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. E

    Commutator Relations vs. Schrodinger Equation

    Some books begin QM by postulating the Schrodinger equation, and arrive at the rest. Some books begin QM by postulating the commutator relations, and arrive at the rest. Which do you feel is more valid? Or are both equally valid? Is one more physical/mathematical than the other? I...
  2. L

    Equivalence Relations on [0,1]x[0,1] and Hausdorff Spaces

    We have a equivalence relation on [0,1] × [0,1] by letting (x_0, y_0) ~ (x_1, y_1) if and only if x_0 = x_1 > 0... then how do we show that X\ ~is not a Hausdorff space ?
  3. J

    How to Calculate Symmetric Relations in Set Theory?

    Hi. Let A = 1,2,3,4,5,6,7 How many symmetric relations on A contain exactly (a) four ordered pairs, (b) 5 , (c) seven and (d) eight The book has solutions to the first two, which I didn't understand at all. Please look the pic below Can someone guide me through how to approach the problem...
  4. I

    Formal power series and non/homogeneous recurrence relations

    Homework Statement Homework Equations We're using generating functions, and recurrence relations of homogeneous and non-homogeneous types The mark allocation is 2, 3, 3 and 2 The Attempt at a Solution I think I've done the first part correctly. The closed form is in terms...
  5. I

    Generating functions and Recurrence relations using the Fibonacci sequence

    We're using generating functions, and recurrence relations of homogeneous and non-homogeneous types The mark allocation is 2, 3, 3 and 2 The Attempt at a Solution I think I've done the first part correctly. The closed form is in terms of z, right? I get: F(z) = z / (1 - z - z2)...
  6. S

    Calculating all possible relations of 2 sets?

    A={1,3,5} B={4,6,8,10} The set AXB that we have been using had 4096 subsets. Why? Can you find a general procedure for calculating the number of possible relations where there are k ordered pairs available? I don't know how to calculate how many relations there are? The only information I...
  7. D

    Proving Equivalence Relations for Real Numbers x, y, z in R

    x,y,z\in\mathbb{R} x\sim y iff. x-y\in\mathbb{Q} Prove this is an equivalence relation. Reflexive: a\sim a a-a=0; however, does 0\in\mathbb{Q}? I was under the impression 0\notin\mathbb{Q} Symmetric: a\sim b, then b\sim a Since a,b\sim\mathbb{Q}, then a and b can expressed as...
  8. D

    Smallest Equivalence Relation on Real Numbers: Proving with Line y-x=1

    1) Recall that an equivalence relation S on set R ( R being the reals) is a subset of R x R such that (a) For every x belonging to R (x,x) belongs to S (b) If (x,y) belongs to S, then (y,x) belongs to S (c) If (x,y) belongs to S and (y,z) belongs to S then (x,z) belongs to S What is the...
  9. S

    Heisenberg Uncertainty Relations - angular momentum and angular displacement

    Homework Statement Starting from one of the more familiar Heisenberg Uncertainty Relations, derive the Uncertainty Relation involving angular momentum and angular displacement and explain its significance. Homework Equations The relevant uncertainty relationship is that between...
  10. H

    Viete's Relations: Solving Cubic Equations

    I'm having trouble with number three. I know Viete's relations are X1+X2+X3, X1X2+X1X3+X2X3, and x1x2x3 for a cubic equation.
  11. N

    Understanding Dispersion Relations in Fluid Dynamics

    I am having trouble understanding a basic problem in fluids that came up during an exam I took last quarter. Namely, we are given a dispersion relation and asked to quantify how a one dimensional surface disturbance propagates in space. (The disturbance is initially an approximate delta function...
  12. I

    Significance of Commutation Relations

    I am aware that the commutation relation between conjugate variables shows that one quantity is the Fourier transform of the other, and so to imply the Heisenberg Uncertainty condition. So for example, the commutation relation between x, p (position and momentum respectively) leads to a non-zero...
  13. T

