Relation Definition and 1000 Threads

Homework Statement This isn't actually a homework question.Actually, it's an example from Rosen's Discrete Math and Its Applications that I'm having difficulty with: "A computer system considers a string of decimal digits a valid codeword if it contains an even number of 0 digits. For...

We all know the famous mass-energy relation E=mC^2,but my question is what does this really mean.I mean if I apply this equation for a normal practical application case e.g. burning of wood,the energy I will get from this combustion reaction will be equal to the mass I used multiplied by C^2.Is...

Someone texted me and asked me if the Earth was half as massive what impact would that have on the rotation period of the moon? I'd think that the moon would rotate slower as it's gravity would more influence on the earth. But I am not sure if that makes sense or not haha

If I were to drop a ball down a fluid with high viscosity, the ball decelerates over time and then reaches close to terminal velocity. How does displacement and velocity relates with time in terms of mathematical equation? Am I right to say: v(t) = Vterminal(1 - exp(-bt)) d(t) = Vterminal*t(1 -...

I'm doing a small research project on group theory and its applications. The topic I wanted to investigate was Noether's theorem. I've only seen the easy proofs regarding translational symmetry, time symmetry and rotational symmetry (I'll post a link to illustrate what I mean by "the easy...

Hi, Assume a matrix H n\times m, with random complex Gaussian coefficients with zero-mean and unit-variance. The covariance of this matrix (i.e., expectation [HHH]) assuming that m = 1 is lower than another H matrix when m > 1 ?? If this holds, can anyone provide a related reference? Thanks...

In quantum mechanics, a physical quantity is expressed as an operator G, then the unitary transformation coresponding to the physical quantity is expressed as exp(-iG/ħt), being also an operator, where t is the tranformation parameter. G is actually the conservative quantity corresponding to the...

Homework Statement In a certain region of space, the electric field along the x-axis is given by: E = 1.2x - 3.06, where E is in N/C and x is in meters. If you set the electric potential equal to zero at (4.39 m,0), find the electric potential, in V, at the point (7.22 m,0). Homework...

I am reading this: http://arxiv.org/pdf/quant-ph/0609163.pdf And Demystifier claims that "The time-energy uncertainty relation is not fundamental" However the proof is done in non-relativistic QM, where t and x are treated differently. My question is, what's about relativistic QM?

Homework Statement Let ##G## be a group and ##\sim## and equivalence relation on ##G##. Prove that if ##\sim## respects multiplication, then ##\sim## is the equivalence relation associated to some normal subgroup ##N\trianglelefteq G##; i.e., prove there is a normal subgroup ##N## such that...

hi, i have studied the annihilation and creation operators and number operator N in relation with the simple harmonic oscillator that is governed by: H = hw(N+1/2) i don't understand the relation between the harmonic oscillator and for example, this hamiltonian: H = hw1a+a+hw2a+a+aa that i...

Hey! :o We have the following lemma: Assume that the characteristic of $F$ is $p$ and $p>2$. Then $(t^m-1)/(t^n-1)$ is a square in $F[t, t^{-1}]$ ($F[t,t^{-1}]$: the polynomials in $t$ and $t^{-1}$ with coefficients in the field $F$) if and only if $(\exists s \in \mathbb{Z}) m=np^s$. Can...

Electrons are accelerated in an electrical potential of: ΔΦ = 105 V and are focused on a biological specimen. Assume that the kinetic energy of an electron is given by eΔΦ where e is the charge of an electron. What is the smallest possible object that can be resolved assuming that the...

I almost feel embarrassed to ask this. I've always understood it to be that the higher the frequency, the higher the energy (at least from what I've been taught). However, something has always bugged me: why then, when a medium is involved, are the lower frequencies the ones that make it...

Homework Statement Which solid-line curve most accurately represents the distribution of molecular energies in a gas at 500 K if the dotted-line curve represents the corresponding distribution for the same gas at 300 K? Homework Equations - The Attempt at a Solution Not sure how this...

Hi, just curious. Sorry I am trying to get a handle on this , will try to make it more precise: I am trying to see if the following has a categorical parallel/counterpart. Consider the case of measure spaces (X,S,m) : X any space, S a sigma algebra, m a measure and that of metric spaces (Y,d)...

[don't know whether i is the correct thread prefix, will change if requested/possible] Now I will start off by saying I'm only an interested lay person, and haven't studied this but was thinking about time dilation and it's correlative effects with gravity. Higher gravity, time slows down...

