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. S

    MHB Equivalences and Partitions and Properties of binary relations

    If someone could explain some of the steps needed to work out these 2 questions it would be much appreciated!
  2. Astronuc

    News Can Obama and Castro turn the page for US and Cuba relations?

    In historic face to face, Obama, Castro vow to turn the page http://news.yahoo.com/anticipation-grows-obama-castro-meet-saturday-panama-070657182--politics.html Seems somewhat similar to Nixon in China. About time!
  3. S

    Learning Recurrence Relations: Challenges & Solutions

    Homework Statement : [/B] I am just learning recurrence relations, and they are proving challenging.Homework Equations -- [/B]Let's have xn = 3xn-1 + 6xn-2. I wanted to look at it with two scenarios. The first is x0 = 1 and x1 = 3. The second is x1=3 and x2 = 4 The Attempt at a Solution Is...
  4. M

    How Do Fermion Commutation Relations Affect Current Operators in 2D Spacetime?

    Homework Statement Consider left-handed fermions in two spacetime dimensions ##(t,x)##: ##\psi_L=\frac{1}{2}(1-\gamma_5)\psi_D## with ##J_0^\epsilon(t,x)=\psi_L^+(x+\epsilon)\psi_L(x-\epsilon)##. (a). Use canonical equal-time anti-commutation relations for fermions to compute...
  5. R

    Questions related to Relations and Functions

    Homework Statement 1. Range of the function ## \sqrt {x^2+x+1} ## is equal to? 2.ƒ:R---->R is defined as ƒ(x) = x2 -3x +4, then f -1 (2) is equal to?Homework Equations NA The Attempt at a Solution For the first one tried squaring on both the sides but that does not give linear x in terms of...
  6. ugenetic

    Relations between workfunction, ionization, redox and fermi

    My understanding so far, critique appreciated: [1] workfunction closely relates to reduction potential Since workfunction is about boundaries and chemical reaction are mostly happening at the boundaries between bulk material, Workfunction should have a direct correlation with reduction...
  7. C

    MHB Proof of Unique Equivalence Relation on Set w/ Partition Classes

    Hello, I've to construct a proof of the following statement: Prove that if S is a set and S_1... S_k is a partition of S, then there is a unique equivalence relation on S that has the S_i as its equivalence classes. I'm really not sure how to go about this proof at all, so any help would be...
  8. N

    Equivalence Relations on Z: Proving m~n and Describing the Partition

    Prove that the following is an equivalence relation on the indicated set. Then describe the partition associated with the equivalence relation. 1. In Z, let m~n iff m-n is a multiple of 10.2. The attempt at a solution Reflexive: m-n = 0 0 ∈ Z, and 0 is a multiple of every number...
  9. A

    What Are the Canonical Commutation Relations for r and p Components?

    Hi , I need help with the this exercise: a) Work out all of the canonical commutation relations for components of the operators r and p: [x,y] [x,py] [x,px] [py,pz] and so on. Answer: [ri,pj]=−[pi,rj]=iℏδij [ri,rj]=−[pi,pj]=0 , where the indices stand for x, y, or z and rx=x ry=y rz=z where...
  10. D

    Confusion over definition of relations in set theory

    I'm coming from a physics background, but find pure mathematics extremely interesting, so have decided to try and gain a more fundamental understanding of the subject. I've recently been reading up on relations and how one can define them as sets of ordered pairs. I am particularly interested in...
  11. D

    Difference between equivalence and equality

    Apologies if this is in the wrong forum, but I chose to post here as the question pertains to equivalence relations and classes. Sorry if it's such a trivial question, but what is the mathematical difference between equivalence and equality? My understanding is the following, but I'm a little...
  12. J

    Question on solving linear recurrence relations

    Why does the characteristic equation of a linear recurrence relation always look like an = series of constants multiplied by a number raised to n
  13. P

    Find unknown vector X if these relations hold true

    Homework Statement If an unknown vector X satisfies the relation X · b = β X × b = c express X in terms of β, b, and c. Homework Equations X · b = |X||b|cos(θ) X × b = |X||b|sin(θ) The Attempt at a Solution I don't know where to start... :( someone pls give me a hint
  14. nuuskur

    What Determines the Transitivity of Relations in a Set?

    Having trouble understanding the concept of transitivity. By definition: If (a,b)\in R\wedge (b,c)\in R \Rightarrow (a,c)\in R - Great. Consider the set \{a,b\}. What makes the relation \{(a,a)\} or \{(a,a),(a,b)\} transitive? How do I translate this in terms of the definition? What makes an...
  15. B

    Exploring Algebra in Energy-Momentum-Mass Relations

    <<Mentor note: Please always use descriptive thread titles.>> First of all, the title is such that it attracts most views.You see, in class our professor did some goofing around numbers and variables in the relativistic energy momentum relation: E2=(pc)2+m02c4 Since the energy required to...
  16. G

    How to Determine Group from Commutation Relations?

