please answer all the questions. question 1 to question 5 Given an integral domain R we...
Please answer all parts. Thank you! 20. Let R be a commutative ring with identity. We define a multiplicative subset of R to be a subset S such that 1 S and ab S if a, b E S. Define a relation ~ on R × S by (a, s) ~ (a, s') if there exists an s"e S such that s* (s,a-sa,) a. 0. Show that ~ is an equivalence relation on b. Let a/s denote the equivalence class...
Correction: first problem is #2, not #1. Please show all steps in the proofs. Definitions for problems #2 through #5: Let C be the set of all Cauchy sequences of rational numbers, with the operations of addition and multiplication defined on C by (an) + (bn) = (an + bn) and (an)(bn) = (anbn). Let N be the subset of C consisting of all null sequences in c. Properties of a ring: A1. (a + b) +c= a + b...
Question 1 (10 Marks) This question consists of 10 true false ansers. In cach ease, answer true if the statement is always true and false otherise. If a statement is false, 1. The set rER0 isa group under the binary operation o defined ad-be is a group under matrix addition. 3. Tho sot eRzs not an Abelian group under the binary erplain why. There is no need to show working for true statements. by a ob vab. 2. The set...
Please answer all the questions. QUESTION 1 ; a question like, "Isn't that the guy we usually see on the bus?" requires (2006) A question like, "What's the name of the waiter?" requires a. recognition; recall b.familiarity, source memory Oc source memory; familiarity d. recall; recognition QUESTION 2 (2001) When faced with an ill-defined problem, which of the following is the best first step? O a reduce the number of subgoals b. hill climbing ocadd structure to better define the...
plz help me solve the question. plz dont copy anyother wrong answer. Ouestion 2. 2/2 -Throughout this question, z E C \ R and we define do (a) Locate and classify all singularities in the complex plane of Determine any associated residues (b) Evaluate Φ(z) by completing the contour in the upper half-plane. (c) Evaluate Ф(z) by completing the contour in the lower half-plane. (d) Verify that your answers to (b) and (c) are the same. (e) If r e...
Use the following information To help you solve the following questions. Show all work for thumbs up. 3.1 Rotations and Angular-Momentum Commutation Relations 159 We are particularly interested in an infinitesimal form of Ry: (3.1.4) where terms of order & and higher are ignored. Likewise, we have R0= ° :- R(E) = 1 (3.1.5) and (3.1.5b) - E01 which may be read from (3.1.4) by cyclic permutations of x, y, zthat is, x y , y → 2,2 → x....
Answer ALL the questions. Some or all of them shall be marked. Question 1. Consider the following system of differential equations: P.(D) [x] + P (D)) -(0) Px(D) [x] + P (D) x = f(t). (1) How do we determine the correct number of arbitrary constants in a general solution of the above system. (0) Explain briefly the difference between the operator method and the method of triangu- larization when used for solving the above system. Question 2. Determine whether...
PLEASE ANSWER ALL OF THE QUESTIONS Question 1 1 pts Each of three objects has a net charge. Objects A and B repel each other. Objects B and C attract each other. Which one of the following table entries is a possible combination of the signs of the net charges on these three objects? A B с (1) + + - + (2) + + (3) (4) - (5) + - 0 1) 3) 0 (3) and (5) O (1)...
2. Consider a mass m moving in R3 without friction. It is fasten tightly at one end of a string with length 1 and can swing in any direction. In fact, it moves on a sphere, a subspace of R3 1 0 φ g 2.1 Use the spherical coordinates (1,0,) to derive the Lagrangian L(0,0,0,0) = T-U, namely the difference of kinetic energy T and potential energy U. (Note r = 1 is fixed.) 2.2 Calculate the Euler-Lagrange equations, namely...
*Please, answer all the literals and be detailed with the answer (do all the procedure and calculations) *Do it with a clear letter Homework (scattering) 1. Consider the time dependent Schrödinger equation written in the form where 0 2mo As it is well known the temporal evolution of a wave function ψ( t) known at a specific time t is uniquely determined for all future times t, > t as well as for all past times t' < t. Moreover,...