Relation Definition and 1000 Threads

Homework Statement Given the following recursion formula: b_{j} = 2 \frac{kj - a}{j(j+1)-l(l+1)} \cdot b_{j-1} (where a, k and l are constants) how can b_{j = l} \neq 0 if b_{j - 1} = 0. Homework Equations The Attempt at a Solution This is a part question and I really can't see why. if...

Hi, On a conducting planar surface, with a plane wave illuminated,(s for scattered field, i for incident field) in spherical coordinates under the tangential boundary condition that: E_{s}(\theta,\phi)=-E_{i}\theta,\phi), which is E_{s,\phi}(\theta,\phi)=-E_{i,\phi}(\theta,\phi) and...

Homework Statement show that the roots of a polynomial with real coefficients are real of form complex conjugate pairs .The inverse is not true ,in general. Homework Equations The Attempt at a Solution

I'm reading a paper on photovoltaic hydrogen production and the author claims that for reasonable solar efficiencies the band gap must be less than 2.0eV. This I understand. My question is how will it effect the photon absorption if the band gap is much smaller. Say the band gap energy is...

Can anybody clear this up for me? In his Chicago lectures in 1930, Heisenberg is quoted as saying “The uncertainty relation does not hold for the past…If the velocity of the electron is at first known, and the position then exactly measured, the position of the electron for times previous...

Homework Statement I am on the final part of a question and I have to prove that the following is a irreflexive symmetric relation over A or if it is not then give a counter example. R is given as an irreflexive symmetric relation over A. Relation: {(X, Y) | X ⊆ A ∧ Y ⊆ A ∧ ∀x ∈ X.∀y ∈...

The relation between two terminology "cusp" (group & algebraic curve) Dear Folks: I come across the word "cusp" in two different fields and I think they are related. Could anyone specify their relationship for me?? Many thanks! the cusp of an algebraic curve: for example: (0,0)...

Equation (p=i^2 * R) seems to suggest that the rate of increase of thermal energy in a resistor is reduced if the resistance is made less. "Eq" : p =v^2/R seems to suggest just the apposite . How do you reconcile this apparent paradox?

Hi Guys I have a very simple and basic question. Assume interface of two dielectric mediums. If the t is transmition cofficient for electricfield from medium 1 to medium 2 with refractive indexs n1 and n2, what is the transmitivity of power from medium 1 to medium 2? I know it is...

The only reason I can think of is: By defining S=k_b \log \Omega, it just works out; for an ideal gas as well as for other systems (that I can't come up with right now). \frac{dS}{dE}=\frac {1}{T(E,...)}\, states that temperature is a measure of the increase in entropy when some energy is...

Where does the 3/2 come from? \frac{1}{2} mv^2 = \frac{3}{2} kT

relation between "commutation" and "quantization" Hi people; Over the several texts I have read, I got the impression that position-momentum commutation relations is the cause of "quantization" of the system. Or, they are somehow fundamentally related. The only relation I know of, is to...

what does more damage an object w/ a high acceleration or a greater momentum i was watching one of my favorite tv shows "Justified" and i started to wonder would a bullet moving at a greater acceleration hence greater force (F=ma) inflict more damage or would a bullet w/ a greater velocity...

A non Ohmic relation of current and voltage is I=α(exp(eV/kT)-1). Where α,K,T,e are constant. What will be the incremental resistance? My question is if it don't follow the Ohmic equation then how it possible to find the resistance?

From mathhelpforum.com... Hi. This is my first post here so I hope I've posted in the right place. My question concerns finding closed forms of nonlinear recurrence relations such as the following... $\displaystyle a_{n+1}= a^{2}_{n}-1\ ;\ a_{0}=a$ (1) This one is both nonlinear and...

Indicate which of the following relations on the given sets are reflexive on a given set, which are symmetric and which are transitive. {(x,y)\inZxZ: x+y=10} Tell me if I'm thinking about this correctly It is not reflexive because the only 5R5. It is symmetric because any xRy and yRx where...

I am trying to prove this as I am practicing for a test but I am pretty much clueless on this problem: Prove that if ~ is an equivalence relation on a set s and [a] denotes the equivalence class of a in s under ~, then a ~ b if and only if [a] = [b]. If anyone can give me some points on...

Would it be possible if you would help me with a quick question, (as none of the staff here, or postgraduates can answer this question)? My group are designing a gamma ray telescope to look at nucleosynthesis in Supernovae. We have found a thing called the 'mass cut' (the separation between...

