Terms Definition and 1000 Threads

I"m starting to suspect that the existence of time is contingent upon the expansion of the universe. In other words, were the expansion to cease, time itself would come to a halt. As we know, as space accumulates thru expansion, time also accumulates. Thus, the space/time continuum is in fact...

Express Max height in terms of g and T?!? I need to express the y_max in terms of g and T... do i need to put in my V_0y value? or leave it as a variable? i've tried V_0y*T + 1/2gT^2

Homework Statement Show that the series \displaystyle\Sigma_{n=1}^{\infty} \frac{(-1)^n}{n} is not absolutely convergent. Do so by permuting the terms of the series one can obtain different limits. Homework Equations The Attempt at a Solution I don't have a total solution...

The terms "function" and "map". I have noticed that the term "map" is used more often than "function" when a map/function is defined using the "mapsto" arrow, as in "the map x\mapsto x^2 ". It has occurred to me that when a function is defined this way, it's usually not clear what the codomain...

So I've been stuck on this problem for hours, I just can't seem to put the pieces together... Homework Statement Two basketball players of equal height, (and jumping with same initial velocity, etc.) by jumping they raise their centers of mass the same distance "H". The first player (A)...

Homework Statement L = \frac{a}{\sin{\theta}} + \frac{b}{\cos{\theta}} find L in terms of a and b where L is a maximum ... Homework Equations place long list of trigonometric identities here??The Attempt at a Solution so my attempt looks something like this: as a cause of the chain rule...

Any suggestions on how to simplify the log (m+1) terms that arise when proving the following statement using induction for m >= 1? (log to the base 2) [PLAIN]http://dl.dropbox.com/u/471735/recurrence%202.png

Could you please help me understand how these terms relate to one another? Scalar, Vector, Displacement, Distance, Speed, Velocity, Accelaration, Position? So Distance is a scalar Quantity, what is a Scaler? Displacement is a vector quantity, what is a Vector? Is velocity just the unit...

Homework Statement sum of first 11 terms of Ap is 17 and sum of first 17 terms is 11 find the sum of first 28 terms?Homework Equations Sum=n/2[2a+(n-1)d]The Attempt at a Solution i tried solving it by using obove formula but i am not able to do so as the value of d is coming in fraction

How could you describe qualitatively how diffraction of a wave through a aperture in terms of the uncertainty principle? Cat

Hello, do you have a hint on how to solve this limit? \lim_{x\to +\infty}(\sqrt{x^2+ax+b}-\sqrt{x^2-ax+b}) Thanks!

Hi, I'm am trying to calculate the radius of curvature of a trajectory in a plane. I am using Frenet-Serret formulas and perpendicular bisector approach to calculate the radius. It comes out that both the approaches lead to same answer when I calculate the radius for a trajectory generated...

Or provide any additional information or resources about them? I'm thinking about how light would react when passing through certain substance/or geometric medium 3 concepts come to mind when considering the idea 1 the light (beam, frequency notwithstanding) enters a prism and is...

Homework Statement The problem is in the attachment along with my answer. Can please one check if I got a correct answer? Some sources say the answer is 2Pi instead of just Pi. Homework Equations The Attempt at a Solution

So, the common high school physics example of a transverse wave is a "stadium wave" ... but, I'm wondering if this is actually longitudinal in terms of particle transmission. Each particle (audience member) is only standing up/down. The particles/audience stay in place and don't propagate/run...

Homework Statement Find x and y in terms of a and b from the following equations x * √x + y * √y = a x * √y + y * √x = b Homework Equations the general algebra equations The Attempt at a Solution adding the equations (x + y) * (√x + √y) = a + b x + y = a + b...

Hi everyone, nobody seemed able to answer on the PDE mathematics forum so I am posting here. I could use some help to validate (or invalidate) and improve my equations as I am trying to model 2D heat dispersion in a Spa. Basicaly my model consist of some air inside a cabinet, the cabinet is...

I'm reading a QFT text right now and to fully understand the physical perturbation theory method I would like anyone to suggest a refrence or supply an example of a calculation using the physical perturbation theory: As an example to start a discussion consider. L = \frac{1}{2}((\partial...