    Beginner's mathematical proof / composition of relations

    Homework Statement Suppose r and s are two positive real numbers. Let Dr and Ds be defined as in part 3 of Example 4.3.1. What is D_r \circ D_s? Justify your answer with a proof. (Hint: In your proof, you may find it helpful to use the triangle inequality.) Homework Equations Example 4.3.1...
  14. D

    References for non-vacuum dispersion relations

    Hi guys, I'm looking for some references where dispersion relations, say for photons, are explicitely written out in a generic medium. In other words, the dispersion relation for particles not propagating in the vacuum is a different one than the standard vacuum one E^2 = p^2 + m^2 and I'm...
  15. U

    N-ary relation as a combination of binary relations

    Hello, I am looking for a formal way to represent an n-ary relation as a combination of binary relations and logical connectives. Suppose we have a set A, a set B = \{b: b\subseteq A^2\} of binary relations over A, and a set of logical connectives C = \{\neg, \wedge, \vee\}. We define a set...
  16. K

    Understanding Equivalence Relations in Real Numbers and Vector Spaces

    Homework Statement I have got myself very confused about equivalence relations. I have to determine whether certain relations R are equivalence relations (and if they are describe the partition into equivalence classes, but I'll worry about that once I understand the first part). Here are...
  17. S

    Is RxS an Equivalence Relation on ExF?

    Homework Statement I need a little help in understand this question: Let E and F be two sets, R a binary relation on the set E and S a binary relation on the set F. We define a binary relation, denoted RxS, on the set ExF in the following way ("coordinate- wise"): (a,b) (RxS) (c,d) <-->...
  18. R

    Equivalence relations and equivalence classes

    Hey! Hoping you guys could help me with a small issue. No matter how hard I try, I don't seem to fully understand the notion of an equivalence relation, and henceforth an equivalence class. What I do understand that, in order to have and equivalence relation, it is defined to satisfy three...
  19. N

    Quantification logic and equivalence relations

    I wasn't sure whether to post this in the algebra forum or here, but it seems that this is more of a logic question so I'm going with here. I am trying to understand whether there is a difference between the following two definitions of an equivalence relation: Definition 1: A binary relation...
  20. X

    Uncertainty relations aren't Lorentz covariant

    Heisenberg's uncertainty relations are not covariant under Lorentz transformation. That means they don't have the same form in any inertial frame. So, how to modify these relations to leave them invariant in form under a Lorentz transformation ?
  21. L

    Classifying Functions from {1,2,3} to {1,2} and Finding Right Inverses

    Homework Statement List all the functions from {1,2,3} to {1,2} representing each function as an arrow diagram. Which of these functions are (a) injective, (b) surjective, (c) bijective? For each surjective function write down a right inverse. Homework Equations The Attempt at a...
  22. K

    [Differential Geometry] Simple relations between Killing vectors and curvature

    First of all, hello :) I'd like to request some aid concerning a problem that is really getting to me. I know it should be simple but I'm not getting the right results. Homework Statement Given that V^{\mu} is a Killing vector, prove that: V^{\mu;\lambda}_{;\lambda} +...
  23. C

    Hydrogen-powered car relations to science?

    Hi, I am in grade 10 and for my final project, I am writing a report on hydrogen cars. We need to relate hydrogen cars to chemistry, ecology, climate change, and light and geometric optics. Can someone tell me how hydrogen powered cars relate to each of these? I am really unsure and need...
  24. L

    Am I Getting the Hang of Relations

    1. R on the set (the reals) defined by xRy iff (x < 0) or (x > or equal to 0 and x = y) 2. None 3. Reflexive - Yes, since no matter what x I choose, x will always be equal to x, and will therefore fit the conditions of the relation. Symmetric - It is symmetric because if I...
  25. L

    Question about Properties of Relations

    1. The question is: P on the set, A, of all people, where xPy means x is a parent of y. Homework Equations - None 3. Attempts at a Solution Here is where I am confused. Reflexivity is defined by aRa. So I am unclear what to do with more than one variable. So in this question, do I...
  26. M

