1. K

    Finding correlation between orders (DV) and price (IV), with many other IVs at play

    I have a large data set of several million customer orders for a product, over the past two years. Orders have grown steadily over that period (with periodic swings due to seasonality or other factors), thanks to a combination of organic growth (e.g. word of mouth), and paid marketing. The...
  2. M

    How would I write a proof for these partial orders?

    Let R 1 and R 2 be relations on N defined by xR 1 y if and only if y=a+x for some a∈N 0 . xR 2 y if and only if y=xa for some a∈N For all x;y∈N. Also N 0 denotes all integers x≥0 , while N denotes all integers x≥1 . There are two different things I want to prove...
  3. A

    Orders of elements for rotational symmetries of cube

    I am having lots of trouble doing this problem because I have particularly poor visualization skills. (Or maybe haven't developed them well yet). I would appreciate any help on this math problem. Here is the question: Suppose a cube is oriented before you so that from your point of view...
  4. C

    Partial Orders

    OK, so I have managed to prove a couple of partial orders already so understand the reflexive, anti-symmetric and transistive properties to some degree but this question has really thrown me, especially for the latter two properties. Could someone please help me out. Thanks x Let X = {1,2,3}...
  5. W

    Partial Orders : Hasse Diagrams

    For A  {a, b, c, d, e}, the Hasse diagram for the poset (A, R) is shown in Fig. 7.23. (a) Determine the relation matrix for R. (b) Construct the directed graph G (on A) that is associated with R. (c) Topologically sort the poset (A,R ). e...
  6. T

    Prove the following statements about the orders of elements...

    L = Z5[x]/(x^2+2x+4) is a field and the multiplicative group L* is generated as a cyclic group by s+3, where s is the congruence class of x modulo x^2+2x+4. Prove the following statements about the orders of elements in L*. (a) s has order 12. (b) s+1 has order 8. (c) s+2 has order 12. (d) 2s...
  7. B

    second derivative of Bessel Function in terms of higher and lower orders of Bessel fn

    I have been trying to replicate a result given in a textbook that says J_{n}^{''}(x)=\frac{1}{4}\{J_{n-2}(x)-2J_{n}(x)+J_{n+2}(x)\} where J_{n}(x) is the Bessel Function of the First Kind. Can someone show me how to get this from the recurrence formulae for Bessel derivatives found in the...
  8. A

    Switches and Number of orders

    Hello, So here is the question: A special-purpose computer has 2 switches, each of which can be set in 3 different positions and 1 switch that can be set in 2 positions. In how many ways can the computer's switches be set? What i tried: is 2 * 2 * 2 * 2 (because in every position there can be...
  9. A

    Orders of convergence

    Hi Guys, I have a small question on orders of convergence. I'm happy with the idea that for $N\in\mathbb{N}$ if, $\text{error} \le C_1N^{-\alpha}+C_2N^{-\beta}$, where $\alpha<\beta$, $\alpha, \beta \in\mathbb{R}$, $\alpha,\beta>0$, $C_1, C_2 \in\mathbb{R}$ are constants $\Rightarrow...
  10. J

    Probability with batting orders

    How many batting orders (the order in which baseball players face an opposing pitcher in a game) does a manager have available for the nine baseball players of a team, if the center fielder must bat 4th and the pitcher must bat 9th? 1. 5040 2. 362,880 3. 181,440 4. 40,320
  11. A

    Group element orders.

    Let G be an abelian group. Suppose \alpha, \beta \in G are of finite order with |\alpha| = m = m'p^{v'} and |\beta| = n = p^v where p is prime, v' < v and \mathrm{gcd}(m,n) = p^{v'} (i.e. p does not divide m'). Prove that |\alpha \beta| = \mathrm{lcm}(m,n).
  12. I

    Theorem about the Set of total orders on a given set

    Hello Here is a problem I am doing. Suppose |A|=n and let F=\{f|f\mbox{ is a one to one,onto function from }I_n\mbox{ to }A\} . Let L=\{R|R\mbox{ is a total order on }A\} Prove that F\sim L and therefore |L|=n!. Velleman gives some hints at the back of the book. To prove F\sim L...
  13. Bernhard

    Orders of elements of Dihedral Group D8

    R = \left(\begin{array}{cccc}1&2&3&4 \\ 2&3&4&1\end{array}\right) Peter Moderator edit: Latex fixed. @OP: Please add the rest of the question by replying to this post.
  14. A

    modulo orders

    Hi, I am not sure about my answer. Given a is an integer with (a,66)=1, what are the possible orders for a modulo 66? Working: Since phi(66)=20 then the possible orders of a modulo 66 have to divide this. So the possible orders are 1,2,4,5,10,20. Is this adequate? Thank you
  15. H

    Mathematical logic--> Binary relations, orders, and equivalence relations/classes

    For each of the following binary relations on the set of natural numbers including 0, state (yes/no) whether it is (i) reflexive, (ii) irreflexive, (iii) symmetric, (iv) antisymmetric and/or (v) transitive. Briefly justify your answers. Identify which relations (if any) are partial orders...
  16. R

    Integration of high orders

    Hi there, I havnt done much integration in a while but i believe i have a pretty solid background. I am really struggling to figure out whether this integration is even possible. Int (dT/(a-bT-cT^4)) Will i have to simplify the problem or is there a method i have overlooked? Thanks
  17. Bernhard

    Isomporhisms preserve orders - help with proof

    I am a math hobbyist studying Joseph Gallian's "Contemorary Abstract Algebra" (Fifth Edition). Part of Theorem 6.2 on page 124 states that if \phi :G \rightarrow G' is an isomorphism then the order of an element a \in G is equal to the order of \phi (a) ; that is \ \mid a \mid \ = \...
  18. F

    orders of elements and isomorphisms

    Show that if \gamma: G_1 \rightarrow G_2 is an isomorphism, then for each g \in G_1, o(\gamma(g)) = o(g) Does this argument work? if g \in G_1 has order l \Rightarrow g^l = e_1 then \gamma (g^l) = \gamma (e_1) then as the identity element of G_1 is mapped to the identity element e_2 \in G_2...
  19. G

    Number of diffracted orders produced

    Hi A liitle help will be appreciated. The question is as follows: A laser beam of wavelength 630nm is directed normally at a diffraction grating with 300 lines per millimetre. Calculate: a) The angle of diffraction of each of the first 2 orders b) The number of diffracted orders produced...
  20. H

    Proposition Regarding Cosets and Orders

    Let A be a finite subset of a group G (not necessarily a subgroup). Denote by A^2 the set \{a_1 a_2 | a_1, a_2 \in A\}. Prove that |A^2| = |A| \iff the following is true: A equals a left coset aH for some subgroup H \leq G and some element a \in G, and A also equals some right coset Hb...