    Is there a way to determine the group from the commutation relations? For example, the commutation relations: [J_x,J_y]=i\sqrt{2} J_z [J_y,J_z]=\frac{i}{\sqrt{2}} J_x [J_z,J_x]=i\sqrt{2} J_y is actually SO(3), as can be seen by redefining J'_x =\frac{1}{\sqrt{2}} J_x : then J'_x , J_y and...
  17. A

    Navigating Superstitions in Medical Ethics: A Case Study

    Hi everyone. I tried searching this up, but I could not come with anything conclusive. I was reading a medical ethics book that leaves this question as "food for thought": You live with your stepmother. You study medicine. You work very hard in the library, go to your classes and take air...
  18. evinda

    MHB Prove Relations: $e,b,d\in \mathbb{Z},d\neq 0$

    Hello! (Wave)Let $e,b \in \mathbb{Z}, d \neq 0$. How could we prove the following? Could you maybe give me a hint? If $d>0$ then $e \text{ div } d = \lfloor \frac{e}{d} \rfloor$ $$$$ If $d<0$ then $e \text{ div } d = \lceil \frac{e}{d} \rceil $ Could we show the above, using the...
  19. S

    Analytic verification of Kramers-Kronig Relations

    Homework Statement Show that the real and imaginary parts of the following susceptibility function satisfy the K-K relationships. Use the residue theorem. $$ \chi(\omega) = \frac{\omega_{p}^2}{(\omega_0^2-\omega^2)+i\gamma\omega} $$ Homework Equations The Kramers-Kronig relations are $$...
  20. C

    Dispersion Relations (tight binding energy)

    The nearest neighbour tight-binding energy band for an fcc metal can be written as: E(kx; ky; kz) = Ei - A - 8t[cos(pi*kx)cos(pi*ky) + cos(pi*ky)cos(pi*kz) + cos(pi*kz)cos(pi*kx)]where kx; ky; kz are express in units of 2*pi/a . Sketch this band dispersion (a) between the (capital Gamma) point...
  21. T

    Maxwell relations Thermodynamics

    Homework Statement Show that: (\frac{∂T} {∂V})_S,_n=-(\frac {∂P} {∂S})_V,_n Homework Equations dU=TdS-PdV+μdn The Attempt at a Solution \frac {∂} {∂S} (\frac{∂U} {∂V})_S,_n=-(\frac {∂P} {∂S})_V,_n \frac {∂} {∂V} (\frac{∂U} {∂S})_V,_n=(\frac{∂T} {∂V})_S,_n I tried to isolate T and P...
  22. evinda

    MHB Calculate Relations with Hey! (Nerd)

    Hey! (Nerd) Given the relation: $R=\{ \langle\{ \{ \varnothing \} \}, \varnothing \rangle, \langle \varnothing, \{ \varnothing \}\rangle, \langle \{ \varnothing \},\{ \{ \varnothing \} \}\rangle \}$, I want to calculate $R^{-1}[\{ \varnothing \}], R \circ R, \mathcal{P}R$. That's what I have...
  23. evinda

    MHB Does it suffice to show these relations?

    Hi! (Wave) If I want to prove that $A \cap B=A \text{ iff } A \subset B \text{ iff } A \cup B=B$. Do I have to prove the following: $A \cap B=A \rightarrow A \subset B$, $A \subset B \rightarrow A \cap B=A, A \subset B \rightarrow A \cup B=B, A \cup B=B \rightarrow A \subset B $ and $A \cup B=B...
  24. K

    Relations- reflexive, symmetric, anit-symmetric, transitive

    Suppose that R1={(2,2),(2,3),(2,4),(3,2),(3,3),(3,4)}, R2={(1,1),(1,2),(2,1),(2,2),(3,3),(4,4)}, R3={(2,4),(4,2)} , R4={(1,2),(2,3),(3,4)}, R5={(1,1),(2,2),(3,3),(4,4)}, R6={(1,3),(1,4),(2,3),(2,4),(3,1),(3,4)}, Determine which of these statements are correct. Check ALL correct answers...
  25. S

    Can someone check this for me? (Equivalence classes)

    Question: Find the equivalence classes and the number of equivalence classes of the following relations. A is the set of all possible strings of 3 or 4 letters in alphabet {A, B, C, D}, and (x, y) ∈ R if and only if x and y have the same first letter and the same third letter. My attempted...
  26. P

    Ordered relations, lower upper bounds of a set

    Homework Statement Suppose that R is a partial order on A, B1 ⊆ A, B2 ⊆ A, x1 is the least upper bound of B1, and x2 is the least upper bound of B2. Prove that if B1 ⊆ B2 then x1Rx2. Homework EquationsThe Attempt at a Solution I split the proof into two different cases: case 1: x_1 is an...
  27. P

    Canonical Commutation Relations in finite dimensional Hilbert Space?

