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. Hibarikyoya

    Prove the following commutation relations

    I tried in this way: $$[J^k, J^i] = \frac{1}{M^2}\ (L^{-1})^k_{\mu}\ (L^{-1})^i_{\nu}\ [W^{\mu}, W^{\nu}] $$ $$ = \frac{1}{M^2}\ (L^{-1})^k_{\mu}\ (L^{-1})^i_{\nu}\ (-i) \epsilon^{\mu \nu \rho \sigma} W_{\rho} P_{\sigma}.$$ At this point I had no idea how to going on with the calculation. Can...
  2. bella987

    Deriving the commutation relations of the Lie algebra of Lorentz group

    This is the defining generator of the Lorentz group which is then divided into subgroups for rotations and boosts And I then want to find the commutation relation [J_m, J_n] (and [J_m, K_n] ). I'm following this derivation, but am having a hard time to understand all the steps: especially...
  3. dim_d00m

    A Recurrence relations for series solution of differential equation

    I am currently looking at section IIA of the following paper: https://arxiv.org/pdf/gr-qc/0511111.pdf. Eq. (2.5) proposes an ansatz to solve the spheroidal wave equation (2.1). This equation is $$ \dfrac{d}{dx} \left((1-x^2) \dfrac{d}{dx}S_{lm} \right) + \left(c^2x^2 + A_{lm} -...
  4. L

    MHB Equivalence Relations: Solving & Proving Reflexivity, Symmetry & Transitivity

    Dear All, I am trying to solve the attached two questions. In both I need to determine if the relation is an equivalence relation, to prove it if so, and to find the equivalence classes. In both cases it is an equivalence relation, and I managed to prove both relations are reflexive. Now I...
  5. P

    Commutation relations between Ladder operators and Spherical Harmonics

    I've tried figuring out commutation relations between ##L_+## and various other operators and ##L^2## could've been A, but ##L_z, L^2## commute. Can someone help me out in figuring how to actually proceed from here?
  6. D

    A What happens when you commute Sx and Sz in spin operators?

    So we know [Sz, Sx] = ihbar Sy (S with hats on) so what happens if you get [Sx, Sz]? Is it the same result? Just trying to work out if I've gone wrong somewhere
  7. E

    I Commutation relations for an interacting scalar field

    Hi there, In his book "Quantum field theory and the standard model", Schwartz assumes that the canonical commutation relations for a free scalar field also apply to interacting fields (page 79, section 7.1). As a justification he states: I do not understand this explanation. Can you please...
  8. G

    Is it a good idea to connect concepts through dependency relations?

    When I learn a concept, I often find that to understand it, I have to learn some other concepts and I don't know if they also require learning new concepts. During this procedure, I find learning frustrating, as the teacher always presume that I should have learned them. So I think I can build...
  9. redtree

    B One-to-many relations in group theory

    I apologize for the simple question, but it has been bothering me. One can write a relationship between groups, such as for example between Spin##(n)## and SO##(n)## as follows: \begin{equation} 1 \rightarrow \{-1,+1 \} \rightarrow \text{Spin}(n) \rightarrow \text{SO}(n) \rightarrow 1...
  10. M

    MHB Transactions & schedules - Dependency relations

    Hey! :giggle: The below transactions are given : and the below schedules : Give the respective dependency relations as well as the precedence graphs. Which schedules are conflict serializable? Which schedules are equivalent? I reread some notes and looked also for some examples in Google...
  11. elcaro

    Storing program source as relations in a database instead of text file

    Almost all (compiled or interpreted) programming langues store the program source in the form of a series of bytes (using an encoding like ASCII or UTF-8) into a text file, enforcing the grammer of the programming language using a parser (as part of the compilation process or interpretation of...
  12. M

    MHB Relation between Sets AUFTRAG & KUNDE

    Hey! :giggle: The below relations are given AUFTRAG($A_1, A_2, A_3$) and KUNDE($B_1, B_2, B_3$) with $A_1$ = AUFTRNR, $A_2$ = DATUM, $A_3$ = KUNDNR, $B_1$ = KUNDNR, $B_2$ = NAME and $B_3$ = ORT. Determine the below sets or justify why it is not possible to determine them. Let $A = A_1...
  13. cwill53

    I Maxwell’s Relations and Differentiating With Respect to ##N_i##

    I was wondering if anyone could write out Maxwell's relations for partial derivatives with respect to particle count ##N_i##. Starting from the fundamental thermodynamic relation, $$dU(S,V,N_i)=TdS-PdV+\sum_{i}\mu _idN_i$$ $$dU(S,V,N_i)=\left ( \frac{\partial U}{\partial S} \right )_{V,\left...
  14. Ssnow

    Quantum References for generalized canonical commutation relations

    Hi to all, I ask if somebody of the Physics community know good references for article where the author works with generalized canonical commutation relations ( I mean that the author works with ##[x,p]=ic\hbar## with ##c## a real constant instead of ##[x,p]=i\hbar##). Thank you for the answers...
  15. WMDhamnekar

    MHB When to use equivalence relations? How to write it in octave?

