In the early days of commutative algebra people did not use the language of localization, so probably such proof exists. In particular, I have been told Kaplansky's early book (around 1950?) might be such reference, but I don't have it right now. In any case, Exercise 2.3 ...
Let $\mathbb{PD}_3 \subset \mathbb{R}^{3 \times 3}$ be the set of the positive-definite $3 \times 3$ real matrices. For given $v \in \mathbb{R}^{3 \times 1}$, consider the function $f_v: \mathbb{PD}_3 \times \mathbb{R}^{3} \rightarrow \mathbb{R}_{\geq 0}$ defined as $$ f_v(X,y) := y^\top X y + 2 y^\top X v + v^\top X v $$ We ...
Let $T:V \rightarrow V$ linear transformation over field $F$. Let $W$ be a non zero proper $T$-invariant subspace of $V$. Suppose that the characteristic polynomial $f_T$ of $T$ satisfies that $f_T(0)\neq 0$. Show that if $T$ has a cyclic vector, then the restricted $T|_W:W \rightarrow W $ has a cyclic ...
I'm having trouble showing $$\lim_{n\to\infty}\int_{0}^{\infty}e^{-x}\sin\left(\frac{n}{x}\right)~\text{d}x=0$$ The integrand doesn't converge for any $x$ so I don't know how to use the standard Lebesgue convergence theorems. Thank you for any hints. ...
Is there a way to answer the following preferably without a calculator What digit appears in unit place when $2^{320}$ is multiplied out ? a)$0$ b)$2$ c)$4$ d)$6$ e)$8$ ---- Ans(d) ...
I am trying to find the moment generating function of a random variable $X$, which has probability density function given by $$f_{X}\left( x\right) =\dfrac {\lambda ^{2}x} {e^{\lambda x}}$$ Where $x>0$ and $λ>0$. The standard approach to doing this i believe is to follow the following algorithm The moment generating function (mgf) of a ...
python function nthOddDigits, which takes a positive integer x and returns the nth number that only has odd digits 1,3,5,7,9,11, 13, 15, 17, 19, 31 etc. nthOddDigits(0)returns 1, etc. def nthOddDigits(x): if x % 2 == 0: return x + ...
Good morning Gentlemen, My goal with this program is to record 4 pieces of information (Employee Number, Employe Name, Shift Number, and Hourly Pay Rate) and then display them. I need to use classes in this program. Here is the Class code: class Employee(object): def __init__(self, name, number): ...
I have here three classes that asks for input and should display an array of strings in a dialog box. Class 1: public class Card { public int rank; public int suit; public String rankName; public String suitName; public String cardName; public Card () { ...
Possible Duplicate: A Game (similar to tic tac toe) algorithm needed. first of all i'm beginner to Java programming. I want to make an application for School project. I have decided to make a board game! pretty straight forward. ![Board][1] This is the board and ...
I have a homework to write a test for the following method in other to show that the Object and its duplicate ,which has been created using this method, are equal. /** * Creates a new object that is a duplicate of this instance of * Parameter. ...
Alright, so I'm supposed to do an assignment: Say you have chat logs sorted like this: System-0/Server-#channel.log System-0/Server-#channel1.log System-0/Server-#channel2.log System-1/Server-#channel.log System-1/Server-#channel2.log System-2/Server-#channel3.log System-0 being my first system, system 1 and 2 being other computers. How would I go on about merging System-0/#channel with System-1/#channel log files? I've already figured out how to get them, however, BufferedWriter randomly stops ...
I found this potential solution in previous stack question. My problem is that it's not outputting to the file. The program terminates without errors and actually does what it's supposed to do as I have verified this with a cout. The program takes in a 7-digit phone number. Then writes to a ...
How could I create a program that has an array of 25 integers with a mixture of values positive and negative and display the average of all the numbers, the positive numbers and the negative numbers? Please help ...
I was thinking that doing java code for executing DDL, DML etc is cumbersome and involves a lot of typing. So, I was thinking if databases have/can be made to have the following feature -Take a script in a text file and execute the entire script. If we had something ...
All I am looking for is when the below code is run and the Albums or the Music links are clicked it posts to the same page, correct? hence the url changes and add the href on the end of it depending on the link clicked. Well how can ...
hand = ['A','Q'] points = 0 player_cards1 = ['2'] value1 = 2 player_cards2 = ['3'] value2 = 3 player_cards3 = ['4'] value3 = 4 player_cards4 = ['5'] value4 = 5 player_cards5 = ['6'] value5 = 6 player_cards6 = ['7'] value6 = 7 player_cards7 = ['8'] value7 = 8 player_cards8 = ['9'] value8 = 9 player_cards9 = ['T'] value9 = 10 player_cards10 = ['Q'] value10 = 10 player_cards11 = ['K'] value11 = 10 player_cards12 = ...
This is related to a Think-A-Dot college project. I have a list of objects of type Flipper as so: flipper1, flipper2, flipper3... flipper8 My thought was to do a recursive function to iterate through each flipper and process each one individually instead of dealing with many if-statements; i figure going with something such ...
I currently have a table called TblTables which has fields as the following TableID Available InUse I am trying to link it to my tblOrders and my Reports so that when they order from the tblOrders it makes the table [InUse] via TblTables Table. After they have paid through the Report (RptOrderSubTotal) and the ...