Relation Definition and 1000 Threads

Hi I'm doing Fourier analysis in my signals and system course and I'm looking at the solution to one basic problem but I'm having trouble understanding one step Can anyone explain to me why becomes From Eulers formula: http://i.imgur.com/1LtTiKX.png for example the Cosine in my problem. I...

Ultra cold atom is achieved by laser cooling. For optical lattice, it is achieved by the interference of counter-propagating laser beams. What is the relation between Ultra-cold atom and optical lattice? Why do people load Ultra-cold atom in optical lattice? Thank you for your answer.

Hello Want to know if constant speed of light is a result cause by time dilation? When your time slow down as you approach speed of light you take a longer time to measure light speed in your spaceship, there for you think speed of light relative to your current speed is still c? When one...

So I am given B=\begin{array}{cc} 3 & 5 \\ 5 & 3 \end{array}. I find the eigenvalues and eigenvectors: 8, -2, and (1, 1), (1, -1), respectively. I am then told to form the matrix of normalised eigenvectors, S, and I do, then to find S^{-1}BS, which, with S = \frac{1}{\sqrt{2}}\begin{array}{cc} 1...

Homework Statement I am wondering what is the relation of sinθ & time of flight in projectile motion with angle. (under the case of same velocity) Is the graph of this in a parabola shape?? Homework Equations t = (2u sinθ) / g (u in constant) The Attempt at a Solution would it be...

This is a question out of model theory. (This preamble is due to the fact that "model" and "theory" are used in different ways in different fields.) Is there any specific relationship between two theories which have the same models? A knee-jerk reaction would be to say that they are isomorphic...

Homework Statement Find a recurrence relation for the number of stricly increasing sequences of positive integers that have 1 as their first term and n as their last term, where n is a positive integer. that is, sequences a1, a2, ..., ak, where a1 = 1, ak = n, and aj < aj+1 for j = 1, 2...

Homework Statement Hi guys, I'm stuck at some step in a QM exercise. Here it is: Consider a free particle of mass m that moves along the x-axis (1 dimensional). Show that ##\frac{dA}{dt}=\frac{2 \hbar ^2}{m^2}\int \frac{\partial \psi}{\partial x} \frac{\partial \psi ^*}{\partial...

I am trying to figure out the torque vs weight relationship. I am working on a software project where I want to create an application to determine the maximum payload on vehicle with rubber tyre on asphalt road. I am having three parameter 1. Torque 2. RPM 3. Diameter of tyre based on...

What is the relation between the pressure that is exerted on the internal walls of a cylinder and the characteristics of a flow of water running inside it? Let's assume that the flow velocity is constant and that we have an inviscid flow of pipe flow type. Furthermore let's assume that the...

Hello all, Is the following equality true \int(f(x))^*\,dx=\left(\int(f(x))\,dx\right)^*. Thanks

In GR for orbits about a central mass in the Schwarzschild metric one can show that \dot r^2 = \frac{E^2}{m^2 c^2} - (1-\frac{r_s}{r})(c^2 + \frac{p_\phi^2}{r^2}). where E=-p_t, r_s is the Schwarzschild radius and 'dot' represent differentiation with respect to proper time. Similarly for...

The integral form of Ampere's law in vacuum is ∫B\cdotdl=μ_{0}I (a) Using the relation between I and J, obtain the differential form of Ampere's law. You may ignore any displacement current. (b)Define the displacement current density J_{d} in terms of the displacement field D and show...

Homework Statement I have seen case studies of the 3D Debye model where the vibrational modes of a solid is taken to be harmonic with dispersion relation \omega = c_sk. It is said that for temperatures much less than the Debye temperature, the heat capacity at constant volume C_V\sim T^3...

Regarding the relation between atoms' kinetic energy and the energy levels of their electrons upon excitation: In other words, what really happens when an atom is excited, either by radiation or by collisions, or otherwise ? What are the mechanisms under which the transferred energy goes to...

When making the transition from the dispersion relation for a beaded string to the relation for a continuous string, I'm confused about the following issue. Take a to be the spacing between beads, m the mass of each bead, and T the tension in the string. We assume these to be constant. For the...

