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. Mayan Fung

    Problems related to Maxwell relations

    Homework Statement Given the entropy of a system : $$ S = AU^αV^βN^{1-α-β} $$ The problem requires me to write $$ (\frac{∂T}{∂U})_{V,N} > 0, 　(\frac{∂P}{∂V})_{U,N} < 0, (\frac{∂μ}{∂N})_{U,V} > 0$$ to find the mathematical constraint of α and β Homework Equations dU = TdS - PdV + μdN The...
  2. Dewgale

    Application of Maxwell's Relations

    Homework Statement This is question 2.18 from Bowley and Sanchez, "Introductory Statistical Mechanics" . Show with the help of Maxwell's Relations that $$T dS = C_v dT + T (\frac{\partial P}{\partial T})_V dV$$ and $$TdS = C_p dT - T( \frac{\partial V}{\partial T})_P dP.$$ Then, prove that...
  3. Erenjaeger

    Which of these relations are functions of x on R

    Mentor note: moved to homework section y = sin(x) y = cos(x) y = tan(x) y = csc(x) y = sec(x) y = cot(x) (a) 0 (b) 4 (c) 6 (d) 2 I thought it was (c) because i graphed all the trig functions and they passed the vertical line test but the answer sheet is saying (d) 2
  4. E

    Difficulty proving a relation is an equivalence relation

    Homework Statement Homework Equations I don't think there are any in this case The Attempt at a Solution I know that in order to prove R is an equivalence relation, I'd have to show that it is Reflexive, Symmetric, and Transitive. I'm not sure why, but I'm finding this a bit difficult in...
  5. B

    B Why are these relations reflexive/symmetric/transitive?

    The definition of these relations as given in my textbook are : (1):- Reflexive :- A relation ##R : A \to A## is called reflexive if ##(a, a) \in R, \color{red}{\forall} a \in A## (2):- Symmetric :- A relation ##R : A \to A## is called symmetric if ##(a_1, a_2) \in R \implies (a_2, a_1) \in R...
  6. E

    A Maxwell field commutation relations

    Maxwell field commutation relations I'm looking at Aitchison and Hey's QFT book. I see in Chapter 7, (pp. 191-192), they write down the canonical momentum for the Maxwell field A^\mu(x): \pi^0=\partial_\mu A^\mu \\ \pi^i=-\dot{A}^i+\partial^i A^0 and then write down the commutation...
  7. sa1988

    Not sure I understand commutation relations

    Homework Statement Firstly, I'm looking at this: I'm confused because my understanding is that the commutator should be treated like so: $$[a,a^{\dagger}] = aa^{\dagger} - a^{\dagger}a$$ but the working in the above image looks like it only goes as far as $$aa^{\dagger}$$ This surely...
  8. S

    A Relations between statistical physics and theoretical CS

    Hi everyone. I wasn't sure where to post this thread, so I figured I'll post this under General Physics. Out of interest, I've been perusing online about connections that exist between statistical physics and theoretical computer science. For example, consider the following report by Pietro...
  9. S

    A Complex scalar field - commutation relations

    I find it difficult to believe that the canonical commutation relations for a complex scalar field are of the form ##[\phi(t,\vec{x}),\pi^{*}(t,\vec{y})]=i\delta^{(3)}(\vec{x}-\vec{y})## ##[\phi^{*}(t,\vec{x}),\pi(t,\vec{y})]=i\delta^{(3)}(\vec{x}-\vec{y})## This seems to imply that the two...
  10. S

    How various CAD programs create relations among objects?

    I'd like a comparison of how various CAD programs handle the task of creating relationships among objects that have been created independently and where the uses wants to change some parameters of one object and have the program adjust the parameters of the others automatically. I'm interested...
  11. J

    MHB Binary Relations and Equivalence Classes | Proving R is an Equivalence Relation

    So the question I am trying to solve is this: Define a binary relation R on R as follows: R={(x,y)∈ R×R:cos⁡(x)=cos⁡(y)} Prove that R is an equivalence relation, and determine its equivalence classes. I've figured out the first two requirements for being a binary relation: 1. cos(x) =...
  12. S

    A Algorithms for solving recurrence relations?