Hello all, Is there any direct relation ship exists between the thermal expansion and density of polymer material (eg. PMMA, Teflon) ? Like, Lorentz- lorentz law relates directly the refractive index and density of the polymer. similarly any laws relating (thermal expansion and density of...

I'm very sure this is wrong. I think the f^i(x) should be changed to a g^i(x) where g^i(x) is some function (I'm guessing either Gamma or Beta) and that the infinity sign should be changed to a i-->k where k is some arbitrary value. Reason being f^i(x) will always equal zero and j/i! will also...

My textbook says "The lower the gas pressure, the higher the mean-free-path". But it does not explain why. Can someone please explain it briefly? Thank you very much.

Good day (or night). I am new here, so I hope my question doesn't bother many. If (forgetting other laws of nature) a shoebox where to hit the sound barrier and an F-35 were to do the same. Would the sound waves be equal. Would it sound the same to a ground observer? I always assume that mass...

Hi first post so forgive any break in widely accepted conduct, Currently involved in a physics competition one of the question is to investigate geysers. Time and time again I have stumbled upon reference to Clausius-Clapeyron relation. Probably the best source I have come across is a youtube...

I have come across this inequality:$$ g≤ log\ n <g + 1$$ We assume that the base of the log is b >1 and n is all the natural numbers. I would like to know if anyone could provide a proof regarding this and mention for what g ? Is it for all the g which are integers ?

Where is the fifth energy level in relation to the fourth energy level? Well, it shows that energy level five is at n= 5 and energy level four is at n=4 away from the nucleus, so that means that the fifth energy level is at the 16th orbital and energy level four is at the 25th orbital?? I am not...

Hello. I'm having trouble understanding what is required in the following problem: Find the relation between the matrix elements of the operators $\widehat{p}$ and $\widehat{x}$ in the base of eigenvectors of the Hamiltonian for one particle, that is, $$\widehat{H} = \frac{1}{2M} \widehat{p}^2...

With the increase in RPM could the electric out put of a generator be increased.

I need a equation relating no. of turns of primary+ secondary, temperature increased due to eddy currents.

Is this equation of any use or in any way interesting? c = speed of light (m/s) e = euler's number I don't know much about physics but 2^6=log_2(64), this is a binary logarithm so would this mean that computers, the world (c and e) and circles(pi) all be related somehow by this equation?

I have a problem. As I was finding the torque for an engine. I have. I get a question about the relation of acceleration and time. How will be the graph of varying acceleration and time if acceleration decreases? Will it be a straight line with negative slope or any other shape?

Hi, If f'(x) >= f'(y) can we say that f''(x) >= f''(y) also holds ? And if yes under which conditions ? Thanks

What is the relation between classical from quantum vs measurement problem. On one hand they seem to be related on the other they seem to be of different nature. We always see our screens on front of us and not 100 meters away, that we say is classical object although the screen is a quantum...

Homework Statement I need to calculate the energy dispersion relation in the tight binding for simple cubic, base centered cubic and face centered cubic crystals. There are no values given, they just need the result depending on the lattice constant a. Homework Equations E (k) = alpha + beta *...

Hi, I was wondering if anyone here could help me prove or disprove this empirical observation or explain why there seems to be a connection between automorphic generators described below and the automorphisms of these groups: Consider the p-group expansion: ##\mathbb{Z}_n^*\cong S_2\times...

Homework Statement To show [J2, J+] = 0 2. Homework Equations J+ = Jx + i Jy [J2, Jx ] = 0 [J2, Jy ] = 0The Attempt at a Solution Step 1: L.H.S. = [J2, J+] Step 2: L.H.S. = [J2, Jx + i Jy ] Step 3: L.H.S. = [J2, Jx ] + i [J2, Jy ] Step 4: L.H.S. = 0 + 0 Step...

Hey! :o If the space $W$ is constant (doesn't move with the flow), show that $$\frac{d}{dt}\int_{W}\left (\frac{1}{2}\rho |\overrightarrow{u}|^2+\rho \epsilon\right )dV=-\int_{\partial{W}}\rho \left (\frac{1}{2}|\overrightarrow{u}|^2+i\right )\overrightarrow{u} \cdot \overrightarrow{n}dA$$...

