Relation Definition and 1000 Threads

Given a group G acting on a set X we get an equivalence relation R on X by xRy iff x is in the orbit of y. My question is, does some form of "reciprocal" always work in the following sense: given a set X with an equivalence relation R defined on it, does it always exist some group G with some...

Homework Statement Compute the numerical constant C for an electron gas (take Z = 6 and A = 12) and determine the radius of a white dwarf whose mass is 0.6 solar masses. h\ =\ 6.62606876(52)\ \times\ 10^{-34}\ Jh\ =\ 6.62606876(52)\ \times\ 10^{-34}\ J\ s\ s m_{e}\ =\ 9.10938188(72)\...

Homework Statement Assume a relation P that is negatively transitive on a set X that is not empty. Define the binary relation R on X by xRy iff y P x is false. Prove that R is transitive.Homework Equations Negative Transitivity: xPz \rightarrow xPy \vee yPz Like in the previous thread...

Homework Statement Assume a relation P that is asymmetric on a set X that is not empty. Define the binary relation R on X by xRy iff y P x is false. Prove that R is complete Homework Equations Asymmetry: xRy \rightarrow \neg (yRx) Now, I think I got a proof, but I am not sure...

Do you believe genetics can cause one to have a particular accent in a given language? Or are accents only related to post-birth personal development? Are there ethnicities having anatomically distinct voice boxes, that have more difficulty in emulating specific accents? I tend to...

I was trying to Go from the uncertainty principle to its energy-time counter part. i know the maths is a bit off,but the idea is correct? dx=position p=momentum e=energy \upsilon=frequency \lambda=wavelength c=velocity of electromagnetic radiations dt=time now , \lambda=h/p....(i)...

Should I in any way find this intuitive? Apart from the fact that the idea of a commutation relation resembles the idea of a poisson bracket for operators I can't see how I should find it intuitive.

i don't know in which section it belongs, so i am putting it here... according to various theories proposed by various researchers, time travel depends on the speed of light. as far as i have read/heard - i) anything traveling faster than the speed of light moves back in time. ii) anything...

Homework Statement find the relationship between the 2 particles' accelerations. Homework Equations m1=20kg m2=40kg wheel doesn't weigh but can move. both particles move with friction. μs=μk=0.2 F(t)=98e0.1t The Attempt at a Solution I came up with 3 equations...

Homework Statement Suppose f:R^2 - {0} → R is a differentiable function whose gradient is nowhere 0 and that satisfies -y(df/dx) + x(df/dy) = 0 everywhere. a) find the level curves of f b) Show that there is a differentiable function F defined on the set of positive real numbers so that...

This is a conceptual question on the region of convergence (ROC) and the inverse Laplace transform (ILT). Here the bilateral laplace transform (LT) and the ILT are given by F(s)=L\{f(t)\}=\int_{-\infty}^{+\infty} f(t) e^{-st} dt and f(t)=L^{-1}\{F(s)\}=\frac{1}{i...

Friction causes a torque that opposes angular momentum. It gets reduced. how can we derive a relation connecting these. friction starts with maximum and becomes zero. angular velocity and its corresponding momentum decreases maximum in the beginning and increases towards the end. the radial...

ok, so, I know e=mc2 is a way i can find what quantity of energy a mass has. and i know that as objects increase in speed they become more massive, which i assume is also elegantly portrayed in this equation. but, this kind poses a problem for me, because i am wondering how much velocity...

What makes, for example, blue color appear darker or lighter? Is it just amount of photons (intensity) or is there any relation between brightness and wavelength? Or is there something else that comes into equation as well?

So this is more so a general question and not a specific problem. What exactly is the diefference between closed and boundedness? So the definition of closed is a set that contains its interior and boundary points, and the definition of bounded is if all the numbers say in a sequence are...

Homework Statement A security fence is to be built around a rectangular parking lot. The front side of the fence costs $60 per meter and the other three sides cost $30 per meter. The total cost of the fence is budgeted to be $7500. Part a). Express the area of the lot enclosed by the...