    Is there good survey of known algorithms for solving recurrence relations ? By "solving" a recurrence relation such as a_n = \sum_{i=1}^{k} { c_k a_{n-k}} , I mean to express a_n as a function of n . In the case that the c_i are constants the algorithm based on the "characteristic...
  13. M

    I Relations & Functions: Types, Examples, Homomorphism

    Hello every one . A relation ( is a subset of the cartesian product between Xand Y) in math between two sets has spatial types 1-left unique ( injective) 2- right unique ( functional ) 3- left total 4- right total (surjective) May question is 1- a function ( map...
  14. DaTario

    I Dispersion Relations: Most Famous DR & Contexts Explained

    Hi All, The equation: ## v = \lambda f ## is presented as a dispersion relation (DR) for it is a formula that specifies the velocity of a wave of certain frequency. This equation seems to be the most famous DR in physics. My questions are the following: What is the second most famous DR? Which...
  15. W

    I Relations resolves singularity -- new paper on arxiv

    A new paper on arXiv today claims that relationsism allows one to evolve the universe through the big bang. Alas I am not familiar with relationsism, is it related to shape dynamics? can anyone explain? https://arxiv.org/pdf/1607.02460v1.pdf
  16. Battlemage!

    B How many possible relations between two sets?

    Say you have set A with n elements and set B with m elements. If I recall, there are a total of 2nm relations between them. But my question is, does this count redundancies? What I mean is, if in the relation A~B = B~A. I don't want to count identical relations twice. Thanks!
  17. Danielm

    Proving R = I_X: Equivalence Relation and Function Homework Solution

    Homework Statement Let X be a set and R ⊂ X × X. Assume R is an equivalence relation and a function. Prove that R = I_X, the identity function. Homework EquationsThe Attempt at a Solution Proof We know that R has to be reflexive, so for all elements b in X, bRb but b can't be related to any...
  18. T

    I Understanding commutator relations

    I am reading through a quantum optics book where they are deriving the equations for a quantized EM field and one of the paragraphs state: "In Section 6.1, the problem has been set in the Hamiltonian form by expressing the total energy (6.55) of the system comprising charges and electromagnetic...
  19. Danielm

    Counting Reflexive and Anti-Symmetric Relations on a Finite Set

    Homework Statement Let X = {1, 2, 3, 4, 5, 6}. Determine the number of relations on X which are reflexive and anti-symmetric Homework EquationsThe Attempt at a Solution This problem looks a little bit hard. Approach: consider R={(x,x),... } If there is just one pair in the relation in the...
  20. S

    A Commutation relations - field operators to ladder operators

    I would like to show that the commutation relations ##[a_{\vec{p}},a_{\vec{q}}]=[a_{\vec{p}}^{\dagger},a_{\vec{q}}^{\dagger}]=0## and ##[a_{\vec{p}},a_{\vec{q}}^{\dagger}]=(2\pi)^{3}\delta^{(3)}(\vec{p}-\vec{q})## imply the commutation relations...
  21. A

    I Exact meaning of the Uncertainty Relations

    In another thread I quoted a paper Bill pointed me to. It included the statement "It is the measurement results that fluctuate, not the underlying object." Bill indicated that this was a misconception but would need a new thread to discuss it. So please discuss... Thanks Andrew
  22. F

    I What does "completeness" mean in completeness relations

    From my humble (physicist) mathematics training, I have a vague notion of what a Hilbert space actually is mathematically, i.e. an inner product space that is complete, with completeness in this sense heuristically meaning that all possible sequences of elements within this space have a...
  23. QuantumRose

    Commutator relations of field operators

    Here is the question: By using the equality (for boson) ---------------------------------------- (1) Prove that Background: Currently I'm learning things about second quantization in the book "Advanced Quantum Mechanics"(Franz Schwabl). Given the creation and annihilation operators(), define...
  24. D

    A The commutations relations for left/right handed fermions

    I have a problem where I have to know the commutation relations for left handed fermions. I know ##\psi_L=\frac{1}{2}(1-\gamma^5)\psi## ##\psi^\dagger_L=\psi^\dagger_L\frac{1}{2}(1-\gamma^5)## and ## \left\{ \psi(x) , \psi^\dagger(y)\right\} = \delta(x-y)## So writing ## \left\{P_L\psi(x) ...
  25. C

    Quantum operators and commutation relations

    Homework Statement Given the mode expansion of the quantum field ##\phi## and the conjugate field one can derive $$\mathbf P = \int \frac{d^3 \mathbf p}{(2\pi)^3 2 \omega(\mathbf p)} \mathbf p a(\mathbf p)^{\dagger} a(\mathbf p)$$ By writing $$e^X = \text{lim}_{n \rightarrow \infty}...
  26. Y