    Sometimes to help describe one expression, another expression is shown that produces identical results. The exact equivalence of expressions is indicated with ‘ ≡’. For example: rot90 ([1, 2; 3, 4], -1) ≡ rot90 ([1, 2; 3, 4], 3) ≡ rot90 ([1, 2; 3, 4], 7) What is the meaning of 'rot90;? What...
  16. snypehype46

    Exercise involving Dirac fields and Fermionic commutation relations

    I'm trying to the following exercise: I've proven the first part and now I'm trying to do the same thing for fermions. The formulas for the mode expansions are: What I did was the following: $$\begin{align*} \sum_s \int d\tilde{q} \left(a_s(q) u(q,s) e^{-iq \cdot x}+ b_s^\dagger(q) v(q,s)...
  17. Like Tony Stark

    Partial derivatives of enthelpy and Maxwell relations

    I've attached images showing my progress. I have used Maxwell relations and the definitions of ##\alpha##, ##\kappa## and ##c##, but I don't know how to continue. Can you help me?
  18. JD_PM

    Deriving Fourier Transform of Operators for Relativistic Quantum Field Theory

    I would say we first need to take the inverse Fourier transform of ##\chi## and associated quantities i.e. \begin{equation*} \chi_{\vec k} = \int d^3 \vec x \left( a_{\vec k} \chi e^{-i \vec k \cdot \vec x} + a^{\dagger}_{\vec k}\chi^* e^{i \vec k \cdot \vec x} \right) \tag{2}...
  19. Arman777

    The contracting relations on the Christoffel symbols

    I am trying to find $$\Gamma^{\nu}_{\mu \nu} = \partial_{\mu} log(\sqrt{g})$$ but I cannot. by calculations, I manage to find $$\Gamma^{\nu}_{\mu \nu} = \frac{1}{2}g^{\nu \delta}\partial_{\mu}g_{\nu \delta}$$ and from research I have find that $$det(A) = e^{Tr(log(A))}$$ but still I cannot...
  20. M

    I Discrete Orthogonality Relations for Cosines

    Hi all, I've come across some problem where I have terms such as ##\sum_{j=1}^N \cos(2 \pi j k /N) \cos(2 \pi j k' /N)##, or ##\sum_{j=1}^N \cos(2\pi j k/ N)##, or ## \sum_{j=1}^N \cos(2\pi j k/ N) \cos(\pi j) ##. In all cases we have the extra condition that ##1 \le k,k' \le N/2-1## (and...
  21. Decimal

    I Completeness relations in a tensor product Hilbert space

    Hello, Throughout my undergrad I have gotten maybe too comfortable with using Dirac notation without much second thought, and I am feeling that now in grad school I am seeing some holes in my knowledge. The specific context where I am encountering this issue currently is in scattering theory...
  22. L

    MHB How many reflexive relations on set A with 4 elements?

    Question: How many reflexive relations are on set A if A has 4 elements? I'm thinking that the answer to this question is 4, but I don't know whether it is truly that simple. I know that a reflexive relation, R, occurs when for all x in A, x R x. so let's say A = {1,2,3,4}. 1~1 2~2 3~3 4~4. So...
  23. S

    Deriving relations for a hard sphere phase diagram

    Ornstein-Zernike states that ##h(r_{12}) = c(r_{12}) + \rho \int d\mathbf{r}_3 c(r_{13})h(r_{32})## which after a Fourier transform becomes ##\hat{C} (\mathbf{k}) = \frac{\hat{H}(\mathbf{k})}{1+\rho \hat{H}(\mathbf{k})}## However, I don't see how to simplify this to the second equation he has...
  24. cianfa72

    Relations between ##k## Currents & Voltages for Black-Box Device

    Hi, I'm aware it is an odd question. Consider a ##k##-terminal electrical device as black-box. We know from KLC and KLV that just ##k-1## currents and ##k-1## voltages are actually independent (descriptive currents and voltages). Furthermore we generally expect there exist ##k-1## relations...
  25. J

    Legendre polynomial - recurrence relations

    Note: $P_n (x)$ is legendre polynomial $$P_{n+1}(x) = (2n+1)P_n(x) + P'_{n-1}(x) $$ $$\implies P_{n+1}(x) = (2n+1)P_n(x) + \sum_{k=0}^{\lfloor\frac{n}{2}\rfloor} (2(n-1-2k)+1)P_{n-1-2k}(x))$$ How can I continue to use induction to prove this? Help appreciated.
  26. M

