What is Relations: Definition and 579 Discussions

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. John Greger

    Showing That $\frac{d}{d_a} F_a(\hat{X}) \cdot \psi = F'(x) \psi$ at a=0

    Homework Statement Consider the operator ##F_a(\hat{X}) =e^{ia \hat{p} / \hbar} \cdot F(\hat{X}) e^{-ia \hat{p} / \hbar}## where a is real. Show that ##\frac{d}{d_a} F_a(\hat{X}) \cdot \psi = F'(x) \psi## evaluated at a=0. And what is the interpretation of the operator e^{i \hat{p_a} /...
  2. J

    A Holographic Relations for OPE Blocks in Excited States

    Holographic Relations for OPE Blocks in Excited States https://arxiv.org/pdf/1809.09107.pdf Jesse C. Cresswell†1 , Ian T. Jardine†2 , and Amanda W. Peet†§3 †Department of Physics, University of Toronto, Toronto, ON M5S 1A7, Canada §Department of Mathematics, University of Toronto, Toronto, ON...
  3. K

    I Weinberg gives relations of SO(3)

    (Weinberg QFT, Vol 1, page 68) He considers Mass-Positive-Definite, in which case the Little Group is SO(3). He then gives the relations Is it difficult to derive these relations? I'm asking this mainly because I haven't seen them anywhere other than in Weinberg's book. Also, I'm finding...
  4. S

    How can I prove that these relations are bijective maps?

    <Moderator's note: Moved from a technical forum and thus no template. Also re-edited: Please use ## instead of $$.> If ##R_{1}## and ##R_{2}## are relations on a set S with ##R_{1};R_{2}=I=R_{2};R_{1}##. Then ##R_{1}## and ##R_{2}## are bijective maps ##R_{1};R_{2}## is a composition of two...
  5. C

    Heat Capacity relations for 1st order phase transition

    Homework Statement Prove the following relation for which clausius equation holds : Cs=Cp-αV(ΔH/ΔV) Where Cs=∂q/∂T at constant S and is the heat capacity in the coexistence line of 2 phases Homework Equations dq=dU+dW dP/dT=ΔH/(ΔV*T) The Attempt at a Solution I do not fully understand why q...
  6. S

    Solving Maxwell Relations Homework with Van der Waals Gas

    Homework Statement [/B] I'm stuck on part c of the attached problem: Homework Equations $$C_P - C_V = \left[P + \left( \frac {∂U}{∂V} \right)_T \right]\left( \frac {∂V}{∂T} \right)_P$$ $$P + \left( \frac {∂U}{∂V} \right)_T = T \left( \frac {∂P}{∂T} \right)_V$$ $$\left(P + \frac {a}{V^2}...
  7. M

    Solving for Attenuation Constant with Power Relations

    Hello. In fields and waves and transmission lines We have a attenuation constant formula with power relations: 1- Alpha = 1/2R0(R+G|Z0|^2) 2-Also we can calculate attenuation constant from these : Z0= radical[(R+jwL) / (G+jwc)] gamma = radical[(R+jwL)(G+jwc)] I want show alpha from 1...
  8. opus

    B Inverse Functions vs Inverse Relations

    If we have a relation, ##R##, and it's inverse, ##R^{-1}## they behave such that a point on ##R##, say (a,b), corresponds to the point (b,a) on ##R^{-1}## This is a reflections across the line y=x. This relation does not mean that ##R^{-1}## is a function. For example, Let ##R## be...
  9. H

    A Commutation relations for bosons and fermions

    For the free boson, the field operators satisfies the commutation relation, $${\varphi}_{x'}{\varphi}_{x} - {\varphi}_{x}{\varphi}_{x'} = 0$$ at equal times. While the fermions satisfies, $${\psi}_{x'}{\psi}_{x} + {\psi}_{x}{\psi}_{x'} = 0$$ at equal times. I interpret ##{\varphi}_{x}## and...
  10. B

    Mastering Maxwell Relations in Thermodynamics: Derivation & Problem-Solving Tips

    I'm studying Thermodynamics and I'm a little stuck at this problem. 1. Homework Statement Starting with the first Maxwell relation, derive the remaining three by using only the relations: $$\left(\frac{\partial x}{\partial y}\right) _{z} \left(\frac{\partial y}{\partial z}\right) _{x}...
  11. K

    MHB Problem understanding relations syntax.

    I have this question:2. Let R be a relation on Z with R = {(a,b) : |a−b| < 3}. (1) Is R reflexive? (If yes, prove it; if no, give a counterexample) (2) Is R symmetric? (If yes, prove it; if no, give a counterexample) (3) Is R antisymmetric? (If yes, prove it; if no, give a counterexample) (4) Is...
  12. Mr_Phil_Osophy

    Which forum should I post in for....

