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. M

    Restore indirect relations within a transitive relation

    Hi, I have a transitive relation and wana build a complete set of pairs that reflect all (direct/indirect) relations among the pairs. Ex.: suppose I have this relation R = { (1,2), (2,3), (3,5), (5,7), (3,4) } I wana to produce this relation R oper R = { (1,2), (1,3), (1,4), (1,5)...
  2. E

    Sets - Relations - proof involving transitivity

    I'm having trouble with the following: Let R be a relation on A. Prove that if Dom(R) \bigcap Range(R) = ø, then R is transitive. I took the negation of the "R is transitive" to try proof by contrapositive (as the professor suggested), and have the following: \exists x,y,z \in A s.t. (x,y)...
  3. B

    MacroEcon, Stock Prices, Recurrence Relations (and Linear Algebra?)

    Homework Statement This is a question from an upper level econ course that is giving me quite a bit of trouble. Fluency in linear algebra is assumed for the course. I'm taking a linear algebra course for the first time this semester so I'm still scrambling to learn the basics. If anyone has a...
  4. B

    Kramers-Kronig relations for the wavenumber

    Hi all, I am wandering if I can apply the Kramers-Kronig (KK) relations to the complex wavenumber k(ω) = k'(ω) + i k"(ω). I have a measurement that easily gives me k'(ω) for a certain range of frequencies, but where k"(ω) is unreliable. I would like to use KK to find k" from k'. According...
  5. N

    Functions and Relations: Solving for f, g, and h

    If f(x)= 2x+5, g(x)=0.5 and h(x)=3-1 find: fg(x), gf(x), fh(3) fg(x) fg(x)= 2(0.5x)+5 fg(x)= x+5 gf(x)= 0.5(2x+5) = x+2.5 fh(3) fh (x) =2(3-1)+5 = 6-2+5 = 4+5 this last part of the question been puzzling me... could I get a little...
  6. liometopum

    Unusual uncertainty relations question

    What are the uncertainty relations for the following: 1. position and energy? 2. position and time?
  7. O

    Showing Commutator Relations for [L^2, x^2]

    I'm doing something horribly wrong in something that should be very easy. I want to show that: [L^2, x^2] = 0 So: [L^2, x x] = [L^2, x] x + x [L^2, x] L^2 = L_x^2 + L_y^2 + L_z^2 Therefore: [L^2, x] = [L_x^2 + L_y^2 + L_z^2, x] = [L_x^2, x] + [L_y^2, x] + [L_z^2, x] = L_y [L_y...
  8. M

    Finding 8 Relations on a Set of 3 Elements with the Same Symmetric Closure

    Homework Statement Show that if a set has 3 elements, then we can find 8 relations on A that all have the same symmetric closure. Homework Equations Symmetric closure ##R^* = R \cup R^{-1} ## The Attempt at a Solution If the symmetric closures of n relations are the same then...
  9. M

    Understanding Set Relations: Exploring Principles and Notations

    Homework Statement I've actually got a couple questions, I'll provide an example for each question, but I'm not really looking for an answer to the example, but an explanation of the concept. I have very little to go on from class notes. We've had some inclement weather in these parts leading...
  10. 3

    Equivalence Relations, Cardinality and Finite Sets.

    Hey everyone, I have three problems that I'm working on that are review questions for my Math Final. Homework Statement First Question: Determine if R is an equivalence relation: R = {(x,y) \in Z x Z | x - y =5} and find the equivalence classes. Is Z | R a partition? Homework...
  11. R

    Hyperbolic geometry - relations between lines, curves, and hyperbolas

    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?)...
  12. M

    Two relations between bounded variation and Riemann-Stieltjes integral

    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...
  13. H

    Beam Splitter - Commutation relations

    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)] =...
  14. 4

    Is R Transitive if R^2 is a Subset of R?

    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...
  15. C

    Commutation relations between P and L

    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...
  16. D

    Pauli matrices and the Levi-Civita tensor : commutation relations

    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!
  17. K

    Binary Relations Between Sets A and B: Quick Question

    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.
  18. H

    SHO ladder operators & some hamiltonian commutator relations

    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...
  19. L

    Commutator Relations; Conjugate Product of a Dimensionless Operator

    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] =...
  20. D

    Finding the elements of a group given two generators and relations

    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...
  21. R

    Abstract Algebra: Relations; Find a symmetric and transitive relation in Z x Z

    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...
  22. B

    Partial order relations, on boolean algebra

    I am a bit confused about a question on proving partial order relation. here is the question and what i done so far. "define the relation '≤' on a boolean algebra B by for all x,yεB x≤y if and only if xVy=y, show that '≤' is a partial order relation" first of all what exactly does...
  23. N

    Kramers-Kronig relations on a finite data set

    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...
  24. H

    MHB Proving Equivalency Relations: Help from Henry

    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...
  25. R

    Transformation relations tensors

    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...
  26. A

    MHB Equivalence Relation: Partition of {a,b,c} - Andy

    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
  27. P

    Help proving some basic properties of relations

    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...
  28. M

    How Do I Prove These Mathematical Limit Relations?

    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...
  29. J

    Maxwell's Relations of Thermodynamic Functions

    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...
  30. F

    Asymptotic relations for equations Euler-Bernoulli

    Homework Statement I need help with asymptotic relations of the equation below x=f(y) with f(y)=0 I not know how to address the problem Homework Equations σzz={β3∇4h(x,y) if x<f(y) 0 if x>f(y)...
  31. S

    MHB Partial Order Relation on Positive Rational Numbers and Numbers Greater Than 1/2

    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.
  32. E

    [Group Theory] Constructing Cayley Graph from Given Relations

    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...
  33. P

    Verify the commutation relations for x and p by definition.

    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...
  34. M

    MHB Solving Recurrence Relations: Are My Results Right?

    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)...
  35. Fernando Revilla

    MHB Total order relations on a finite set

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

    Speed of light and relations to mass

    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...
  37. H

    Will you check my solution to a relations question.

    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...
  38. J

    Proving Modular Relations: b ≡ 1 (mod 2) ⇒ b² ≡ 1 (mod 8)

    \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?
  39. A

    Is the Calculation for Sin and Tan Correct Given Cos in the Third Quadrant?

    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...
  40. M

    Do Manifolds have distance relations between points?

    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...
  41. J

    Isentropic Relations for Real Gas in Converging-Diverging nozzle

    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...
  42. MarkFL

    MHB Bryan's question at Yahoo Answers regarding linear recurrence relations

    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.
  43. T

    Prove Green's Relations for Semigroup Morphism

    Homework Statement If \phi : S \to T is a semigroup morphism then show that if a\; \mathcal{R} \;b in S then a\phi \; \mathcal{R} \; b\phi in T. Homework Equations Recall that if S is a semigroup then for a\in S aS = \{as : s \in S \}\text{,}\;\;\;aS^1 = aS \cup \{a\}\text{.} The...
  44. S

    Total Angular Momentum Commutation Relations for 2 Particle

    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...
  45. A

    Differential Geometry Relations, relating to plasma physics.

    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...
  46. H

    Recurring relations solving differential equations

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

    Electromagnetic levitation Relations

    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...
  48. J

    Composition of two equivalence relations

    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...
  49. C

    RLC circuit, finding relations and forming a differential equation

    Hello. I'm having a hard time solving this homework question, even though I know I shouldn't... but well. Here's the problem : -The K switch is closed for a long time, so as to be in a steady state. What's the electric charge of the capacitor ? Infer vs tension from this. Which...
  50. B

    Equivalence relations and classes

    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...
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