Relations Definition and 540 Threads

Hi. I studied calculus a while back but am far from a math god. I have been reading around online about hyperbolic geometry in my spare time and had a simple question about the topic. If a straight line in Euclidean geometry is a hyperbola in the hyperbolic plane (do I have that right?)...

I am reading Apostol's section on Riemann-Stieltjes integral and I have doubts on one statement: Let ##α## be a function of bounded variation on ##[a,b]## and suppose ##f \in R(α)## on ##[a,b]##. We define ##F## as ##F(x)=\int_a^x f(x)dα## if ##x \in [a,b]##, then ##F## is a function of...

Hi guys, why does the following mean B is unitary? if we have two rotations such that; b1 = B11a1 + B12a2 b2 = B21a1 + B22a2 and the following commutator results are; [b1, b1(dagger)] = |B11|^2 + |B12|^2 --> 1 [b2, b2(dagger)] = |B21|^2 + |B22|^2 --> 1 [b1, b2(dagger)] =...

I'm currently reading the section on relations in Velleman's "How to prove it" and I have found a statement somewhere that I want to prove, but I'm not sure whether what I have come up with is reasonable and I also have some questions on the logic used in these type of proofs. The theorem is...

Homework Statement Compute the commutation relations of the momentum operator ##\underline{\hat{P}}## and the angular momentum operator ##\underline{\hat{L}}## Homework Equations $$\hat{L_i} = -i\hbar \epsilon_{ijk} x_j \frac{\partial}{\partial_k} = \epsilon_{ijk}x_j \hat{P_k}$$ The...

Homework Statement Whats up guys! I've got this question typed up in Word cos I reckon its faster: http://imageshack.com/a/img5/2286/br30.jpg Homework Equations I don't know of any The Attempt at a Solution I don't know where to start! can u guys help me out please? Thanks!

Homework Statement True or False: Given that A = {a,b,c} and B={0,1,2,3,4}, there are 32768 binary relations from A to B I assume there is some simple way to tell how many relations there are given two different sets, but I don't know it. Factorials? Powers? I'm not sure what.

Homework Statement For the SHO, find these commutators to their simplest form: [a_{-}, a_{-}a_{+}] [a_{+},a_{-}a_{+}] [x,H] [p,H] Homework Equations The Attempt at a Solution I though this would be an easy problem but I am stuck on the first two parts. Here's what I did at first...

Consider the following commutator for the product of the creation/annihilation operators; [A*,A] = (2m(h/2∏)ω)^1 [mωx - ip, mωx + ip] = (2m(h/2∏)ω)^1 {m^2ω^2 [x,x] + imω ([x,p] - [p,x]) + [p,p]} Since we have the identity; [x,p] = -[p,x] can one assume that.. [x,p] - [p,x] =...

Hey everyone Let's say I have two generators, a and b, with the following relations: a^{5}=b^{2}=E bab^{-1}=a^{-1}; Where E is the Identity element. What I've done so far is this - the number of elements of the group is the product of the exponents of both generators, which is 10...

Abstract Algebra: Relations; Find a relation that is symmetric, etc Homework Statement Find a relation that is symmetric and transitive but not reflexive. Homework Equations None, other than my chosen condition on the relation, namely: xy > |x + y|. The Attempt at a Solution...

Hi Say I have a finite data set (frequency, absorption) and I would like to find the corresponding dispersion. For this I could use the Kramers-Kronig (KK) relation on the absorption data. What I would do is to make a qubic spline and then perform the KK-transformation. However, the absorption...

I'm having copious amounts of trouble with this question and an amount of help would really be appreciated. Let S be the relation on the set of real numbers defined by x S y iff x-y is an integer 1. prove that S is an equivalence...

I'm trying to understand the transformation relations for 2d stress and the book doesn't show the derivation of the 2d stress transformation relations from the directional cosines. The 2d stress transformation relations are found by using the transformation equation and the 2d directional...

If {{a,b},{c}} is the partition of {a,b,c}. When finding the equivalence relation used to generate a partition, is it enough to say {a,b}x{a,b} U {c}x{c}? Thanks Andy

Homework Statement Prove the following properties of relations: 1) If R is asymmetric then it's antisymmetric. 2) If R is asymmetric then it's irreflexive. 3) If R is irreflexive and transitive then it's asymmetric. The Attempt at a Solution 1) If R is asymmetric on a set X, then for all...