Hi, How can I write, for instance, the square root of (a2 + b2) in another form? Is there another expression which equals √(a2 + b2), and is it possible for that expression to have its √() holding one term whereas other factors exists outside the √() in that expression... Thanks...

edit: Oh nuts, embarrassing typo. Should be "...rearranged in terms of y" Ok, I swear this isn't homework but if it seems too much like homework I'm happy to have it moved there. So I need to be able to find x given y in: y = 1/(1+x)^x Possibly important: y will always be between 0 and 1 and...

um, I'm having a hard time understanding some terms and equations in semiconductors, particulary 2 equations and 1 term(fermi function,density of state function, and fermi level). My understanding of fermi function is somewhat the probability of an energy state to be occupied by an electron. for...

As it says in the title, will anyone please give me the equation (in pre-algebraic terms) for discrete choice probability? I can see that the equation is P = Prob( Person n chooses Alternative i ) = G(xni, xnj(forall j inequal to i), sn, β), where xni is a vector of attributes of...

I have been researching generators lately, whilst contemplating building my own wind powered generator. I think I understand the general layout: a central magnetic core that rotates with an outside ring of conductive coils spun in specific alternating turns with their own magnetic cores. If I am...

The terms "length contraction" and "time dilation" Is there a particular reason why we say length contraction but time dilation? A Lorentz transformation \Lambda=\gamma\begin{pmatrix}1 & -v\\ -v & 1\end{pmatrix} takes \begin{pmatrix}1\\ 0\end{pmatrix} to \gamma\begin{pmatrix}1\\...

sum up the series : 1/(1.3.5)+1/(3.5.7)+1/(5.7.9)+.......n terms.

Homework Statement Hi, I need to find the spectrum of the following function: i=I_0[e^{\frac{-0.01(cos(2\pi 1000t)+cos(2\pi 100000t))}{0.026}}-1]Homework Equations the Fourier Transform would be: \int_{-\infty }^{\infty }I_0[e^{\frac{-0.01(cos(2\pi 1000t)+cos(2\pi...

http://upload.wikimedia.org/math/1/9/8/1983171154842b0b061fc42aa5eb7642.png" How to rewrite this 2D Gaussian eqn in terms of x? i need to calculate the x and y values. let x0=0 and y0=0. is it complex?

I understand why dE=TdS-PdV ...[1] at constant temperature and pressure Also, I see that F=E-TS and therefore dF=dE-SdT-TdS ...[2] and how combining [2] and [3] gives dF=-SdT -PdV QUESTION: shouldn't [1] be expressed as dE=TdS+SdT-PdV i.e if you're going to substitute...

For instance: 1/(e^.5t) + 1/(e^-7t) As t grows larger, the left term goes to 0, but the right term goes to infinity. Would I be correct in saying that the limit of the sum is infinity because the (absolute value of the) coefficient of t in the term that tends to infinity is larger than...

Homework Statement Put in general terms 1, 1, -1, -1, 1, 1, -1, -1, ... Homework Equations The Attempt at a Solution obviously (-1)^n, alternates 1, -1, 1, -1... I have no idea how to figure this out. I thought it might have a sin function in it possibly. Thanks a lot for...

Homework Statement Find the explicit formula c1=1, c2=2, cn+1 = (cn + cn-1)/2 ; n>2 Homework Equations The Attempt at a Solution c1 = 1 c2 = 2 c3 = 3/2 c4 = 7/4 c5 = 13/8 c6 = 27/16 c7 = 53/32 c8 = 107/64 I know the bottom term is 2^n-2. I cannot find what the top...

Does anybody help me how to find the average (expectation) of terms involving double summation? Here is the equation which I'm trying solve. [\tex]E\Big[2\sum_{k=0}^{N-2}\sum_{j=k+1}^{N-1}f(k,j)\cos[2\pi(j-k)t-\theta_{k,j}]\Big][\tex] where f(k,j) and [\tex]\theta_{k,j}[\tex] are some...

This is a question about solving Einstein's Field Equations for some simple cases, but I'm not sure how to explain this without analogy. So bear with me for a brief discussion. Consider the electrostatic equation: \nabla^2 V = \rho / \epsilon_0 which show explicitly how the charges source the...

Hi everyone. I believe to have read somewhere (but now I can't find it) that any operator in QM is expressible in terms of the x and p operators. Obviously the spin operator is not, so this is not entirely true. But can we say something along those lines? Which operators are expressible in...