    So lately I've been thinking about whether or not it'd be possible to have the commutation relation [x,p]=i \hbar in a Hilbert Space of finite dimension d. Initially, I was trying to construct a lattice universe and a translation operator that takes a particle from one lattice point to the...
  28. R

    Use viscosity/shear stress relations to find torque needed to rotate disk

    The problem asks for an approximation for the torque needed to rotate a disk that is separated from a stationary boundary by a viscous fluid, given that \tau = \mu \frac{U}{H}. I did it first using like this: T = F R F = \tau A = \mu \frac{U}{H} \pi R^2 where U = \Omega R And thus T = \mu...
  29. P

    Relations, power sets and the empty/null set.

    Homework Statement Suppose R is a relation on A, and define a relation S on P (A) as follows: S = {(X, Y ) ∈ P (A) × P (A) | ∀x ∈ X∃y ∈ Y (xRy)}. For each part, give either a proof or a counterexample to justify your answer. (a) If R is reflexive, must S be reflexive? (b) If R is symmetric...
  30. J

    Maxwell Relations: when are they valid?

    Hi, I have a question If I am not mistaken, the Maxwell relations of theromdynamics -----for example: ∂G/∂T) = -S ; ∂G/∂P) = V ----- are valid only for reversible processes. On the other hand, dG = ∂G/∂T)*dT + ∂G/∂P)*dP + ∑ μi dni is valid for any process. This means that dG = -SdT + VdP...
  31. Math Amateur

    MHB Notes & Texts on Sets, Relations and Functions

    On a post involving the proof of the Fourth Isomorphism Theorem for vector spaces (in which I was immeasurably helped by Deveno) I have become aware that my knowledge of sets and functions was not all it should be when it comes to things like inverse images, left and right inverses and the like...
  32. J

    Recurrence relations with rabbits pairs

    A single pair (male and female) of rabbits is born at the beginning of the year. Assume the following: 1) Each pair is not fertile for their first month bet thereafter give birth to four new male/female pairs at the end of every month 2) no rabbits die a) let r_{n} be the number of pairs of...
  33. D

    QFT - Commutator relations between P,X and the Field operator

    Hi all, I haven't been able to find an answer online but this seems like a pretty basic question to me. What are the commutator relations between the position/momentum operators and the field operator? I'm not even certain what the commutation relations between X/P and a single ladder operator...
  34. A

    MHB Proving Binary Relations: R & S

    Hi, I'm currently stuck on a few questions regarding binary relations as I'm unsure on how to prove their properties. R is defined on N by aRb if and only if a <= b and b <= a+5 Is R reflexive, symmetric, antisymmetric, transitive? S is defined on Z (union) {x + 1/2 : x is an element of all...
  35. kelvin490

    Questions about thermodynamic relations

    We know that for constant pressure thermodynamic processes which only expansion work is possible, dH=dQp. My question is, is it necessary that both work W and Qv be reversible to arrive this relation? What if the heat transfer is irreversible? Similar question for dU=dQv, does the heat...
  36. evinda

    MHB How Do We Derive and Verify the Taylor Series for \(\arctan(x)\)?

    Hello! (Cool) I want to find the Taylor series of $f(x)=\arctan(x), x \in [-1,1], \xi=0$ $$f'(x)=\frac{1}{1+x^2}$$ According to my notes: $$\frac{1-(-t^2)^n}{1+t^2}=1-t^2+ \dots + (-1)^{n-1} t^{2n-2}$$ So, $\frac{1}{1+t^2}=1-t^2+ \dots +(-1)^{n-1}t^{2n-2}+\frac{(-t^2)^n}{1+t^2} \Rightarrow...
  37. H

    4-force, 4-momentum, energy and mass relations.