    Hi, I have a question about the bending of spacetime and its proportion and relation to the mass which causes the bending; and also how the bent space would interact with other objects as they come closer. I'm going to ask a more detailed question with some possible problems I would like to...
  13. Mr Davis 97

    Proving that a sequence is always positive given two constraining relations

    Homework Statement Given that ##t_1 = 1## and ##\displaystyle t_{n+1} = \frac{t_n^2 + 2}{2t_n}## for ##n \ge 1##. Show that ##t_n > 0## for all ##n##. Homework EquationsThe Attempt at a Solution Intuitively this is obvious. Since ##t_1## is positive, so is ##t_2##, and so on. But I am having...
  14. B

    MHB Recurrence Relations - Determining a solution of the recurrence relation

    Hello - I am having a tough time understanding the problems in the attached picture (Problem 13). My issue is understanding how I plug in the proposed solutions, specifically those that include n. I am able to solve A and B but unable to solve the rest. For instance, how do I plug in C or...
  15. A

    Quantum Field Theory, Momentum Space Commutation Relations

    Homework Statement Derive, using the canonical commutation relation of the position space representation of the fields φ(x) and π(y), the corresponding commutation relation in momentum space.Homework Equations [φ(x), π(y)] = iδ3(x-y) My Fourier transforms are defined by: $$ φ^*(\vec p)=\int...
  16. pairofstrings

    B Can Multiple Outputs from a Single Input Help in Constructing Non-Linear Curves?

    <Moderator's note: This is a spin-off from another thread.> I will find out axioms to find out an answer to a question - axioms guarantees that my solution to a mathematical problem is correct. I have another question: A function 'y' in 'x' yields a single value as output on an input. Is there...
  17. C

    MHB Can you explain how the law of logic was used to reach this conclusion?

    New to set and graph theory and need help on how to approach these exercise questions: For each of the following relations, state whether the relation is: i) reflexive ii) irreflexive iii) symmetric iv) anti-symmetric v) transitive Also state whether the relation is an equivalence or partial...
  18. M

    MHB Can we simplify the relations of condition number for orthogonal matrices?

    Hey! :o I want to prove the following relations of condition number: $\operatorname{cond}(\alpha A)=\operatorname{cond}(A)$. The matrixnorm is submultiplicativ. $\operatorname{cond}_2(U)=1$ if $U$ is an orthogonal matrix. $\operatorname{cond}_2(UA)=\operatorname{cond}_2(A)$, $U$ is...
  19. Math Amateur

    MHB Antisymmetry & Partial Orderings - H&J Ch.2 Section 5 | Peter's Help

    I am reading "Introduction to Set Theory" (Third Edition, Revised and Expanded) by Karel Hrbacek and Thomas Jech (H&J) ... ... I am currently focused on Chapter 2: Relations, Functions and Orderings; and, in particular on Section 5: Orderings I need some help with H&J's depiction of...
  20. Math Amateur

    MHB What are the properties of partial order relations according to J&W's book?

    I am reading the book: "Discovering Modern Set Theory. I The Basics" (AMS) by Winfried Just and Martin Weese. I am currently focused on Chapter 2 Partial Order Relations ... I need some help with Exercise 1(a) ... indeed, I have been unable to make a meaningful start on the exercise ... :(...
  21. S

    MHB Triangular Relations: Proving (AD)^2+(DE)^2+(AE)^2= \frac{2}{3}(BC)^2

    Given a right ABC trigon with the right angle at A and two points D,E on BC such that: (BD)=(DE)=(EC) Prove: (AD)^2+(DE)^2+(AE)^2= \frac{2}{3}(BC)^2
  22. C

    General commutation relations for quantum operators

    (This is not a homework problem). I'm an undergrad physics student taking my second course in quantum. My question is about operator methods. Most of the proofs for different commutation relations for qm operators involve referring to specific forms of the operators given some basis. For...
  23. S

    I Distinguishing things by relations

    What math is useful for distinguishing and classifying things based only on relations they satisfy? For example the relation ##R_1 = \{(a,b), (b,a)\}## isn't useful for distinguishing "a" from "b" while the relation ##R_2 = \{(a,b), (c,b) \}## let's us distinguish "b" by the description "The...
  24. K

    Relationship between translation and rotation

    Homework Statement Prove or disprove: Every translation is a product of two non-involutory rotations. Homework EquationsThe Attempt at a Solution :[/B] I am not sure if I got the right proof for the special situation: A translation is the product of two reflections with parallel reflections...
  25. Mr Davis 97

    I What is the Definition of a Relation in Set Theory?

