Relation Definition and 1000 Threads

Homework Statement In "Methods of theoretical physics" from the authors Morse and Feshbach is writen: " The displacement (dx,dy,dz) is perpendicular to the surface if the component displacemetn satisfy the equation: How to prove this relation? Homework Equations the relevant...

Fact: The refractive index depends on the medium. Also, in general, to study the pulse propagation in a medium, there is a governing model equation (e.g. Non linear Schrodinger equation). My question is: Will there be any relation between the model equation and the refractive index? Why...

1. Homework Statement . Let A be a chain and B a partially ordered set. Now let f be an injective function from A to B and suppose that if a,b are elements of A and a≤b, then f(a)≤f(b). Prove that f(a)≤f(b) implies a≤b. 3. The Attempt at a Solution . I want to check if this proof by...

Hello, I'm having trouble calculating this commutator, at the moment I've got: \left[a_{p},a_{q}^{\dagger}\right]=\left[\frac{i}{\sqrt{2\omega_{p}}}\Pi(p)+\sqrt{\frac{w_p}{2}}\Phi(p),\frac{-i}{\sqrt{2\omega_{p}}}\Pi(p)+\sqrt{\frac{w_p}{2}}\Phi(p)\right]=i\left[\Pi(p),\Phi(q)\right]=i\int...

A particle moves such that its position vector, as a function of time is r(t) = (5*t^2)*i + (3*t^2)*j − (5*t)*k Im trying to find the unit tangent to the trajectory as a function of time. However I can't seem to find any formula of how to do this. Can someone please help me with a formula or...

Homework Statement The coplanar points A,B,C,D are (2-x, 2,2); (2,2-y,2); (2,2,2-z): (1,1,1) Homework Equations The Attempt at a Solution a(2-x, 2,2) + b(2,2-y,2) + c(2,2,2-z) = (1,1,1) Equating respective components ax=by=cz=k The answer is 1/x + 1/y + 1/z = 1 but in my case...

In relativity spacetime is usually visualized by placing something on a stretchable fabric of some sort. The object placed on the fabric will bend the fabric, just as a planet or star would in real space. Time can be manipulated when something extremely massive like a black hole is in space. But...

Several species, including the squid, cuttlefish, dragonfly fish and many microscopic organisms, move themselves around by a kind of jet propulsion. In each case the animal absorbs fluid in a body cavity and expels it through an orifice by contracting the cavity. If a squid has a mass Ms when its...

Hello I have to check if the following relation is an equivalence relation. \[m\sim n \;\;\mbox{in}\;\;\mathbb{Z}\;\;\mbox{if}\; mn > 0\] I think this relation fails to be reflexive since $(0,0)$ does not belong to this relation. Hence this is not an equivalent relation. Is this ok ? Thanks

We know that radio waves follow the curvature of the earth. Reason? Gravity (I think) The only logical thing I can think of is what Johann Heinrich Winkler discovered in mid 1800's; that when electricity is given multiple paths to choose from, it invariably chooses the best conductor (least...

Hello all, I have an equivalence relation that I need some help with. Normally I find these to be fairly simple, however I'm not sure if I'm over-thinking this one or if it's just tricky. For the relation: aRb $\Longleftrightarrow$ |a| = |b| on $\mathbb{R}$ determine whether it is an...

Homework Statement problem statement is attached as problem.pdf Homework Equations eqn are given in the pdf file The Attempt at a Solution I have tried in vain to connect Fermi energy with dispersion relation. I just don't have any clue ,I also tried to determine the effective...

Hi, I have a question about groups: What is the de Sitter group?? and how does it relate to poncaire's group? Thanks!

can you give an example of symmetric property of equality and transitive property of equality. the generalization of these properties are a bit abstract for me. thanks!

Dears, I wish to measure the entropy of visual data such as image and video. I did transform these image and videos into frequency domain such as DCT, then measured the entropy with these pdfs for each AC components of image and videos. However, when I measured the entropy over spatial domain...

