Relations Definition and 579 Threads

Industrial relations or employment relations is the multidisciplinary academic field that studies the employment relationship; that is, the complex interrelations between employers and employees, labor/trade unions, employer organizations and the state.
The newer name, "employment relations" is increasingly taking precedence because "industrial relations" is often seen to have relatively narrow connotations. Nevertheless, industrial relations has frequently been concerned with employment relationships in the broadest sense, including "non-industrial" employment relationships. This is sometimes seen as paralleling a trend in the separate but related discipline of human resource management.While some scholars regard or treat industrial/employment relations as synonymous with employee relations and labour relations, this is controversial, because of the narrower focus of employee/labour relations, i.e. on employees or labour, from the perspective of employers, managers and/or officials. In addition, employee relations is often perceived as dealing only with non-unionized workers, whereas labour relations is seen as dealing with organized labour, i.e unionized workers. Some academics, universities and other institutions regard human resource management as synonymous with one or more of the above disciplines, although this too is controversial.

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  1. N

    Matrices satisfying certain relations

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

    Mathematica Mathematica 8.0 - solve two recursive relations

    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...
  3. J

    MHB Question about generators and relations.

    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...
  4. 9

    Financial mathematics-recurrence relations

    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...
  5. A

    Proving Injectivity of Group Homomorphism Given Relations

    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...
  6. K

    Derivation of Maxwell's relations

    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...
  7. L

    Equivalence Relations in A={a,b,c,d}: Proving the Bell Number Theorem

    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...
  8. G

    Finding Equivalence Relations in a Set of 4 Elements - Juan's Question

    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...
  9. S

    Relations between compactness and connectedness

    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...
  10. K

    Thermodynamics: Show that the two relations give Pv = RT

    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...
  11. C

    Recurrence relations for Associated Legendre Polynomials

    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...
  12. F

    How Does Frequency Affect Phase in a Resistor-Capacitor Circuit?

    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...
  13. P

    Uncertainty Relations & Wave Packets

    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...
  14. L

    Fermion Anticommutation Relations (nightmare)

    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...
  15. C

    Relations, Set Theory, Reflexive, Symmetric, Transitive

    Homework Statement Determine whether the relations on three sets are Reflexive, Irrelfexive, Symmetric,, Asymmetric, Antisymmetric, Transitive, and Intransitive. The relation \subseteq on a set of sets. Homework Equations The Attempt at a Solution I am having trouble figuring out...
  16. B

    Basic Set Theory: Determining Relations: Reflexive, Symmetric, Transitive

    I am taking a philosophy course that covers basic set theory as part of the introduction. I’m not sure in which section of the forum set theory should be, but I think this is the right place. Homework Statement For each of the following relations, indicate whether it is Reflexive...
  17. A

    Why define equivalence relations, posets etc.

    I am studying set theory and I came across various definitions like equivalence relations, partial order relations, antisymmetric and many more. I am aware mathematicians don't care about real life applications but still - why are we defining so many relations? What is the use of defining...
  18. S

    Are These Relations Symmetric?

    Determine which of these relations are symmetric 1) x~y if and only if x-y is positive 2) x~y if and only if xy >= 0 3) x~y if and only if x+2y is positive 4) x~y if and only if x+y is positive 5) x~y if and only if x+y is odd I thought all but 1) but this was wrong. The only one I...
  19. U

    Partial differentiation: thermodynamic relations

    Homework Statement This question is about entropy of magnetic salts. I got up to the point of finding H1, the final applied field. The Attempt at a Solution But instead of doing integration I used this: dS = (∂S/∂H)*dH = (M0/4α)(ln 4)2 I removed the negative...
  20. S

    Discrete Mathematics : Functions and Relations : Question 2c

    Homework Statement c) Is 'g' a surjective function (onto) ? Justify your answer. Homework Equations Let 'f' be a relation on ℤ (the set of integers) , defined by the entrance requirement : (x;y) ∊ ƒ iff y = x + 15 and let 'g' be the function on ℤ defined by the...
  21. S

    Discrete Mathematics : Functions and Relations : Question 2

    Homework Statement Determine the dom(g) Homework Equations Let 'f' be a relation on ℤ (the set of integers) , defined by the entrance requirement : (x;y) ∊ ƒ iff y = x + 15 and let 'g' be the function on ℤ defined by the entrance requirement : (x;y)...
  22. R

    Hyperbolic relations in deriving Lorentz transformations

    Preface to my question: I can assure you this is not a homework question of any kind. I simply have a pedagogical fascination with physics outside of my own studies in school. Also, I did a quick search through the forum and could not find a question similar enough to what I want to know, so i...
  23. J

    Showing that Equivalence Relations are the Same.