    NESC Line Relations: Clarifying Section 220.B.2.b

    I have a question about a confusing section of the NESC (not that many sections are not confusing, but this is my current issue). Section 220.B.2.b reads as follows That the supply circuits be placed on the end and adjacent pins of the lowest through signal support arm and that a 750 mm (30...
  27. D

    Transitive Relations on Finite Sets of Size n

    How many transitive binary relations are there on a finite set of size n?
  28. B

    Deriving Relations Between Generating Functions via Legendre Transformations

    Homework Statement Problem 9.7(a) of Goldstein, 3rd edition: If each of the four types of generating functions exists for a given canonical transformation, use the Legendre transformations to derive the relations between them. Homework Equations F = F1(q,Q,t) p = partial(F1)/partial(q) P =...
  29. G

    Combined gas law vs. adiabatic relations

    Why is there a difference when calculating pressure temperature and volume using the combined gas law, or when using adiabatic relations? As an idiot I am very confused. Why must I use a very similar equation to calculate the final temperature of an ideal gas but resulting in very different...
  30. T

    Incertitude relations from QFT

    Hello, There are no incertitude relations in QFT. On the other hand, these incertainty relations do exist in non-relativistic QM. How can we reconcile these two facts ? Is it possible to "derive" uncertainty relations from QFT by "taking the non-relativistic limit" ? Thanks !
  31. H

    Transitive Closure of Binary Relation T on A={0,1,2,3}

    Homework Statement T is a binary relation defined on A = {0, 1, 2, 3}. Let T = {(0,2), (1,0), (2,3), (3,1)} Find T^t, the transitive closure of T.The Attempt at a Solution I'm going to skip using commas cause it takes to long 02 23 = 03 31 10 = 30 23 31 = 21 10 02 = 12 12 23 = 13 02 21 = 01...
  32. D

    Equivalence Relations on Integers with a Unique Property

    This is a question from A consise introduction to pure mathematics (Martin Liebeck) Hi guys, just stuck on one problem was wondering if someone could lend me hand. Let ~ be an equivalence relation on all intergers with the property that for all "m" is an element of the set of intergers ...
  33. V

    Dirac Gamma Matricies and Angular Momentum Commutation Relations

    Homework Statement This isn't really the problem, but figuring this out will probably help me with the rest of the problem. I want to know what [\gamma^0, L_x] is. Homework Equations I know the commutation (or rather anticommutation) relations between the gamma matricies, and I know the...
  34. D

    Equivalence Relations on Integers: Proving Equivalence for All Elements

    This is a question from A consise introduction to pure mathematics (Martin Liebeck) Hi guys, just stuck on one problem was wondering if someone could lend me hand. Let ~ be an equivalence relation on all intergers with the property that for all "m" is an element of the set of intergers ...
  35. I

    Binary relations: weak order, strict partial order, equivalence

    Homework Statement I'm totally lost about this. I know the properties of binary relations (or at least I think I know them, what it means to be transitive, complete etc). This exercise asks me to show that P and I are strictly partial and equivalent respectively when P and I are defined...
  36. N

    Recovering the generator of rotation from canonical commutation relations

    I'm having a course in advanced quantum mechanics, and we're using the book by Sakurai. In his definition of angular momentum he argues from what the classical generator of angular momentum is, and such he defines the generator for infitesimal rotations as...
  37. K

    Commutation Relations and Ehrenfest

    Homework Statement Let \psi(\vec{r},t) be the wavefunction for a free particle of mass m obeying Schrodinger equation with V=0 in 3 dimensions. At t=0, the particle is in a known initial state \psi_0(\vec{r}). Using Ehrenfest's theorem, show that the expectation value <x^2> in the state...
  38. C

    Q: About the relations bitween the inflation and matter's properties

    My question goes like this: Did the inflation following the Bing Bang caused matter to emerge as it is in our universe? In other words, was it the inflation itself that gave matter - electrons, neutrons and protons - its properties (physical size, quantums, velocity, mass), or perhaps the two...
  39. D

    Defining relations for an n-tuple

    Given an element (6, 5, 4) of S (that is {(6, 5, 4)} is a subset of S); assuming S is a relation, how exactly do we donate the relations between the elements of the 3-tuple formed in this case; the relation can be of 3 sorts (in a 3-tuple) - 6S5 6S4 5S4 Out of these 3 how many relations...
  40. J

    Is a Symmetric and Transitive Relation Always Reflexive?