Hi! (Wave) I want to show that the Euler equation for the functional $J(y)= \int_a^b f(x,y) \sqrt{1+y'^2}dx$ has the form: $$f_y-f_xy'-\frac{fy''}{1+y'^2}=0$$$$L(x,y,y')= f(x,y) \sqrt{1+y'^2} dx$$ Substituting $L_y(x,y,y')=f_y(x,y) \sqrt{1+y'^2}, \ L_{y'}(x,y,y')= f(x,y)...

Hello. I am trying to wrap my head around where from did he got the x = sin of theta equation at the 32:44 mark of the video: . Isn't sine of theta x over the hypotenuse in the diagram ? Thanks in advance!

In class I learn that we can get the dispersion relation for particles by using E=hbar*w and p=hbar*k. The calculated phase velocity is w/k = hbar*k/2m, while the group velocity is dw/dk=hbar*k/m. All these make sense to me, except one thing: I always thought that E=hbar*w=hf is only applicable...

Hi, I have a question about how to find the particular solutions when trying to solve recurrence relations. For example, trying to solve an+2 = -4an + 8n2n , I begin with finding the roots in the characteristic polynomial associated with the homogeneous equation, so r1 = 2i and r2 = -2i...

Hi. Here's the dispersion relation for a diatomic linear chain, where the distance is a/2 between each atom. My issue here is that if you set m_1=m_2=m, i.e. set both atoms equal to each other, it doesn't automatically reduce to the old acoustic dispersion relation as the ± term doesn't...

Hi Friends! Please tell me if the question below is valid? "If the frequency of the source is changed from f to 2f ,keeping amplitude same,then total energy is changed by what amount?" What I conclude is"We can think it in two ways: 1 In classical sense,where I could not find any...

Homework Statement If matrix ## C = \left[ {\begin{array}{c} A \\ B \ \end{array} } \right]## then how is N(C), the nullspace of C, related to N(A) and N(B)? Homework Equations Ax = 0; x = N(A) The Attempt at a Solution First, I thought that the relation between A and B with C is ## C = A...

Homework Statement If S2 = at2+ 2bt+c, then the acceleration is A) Directly proportional to S B) Inversely proportional to S C) Directly proportional to S2 D) inversely proportional to S3 Homework Equations dS/dt = v dv/dt = A The Attempt at a Solution Differentiating both sides, 2Sv = 2at +...

Homework Statement Given an NxN symetric tri-diagonal matrix, derive the recursion relation for the characteristic polynomial Pn(λ) Homework Equations Pn(λ) = |A -λI | Pn(λ) = (An,n - λ)Pn-1(λ) - A2n,n-1Pn-2(λ) The Attempt at a Solution This was easy to do by induction, but I am always...

Regarding interacting green's function, I found two different description: 1. usually in QFT: <\Omega|T\{ABC\}|\Omega>=\lim\limits_{T \to \infty(1-i\epsilon)}\frac{<0|T\{A_IB_I U(-T,T)\}|0>}{<0|T\{U(-T,T)\}|0>} 2. usually in quantum many body systems...

Hello guys, I'm currently working on a car simulation just for fun, but I'm stuck... The force to move a car is generated by burning fuel ( to be more percise, diesel or gasolin). But there are more variables: Pressure (i know this because of turbos and such) amount of fuel amount of air (or...

how can we relate innermost stable circular orbits, keplerian, epicyclic, frame dragging precession frequency with dipole moment.

Homework Statement We know about the equation: ##Fe+2HCl(g) \longrightarrow FeCl_2+H_2##. In my textbook it's written that liberation of ##H_2## prevents formation of ##FeCl_3##. But why?And how?Homework EquationsThe Attempt at a Solution I think it is related to the Le-Chatelier principle . As...

Homework Statement If a,b,c,d ∈R+ and a,b,c,d are in H.P. Then 1. a+ d > b+ c 2. a+ c > b+ d 3. a + b > c+d 4. a-b > c-d Homework Equations Don't know which equation to apply The Attempt at a Solution 1/a, 1/b , 1/c and 1/d would be in A. P 1/b -1/a = 1/d - 1/c

The closure relation in infinite dimension is : ∫|x><x|dx =I (identity operator),but if we apply the limit definition of the integral the result is not logic or intuitive. The limit definition of the integral is a∫b f(x)dx=lim(n-->∞) [i=1]∑[i=∞]f(ci)Δxi, where Δxi=(b-a)/n (n--.>∞) and...