    Exploring Composition Relations: A and B

    Homework Statement Suppose that A = { 1, 2, 3} , B = { 4, 5, 6} , R = { (1, 4), (1, 5), (2, 5), (3, 6)} , and S = { (4, 5), (4, 6), (5, 4), (6, 6)}. Note that R is a relation from A to B and S is a relation from B to B . Find the following relations: (a) S ◦ R . (b) S ◦ S−1...
  27. S

    Anticommutation relations Fermion creation and annihilation

    Homework Statement This problem is from Lahiri and Pal (2nd edition) Exercise 1.4: Suppose in a system there are operators which obey anticommutation relations ##[a_{r},a^{\dagger}_{s}]_{+}\equiv a_{r}a^{\dagger}_{s}+a^{\dagger}_{s}a_{r}=\delta_{rs}## and ##[a_{r},a_{s}]_{+}=0,## for...
  28. RJLiberator

    Is This a Valid Equivalence Relation on ℚ?

    Homework Statement For each of the relations defined on ℚ, either prove that it is an equivalence relation or show which properties it fails. x ~ y whenever xy ∈ Z Homework EquationsThe Attempt at a Solution Here's my problem: I am starting off the proof with the first condition of...
  29. RJLiberator

    Equivalence Relations Questions

    Homework Statement For the set ℤ, define ~ as a ~ b whenever a-b is divisible by 12. You may assume that ~ is an equivalence relation and may also assume that addition and multiplication of equivalence classes is well defined where e define [a]+[ b ] = [a+b] and [a]*[ b ] = [ab] for all [a],[ b...
  30. A

    Gibbs Free Energy, Maxwell Relations

    Homework Statement We have a Gibbs Free Energy function G=G(P, T, N1, N2) I am not writing the whole function because I just want a push in the right direction. Find expressions for the entropy, volume, internal energy, enthalpy and chemical potential. Homework Equations Maxwell Relations...
  31. S

    More ebooks about Maxwell relations of Thermodynamics

    I'm learning about Maxwell relations of Thermodynamics, but it's difficult for me to find more books about this in Vietnamese. So, I want to ask you about some english ebook about this. Thanks a lot!
  32. X

    Relations (Relation inside a Relation)

    I have a question about what I would call a relation inside a relation. Like: A={1,2,3) and B={a,b,c} R1={(a,1) ,(a,3), (b,2), (c,1,), (c,3) } R2={(a,a), (b,a), (b,c), (c,a) } R3=R1R2 Like this. I have 2 regular relations. Then I form another relation using these 2. How do I do that? Like...
  33. S

    Commutation relations for angular momentum operator

    I would like to prove that the angular momentum operators ##\vec{J} = \vec{x} \times \vec{p} = \vec{x} \times (-i\vec{\nabla})## can be used to obtain the commutation relations ##[J_{i},J_{j}]=i\epsilon_{ijk}J_{k}##. Something's gone wrong with my proof below. Can you point out the mistake...
  34. M

    MHB How can we define the relations?

    Hey! :o Consider the ring $R=\mathbb{C}[e^{\lambda x} \mid \lambda \in \mathbb{C}]$. I want to define the relation $e^x-1 \mid e^{kx}-1$ (where $k \in \mathbb{Z}$) in the language $\{+, \cdot , \frac{d}{dx} , 0, 1\}$, so we can use only these operations, the addition, the multiplication and...
  35. T

    Discrete Math: Poset Characteristics and Minimum Element Count

    Homework Statement My task is to find out what is the lowest # of elements a poset can have with the following characteristics. If such a set exists I should show it and if it doesn't I must prove it. 1) has infimum of all its subsets, but there is a subset with no supremum 2) has two maximal...
  36. S

    Deriving the commutation relations of the so(n) Lie algebra

    The generators ##(A_{ab})_{st}## of the ##so(n)## Lie algebra are given by: ##(A_{ab})_{st} = -i(\delta_{as}\delta_{bt}-\delta_{at}\delta_{bs}) = -i\delta_{s[a}\delta_{b]t}##, where ##a,b## label the number of the generator, and ##s,t## label the matrix element. Now, I need to prove the...
  37. C

    IBP Relations in Feynman integrals

    I am wondering if anyone has experience in using IBP( Integration by parts) identities in the evaluation of Feynman diagrams via differential equations? My question is that I can't seem to understand where equation (4.8) on P.8 of this paper: http://arxiv.org/pdf/hep-ph/9912329.pdf comes from...
  38. E