Hello, In the book physical chemistry (P. Atkins & Julio de Paula, 2009, 5 ED) the authors derive a justification of the Schrödinger equation. 1.) \frac{-\hbar^{2}}{2m} \frac{d^{2}\psi}{dx^{2}}+V(x)\psi=E \psi The derivation goes as follows: Derivation: We can justify the form of...

Homework Statement Let d0, d1, d2,... be defined by the formula dn = 3n - 2n for all integers n ≥ 0. Show that this sequence satisfies the recurrence relation. dk = 5dk-1 - 6dk-2.Homework Equations The Attempt at a Solution I found that dk = 3k - 2k dk-1 = 3k-1 - 2k-1 dk-2 = 3k-2 - 2k-2...

I'm reading some quantum optics and I stumbled on the following completeness relation for the polarization vectors of the electromagnetic field. \sum_{a} (\epsilon_{\vec{k} a } )_i ( \epsilon^*_{ \vec{k} a} )_j = \delta_{ij} -\frac{k_i k_j}{\vec{k}^2} Does anyone know how to derive...

There is a certain equation relating both Mp (max. overshoot) and damping ration. Which is; Mp = e(-ζ*pi)/(1-ζ2)1/2 What I get from that equation is for every system a certain damping ratio will result the system in a certain amount of max. overshoot. That sounds ridiculous, because...

Ok, I am barely beginning to understand the subject. I understand that the relation ≥ on N(naturals) is reflexive, not symmetric, and transitive. I don't understand why it is transitive though. Can someone explain? Also, I understand why x2 = y2 is reflexive and symmetric, but I don't...

Hi, D=εE, and E=Q/(4πεr^2). We may suppose generally that, E is inverse proportional to permittivity. Combining the interpretation to the first equation, E is dependent variable, and D is the independent variable. That is, D is medium dependent. Anyway, E is dependent on the permittivity...

greetings, how a sampling rate can define bandwidth required for transmission of that signal.if sampling rate is high then bandwidth requirement is also high,how?

Hi. I have a problem to understand the following situation regarding observation of a quantum system: Imagine we have an unstable particle in a box, together with many sensors where each is connected to a lamp. The sensors continuously monitor the particle, the lamp turns on whenever the...

Determining the commutation relation of operators -- Einstein summation notation Homework Statement Determine the commutator [L_i, C_j] . Homework Equations L_i = \epsilon_{ijk}r_j p_k C_i = \epsilon_{ijk}A_j B_k [L_i, A_j] = i \hbar \epsilon_{ijk} A_k [L_i, B_j] = i \hbar...

Homework Statement In Einstein's energy mass relation, the unit for the energy released is Joules, this means that the unit for the mass must be a. g b. kg c. it could be either grams or kilograms d. Newtons Homework Equations E = mc2 The Attempt at a Solution I believe the...

I know the physical meaning of phase as well as the group velocity. I want to know the mathematical relationship between the phase velocity and group velocity. Thanks a lot.

Hi there, I want to modify a equation which is written for Singal to Noise Ratio. Now I want to change for logical interference. But I could not find any reliable source of explanation, " [FONT="Arial Black"]what is the relation between SNR/SINR and interference(Logical/Physical)?"

Hi all, I am brand new here and need some help - i hope it is the right category i am posting in. I am no expert in physics - i am working at sea as a mate on board producttankers. I would like some advice for calculating or formulas for the following scenario: - A closed tank 10m3 is...

Hi Let's stick to the classical limit. We have 2 monochromatic light waves of same intensity. Let's say one is blue and one is red. Now this means the individual photons of the blue light have more energy(obviously, higher frequency) and the red light photons have lower energy. But since...

Friction and Relation of Coefficient of Friction to "Smoothness" In my physics class today my teacher began discussing a very peculiar characteristic concerning the static and dynamic coefficients of friction. Apparently, when one makes an object's surface "smoother" (meaning with less...

"Show that the uncertainty relation forces us to reject the semiclassical Bohr [...]" Homework Statement The problem along with the solution is attached as TheProblemAndSolution.jpg. Homework Equations Uncertainty principle/relation. The Attempt at a Solution Why is it the consideration of...