Hey PF, I'm just being stupid today, because I can't figure out the way HR diagram is constructed, hope you guys can help. So suppose that you complete an observation in several different filters, and you need to work out the luminosity and temperature for each object in your field of view...

Hi all, so my question is can i carryout normal algebraic operations on derivatives, for example: v=ds/dt and a=dv/dt then eliminating dt a=(dv/ds) *v then, a *ds= v*dv is that how you derive the relationship between acceleration, velocity and displacement?

Here is the question: Here is a link to the question: Equivalence Relation question? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement A particle moves counterclockwise around the ellipse with equation 9x^2 + 16y^2 = 25. a). In which of the four quadrants in dx/dt > 0? Explain. b). Find a relation between dx/dt and dy/dt. c). At what rate is the x-coordinate changing when the particle passes the point...

Please help me in proving the following expression $$H_{2n}(x)=(-1)^n2^{2n}n!L_n^{-\frac{1}{2}}(x^2)$$ where $$H_n$$ is the Hermite polynomial and $$L_n^{-\frac{1}{2}}$$ is the associated Laguerre polynomial.

https://www.google.com/search?hl=pt-PT&q=potential+energy+curve&tbm=isch&tbs=simg:CAQSWgmiv8BdfMuabhpGCxCwjKcIGjQKMggBEgzUBt8GogeoB6cHpgcaINsvJGealnimdPrsI3wtVoz6gqeyB8qrabdVeAx3e1vHDAsQjq7-CBoADCGpFP3k7rrt1w&sa=X&ei=sW4uUd7TDY6xhAelv4CIDg&ved=0CCYQwg4&biw=1366&bih=643#imgrc=or_AXXzLmm6FRM%3A%3Bq...

Here is the question Here is a link to the question: 2nd order homogeneous linear recurrence? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

For part b), I can see that, as p = \frac{E}{c}, then a photon with twice the momentum must have twice the energy. However, I cannot see the answer to part a). My book states that k_2 = 4k_1, but I would have thought that, as per the answer to b), the KE is just twice that of the other, not four...

I know that function is a type of relation. What i acctually need to know is that; Are these relations Equivalent all the times?, or it depends on the types of function?

hey all i know and understand the component of curl/line integral relation as: curlF\cdot u=\lim_{A(C)\to0}\frac{1}{A(C)} \oint_C F\cdot dr where we have vector field F, A(C) is the area of a closed boundary, u is an arbitrary unit vector, dr is an infinitely small piece of curve C my...

A hot-air balloon has just lifted off and is rising at the constant rate of 1.8 . Suddenly one of the passengers realizes she has left her camera on the ground. A friend picks it up and tosses it straight upward. If the passenger is 3.1 above her friend when the camera is tossed, what is the...

Homework Statement 'Show that row equivalence is an equivalence relation'. Homework Equations The definition for 'row equivalence' given in the text is, 'two augmented matrices corresponding to linear systems that actually have solutions, are said to be (row) equivalent if they have the...

Homework Statement let X = {1,2,3,..,10} define a relation R on X x X by (a,b)R(c,d) if ad=bc. show that R is an equivalence relation on X x X. Homework Equations The Attempt at a Solution I think that the R have to be reflexive (because ad=bc). Eg. one of the subset is (1,1)...

Homework Statement (b) A steel alloy has an ultimate tensile strength of 820MN/m2 and a fatigue endurance limit of 390MN/m2. The steel is used in a fatigue application in which the alternating stress is 0.3 times the mean stress. Using the Goodman method with a factor of safety of 1.5...

Dear ForumersI am having a bit problem understanding the phase relation between current source and the generated eletromagnetic field components. Assume a very small current element( a very small current running in direction x)(essentially an electric dipole) in a non-homogenous loss periodic...

One of stokes relation is that r=r'. What does this mean exactly? Is the phase difference between incident beam and reflected beam on a boundary between 2 mediums of different refractive indices ∏??

Homework Statement A planet orbits a massive star in a highly elliptical orbit, i.e, the total orbital energy is close to Zero. The initial distance of closest approach is 'Ro'. Energy is dissipated through tidal motions until the orbit is circularized with a final radius of 'Rf'. Assume the...