So, I technically got this problem correct (our professor gave us the answers but not the total solution). My question is more of a logic one- an answer that I'll need to apply this concept to problems on the exam. I included it at the bottom of the post, after I explained the problem Find...

Homework Statement Find the relation P=P(V) for a transformation dQ=0 in an ideal gas (PV=nRT and U=CnRT).Homework Equations dU=dQ-PdV.The Attempt at a Solution If I assume that C and R are constant I get dU=CR \left [ \frac{\partial (nT)}{\partial n} dn + \frac{\partial (nT)}{\partial T } dT...

It is known that the area of a sector of a polar curve is \frac{1}{2}\int r^{2} d \theta This of course comes from the method of finding the area of an arc geometrically, by multiplying the area of the circle by the fraction we want \frac{\theta}{2\pi}\pi r^{2} Today I learned how...

I'm having trouble doing a classic proof (integration par part and induction on r) for this : Pr(X>t)=Pr(Y ≤r−1), where X follows a gamma Γ(α = r, β = 1/λ) and Y a Poisson P (λt). Start with r = 1 (exponential distribution). I don't really understand what induction on r really means...

Homework Statement Let H and K be subgroups of the group G. Let a,b \in G and define a relation on G by a ~ b if and only if a = hbk for some h \in H and k \in K. Prove that this is an equivalence relation.Homework Equations a = hbkThe Attempt at a Solution The goal is to prove the reflexive...

Hi all, this is my first post; apologies if it seems a bit basic, I suspect there's something fundamental I'm not getting here :smile: Say I observe the spectrum of a galaxy, and I calculate its redshift. I then use the Hubble Relation to find its distance, which is, say, ten billion light...

So my professor gave us this recurrence relation to prove combinatorially for extra credit, but I was unable to figure it out. h(n) = 5h(n-1) - 6h(n-2) + 1 This was my solution, but I couldn't figure out how to factor in the +1: Let hn be the number of ways to arrange 0,1,2,3,4 on a 1xn...

Hi All A question that bothering me and I can't find answer for: a charged particle in empty space will generate an electromagnetic field that has energy density and can be described by Energy-Momentum Tensor. A non charged particle at rest also has energy due to mass energy...

Derive the relation Δn.Δσ ≥ 1/2 where n is number of photons in an EM field and σ is phase Using heisenburgs uncetertainty principle? Tried subbing in frequency into heisenburgs uncertainty principle to get to the number of photons and to get rid of mometum is this the right line? Dont...

Homework Statement I have these two sets: Pairwise, (1, 1) (2, 4) (3, 9) (4, 16). Clearly this is just squared. How can I get a function relation with like: (1, 1) (2, 3) (3, 9) (4, 10) or like (1, 1) (2, 5) (3, 12) (4, 22) Homework Equations The Attempt at a...

Homework Statement For n ≥ 1, let g(n) be the number of ways to write n as the sum of the integers in a sequence of any length, where each integer in the sequence is at least 2. For n≥3, show that g(n) = g(n-1) + g(n-2).2. The attempt at a solution I've gone through values of g(n) for...

Hello Forum, when a wavefield is incident of an atom and the photon have the right energy (equal to the band gap energy), the photon is absorbed and disappear... But isn't the photon re-emitted later on and allowed to propagate through the material or does all its energy get lost into heat...

Hi everyone: How is the following derived? Just for example: \Deltax\alphae\alpha=\Deltax\alpha(\delta/\deltax\alpha) does it not mean? e\alpha=\delta/\deltax\alpha But How?

Homework Statement The question is to show that Cos^2(x) + Sin^2(y) = 1 is an equivalence relation. The Attempt at a Solution I know that there are three conditions which the equation must satisfy. (reflexivity, symetry, transitivity) For reflexivity I tried: Cos^2(x) - Cos^2(x) = Sin^2(y)...

Hey everyone, I'm in the process of designing a rocket that could achieve high(er) altitudes. Of course, I want to make the rocket as small as possible, but maximize the height. I understand that the Mass fraction of the craft should be 0.91, where 91%~ is fuel/propellant, 6%~ is payload, and 3%...

Homework Statement A beam contains 4.0x10^8 doubly charged positive ions per cubic centimeter, all of which are moving north with a speed of 1.2x10^5 m/s. (a) What is the magnitude of the current density ? (b) What is its direction? (c) What additional quantity or quantities are needed...