    Let G be a group and let H be a subgroup of G. Define ~ as a~b iff ab-1εH. Define ~~ as a~~b iff a-1bεH. The book I am using wanted us to prove that each was an equivalence relation, which was easy. Then, it asked if these equivalence relations were the same, if so, prove it. My initial...
  24. W

    Determining Defining Relations for a Group

    Homework Statement Given some group G with generators g_{1},g_{2},...,g_{n} as well as a description of the action of g on the elements of some set S={s_{1},s_{2},...,s_{k}}, how in general does one go about finding a complete defining relations (and showing they are complete)? Homework...
  25. S

    Is the delta in the commutation relations of QFT a dirac delta or a kronecker?

    If it's a dirac delta doesn't it mean it's infinite when x=y? Or is it a sort of kronecker where it's equal to one but the indices x and y are continuous? I'm confused.
  26. H

    Equivalence Relations on {0, 1, 2, 3}: Understanding Reflexivity and Properties

    Homework Statement Which of these relations on {0, 1, 2, 3} are equivalence relations? Determine the properties of an equivalence relation that the others lack a) { (0,0), (0,2), (2,0), (2,2), (2,3), (3,2), (3,3) } This one is not reflexive Homework Equations I understand that...
  27. N

    [group theory] Finite presentations and relations <S|R>

    Homework Statement Let G be a finitely presented group. Suppose we have a finite generating set S. Prove that there is a finite set of relations R \subset F_S such that <S|R> is a presentation of G. Homework Equations NA The Attempt at a Solution I don't know how to do this. I think...
  28. W

    Generators and Defining Relations on the Symmetric Group of degree n

    Homework Statement I am working through MacLane/Birkhoff's Algebra, and in the section on Symmetric and Alternating groups, the last few exercises deal with generators and Defining relations for Sn (the symmetric group of degree n). These read: 11. Prove that Sn is generated by the cycles (1...
  29. G

    Prove some relations but going round in circles

    Homework Statement I need to prove some relations but going round in circles. ## [\hat{J}_z, \hat{J}_+] = \hbar J_+ ## I've got this: ##\left(a_+^{\dagger }a_+-a_-^{\dagger }a_-\right)\left(a_+^{\dagger }a_-\right)-\left(a_+^{\dagger }a_-\right)\left(a_+^{\dagger }a_+-a_-^{\dagger...
  30. C

    Recurrence relations discrete math problem

    Homework Statement Find the general solution to the following recurrence relations (defined n≥2). c) an=6an-1-9an-2+8n+4 Homework Equations The Attempt at a Solution an=6an-1-9an-2+8n+4 8n+4= an -6an-1+9an-2 R2-6R+9=0 R=3,3 So hn=A(3)n+B(3)n Assume pn=Cn+Cn2 → This is where I got...
  31. S

    What is the meaning of ∅ used in the context of a relation?

    Hi. I am reading Halmos's Naive Set Theory book. I have the following doubts. 1. In chapter 7. on relations, he says "The least exciting relation is the empty one. (To prove that ∅ is a set of ordered pairs, look for an element of ∅ that is not an ordered pair) ". Whenever someone talks...
  32. Dembadon

    Intro to Proofs: Properties of Relations

    Hello, I would like to check my arguments for this problem. Homework Statement Consider the relation R = \{(x,y) \in \mathbb{R} \times \mathbb{R}: x-y \in \mathbb{Z}\} on \mathbb{R} . Prove that this relation is symmetric, reflexive, and transitive. Homework Equations Supposing a relation...
  33. G

    Proving Recursion relations for Bessel Functions

    Homework Statement Solve equations 1) and 2) for J_{p+1}(x) and J_{p-1}(x). Add and subtract these two equations to get 3) and 4). Homework Equations 1) \frac{d}{dx}[x^{p}J_{p}(x)] = x^{p}J_{p-1}(x) 2) \frac{d}{dx}[x^{-p}J_{p}(x)] = -x^{-p}J_{p+1}(x) 3) J_{p-1}(x) + J_{p+1}(x) =...
  34. E

    Transition from Poisson bracket into Canonical Commutation Relations

    In book http://www.phy.uct.ac.za/people/horowitz/Teaching/lecturenotes.pdf in section 2 it is described transition from Poisson bracket into Canonical Commutation Relations. But it is written The experimentally observed phenomenon of incompatible measurements suggests that position and...
  35. L

    Weinberg QFT - Inner product relations, Standard momentum, Invariant integrals

    Weinberg in his 1st book on QFT writes in the paragraph containing 2.5.12 that we may choose the states with standard momentum to be orthonormal. Isn't that just true because the states with any momentum are chosen to be orthonormal by the usual orthonormalization process of quantum mechanics...
  36. 1