Can we approach spin by gradient. For example, spin 1/2 can be written as 180 degree turning in 360 degree space while spin 2 is 720 degree turning in 360 degree space? If I have a ball spinning with angular momentum perpendicular to rotation plane, what is the spin value of the ball? Can some...

Homework Statement This is part of the derivation of the direction of rotation of an ellipse in EM wave polarization. I need to find the direction of the change of phase \psi of the electric field vector with increase of time t. To make the long story short, for example: \psi\;=\...

Let A ∈ Mn×n(F ) Why dim span(In, A, A2, A3, . . .) = deg(mA)?? where mA is the minimal polynomial of A. For span (In,A,A2...) I can prove its dimension <= n by CH Theorem but what's the relation between dim span(In,A,A2...)and deg(mA)

1. The problem statement: Show that if the operator relation e^(ipa/ħ)xe^(-ipa/ħ) = x+a holds. The operator e^A is defined to the ∞ e^A= Ʃ(A^n)/n! n=0 [Hint: Calculate e^(ipa/ħ)xe^(-ipa/ħ)f(p) where f(p)is any function of p, and use the representation x=iħd/dp]...

On a smooth triangulation of a manifold differential forms can be viewed as real cochains by integration. The wedge product of two forms gives another real cochain. So does their cup product. - are they cohomologous? - Is there a limiting process that relates them?

I posted a link to this topic, so the OP could find my response. Here is a link to the original question: Recursive formula help on real world situations? - Yahoo! Answers Let $A(t)$ represent the amount, in mg, of antibiotic in Jonah's bloodstream at time $t$, measured in hours. With a...

Can the Planck relation, and the Heisenberg and the time-energy uncertainty principles be derived, or produced, from the equations of General Relativity?

Finally I found the time to write my account on the interpretation of the Heisenberg uncertainty principle vs. the question whether it can be interpreted as Heisenberg did in his very first paper on the subject. Although it is well known that this interpretation is not compatible with quantum...

Hi, The Fourier series can (among others) expressed in terms of sines and cosines with coefficients a_n and b_n and solely by sines using amplitudes A_n and phase \phi_n. I want to express the latter using a_n and b_n. Using a_n = A_n \sin(\phi_n) \\ b_n = A_n \cos(\phi_n) I...

Hey All! My question is regrading a subtle observation that i made when i was straing at my "spring coil type" room heater. Accidently i pulled up some stands of heating coil spring to make them straight section (obviuosly when it was switched off). Then, when i passed current through it...

I have a very trivial question to ask and it would be great if someone could help me in this. The statement that '3-point amplitudes' and the location of poles are sufficient to determine any n-point amplitude at tree level is confusing to me. Don't I also need to know 4-point amlitudes, for...

What is the commutator [\hat{A}\hat{B}, \hat{C}\hat{D}] equal to? How to distribute what's inside?

Hello, What does the Faber Jackson relation tells? Does it establish the relation between: higher the Luminosity, higher the velocity dispersion? Does it calculate in Elliptical galaxies? What does Tully-Fisher relation explains? -- Shounak

what is the "form" of the following recursion relation? Hi all, I have a recursion relation I am trying to solve: {X_n} = \frac{1}{{1 - {\alpha _0} \cdot {X_{n - 1}}}} \to {X_n} = ? What is the "mathematical form" of this recursion-relation? E.g., I know what a homogeneous, linear...

May I know what is the difference between the dispersion relation for 100 and 001 on the E-K diagram? Can i say 001 has lesser dispersion? But why is it so?

Homework Statement Find all the primes p and q such that p^2-p-1=q^3 The Attempt at a Solution Trying out the first prime number 2, it is clear that p>q and that the difference is larger than 1. Then when factorizing it p^2-p=q^3+1 \Rightarrow p(p-1)=(q+1)(q^2-q+1), I get that p must...

Homework Statement Find the matrix that represents the given relation. Use elements in the order given to determine rows and columns of the matrix. R on {2, 3, 4, 6, 8, 9, 12} where aRb means a|b. Homework Equations The Attempt at a Solution 1 0 1 1 1 0 1 0 1 0 1 0 1 1 0 0...