{\infty}dx\int_{0}^{\infty}dy\int_{0}^{\infty}dzK(sx)K(py)K(uz)f(x,y,z) then my question is if we could "seek" for a solution in the form: f(x,y,z)=A(x)A(y)A(z) where the function A satsify (for x y and z) the integral...

http://album6.snapandshare.com/3936/45466/844588.jpg

xdv/dx=(1-4v^2)/3v I used separation of variables to get x/dx=(1-4v^2)/3v dv I'm not sure if that's even right. But if it is right, how do I integrate that?

In Metric units: A vapor-liquid separator drum is a vertical vessel into which a liquid and vapor mixture (or a flashing liquid) is fed and wherein the liquid is separated by gravity, falls to the bottom of the vessel, and is withdrawn. The vapor travels upward at a design velocity which...

Two boats leave the shore at the same time and travel in the directions shown. If v_A\,=\,20\,\frac{ft}{s} and v_B\,=\,15\,\frac{ft}{s}, determine the speed of boat A with respect to boat B. How long after leaving the shore will the boats be 800 ft apart...

Is this for real? http://www.smh.com.au/news/national/laser-enrichment-could-cut-cost-of-nuclear-power/2006/05/26/1148524888448.html

I'm sure most people are familiar with the 6 degrees of Kevin bacon game. Here's something for folks to have fun with. The rules are: 1) You must name 2 relatively well known celebreties who have both appeared in at least one theatrical movie (i.e., not made for TV nor TV series). 2) You...

Hello, Could someone please help me to simplify my solution to my ODE? Here is the solution I get when I check it using Maple 10, http://img524.imageshack.us/img524/415/ode2hx.jpg Here are my steps: \left( {1 + x^3 } \right)\frac{{dy}}{{dx}} - 3x^2 y = 0 \left( {1 + x^3...

My text doesn't seem to talk about average separation of molecules, so I can only get so far with this problem. Help would be appreciated. The problem reads: From the average separation between air molecules at STP, and their mean speed, estimate how long it would take one molecule to move...

I never thought I would see this day. Oh well. http://www.washingtonpost.com/wp-dyn/content/article/2006/03/21/AR2006032101723.html" Granted that previous administrations gave taxpayer money to organizations allied with them, atleast on social issues, it promoted the separation of the church...

ive done a test were, i get someone to try and distinguish to lines that are 0.25mm apart from varying distances. then I am going to do some kind of calculation to tell me somthing (hopefully) and i have done this experiement in different light levels, controlling the lux. and i have...

hi i have been trying to solve the diffusion equation using separation of variables. i know the answer should turn out something like the normal probability density function but its just turns into a mess when i try it. i am given the following information: \frac{\partial p}{\partial...

1] Is the placenta and cord an extension of the fetus or of the host? We were talking about this, and have tentatively concluded that the DNA of placenta and cord would reflect the fetus rather than the host. This came up in a discussion about 'two vessel cord'. I was wondering if that would...

Hey, I need some guidance in this problem. Consider a rocket taking off vertically from rest in a gravitational field g, the equation of motion (which I had to derive in the previous part of this problem) is: m \dot{v} = -\dot{m}v_{ex} - mg where m is the mass of the rocket...

Slve by separation of variables \frac{\partial u}{\partial t} - k \frac{\partial^2 u}{\partial x^2} = 0 for 0 <x < pi, t > 0 u(0,t) = u(\pi,t) = 0 u(x,0)= \Sin^2 x let u (x,t) = X(x) T(t) \frac{X''}{X} = \frac{T'}{T} = -\lambda = \mu^2 also lambda must be positive...

we are given the laplacian: (d^2)u/(dx^2) + (d^2)u/(dy^2) = 0 where the derivatives are partial. we have the B.C's u=0 for (-1<y<1) on x=0 u=0 on the lines y=plus or minus 1 for x>0 u tends to zero as x tends to infinity. Using separation of variable I get the general solution u =...

I am to reduce the following PDE to 2 ODEs and find only the particular solutions: u_tt - u_xx - u = 0; u_t(x,0) = 0; u(0,t) = u(1,t) = 0 I guess u = X(x)T(t), and plug u_tt, u_xx into PDE and divide by u to get: T''/T = X''/X + 1 = K I solve X'' + (1-K)X = 0 first. From...

A telescope has an objective mirror of 6m. An astronomer uses it to determine if a certain object is a binary star, i.e. two stars in orbit around a common point. If the object is 25 light years away (a light year is the distance light travels in one year) what is the minimum separation of...

Oh boy...this problem has stumped me. I am not even sure I know where to start: The potential energy of a diatomic molecule (a two-atom system like H2 or O2) is given by U= (A/r^12) - (B/r^6) where r is the separation of the two atoms of the molecule and A and B...