I have been asked to prove the following limit relations. (a) lim(as x goes to infinity) (b^x-1)/x = log(b) (b) lim log(1+x)/x = 1 (c) lim (1+x)^(1/x) = e (d) lim (1+x/n)^n =e^x Unfortunately, I really have no idea where to start. We have a theorem that says if f(x)=the sum of (c...

The following are Maxwell's Relations right? \left(\frac{\partial s}{\partial v}\right)_{T} = \left(\frac{\partial p}{\partial T}\right)_{v} \left(\frac{\partial s}{\partial p}\right)_{T} = - \left(\frac{\partial v}{\partial T}\right)_{p} Are these all? And BTW, these are derived from the...

need help on this ..any suggestions are highly appreciatedConsider the set of positive rational numbers Q+ . Consider the relation r defined by (x,y) ∈ r<=> x/y ∈ Z. Show that r is a partial order and determine all numbers greater than 1/2.

Homework Statement Show that there exists a group of order 21 having two generators s and t for which s^3 = I and sts^{-1} = t^2. Do this exercise by constructing the graph of the group.Homework Equations Based on the given relations, we have t^7 = I.The Attempt at a Solution Since ##s## and...

Homework Statement Verify ##\left[ x^{i} , p_{k}\right] = i \hbar \delta^{i}_{k}## Homework Equations ## p_{j} = -i \hbar \partial_{j}## The Attempt at a Solution Writing it out i get $$ i \hbar \left( \partial_{k} x^{j} - x^{j} \partial_{k} \right)$$ The Kronecker makes perfect sense, it's...

Helloo! I have to solve the following recurrence relations: (a) T(n)=sqrt(2)*T(n/2)+lgn (b) T(n)=3*T(n/4)+nlgn (c) T(n) 3*T(n/3)+n/2 (d) T(n)=5*T(n/2)+Θ(n) (e) T(n)=9*T(n/3)+O(n^2) Could you tell me if my results are right? Using the master theorem I found: (a)T(n)=Θ(sqrt(n)) (b)T(n)=Θ(nlgn)...

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

Being that anything accelerated to the speed of light gains infinite mass and will require infinite energy thus providing a barrier to achieving the speed of light but wouldn't the fuel source become infinite and in turn the potential for energy become infinite effectively canceling out this...

Homework Statement I want to compose the relation "equality" with the relation "less than" in the form: equal o less than. Homework Equations The Attempt at a Solution Firstly I determine the y in (x,y) such that this is true. Graphically, it is just the values less below y=x...

\forall b\in Z b \equiv 1 (mod 2) \Rightarrow b^{2} \equiv 1 (mod 8) How do I go about proving this? Can the Chinese Remainder Theorem be used to prove this or is there something easier?

Q If cos(alpha)=-sqrt3/5 and alpha is in the third quadrant, find exact values for sin(alpha) and tan(alpha). A. Well what I did was use the pythagorean theorem so (-sqrt3)^2+(opposite)^2=5^2. then in the end I got sqrt22 for opposite so then sin(alpha)=sqrt22/5 and tan alpha =sqrt22/-sqrt3...

Hello everyone, I am currently reading 'Geometrical Methods of Mathematical Physics' by Bernard Schutz and I have some questions about manifolds. I'm fairly new to Differential Geometry so bear with me! On P33 he states that 'manifolds need have no distance relation between points, we...

Hello, I am looking at a problem concerning flow through a converging-diverging nozzle. The governing equations are relatively straight-forward for gasses that closely follow the ideal gas law. However I am looking at an unusual gas which is certainly not represented by the ideal gas...

Here is the question: Here is a link to the question: Discrete Mathematics Question? - Yahoo! Answers I have posted a link there to this topic so the OP may find my response.

Hey, I'm not exactly sure how much this question wants, however the two in question are parts a) and b) below. So part a) asks to write the expression for the total angular momentum J, I though this was just: \hat{J}=\hat{J}^{(1)}+\hat{J}^{(2)} but when we come to showing it...

The context of this question is looking at straggling in plasma. I was told there was a simple differential geometry relationship between the following entities: dE/dx, dE/dy and dE/dt, where x,y are distance in perpendicular directions (axes on a plane), t is time and I'm using E to...