    I have an exercise in my set theory book that states the following: Show that a set ##A## is a relation iff ##A \subseteq \operatorname{dom} A\times \operatorname{ran} B##. This is an easy exercise, so I am not asking how to prove it. However, I am confused about one thing. The forward...
  26. S

    I Are there relations that are valid for any field?

    I use the word «field» in purely algebraic sense here. Sometimes, when reading textbooks I encounter sentences like «Although the formulae in this section derived for the field of real numbers, they remain valid for complex numbers field as well». Or even more general variant of it: «...remain...
  27. TeethWhitener

    I Complex scalar field commutation relations

    I'm trying to derive the commutation relations of the raising and lowering operators for a complex scalar field and I had a question. Let's start with the commutation relations: $$[\varphi(\mathbf{x},t),\varphi(\mathbf{x}',t)]=0$$ $$[\Pi(\mathbf{x},t),\Pi(\mathbf{x}',t)]=0$$...
  28. S

    I Understanding the Dirac Commutation Relations in QFT

    Hello! I am reading Peskin's book on QFT and at a point he wants to show that the Dirac field can't be quantified using this commutation relations: ##[\psi_a(x),\psi_b^\dagger(x)]=\delta^3(x-y)\delta_{ab}## (where ##\psi## is the solution to Dirac equation). I am not sure I understand the math...
  29. M

    Angular momentum commutation relations

    Homework Statement Show that ##|l, m\rangle## for ##l=1## vanishes for the commutator ##[l_i^2, l_j^2]##. Homework Equations ##L^2 = l_1^2 + l_2^2 + l_3^2## and ##[l_i^2,L^2]=0## The Attempt at a Solution I managed to so far prove that ##[l_1^2, l_2^2] = [l_2^2, l_3^2] = [l_3^2, l_1^2]##. I...
  30. Y

    MHB Different Number of Equivalence Relations

    Hello all, I have a few questions related to the different number of equivalence classes under some constraint. I don't know how to approach them, if you could guide me to it, maybe if I do a few I can do the others. Thank you. Given the set A={1,2,3,4,5}, 1) How many different equivalence...
  31. B

    Commutation Relations, 2D Harmonic Oscillator

    Homework Statement Consider a two-dimensional harmonic oscillator, described by the Hamiltonian ##\hat H_0 = \hbar \omega (\hat a_x \hat a_x ^{\dagger} + \hat a_y \hat a_y^{\dagger} + 1)## Calculate ##\hat H_0 \hat L | n_1, n_2 \rangle## and ##\hat L \hat H_0 |n_1, n_2 \rangle##. What does...
  32. F

    Dispersion Relations in Cold Plasma waves

    Homework Statement Im stuck on a old exam in plasma physics. It is about how to determine dispersion relations for high frequency waves in cold plasma's. I'm not sure how they do in the solution manual. Homework Equations B = B_0z^ E = E_0exp(i(kx-wt))z^ The Attempt at a Solution The...
  33. Bunny-chan

    Book demonstration about trigonometric relations

    Homework Statement [/B] In the equation between (3) and (2), why does the author says that ? Isn't the trigonometric identity actually ? 2. Homework Equations The Attempt at a Solution
  34. L

    A Relations between lagrangian and hamiltonian

    Lagrangian is defined by ##L=L(q_i,\dot{q}_i,t)## and hamiltonian is defined by ##H=H(q_i,p_i,t)##. Why there is relation H=\sum_i p_i\dot{q}_i-L end no H=L-\sum_i p_i\dot{q}_i or why ##H## is Legendre transform of ##-L##?
  35. L

    Why Do Authors Use γ=γ(P,T) Instead of γ=γ(P,T,V) in Thermodynamics?

    Thermal coefficient of pressure is defined by \gamma=\frac{1}{P}(\frac{\partial P}{\partial T})_V . Why in books authors uses ##\gamma=\gamma(P,T)## and no ##\gamma=\gamma(P,T,V)##. Could you explain me this. I am sometimes confused with this dependences in thermodynamics.
  36. Larry

    A Non-Heisenberg Uncertainty Relations

    Simultaneous tracking of spin angle and amplitude beyond classical limits Nature 543, 525–528 (23 March 2017) www.nature.com/nature/journal/v543/n7646/abs/nature21434.html The authors remark that "because spins obey non-Heisenberg uncertainty relations, enables simultaneous precise knowledge...
  37. M

    MHB Linear conqruence and relations problem

    Suppose that the relation R is defined on the set Z where aRb means a = ±b. Establish whether R is an equivalence relation giving your justifications. Find the set of solutions of each of the linear congruence: a) x ≡ 3 (mod 5). b) 2x ≡ 5 (mod 9).(please write the full solutions thanks)
  38. S

    I Input-output relations for Y-Junction fiber splitter

    What is the representation of the Y-junction fiber splitter in terms of the creation operators ##\hat{a}^\dagger_P## for each port P?
  39. Eclair_de_XII

    How can relations on three-element set have seven elements?