    MHB Relations between map and matrix

    Hey! 😊 Let $1\leq m,n\in \mathbb{N}$ and let $\mathbb{K}$ be a field. For $a\in M_m(\mathbb{K})$ we consider the map $\mu_a$ that is defined by \begin{equation*}\mu_a: \mathbb{K}^{m\times n}\rightarrow \mathbb{K}^{m\times n}, \ c\mapsto ac\end{equation*} I have show that $\mu_a$ is a linear...
  27. M

    Modeling Pressure Change in a Pressurized Chamber

    I'm trying to model the rate of change of the pressure in a pressurized rigid chamber with normal air (assumed to be an ideal gas). It has an air outflow V̇ (m^3/s) with ρ1. What's the change in p between state 1 and state 2? My assumption is that it can be modeled like an adiabatic expansion...
  28. dykuma

    Hermitian Matrix and Commutation relations

    I think I roughly see what's happening here. > First, I will assume that AB - BA = C, without the complex number. >Matrix AB equals the transpose of BA. (AB = (BA)t) >Because AB = (BA)t, or because of the cyclic property of matrix multiplication, the diagonals of AB equals the diagonals of...
  29. lekh2003

    De Broglie Relations Confusion

    I've been attempting to run through some quantum mechanics and I've seen something extremely odd, and I just can't spot my mistake. I know the relationships: ##p = \frac{h}{\lambda}## and ##E = hf##. I also know the relationship ##E = \frac{p^2}{2m}##. I tried to show using the energy-momentum...
  30. JD_PM

    A Commutation relations between HO operators | QFT; free scalar field

    I am getting started in applying the quantization of the harmonic oscillator to the free scalar field. After studying section 2.2. of Tong Lecture notes (I attach the PDF, which comes from 2.Canonical quantization here https://www.damtp.cam.ac.uk/user/tong/qft.html), I went through my notes...
  31. I

    Equivalence Relations and Counter Examples for Equinumerous Sets

    (a) I present the following counter example for this. Let ##A = \{0,1,2,\ldots \}## and ##B = \{ 2,4,6, \ldots \} ##. Also, let ##C = \{ 1, 2 \} ## and ##D = \{3 \}##. Now, we can form a bijection ##f: A \longrightarrow B## between ##A## and ##B## as follows. If ##f(x) = 2x + 2##, we can see...
  32. L

    I Momentum-Position vs. Energy-Time Uncertainty Relations

    In a few textbooks in introductory quantum mechanics which I have looked through (e.g. Griffiths), it is heavily emphasized that the momentum-position uncertainty relation has a completely different meaning from the energy-time uncertainty relation, and that they are quite unrelated and only...
  33. Diracobama2181

    Does $$S_1^x$$ commute with $$S^2$$?

    $$H$$ can be rewritten as $$H=\frac{1}{2}(S^2-S_{1}^2-S_{2}^2-S_{3}^2-S_{4}^2)$$. Let's focus on the x component, $$J^x=\sum_{i}S_i^x$$. Now $$S_1^x$$ commutes with $$S^2_1, S^2_2, S^2_3, S^2_4$$, but does it commute with $$S^2$$? If not, what is the exact relation between $$S^2$$ and $$S_1^x$$?
  34. Ssnow

    Relations on the Kinetic velocities in a cyclic reaction

    Hi to all, I whant to ask a question about theoretical chemistry. Let us consider a cyclic reaction ##\alpha A\rightarrow \beta B\rightarrow \gamma C\rightarrow \alpha A## where ##\alpha,\beta;\gamma## are the stochiometric coefficients and ##A,B,C## chemical molecules ... there are relations...
  35. binbagsss

    A Reading canonical commutation relations from the action (QHE)

    Hi I'm sure i understood this a week or so ago, and I've forgot the idea now. I'm just really confused, again, how you read the commutator relationships of from the action ? many thanks (source http://www.damtp.cam.ac.uk/user/tong/qhe/five.pdf)
  36. newbie12321

    B Do Wedge Constraint Relations Affect Velocities Parallel to the Contact Surface?

    There’s a rigid rod pushing on a wedge. Velocity of the rod is v, which is vertically downwards, and the wedge is sliding to the right as a result with a velocity u. There is zero friction on the surface of the wedge and the surface of the rod in contact with the wedge. According to wedge...
  37. lohboys

    Engineering Derivation of Thermodynamic Relations

    dG= -SdT + VdP ... now dividing by dV holding temperature constant (dG/dV)T = -S (dT/dV)T + V (dP/dV)T ... now dT and constant temperature cancel out final answer: (dG/dV)T = V (dP/dV)T
  38. M

    I What do the commutation/anti-commutation relations mean in QFT?