:confused: I aim trying to do a problem where I have 2 Equatorial Coordinates, and I need to find the angular distance in between this two points. Thanks in advance. :confused:

I have this Physics Problem which I am not to sure where to start it from. The problem is: A real inverted image I of an object O is formed by a certain lens. The object-image speration is d = 0.40m, measured along the central axis of the lens. The image is just half the size of the...

I missed this class the other day and my prof isn't answering his email right now so I thought I'd ask it here. I want the answer to the question, but really I'm looking for the relationship between the values. Q: A star located 135 degrees from the solar apex on the celestial spehe is at...

How do separation axioms carry over to subspaces? Some are clear -- it's easy to see that if any two points of a space X are separated by neighborhoods, then the same must be true of any subset S of X. But what about the nicer ones? Is it true that if S is a subset of a normal space, that...

is any other chemist on here familiar with trying to separate isomers? I hate how tedious it is, after I run a silica gel column, I have to take each fraction evaporate the eluent, dissolve what is left behind in methanol, prepare LC/MS sample, and wait 3.2 min for each sample to run in order to...

I'm working on a problem that has me baffled mathematically. What equation can I use to calculate the future distance between two galaxies not gravitationally bound receding at a Hubble constant of 70km/sec/Mpc as a function of time. Stated in another way, if two distant galaxies start off...

I'm trying to track down a quantitative proof that the most uniform magnetic field between two Helmholtz coils occurs for a separation equal to their radii. So far I've just been playing around with the Biot-Savart law and proving that B is identical at several trial points along the axis...

Separation of Church and State..."May God Bless"...the rest of us? In the wake of the 2004 election, last count was that the IRS was investigating 60 religious organizations for endorsing Bush from the pulpit. The mixing of religion in politics has become a much more serious problem then most...

Could some kind chemistry pro here tell me the energy required for molecular separation of water into H and O2? Thxs. :smile:

Let c' be the separation vector from a fixed point(x'',y'',z'') to the point (x,y,z) and let c be its length. show that Gradient(1/c) = -c'(hat)/c^2 Thnaks for the help

Hi, In physics, many PDEs' equation can be reduced to a number of ODEs' equations by "Separation of Variables". According to my knowledge, "Separation of Variables", it just subsitutes the function, for example F(x,y,z), by a product of three function, X(x)Y(y)Z(z). Why does it work? I mean...

QM field separation "principle" I came across a term called "QM field separation "principle"" (or theorem, method etc.) and was left thinking, whether this is simply identifiable to general representation of fields (tensor ones typically) as a sum of their symmetric and antimetric components...

Personally, I believe this firmly, but I'm interested in seeing what some of you people who use "secularist" as a dirty word think of the topic, and how you can defend religious involvement in governmental policy... Paz, Jacob

Explain how a polar solvent works in the separation of polar dyes? How might chromatography be useful in forensic science? i only thing i can think of is figuring out what pen the criminal used... i really need help on this... :rolleyes:

A brick is resting atop a piston that is moving vertically with simple harmonic motion of period 1.08 s. At what amplitude will the brick separate from the piston? I came across this question reviewing for my test next Thursday. Anyway, I can calculate the angular frequency using the...

I was wondering if someone could take the time to explain why linear and angular momentum are two separte things that can never be converted from one form to another. Thanks

The final conversatation between Doc Al and Russ_Watters in post 78 in the Speed of light thread went as: Reading this last post led me to question whether the conversation between Doc Al and Russ_Watters ought not be left unanalyzed. I had finished reading the entire thead earlier and began...

I read from a website that the electric field is independent of the separation between the plates if the separation is negligibly small. But how to derive this?

two problems in particular, one i got in calc, the other in physics one asks if a = -v and v = 1 when t = 0 what is a possible position function for this equation the other one is given a = 3x and starting at rest from x = 0 find the velocity at 5 seconds i can't seem to...

Okay, I'm hoping someone here can explain this homework qustion I've got bcause we don't seem to have anything in our notes that covers it, so any help would be great- thanks! Potassium fluoride (K+F-) is an ionic crytal having density 2.48x10^3 kg/m^3 Assuming that the diameters of the K+...

I'm getting tired of waiting. I'm not that smart in science, but I have done a couple of very remarkable engineering feats, and I have figured out what happens when points have distance between them. If you look at the screen that comes up between screens on this website, the screen with a...

This hypothesis basically states that any 2 people on Earth are connected by no more than six levels of acquaintances.

"In God we Trust" I'm sure that this topic came up before, but i cou;detn find it in the search so... I was just talking to a friend and some how we got on the topic of separation of church and state. We both agreed that it is not seprate and the way poloticians who representg our country...

Discuss... (Hell, at least it isn't another thread about Iraq or Israel!)