Homework Statement List the ordered pairs in the relation R from A = {1, 2, 3, 5} to B = {2, 4, 6, 9} where <x, y> is an element of R iff: (i) x ≥ y (ii) x – y < 2 (iii) x – y > 2 (iv) l.c.m. (x, y) = 18 (v) g.c.d. (x, y) = 3 I understand in general ordered pairs and...

I'm doing a much larger problem and I am stuck going from: T(n) = 14 + T (n − 2) + 10(n + (n − 1)) to T(n) = (n − 1)7 + T(1) + 10(Σi=2 to n of i) and I would very much appreciate it if someone could show me the detailed steps. (I've been told something about expanding the recursive...

I know I knew this many years ago and I am sure the answer is simple but I would really appreciate the help. Event That Brought Up The Question: Working on a complany vehicle, there was a heater fan that would keep failing. As we troubleshot, we saw that system voltage was low (bad...

So, my problem statement is: Suppose that two operators P and Q satisfy the commutation relation [Q,P] = Q . Suppose that ψ is an eigenfunction of the operator P with eigenvalue p. Show that Qψ is also an eigenfunction of P, and find its eigenvalue. This shouldn't be too difficult, but...

Homework Statement Suppose two objects have energy fluxes, f and f + Δ
f, where
Δf ≪ f. Derive an approximate expression for the magnitude difference
Δm between these objects. Your expression should have Δ
m proportional to
Δf. Homework Equations Δm = m2 - m1 = 2.5 * log(f1/f2)...

Hello, I have to present Critical Realsim theory to class. I have been coming across words like Ontology and Epistemology. I made effort to see what those terms are and their relation to critical realism but I couldn't understand it. It talks philosophy. Can some help me to understand in simple...

Considering f(z) = z where z is analytic. z = x + iy. f(z) = u + iv = x + iy. Hence u=x and v=y. Using Cauchy Reimann eqns. ∂u/∂x = ∂v/∂y =1 and ∂u/∂y = -∂v/∂x where u=x and v=y hence ∂x/∂y = -∂y/∂x is this relation true in general?

i have two relations given to me which are both defined on the integers Z by relation 1: x~y if 3x^2 -y^2 is divisibale by 2 and relation 2: x~y if 3x^2 -y^2 ≥0 I have used three properties to figure out that relation 1 is eqivalence relation as it stands for all three properties i.e...

Homework Statement Show that one can write U=exp(iC), where U is a unitary matrix, and C is a hermitian operator. If U=A+iB, show that A and B commute. Express these matrices in terms of C. Assum exp(M) = 1+M+M^2/2!...Homework Equations U=exp(iC) C=C* U*U=I U=A+iB exp(M) = sum over n...

Hello, Let me first start off by saying that I have no formal Education or background in Physics or Astronomy save for one course during college. This is simply posing an idea I had while reading an article on the acceleration of the expanding universe and how it could have a correlation with...

Is it true that all the Experiments which are intend to prove Time-Dilation of SR 'directly', are based on radioactive half-lives extension ? For example, cesium atomic clocks in GPS satellites, Muon decay etc. Moreover, if it is true, ... and correlations between nuclear decay rates...

Hey! I was trying to find the expected time an algorithm takes to solve a certain problem, and I ended up in a very nasty recurrence relation of this form: a_{k,k} =...

Hi, I'm confused about the meaning of the term frequency used in electronics. I'm not sure if I understand what it means. For example: There a number of frequencies travel through a single cable television, at the end point does the de-multiplexer recognizes each signal by its voltages...

Hi all, Let λ>0 and define an equivalence relation on ℝn-{0} by (x~y) \Leftrightarrow (there is an s\inZ such that λsx=y) I would like to know what the quotient space ℝn-{0}/~ looks like. I know that it is a set of equivalence classes. To understand it better I wanted to see how it...

I am stuck on one part of my Quantum Mechanics HW. Above the question it says "Try and answer the following question." So I can only assume that he isn't looking for something incredibly detailed. (Ill explain why after the question is given.) Homework Statement What is the meaning of the...

Homework Statement Determine whether the given relation is an equivalence relation on the set. Describe the partition arising from each equivalence relation: xRy in ℝ if x≥y Homework Equations Reflexive: for all x in X, x~x Symmetric: for all x,y in X, if x~y, then y~x Transitive...