    Finding the Composition of Relations

    Homework Statement R = { (1,2), (3,5), (2,2), (2,5) } S = { (2,1), (5,3), (5,1), (5,5) } Explicitly find the relation R^-1 o S^-1 Homework Equations The Attempt at a Solution This was on my test. First I just wrote down the inverses: R^-1 = { (2,1), (5,3), (2,2), (5,2)...
  37. S

    Proving recursion relations. BFGS non linear optimization

    Homework Statement Please see attached thumbnail Here's what I know. 1)Bk is the Hessian 2) sk = \alpha*p 3)pk is the search direction 4) Alpha is the step size Homework Equations yk = \nablaf(xk+1) -\nablaf(xk Bk+1(xk+1-xk) = \nablaf(xk+1) -\nablaf(xk The Attempt at a Solution...
  38. A

    Showing a bijection between a set of functions and a set of relations

    Homework Statement With X and Y being sets, I need to show that there is a bijection between the set of functions (X->P(Y)) and the set of relations P(X x Y) where P(..) is the power set symbol. Homework Equations P(Y) = {Z | Z subset of Y} The Attempt at a Solution I know a bijection...
  39. S

    Commutation relations for Spin opertors

    Dear physicist, I designed an experiment for my undergraduate students. As we know, for spin operators, the commutation relation is [Si,Sj]=ihSk We also know, if we use two polarizers which are perpendicular each other, there is no light other side after polarizers. Namely apparatus is...
  40. H

    Understanding Equivalence Relations: Simplifying Vectors with Linear Algebra

    Hi. I've starting working with vectors in linear algebra but I need to have previous knowledge of equivalence relations so I started studying that but I have a simple doubt with the following relation: $$R = \{ (a,b)/a,b \in A,{\text{ a - b is an integer multiple of 2}}\} $$ In this case could...
  41. sankalpmittal

    Problem regarding relations and functions .

    Problem regarding "relations and functions". There are 3 very mini problems so I thought it would be rather fine to adjust them in a single thread. Homework Statement (i) Find the range of the function : f(x) = 2-3x , x\inR , x>0 Note : R is universal set containing real numbers in all the...
  42. teroenza

    Compositions Of 2 Relations, one is the Entire Plane

    Homework Statement Sketch the compositions S of R R of S Homework Equations The relations to be... "composition'ed?". R= R^2, the XY plane, i.e. {(x,y)}, the set pf all (x,y) S= {(x,y) : y=x^3}, set of all (x,y) such that y=x^3 For example R of S = {(a,c) : \existsb such that a^3=b and...
  43. C

    Trying to verify these work relations

    I need to verify these three work relations and don't know where to even start. Wtotal= ΔK, Wc= -ΔU and Wnc = ΔE The details for the whole problem were A block of mass m1 = 2.40 kg is connected to a second block of mass m2 = 1.80 kg, as shown in the figure. The two masses start from rest...
  44. U

    Closure of relations betweens sets

    Hi all! I am searching for an algorithm (most likely already present in the literature) that could solve the following problem: Instance: Properties of sets of elements and relations between sets of elements Question: Find the closure of the properties and relations Possible properties...
  45. S

    Relations Involving the Directional Cosines

    Greetings, I wonder if a proof of the relation between the directional cosines of two vectors and cosine between two vectors is available? In order to clarify what I meant I put a screen shot from Vector and Tensor Analysis by Hay.
  46. K

    Relations between classical and quantum time-evolution of fields

    This question is going to be a bit vague and might lead to nowhere, but still I'll take the risk and try to ask it here. I know in general how to quantize a field, and from the quantized field one gets the quantized Hamitonian thus the time-evolution operator. However, I wonder what're the...
  47. F

    Pauli-Lubanski pseudovector commutation relations

    Homework Statement Hi. This is not a homework question per se, but more of a personal question, but I thought I'd post it here. I'm trying to prove the commutation relations of the Pauli-Lubanski pseudovector \begin{equation} W_\mu\equiv-\frac{1}{2}...
  48. G

    Maxwell's Relations Derivative P,V,T,Cp,Cv

    Homework Statement Express (dA/dV)p in terms of P,V,T,Cp,Cv and their derivatives. Your answer may include absolute values of S if it is not a derivative constraint or within a derivitiveHomework Equations Maxwell's equations Product Rule Chain&Expansion ruleThe Attempt at a Solution Using the...
  49. F

    Contrapositive proof of irrational relations

    I'm confused with a question and wondered if anyone could help explain where I need to go... let x ε R. Prove that x is irrational thenI'm confused with a question and wondered if anyone could help explain where I need to go... let x ε R. Prove that x is irrational then ((5*x^(1/3))-2)/7)...
  50. T

    Synergistic relations between computer science and technology.

    I need some topics to write about for my research paper. I'm writing about how computer science and technology both force the other to expand. The 3 examples I'm writing about now are hardware/processor enabled security (ie I'm comparing 16bit x86 which had no security to 32bit which did)...
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