    Homework Statement "Determine the max number of elements in a three-element set that is not reflexive, symmetric, or transitive?" Homework Equations ##a R b⇔(a,b)∈R## The Attempt at a Solution Basically, my professor has stated that there are a total number of seven possible elements in a...
  40. doktorwho

    Antisimmetric relations question

    Homework Statement A set ##P=\left\{ \ p1,p2,p3,p4 \right\}## is given. Determine the number of antisimmetric relations of this set so that ##p1## is in relation with ##p3##, ##p2## is in relation with ##p4## but ##p2## is not in relation with ##p1##. Homework Equations 3. The Attempt at a...
  41. P

    MHB Understanding Sets, Relations, and Functions: A Guide for Struggling Students

    I'm having issues with the first four questions and have uploaded them. My attempts are shown below. 1. a) True, all elements of E are even b) False, 0 is not a multiple of 3 c) True, 8 is even and 9 is a multiple of 3 d) No idea e) False, 6 is an element of E and T f) No idea 2. a) You can...
  42. B

    Expectation values and commutation relations

    Homework Statement I am trying to calculate the expectation value of ##\hat{P}^3## for the harmonic oscillator in energy eigenstate ##|n\rangle## Homework EquationsThe Attempt at a Solution [/B] ##\hat{P}^3 = (i \sqrt{\frac{\hbar \omega m}{2}} (\hat{a}^\dagger - \hat{a}))^3 = -i(\frac{\hbar...
  43. B

    Relations between torque for system of pulleys

    Homework Statement In an attempt to find a transfer function of the system, I need to come up with equations that I can use to solve for unknowns. See the attached image to see the diagram of the pulley system. J is the moment of inertia, r is the radius. The smaller radius on pulley 2 is r1...
  44. B

    How Can I Apply Thermodynamic Principles to Solve Homework Equations?

    Homework Statement I need to prove the following equation: Homework Equations The 4 maxwell relations and their derivations: https://en.wikipedia.org/wiki/Maxwell_relations The Attempt at a Solution I started out with the fundamental equations of dU=TdS - PdV and as dS=0, and Cv=(dU/dT)v; I...
  45. F

    I Sets, Subsets, Possible Relations

    Given a set, there are subsets and possible relations between those arbitrary subsets. For a given example set, the possible relation between the subsets of the example set will narrow down to the "true" possible relations between those subsets. a) {1} Number of Subsets: ##2^1 = 2## (∅, {1})...
  46. Mr Davis 97

    I DIfference between vectors and relations of points

    When it comes to analytic geometry, I am little confused about the use of vectors. For example, throughout high school, one works in ##\mathbb{R}^2##, and geometric objects such as lines are described using equations relating two variables, the x and y coordinate, such as y = 2x + 1. However...
  47. F

    I Do these relations have any physical significance

    Photon energy E_p= hv=hc/lamda taking lamda= h/mc which is the electron Compton wavelength and substituting in above E_p=mc^2 L(angular momentum)=r X P=(Lamda/2)*(E_p/c)=h/2 are these results coincident or have any physical meaning, they relate a photon wavelength equal to an electron...
  48. K

    MHB Determining a determinant using recurrence relations

    I'm a little stuck here. I should determine the following determinant. I first tried to simplify it a little by using elemntary transformations. And then I did Laplace expansion on the last row. $\begin{vmatrix}2 & 2 & \cdots & 2 & 2 & 1 \\ 2 & 2 & \cdots & 2 & 2 & 2 \\ 2 & 2 & \cdots & 3 & 2 &...
  49. evinda

    MHB How do we get the relations?

    Hello! (Wave) We set $L_k \equiv u_{tt}+\frac{k}{t}-\Delta u=0, k \in \mathbb{N}_0$. I am looking at the proof of the following proposition: We suppose that $g(x)$ is twice differentiable in $\mathbb{R}^n$. Then the mean value of $g(x)$ at the sphere with radius $t$ and center at $x$, which...
  50. L

    I Let A = {1,2,3,4,5,6.} # of many different relations possible

    How many different relations are possible? Is the question. Is the answer the power set of AxA? 2^36.
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