The Von Neumann entropy is \mathcal{S}(|\psi\rangle) = -Tr[\rho_a ln \rho a] . The linear entropy S_L = \frac{l}{l-1}(1 - Tr[\rho_a^2]) For l =2 the linear entropy is written 4Det(\rho_A) which is also called the tangle \tau. I understand this just fine, I can show that. Now it says the Von...

Can anyone give some help on how I should go about creating a formula for this problem? Bob creates a new shade of paint by mixing black, red and white paint. He uses x litres of black paint. He uses 5 times as many litres of red paint than he uses of black paint. He uses 12 more litres of...

Homework Statement By first expressing the general term in partial fractions, find an expression in terms of n for summation of r=2 to n ( 1 / (r^2 - 1) ). Hence show that summation of r=1 to n ( 1 / r^2) i less than 7/4 for all values of n Homework Equations The Attempt at a...

Homework Statement Hi, I have this function: f(x ) = 0 (x is irrational) or f(x) = 1/q for rational p/q in lowest terms. show that this function is not differentiable anywhere The Attempt at a Solution This is the answer from the solutions book: consider [(f(a+h) - f(a ) ) /...

Hello everyone, Can someone please tell me what is the meaning of "lumped" term in heat transfer? Regards Huygen

Homework Statement Hi. Find the sum of the first 10 terms in the series: 1, (ln2)/1!, (ln2)^2/2!, (ln^3)/3!... Homework Equations I guess the Maclaurin series, which is e^k = 1, k/1!, (k^2)/2!, (k^3)/3!... In my case, k = ln2. The Attempt at a Solution I tried to use the sum of the first...

Homework Statement This is actually part of a probability problem I'm thinking about. I'm trying to find the nth moment of a certain random variable in terms of the gamma function, which is basically equivalent to solving the following integral or expressing it in terms of the gamma function...

Homework Statement a)find the velocity when x = 3, b)find the time taken to travel between x=1 to x=3. when x = 1, v = 0 Homework Equations a=2x The Attempt at a Solution a)using the chain rule I got v = 2x^2 + u (u as a constant), but I think that's wrong. i tried using...

Hi this is the question, I already finished it basically, there is just one small thing I am unsure about So I let that equation be F, and I found Fy, it is Zeyz-x2z/y...so I know this equation can't equal zero if I want there to be a solution for y in terms of x and z, my question is what I...

Hello, I have a long equation and using Mathematica 7 I want to factor out terms such as x,y,xy, x^2y,xy^2, etc. so that I'll have it in a form similar to a + b*x + c*y + d*(xy) + e*(x^2y) + f*(xy^2) + ... I've tried using the Collect by passing {1,x,y,xy,x^2y,x y^2,...} as the terms to be...

Homework Statement Use double-angle and addition formulæ and other relations for trigonometrical functions to find an expression for sin(3x) in terms of sin x alone. My problem is I don't know what is meant by "find an expression for sin(3x) in terms of sin x alone.". I know the relevant...

Homework Statement The first 3 parts of this 4 part problem were to derive the first 5 Hermite polynomials (thanks vela), The first 5 Legendre polynomials, and the first 5 Laguerre polynomials. Here is the last part: Write the polynomial 2x^4-x^3+3x^2+5x+2 in terms of each of the sets of...

Im attempting a problem in relativistic optics that's asking me to write k_x, k_y and k_z in terms of lambda, c, and theta (theta being the angle between a source and an observer, at rest relative to each other). Lamda is the wavelength in this reference frame. I started off using trigonometry...

Homework Statement Hi, How do i determine de result in terms of x of this series for x < 1: (Sum(i=0..+infinity; i*x^i))/(Sum(i=0..+infinity;x^i) Thanks The Attempt at a Solution I know that (Sum(i=0..+infinity;x^i) will tend do 1/(1-x) but i don't know what the numerator...

What restrictions must we place on a real-valued function F for F(x) = \frac{d}{dx} \int_a^x F'(y)dy to hold, where "\int" is the Lebesgue integral?

Hello; What is colour? Is it like the charge between quarks? I can't conceptually understand it, probably because of the wording. Thanks.