    Hello everybody, In all QFT courses one starts very early with commutation and anti-commutation relation. My main question is why do we do this and what is the motivation? I have already asked few people including our professor but could not get a clear answer. I am talking about the...
  39. Eclair_de_XII

    How many ways are there to to climb n steps (recurrence relations)?

    (a) Okay, so if Tom climbs the first step, then he has ##n-1## steps to climb. So the number of ways to climb ##n## steps given he has initially climbed one, is ##s_n=s_{n-1}##. (b) Similarly, ##s_n=s_{n-2}##.
  40. R

    Trying to understand transitive relations

    Obviously R is not transitive because it doesn't contain (2,2). But does it need to contain both (2,2) and (4,4) to be considered transitive?
  41. CharlieCW

    Kramers-Kronig Relations: Principal Value

    I'm kind of confused on how to evaluate the principal value as it's a topic I've never seen in complex analysis and all the literature I've read so far only deals with the formal definition, not providing an example on how to calculate it properly. Therefore, I think just understanding at least...
  42. V

    MHB Limits of Recurrence Relations with $0<b<a$

    Let $0<b<a$ and $(x_{n})_{n\in \mathbb{N}}$ with $x_{0}=1, \ x_{1}=a+b$ $$x_{n+2}=(a+b)\cdot x_{n+1}-ab\cdot x_{n}$$ a) If $0<b<a$ and $L=\lim_{n\rightarrow \infty }\frac{x_{n+1}}{x_{n}}$ then $L= ?$ b) If $0<b<a<1$ and $L=\lim_{n\rightarrow \infty }\sum_{k=0}^{n}x_{k}$ then $L= ?$ I don't know...
  43. Z

    What Are the Anti-Commutation Relations of SUSY Generators?

    I hope I put this in the correct section of this forum, I apologize if I didn't. Homework Statement :[/B] It is well known that the generators $$ Q_\alpha = \frac{\partial}{\partial \theta^\alpha} - i \sigma^\mu_{\alpha \dot \beta} \bar{\theta}^\dot{\beta} \partial_\mu $$ and $$...
  44. S

    MHB Proper Subsets and Relations of Sets

    Q1: Write all proper subsets of S = {1, 2, 3, 4 }. Q2: Let S = {1,2,5,6 } Define a relation R on S of at least four order pairs, as (a,b)  R iff a*b is even (i.e. a multiply by b is even)...
  45. B

    A Covariance of equal time commutation relations

    I have a question regarding the covariance of the equal time commutation relations in relativistic quantum field theory. In the case of a scalar field one has that the commutator is (see Peskin, pag. 28 eq. (2.53) ) $ [\phi(0), \phi(y)] = D(-y) - D(y) $ is an invariant function, which is zero...
  46. W

    Relations on Sets: Need help understanding a mistake

    Homework Statement Suppose ##R## and ##S## are relations on a set ##A##. If ##R## and ##S## are transitive, is ##R \cup S## transitive? Why? Homework EquationsThe Attempt at a Solution Suppose that ##a## is an arbitrarily but particularly picked element of ##R \cup S##, then $$a \in R \...
  47. L

    MHB How Do You Solve the Second Part of an Equivalence Relations Problem?

    I understand that the first part of the equation is an equivalence class due to reflexivity, symmetry, and transivity... but I am confused on the second part. Could someone please help me out? THANKS
  48. F

    A Invariance of Commutator Relations

    Does anybody know of examples, in which groups defined by ##[\varphi(X),\varphi(Y)]=[X,Y]## are investigated? The ##X,Y## are vectors of a Lie algebra, so imagine them to be differential operators, or vector fields, or as physicists tend to say: generators. The ##\varphi## are thus linear...
  49. Destroxia

    I DSP: Recurrence Relations in a Linear Algebra Equation

    Hello, I've been working through some Digital Signal Processing stuff by myself online, and I saw a system that I wanted to write down as a Linear Algebra Equation. It's a simple delay feedback loop, looks like this: The (+) is an adder that adds 2 signals together, so the signal from x[n]...
  50. S

    MHB Functions and Relations: Proving R is a Function from A to B

    Let R\subseteq A*B be a binary relation from A to B , show that R is a function if and only if R^-1(not) R \subseteq idB and Rnot aR^-1 \supseteq both hold. Remember that Ida(idB) denotes the identity relation/ Function {(a.a)|a€ A} over A ( respectively ,B) Please see the attachment ,I...
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