    This is an exercise of Special Relativity the professor asked last week. Sorry for the long post, I hope you don't get bored reading it, also, this is my first post here :shy: Homework Statement Defining the 4-force that acts on a particle as the proper-time variation of the 4-momentum...
  38. J

    Nonhomogeneous recurrence relations

    Homework Statement Solve the recurrence relation an = 3an−1 −2an−2 +3, a0 = a1 = 1.Homework Equations an = general solution + particular solutionThe Attempt at a Solution I started with finding the general solution, which was easy. it ended up being A12n + A0 now I am having trouble solving...
  39. Dishsoap

    Manipulate Commutator Relations in Quantum Mechanics - Help Needed

    This is not a homework question, I just can't find a good resource on this topic. I am working in quantum mechanics on commutator relations. My book (Griffiths) lacks information on how to manipulate the commutator relations. For instance, when I have [AB,C], when can I make it A[B,C]? Or...
  40. K

    What Does Equivalence Relations Mean in Set Theory?

    Hi, I'm reading a book on sets and it mentions a set B = {1,2,3,4} and it says that R3 = {(x, y) : x ∈ B ∧y ∈ B} What does that mean? Does that mean every possible combination in the set? Also the book doesn't clarify this completely but for example using the set B say i had another...
  41. A

    MHB Understanding Binary Relations: Reflexive, Symmetric, Antisymmetric & Transitive

    Hi, I'm having trouble understanding how to determine whether or not a binary relation is reflexive, symmetric, antisymmetric or transitive. I understand the definitions of what a relation means to be reflexive, symmetric, antisymmetric or transitive but applying these definitions is where I...
  42. X

    Is my explanation valid? (commutation relations)

    I am doing a problem on the "super symmetric harmonic oscillator" Defined by.. \hat{H}=\hat{H}_b+\hat{H}_f= \hbar \omega \left( \hat{b}^{\dagger}\hat{b}+\hat{f}^{\dagger}\hat{f} \right) I am given the operator.. \hat{Q}=\sqrt{\hbar \omega} \hat{b}^{\dagger} \hat{f} and asked to show...
  43. T

    MHB Glad I could help! Good luck with your studies.

    Hi guys! First time poster, long time lurker! I can't make any sense out of equivalence relations:confused: These kinda questions crop up every year on the exam and I was wondering if someone could help me understand the concept behind them. (i)Show that relation R defined on the of the set S =...
  44. gfd43tg

    Maxwells relations for an open system

    HelloI have learned about maxwells relations and can derive them. I noticed that we had made an assumption of a closed system. We just learns about chemical potential and the fundamental relations for an open system. I had a thought experiment that there may exist maxwells relations for an open...
  45. K

    What is the equivalence class [3] in a relation defined by powers of 2?

    Homework Statement Let ## H = \{ 2^{m} : m \in Z\}## A relation R defined in ##Q^{+} ## by ##aRb ##, if ## \frac{a}{b} \in H## a.) Show that R is an equivalence Relation b.) Describe the elements in the equivalence class [3]. The Attempt at a Solution For part a, I think I am able to solve...
  46. S

    MHB Partitions and equivalence relations

    i don't have a specific question. i just need an explanation on what this topic is about. i am not understanding it
  47. V

    How can I write down this property of relations

    If I have a relation which is not only antisymmetric (##aRb\rightarrow{}\neg{}bRa##) but it also has a property that ##aRb\land{}bRc\rightarrow{}\neg{}cRa##. How can I be sure that this property holds for any string like that? So that ##aRb\land{}bRc\land{}cRd\rightarrow{}\neg{}dRa## without...
  48. T

    Relations and Inverse Relations

    I am having difficulty understanding the following problem. I feel it should be very simple but am unsure how to interpret it. A relation ##R## is defined on ##N## by ##aRb## if ##\frac{a}{b} \in N##. For ##c, d \in N##, under what conditions is ##c R^{-1} d##? (Exercise 8.6 from Chartrand...
  49. L

    Relations with big oh and big theta

    Hi all, this is a problem that I want to start early on, but I'm not sure how to show my work for this. If i say the theorems it just feels repetitive. So I guess my question is, is using theorems enough to answer this? thank you! Homework Statement determine the properties of each...
  50. evinda

    MHB How Does the Linearity of Integration Work for Sum of Functions?

    Hey! :) Let $f,g: [a,b] \to \mathbb{R}$ integrable functions.Show that: $\int_{a}^{b}(f+g)=\int_{a}^{b}f+\int_{a}^{b}g$ We suppose the subdivision $P=\{a=t_0<t_1<...<t_n=b\}$ of $[a,b]$. Let $t \in [t_k,t_{k+1}]$. $$f(t) \leq sup f([t_k,t_{k+1}])$$ $$f(t) \geq inf f([t_k,t_{k+1}])$$ $$g(t)...
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