Hi friends, I have a system (with unknown properties) which takes an input vector of length 10 and outputs a vector with length 6. I select Inputs vector 'I' which is a 1000x10 matrix, : 1000 samples of 10 elements. And outputs vector 'O' is a 1000x6 matrix,: 1000 samples of 6...

I quote a question from Yahoo! Answers I have given a link to the topic there so the OP can see my response.

Hi there everybody I have a nice little problem which might not be so complicated after all. I need to push a heavy object using torque applied on a bolt. This is done manually, and the necessary torque needed is of interets. The attachment explains it quite well, I think. To overcome...

Homework Statement The position of a 60-gram golf ball sitting on a tee is determined within +- 1μm. What is its minimum possi- ble energy? Moving at the speed corresponding to this kinetic energy, how far would the ball move in a year?Homework Equations ## K\geq\dfrac {\hbar ^{2}} {2ma^{2}}...

If Neanderthals and humans interbred, then they must have had a common ancestor that was also human. What is known about this common ancestor?

When can be used (\frac{\partial S}{\partial V})=\frac{P}{T}?

Hello, Something I have some time wondering and still couldn't find the answer is to this question: if there is some relation between the Spectrum (functional analysis) and the Frequency spectrum in Fourier Analysis. Now that I think about it there seems to be a casuality the use of the...

Is it the absence and presence of an electrical fluid called as positive and negative charges?

Why is dU=-\vec{F}.d\vec{r} Integrating with putting the limits on we get: ΔU=-W Why is this? Here \vec{F} is a conservative force/Force field.

I'm having a gap in understanding the relation between them, and resolving my confusion is really appreciated. For example, the Hamiltonian operator, why do we call its eigenvalues energies? how do we actually measure it in the laboratory, quantum mechanically? And maybe I need a better...

Hello all. This is not a "What is Energy" Thread but rather a question about its relation with work. I understand that energy has been defined as the ability to do work. So why is change in energy is equal to work? Cant energy be equal to work. Also when the force field is doing work on...

I am read the pag 190 of Dodelson bock, where use the following relation \rho_{DM}= \rho \frac{y}{y+1} . where y= a/a_{eq}=\rho_{DM}/\rho_{rad} i tried using the tipically relation \rho = \rho_{rad} a^-4+ \rho_{DM} but, i don't understand, healp please

So I understand that Reynolds number is the ratio of intertial forces to viscous forces but how exactly does this relate to flow? Why is it that when viscous forces dominate one gets a laminar flow? How to conceptualize?

Homework Statement Prove that the relation, two finite sets are equivalent if there is a one-to-one correspondence between them, is an equivalence relation on the collection S of all finite sets. I'm sure I know the gist of how to do it, but I'm a beginner in proofs, and I'm not sure if...

I found this in Srednicki's QFTbook. I don't know what ↔ means. Help me, please

One can show that at around ##p \approx m## where m is the physical mass the full propagator ##D_F## is something like $$D_F = \frac{Z}{p^2 - m^2}.$$ Where ##Z = (1 - \Sigma '(m))^{-1}##, ##\Sigma## is the self energy and m is the physical mass of the particle. If i were now to write a...

Hi,I hope my question will be clear.I need to be explained me one problem.That is: Can be expressed physical law,for example average speed like relation,but not like a function?Or speed can be only the function?I mean,why we use functions to describe physical phenomena?Is possible to describe...

I've just started learning about torque, and understand that tau=Fd, but wondered how this relates to F=ma. For example if there is a rod with a pivot in the middle (say a nail), when one end is pushed down, why does the other end move up? Where is the force that causes the end to move up...

Please explain the relation between electric potential energy and electric field in detail.

Stability, Helmholtz free energy mathematical relation "proof" Homework Statement I must show that \left ( \frac{\partial ^2 F}{\partial V ^2} \right ) _T=\frac{\frac{\partial ^2 U}{\partial S^2} \frac{\partial ^2 U}{\partial V ^2} - \left ( \frac{\partial ^2 U}{\partial S \partial V} \right...