    Wave reflection and refraction, relations between angles

    Hello! This post is strictly related to my previous one. Let's consider the same context and the same image. Regarding the oblique incidence of a wave upon an interface between two dielectric, all the texts and all the lectures write an equation like the following: e^{-j k_1 y \sin \theta_i} +...
  39. B

    Classical Demonstration of Onsager reciprocal relations

    Hello everyone, I am working on the Onsager reciprocal relations, more precisely on the demonstration of those relations. I try to understand the Onsager original paper (1931) but it's really not easy (although he says that the examples are "extremely simple"). I was wondering if any of you...
  40. CivilSigma

    Virtual Work - Determining Relations

    Homework Statement Hello, I'm having problems determining the relationships between delta a and delta c . I don't see how how delta C = 4/9 delta A [/B] http://imgur.com/a/B6eTx Thank you.
  41. L

    Thermodynamics - Maxwell Relations

    Homework Statement 2. The attempt at a solution I've tried using the relation Cp = T(dS/dT), isolating "T" for T = Cv2(dT/dS) and using the maxwell relations to reduce the derivatives, reaching, T = Cv2/D (dV/dS), but i don't think this is the right way to do solve this problem, i couldn't...
  42. E

    Fresnel Relations and the Sensitivity of a Camera

    Reflectance, according to the Fresnel Relations, is given by ##R \equiv \frac{I_r}{I_i}##, and Transmittance is ##T = \frac{I_t \cos \theta_t}{I_i \cos \theta_i}##. Do these values depend on the wavelength of light? For example, if I have a beam of white light rather than a monochromatic...
  43. Yohanes Nuwara

    Are there any relations between entropy and force?

    Is there any relations of S and F? If any, I would like to know what the equation of this relationship will be. Thanks:wink:
  44. F

    Thermodynamics equations and relations

    Homework Statement I don't have a specific problem I'm trying to solve, I'm trying relate all the concepts for basic thermodynamics. I'm not entirely sure where I am misunderstanding 1. What is work 2. What is internal energy? 3. What is heat? 4. What is enthalpy? 5. What is entropy? Homework...
  45. D

    Recurrence relations define solutions to Bessel equation

    I'm trying to show that a function defined with the following recurence relations $$\frac{dZ_m(x)}{dx}=\frac{1}{2}(Z_{m-1}-Z_{m+1})$$ and $$\frac{2m}{x}Z_m=Z_{m+1}+Z_{m-1}$$ satisfies the Bessel differential equation $$\frac{d^2}{dx^2}Z_m+\frac{1}{x}\frac{d}{dx}Z_m+(1-\frac{m^2}{x^2})Z_m=0$$...
  46. S

    Orthogonality relations for Hankel functions

    Where can I find and how can I derive the orthogonality relations for Hankel's functions defined as follows: H^{(1)}_{m}(z) \equiv J_{n}(z) +i Y_{n}(z) H^{(2)}_{m}(z) \equiv J_{n}(z) - i Y_{n}(z) Any help is greatly appreciated. Thanks
  47. W

    Many to Many Relations in Database

    I am pulling my hair trying to find a straight answer to this, after looking it up in different books, websites: Say we have a many-to-many relationship in a RDB (Relational DB). Is there a standard way of creating a junction, bridge, etc. table? From what I know,. the bridge table will contain...
  48. TrickyDicky

    Equivalence between Weyl relations and CCR

    Due to the fact that the operators in the canonical commutation relations(CCR) cannot be both bounded, in order to prove the Stone-von Neuman theorem one must resort to the Weyl relations. Now the Weyl relations imply the CCR, but the opposite is not true, the CCR don't imply the Weyl relations...
  49. C

    Dirac Equation and commutation relations

    Homework Statement Consider the Dirac Hamiltonian ##\hat H = c \alpha_i \hat p_i + \beta mc^2## . The operator ##\hat J## is defined as ##\hat J_i = \hat L_i + (\hbar/2) \Sigma_i##, where ##\hat L_i = (r \times p)_i## and ##\Sigma_i = \begin{pmatrix} \sigma_i & 0 \\0 & \sigma_i...
  50. T

    Relations between chern number and edge state

    I have been doing a literature survey about topological insulators for some time. What surprises me is the close relation between difference of chern number and number of edge states. However, I found most review or tutorial in topological insulator avoided direct proof of the relation. So can...
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