1. S

    Preference relation

    Hi everyone, I have been reading this real analysis /economics book and I came across the following problem with which I have been struggling with. If I have two bundles a=(a1,a2) and b=(b1,b2) then I prefer a over b if and only if a1+a2>=0.5+b1+b2 . My question is , is this preference...
  2. I

    Understanding an Equivalence Relation proof

    Hey guys, I asked this question before but now I got the answer from my prof, but I don't really get the answer. A binary relation R is defined on the set Z2 as follows: (a, b) R (c, d) <---> a= c (mod 2) and b = d (mod 3) Here's what I don't get: From the definition, isn't reflexive (x, x)...
  3. A

    no of reflexive relations on a set cant be 2^(n^2-n).

    no of reflexive relations on a set cant be 2^(n^2-n).as we have to take diagnol elements no of reflexive relations are coming out to be n only.if we have a set{1,2,3,4}.then the reflexive relations are only (1,1);(2,2);(3,3);(4,4)..please correct me with reasoning if i'm wrong.
  4. I

    Prove an Equivalence Relation

    Hey, I would like to prove this equivalence relation: A binary relation R is defined on the set Z2 as follows: (a, b) R (c, d) <---> a= c and b = d I know I need to show that R is reflexive, symmetric, and transitive, but I am not sure how in this kind of question.
  5. Z

    Modelling with Recurrence Relation

    This is a question from my tutorial. A patient is injected with 80 ml of an antibiotic drug. Every 4 hours 40% of the drug passes out of her bloodstream. To compensate for this an extra 15ml of antibiotic is given every 4 hours. Find a recurrence relation for the amount of drug in the...
  6. S

    Relation between curvature and torsion

    In the context of tensor calculus, by using Serret-Frenet formula or otherwise, how to prove that $\tau^2=\displaystyle\frac{r'''^2}{k^2}-k^2-(\frac{k'}{k})^2$ where $\tau$ and $k$ represent respectively torsion and curvature.
  7. K

    Proof of inner product relation in a Hilbert space

    Hello everyone I have been given a task where I need to prove, \forall \textbf{v} \in H, the following formula: <\textbf{v},\sum \limits^{\infty}_{k=1}c_k \textbf{v}_k>=\sum \limits^{\infty}_{k=1}\bar{c_k}<\textbf{v}_k, \textbf{v} > Where < \: \cdot \: , \: \cdot \: > is an inner product...
  8. N

    Describe a relation between the composition of two relations and their domains ...

    Describe a relation between the composition of two relations and their domains and ranges. Any & all help is appreciated.
  9. C

    Define the relation R on the set A = {1,7,21,35,36} as: (a, b) ∈ R if GCD(a,b) > 1

    Define the relation R on the set A = {1,7,21,35,36} as: (a, b) ∈ R if GCD(a,b) > 1 a. Find three distinct paths from node 36 to node 35. (Use the -> symbol to indicate a transition between nodes.)
  10. T

    Recurrence relation problem

    Hello everyone, I tried to solve this one but it isn't consistent with my solution. How can i solve this problem?
  11. Z

    A specific problem on Sobolev's embedding theorem with its relation to Fourier transf

    I have recently encountered this problem in my studies of Sobolev spaces and generalized functions (distributions), on which I can say I might have some intuition but cannot stumble across a final solution, but first some notations: $ \mathcal{S} $ is the Schwartz class of functions and $...
  12. D

    Relation between these numbers

    Can you please help me find the link between the first two columns and the last column please 584.4 662.3 1.207751938 576.2 604.1 0.43255814 464.4 461.2 -0.049612403 509 582.8 1.144186047 523.5 569.1 0.706976744 Thanking you from Australia
  13. C

    Completeness Relation

    Hi I'm currently studying Fourier Analysis and having trouble with the completeness relation. Does the completeness relation hold for A={e_k | k belongs to Z \ 3N}? I know that all multiples of 3 will be removed from the function but am unsure of how to show if the completeness relation holds...
  14. B

    proving the relation

    Hi, I need some help with the following situation i would like to prove. I have three functions (f_a,f_b, f_c). I know the following: f_{a} \geq \frac{f_{b}}{2x} f_{a} \geq \frac{f_{c}}{x+2} what I would like to know is the relation between f_b, f_c( isf_b \geq or \leq or = f_c ).However I...
  15. N

    recurrence relation

    Find a recurrence relation to count the number of n-digit (n ≥ 1) ternary sequences (i.e. strings of 0,1 and 2) with at least one instance of consecutive 1’s.
  16. M

    Recurrence relation

    Can someone assist me with this please.How do i go about doing it?
  17. I

    Relation within Gauss-Newton method for minimization

    If we study model fit on a nonlinear regression model $Y_i=f(z_i,\theta)+\epsilon_i$, $i=1,...,n$, and in the Gauss-Newton method, the update on the parameter $\theta$ from step $t$ to $t+1$ is to minimize the sum of squares...
  18. Krizalid

    Limit relation for events

    Let (\Omega,\mathcal F,P) be a probability space and (A_n)_{n\ge1} be a sequence of events in \mathcal F. Prove that {{I}_{\underset{n\to \infty }{\mathop{\underline{\lim }}}\,{{A}_{n}}}}+\underset{n\to \infty }{\mathop{\overline{\lim }}}\,{{I}_{A_{n}^{c}}}=1. (Rock)
  19. R

    what is the symmetric closure of below relations?

    If I have a relation ,say ,less than or equal to ,then how is the symmetric closure of this relation be a universal relation . I tried out with example ,so obviously I would be getting pairs of the form (a,a) but how do they correspond to a universal relation.
  20. R

    what is the reason behind the below nature of the relation?

    If I have a relation R which is transitive ,then why is the symmetric closure of the relation is not transitive ?Actually I am confused in this ,so please guide me in this.