We know that electrons are nearly massless so their wave funtion is quite easily detectable.So is there any mathematical relation between the mass of the body and the intensity of the wave it exhibits? thanks

Homework Statement Prove the commutation relation ##\left [L_x, p_y \right] = i\hbar \epsilon_{xyz} p_z## Homework Equations ##L_x = yp_z - zp_y## ##p_z = i\hbar \frac{\partial}{\partial z}##The Attempt at a Solution ##\left [L_x, p_y \right] = (yp_z - zp_y)p_y - p_y(yp_z - zp_y)## ##\left...

Homework Statement Have a solution for the temperature u(x,t) of a heated rod, now using the orthogonality relation below show that the coefficients a_n , n = 0,1,2,... can be expressed as: a_n = \frac{2}{L} \int_{0}^{L} cos\frac{n\pi x}{L} f(x) dx Homework Equations \int_{0}^{L}...

Relation between Cooling rate and Viscosity Hi all I have a situation where i have a molten Aluminium Copper alloy melt poured in a mould to be solidified. This means, the mould temperature is lower than than than the poured melt. I am thinking about a relation which associates temperature...

I see there have been many postings about this topic in this forum. The formula for this relation is Luminosity = Mass^3.5 Taking logs of both sides we get log (lum) = 3.5 * log (mass) and using a little algebra we find that the exponent (3.5) should equal log (lum) ÷ log (mass) I have...

I'm confused about the condition for spontaneity for the Helmholtz energy. My textbook (McQuarrie, "Physical Chemistry") derives the conditions as follows. We start with the combined law of thermodynamics: dU = δq + δw ≤ TdS – PdV since δq/T ≤ dS dU – TdS + PdV ≤ 0 For a process at...

Homework Statement Let A be the set that contains all rational numbers, but not zero. Let (a,b),(c,d) \in A×A. Let (a,b)\tilde{}(c,d) if and only if ad = bc. Prove that \tilde{} is an equivalence relation on A×A.Homework Equations The Attempt at a Solution The solution just needs to show...

Hello!Could you help me at the exercie below? Consider a gamble,with the same possibility to win or to lose.If we win,we double our property,but if we lose we halve our property.Let's consider that we begin with an amount c.Which will be the mean value of our property,if we play n...

Hi all, What is the relation between RAMAN Intensity and Energy of the photon and/or bond stregth and/or bond energy? Is there any equation or sth explain it easily? If you can explain it in a simple way, I will appreciate. Thanks

Hello friends, If we consider ##{T}## as coordinate time and ##{\tau}## as proper time, the relationship between them is: ##\frac{T}{\tau}= \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}## so, ##{T}= \frac{\tau}{\sqrt{1-\frac{v^2}{c^2}}}## So we can consider this expression like this: If In...

I am familiar with the equation ΔG=ΔG°+RT ln(Q).But I can't derive it.We have to use the equation to derive nernst equation. So please help.

Homework Statement The **mean value theorem** says that there exists a $c∈(u,v)$ such that $$f(v)-f(u)=f′(c)(v-u).$$ Here is my question. Assume that $u$ is a root of $f$, hence we obtain $$f(v)=f′(c)(v-u);$$ assume that $f$ is a non-zero analytic function in the whole real line. We...

Hi Guys, I am learning some solid state physics. I see a lot of pictures with Phonon Dispersion Relation, with \omega (\vec{k}) on the y-axis and \Gamma, X, M, \Gamma, R on the x-axis. I don't understand, why the angular frequenzy \omega (\vec{k}) is important. Or why is this...

Homework Statement Homework Equations The Attempt at a Solution Is my initial assumption wrong?

Homework Statement a_{n} = a_{n-1} + n a_{0} = 0 The Attempt at a Solution h_{n} = h_{n-1} t^{2} - t = 0 t=0 t=1 h_{n} = B p_{n} = bn + c p_{n} = p_{n-1} + n bn + c = b(n-1) + n bn + c = (b+1)n -b I'm sure I've gone wrong somewhere, I just can't figure out where!