    Statement: Prove or Disprove: A relation ~ on a nonempty set A which is symmetric and transitive must also be reflexive. Ideas: If our relation ~ is transitive, then we know: a~b, and b~a \Rightarrow a~a. Therefore our relation ~ is reflexive, since b~c and c~b \Rightarrow b~b, and c~a...
  41. B

    Equivalence Relations on Set S: Description and Number of Classes

    Hello! I'm a bit lost on these questions pertaining to equivalence relations/classes. If someone could run me through either, or both, of these questions, I'd be very thankful! I'm completely lost as to what to do with the z in terms of set S... Homework Statement Show that the given...
  42. Somefantastik

    Are these the correct cos and sin relations for the given values?

    if \mu = cos(\theta) and \mu_{0} = cos(\theta_{0}) and cos(\pi - \Theta) = \mu_{0}\mu + \sqrt{1-\mu_{0}^{2}}\sqrt{1-\mu^{2}}cos(\phi) Then cos(\pi - \Theta) = cos(\theta_{0})cos(\theta) + sin(\theta_{0})sin(\theta)cos(\phi) Is this not correct?
  43. D

    Looking for a Book on Sets, Groups, and Relations with Exercises?

    Hi, I would like to know if you guys know a good book on sets groups and relations, preferably with lots of exercises. I believe that I am on a beginner level, but I already know all basic concepts, so the text is not that important. It would be even better if it is available online hehe! Thks!
  44. B

    Blast Waves and Scaling Relations

    One of the outstanding questions I have in physics relates to scaling relations. Say you're presented with a problem like: Find X--which has units of y--given that the relevant (dimensional) quantities of this problem are A, B, C, and D. Then you construct a solution using these quantities...
  45. A

    Commutation Relations and Symmetries for SU(2)

    Homework Statement I'm working through a bit of group theory (specifically SU(2) commutation relations). I have a question a bout symmetries in the SU(2) group. It's something I'm trying to work through in my lecture notes for particle physics, but it's a bit of a mathsy question so I thought...
  46. J

    Proving R is an Equivalence Relation on R^2

    A relation R on R^2 is defined by (x_{1},y_{1})\mathit{R}(x_{2},y_{2})\;\;\;if\;\;\;x_{1}^{2}+y_{1}^{2}=x_{2}^{2}+y_{2}^{2} How do you show that R is an equivalance relation?
  47. M

    Help with Binary Relations Homework

    Hello :smile: I was wondering if I could get some help with work on Binary Relations. We've done very little of this in class, and hours of Googling has provided little help. So I was hoping that someone could look over my attempts at the questions and let me know if I've gone wrong...
  48. facenian

    Is the Commutation Relation for Angular Operators in Hilbert Space Valid?

    There must something wrong with my understanding of this relations because I think the usual way they are derived in many textbooks makes no sense. It goes like this, first assume that to every rotation O(a) in euclidean space there exists a rotation operator R(a) in Hilbert space,second: the...
  49. S

    Power/Torque Relations: Exploring the Imperial vs. Metric Equations

    Hi all.. I've been seeing the famous equation which 'converts' horsepower into torque: HP = Torque (lb/ft) * rpm / 5252. The 1/5252 comes from 2*PI/33,000. Power (rotational) is simply torque * angular velocity, isn't it? When I try to plot the imperial version, I get the typical graph with HP...
  50. R

    Pressure Relations in Pipe Flow of Viscous Fluid

    In pipe flow of a viscous fluid, what happens to the head lost due to friction and "minor losses" (pipe bends, valves, etc).?I mean, if you decrease the dynamic pressure by reducing flow velocity, then the static pressure increases. If the dynamic pressure increases then the static pressure...
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