Can anyone explain why we obtain the part where i put the red underline. I understand everything until then

Hello everyone i bought a kit for my senior project on electromagnetic levitation. It uses an electromagnet to suspend a magnet via force of attraction. It is stable because of two hall effect sensors and voltage regulator. The kit can make the magnet move in a sinusoidal and tangential motion...

Homework Statement The question is let E1 and E2 be equivalence relations on set X. A new relation R is defined as the E1 o E2, the composition of the two relations. We must prove or disprove that R is an equivalence relation.Homework Equations The Attempt at a Solution I know that we must...

Show that if R1 and R2 are equivalence relations on a set X, then R1 is a subset of R2 iff every R2-class is the union of R1 classes. Attempt: I don't understand that if R2 has elements nothing to do with the elements of R1, how can an R2 class be a union of those elements belonging to an R1...

How do you find matrices a,b,c satisfying a=b*c*b^-1 b=c*a*c^-1 c=a*b*a^-1 ?

Hi, all! I have trouble by using Mathemtica to solve the following problem as shown on the attachment. You see that the two recursive relations depend one another. I plan to write a "For" loop to evaluate E, instead of using Rsolve (a build-in function in Mathematica), however, I am very new...

I am trying to use generators and relations here. Let M ≤ S_5 be the subgroup generated by two transpositions t_1= (12) and t_2= (34). Let N = {g ∈S_5| gMg^(-1) = M} be the normalizer of M in S_5. Describe N by generators and relations. Show that N is a semidirect product of two Abelian...

A person has inherited a surplus grain mountain of 30000 tonnes held in a warehouse.each year 5% of the grain is eaten by mice.The person is obliged to add N tonnes each year.find the maximum of N such that mountain will decrease in size. This is what I have understood the problem...

Homework Statement Let G = \langle x,y \ | \ x^2, y^3, (xy)^3 \rangle, and f: G \rightarrow A_4 the unique homomorphism such that f(x) = a, f(y) = b, where a = (12)(34) and b = (123). Prove that f is an isomorphism. You may assume that it is surjective. Homework Equations N/A The...

In thermodynamics one of the maxwell relations is: \left( \frac{\partial S}{\partial V} \right)_T = \left( \frac{\partial P}{\partial T} \right)_V When I try to derive it from dU = TdS - PdV i get: T = \left( \frac{\partial U}{\partial S} \right)_V P = -\left( \frac{\partial...

Our math Teacher asked us to find how many equivalence relations are there in a set of 4 elements, the set given is A={a,b,c,d} I found the solution to this problem there are 15 different ways to find an equivalence relation, but solving the problem, i looked in Internet that the number of...

Our math Teacher asked us to find how many equivalence relations are there in a set of 4 elements, the set given is A={a,b,c,d} I found the solution to this problem there are 15 different ways to find an equivalence relation, but solving the problem, i looked in Internet that the number of...

Hello there, This might be probably a simple question, but my wondering was: Is there any relation between the compactness and the connectedness of a topological space? Let us consider the specific example (of interest for me) of a subdomain D of a 3D Riemannian manifold. i) If D is...

Homework Statement For an ideal gas the slope of an isotherm is given by (∂P/∂v) constant T = -P/v and that of an isochore is (∂P/∂T) constant v = P/T Show that these relations give Pv = RT Homework Equations Pv = RT The Attempt at a Solution I have never worked with...

Homework Statement I'm working on problem 6.11 in Bransden and Joachain's QM. I have to prove 4 different recurrence relations for the associate legendre polynomials. I have managed to do the first two, but can't get anywhere for the last 2 Homework Equations Generating Function: T(\omega...

Hi there, I am writing up a labratory report at the moment and I am a little confused about the phase realtive to v(capacitor) relative to v(resistor). In a circuit with a capacitor and a resistor, how will the phase change when the frequency is changed? Say from 100Hz to 1kHz to 10kHz...

PROBLEM: Laser pulses of femptosecond duration can be produced, but for such brief pulses it makes no sense to speak of the ‘color’ of the laser. To demonstrate this, compute the time duration of a laser pulse whose range of frequencies covers the entire visible spectrum (4.0*10^14 Hz to...

Hi. I've been thinking about this proof for over a day now and have reached the point where I can't come up with any new approaches! I'm trying to prove equation (5.15) in these notes: http://www.damtp.cam.ac.uk/user/tong/qft/qft.pdf Just above eqn (5.15) we are told that the proof...