Another vector identity I have been trying to prove. My textbook lists this identity in "properties of cross products" without proving it. I have been trying to prove it, withou much luck, so some insight is appreciated. u \times (v \times w) = (u \cdot w)v - (u \cdot v)w Thanks! BiP

I understand the basic connections between vapor pressure of substances and how this effects their boiling points. However, I am a bit hazy on applying it to some real life situations so I want to give some examples to check where I might be going wrong in my thinking. 1. I have 70F water in...

I was just curious, sorry if it is already asked, I was going through a book on photonics and came across the relation coherence time, t = λ*λ/Δλ I did not find any proof of this. Can anyone explain me how this relation is found?

Like any mathematical relativity between them as per General Relativity?

Fill a bowl with water, lay a piece of fabrics over the bowl, one end touching the water and the other end laying down on the table. Due to the capillarity effect the water will follow the fabrics and after a while it will be all wet. From this little experiment we can deduce that water...

The relation between the vector operator curl and rotation in fluids and vector fields is treated thoroughly in many texts. And the uniform (pure or simple) shear of a solid is adequately described by the strain tensor. I'd like to put the two together. My guess is that an alternative...

Find a simple closed formula for the ordinary generating function of the sequence given by {a_{n}]}n>=0 when a_{n} is given by a_{n} = 6 * 5^n - 5 * 3^n. My question is how do you find the recurrence relation a_{n} = 6 * 5^n - 5 * 3^n. I don't know were to start.

Homework Statement Q. Define an order relation (x,y)<(j,k) if and only if x+k<y+jHomework Equations x<y means x+a=y and viceversaThe Attempt at a Solution I have no idea. To show it is equivalence relation, I simply show that it is reflexive, transitive and symmetric. but how do I show it...

I'm a computer science and engineering student, who has recently developed interest about quantum computers. I can understand that quantum computers are totally linked with quantum mechanics. But I would like to learn whether there is any relation between quantum computing and quantum field...

Homework Statement ~ is a equivalence relation on integers defined as: a~b if and only if 2a+3b is divisible by 5 What is the equivalence class of 0 Homework Equations The Attempt at a Solution [0] = {0, 5n} n is an integer My reasoning for choosing 0 is that if a=0...

Homework Statement Relation on set of integers. a~b if and only if 2a+3b is divisible by 5 show that ~ is an equivalence relation Homework Equations The Attempt at a Solution I have already proved that the relation is reflexive and symmetric, but I'm unsure of my approach...

Hello, It is my understanding that if we have a sequence defined as follows:an+1=(ψ)an + (λ)Then if ψ≥1 or ψ≤-1, the sequence diverges. If -1<ψ<1, the sequence converges to: λ/(1-ψ)I was working problems in a book and one of the problems said that the following sequence converges...

What exactly allows a "differential relation" form of an equation? I understand this in a superficial way but I'd really like some more clarification. If anybody can provide a little better understanding on this subject, please feel free to post anything at all. Even a sentence or two would be...

Homework Statement Suppose that ##\left\{a_n\right\}## is a sequence of complex numbers with the property that ##\sum{a_n b_n}## converges for every complex sequence ##\left\{b_n\right\}## such that ##\sum{|b_n|^2}<\infty##. Show that ##\sum{|a_n|^2}<\infty##.Homework Equations The Attempt at...

Hello. How do I evaluate, in Mathematica, limits like this: "X+Y" when X is much bigger than Y, i.e., when Y/X->0. The unswer should be X+Y->X. Regards.

Homework Statement A 1200 kg car is at a red light on a horizontal road. When the road turns to green, (t0) he starts accelerating and reaches 14 m/s in 7 seconds. He then continues at a constant speed for 10 seconds, then brakes with a -3.5 m/s^2 acceleration. All accelerations are assumed...

a ball is whirling on the end of the string L the max tension is Tbreak the max velocity is vmax find an equation for vmaxin m(mass of ball)Tbreak, L and g

X is a random variable. If Y=g(X). then how do you prove that- fY=Ʃ fX(xi)/|g,(xi)| Thanks a lot.