0
votes
0answers
8 views

Change of Basis for 2x2 matrix

Suppose I have the matrix basis $\begin{bmatrix}1&0\\0&0\\\end{bmatrix}$ , $\begin{bmatrix}0&1\\0&0\\\end{bmatrix}$ , $\begin{bmatrix}0&0\\1&0\\\end{bmatrix}$, ...
-7
votes
0answers
21 views

I need someone to add a very long list of numbers for me. [on hold]

352 197 193 153 144 142 120 109 107 101 93 92 72 61 52 51 49 47 47 46 46 45 44 43 42 42 41 40 40 39 38 37 37 37 37 37 36 35 34 33 33 33 31 31 29 28 27 27 26 25 24 24 23 22 22 20 19.8 19.8 19.5 19.4 ...
0
votes
1answer
13 views

COMBINATIONS OF MEASURABLE FUNCTIONS

If f is such that | f | is measurable, does f have to be measurable ? any help would be appreciated . and proof the answer .
-3
votes
0answers
13 views

how to creat a matlab program?

How can I creat a tridiagonal matrix in matlab if the elements of matrix is again a matrix instead of a scalar.n how to solve them using crouts methods.I am new to matlab.
0
votes
0answers
4 views

numerical solution of drift diffusion equation

0 down vote favorite in this link (in semiconductor physics section) you can see four coupled equations. do you know that finite element method is more accurate for discretization and numerical ...
0
votes
1answer
12 views

Simplify $\frac{\sum_{i = 1}^{n}x_{i}}{n} - \frac{n - \sum_{i = 1}^{n}x_{i}}{1 - \theta} = 0$ to show that $\theta = \bar{x}$

Simplify $\frac{\sum_{i = 1}^{n}x_{i}}{n} - \frac{n - \sum_{i = 1}^{n}x_{i}}{1 - \theta} = 0$ to show that $\theta = \bar{x}$ $\frac{\sum_{i = 1}^{n}x_{i}}{n} = \frac{n - \sum_{i = 1}^{n}x_{i}}{1 - ...
0
votes
0answers
12 views

Antiderivative of an even function

I'm faced with an issue in terms of antiderivatives of even and odd functions. Define $f \in C[-a,a]$ where $a>0$. Let $f$ be an even function on $[-a,a]$. We wish to show that $$\int_{-a}^a ...
0
votes
0answers
3 views

Summation of binomial number of poisson random variables

Z is summation of K random variables that each has Poisson distribution with different means. But, K is a Binomial random with parameters of n and p. I was wondering what is the distribution of Z?
1
vote
1answer
16 views

Determinant of $\lambda I + A^TA$

What properties $\lambda I + A^TA$ have? I know that $A^T A$ is positive semi-definite, and symmetric. I want to show that the determinant of $\lambda I + A^TA$ decreases as $\lambda$ increases!
1
vote
0answers
6 views

Basic questions on convolution

I am new to convolution. Below is some derivation related to convolution I saw in a paper. Hope to get some help here. (The paper is "Comparing nonparametric and parametric regresssion fit" published ...
-1
votes
1answer
14 views

Vector spaces and multiplicative inverse?

Do vector spaces have multiplicative inverses? They seem to be monoids under $+,\times$, so monoids $(\Bbb F, +)$ and $(\Bbb F, \times)$ where $\Bbb F=\Bbb R \,or\, \Bbb C$ And it is even a group ...
1
vote
2answers
22 views

Suppose $\sqrt2=a/b$, with $gcd(a,b)=1$. Then $3|(a^2+b^2)$ implies that $3|a$ and $3|b$,

Suppose $\sqrt2=a/b$, with $gcd(a,b)=1$. Then $a^2=2b^2$, so that $a^2+b^2=3b^2$. But $3|(a^2+b^2)$ implies that $3|a$ and $3|b$, a contradiction. I don't understand how $3|(a^2+b^2)$ implies that ...
1
vote
1answer
18 views

Example of a Non-Commutative Division Ring With Finite Characteristics

Wedderburn's Little Theorem says that every finite Division Ring is commutative. What is about an infinite Division Ring with prime characteristics? Is this also a Field?
-1
votes
1answer
20 views

Simplify the function

I am having problems solving this, any help would be appreciated. Find $f(x+h)-f(x)$ and simplify if $f(x)=2+3-x^3$ Thanks in advance.
0
votes
1answer
4 views

A symmetric algebra that is not a C* algebra

Recall that a commutative Banach $*$-algebra $A$ is called symmetric if the Gelfand transform replaces involution in $A$ by complex conjugation in $\mathbb{C}$. Moreover, any commutative C* algebra is ...
1
vote
3answers
61 views

Show that $n^4+4$ is not a prime number

How do you show that for all $n ∈ N, n ≥ 2,$ $n^4 + 4$ is not a prime number? My attempt: I see that whatever number $n^4+4$ makes when $n$ is an even number would result to an even number. Thus ...
0
votes
2answers
15 views

Need help in clarifying relation of square root and logarithm to do a correct substitution

This might be so basic and obvious, but I am stuck on how to do substitution that involves logarithm and square root. If we have $$\lfloor\sqrt{n}\rfloor$$ and we do the following substitution ...
0
votes
2answers
19 views

What is the minimum number of painted edges in the chessboard?

Some edges of the squares of an 8×8 chessboard are painted red. What is the minimum number of edges that must be painted, so that each square has at least two red edges? What is the meaning of this ...
1
vote
1answer
16 views

basic question about Group structure (answering a small exercise..)

The operation * defines a binary operation in $\mathbb R\times \mathbb R$ by $(X_1,Y_1)*(X_2,Y_2) = (X_1X_2, Y_1X_2+Y_2)$ defines a group structure (i found out..), but shouldn't we exclude the ...
0
votes
2answers
16 views

Prove that the ideal generated by $x^3 + x + 1$ is not maximal in $\mathbb Z_3[x]$

This is part of a larger homework problem. I am trying to prove that a quotient ring is not a field by showing that $\langle x^3+x+1\rangle$ is not maximal in the ring of polynomials in the integers ...
0
votes
1answer
11 views

Calculate perimeter of rhomboid

I am trying to solve the following problem but I got stuck In a rhomboid with an area of $48 \space cm^2$, the major diagonal is $4$ cm shorter than the double of the minor diagonal. Calculate the ...
1
vote
2answers
12 views

Find the general expression from the antiderivative

I am having trouble computing the original function. Question states: Let $f$ be a differentiable, positive function, such that $$f'(x)=x*f(x)$$ for all real numbers x. A) Find the general ...
0
votes
0answers
14 views

$\sigma$-algebra generated by a topology

Suppose that $(X, \mathcal{T})$ is a topological space. My hunch is that the smallest $\sigma$-algebra on $X$ containing $\mathcal{T}$ is the collection of Borel sets obtained from $\mathcal{T}$. Is ...
-1
votes
1answer
15 views

Determine average rate of change of function

How to determine the average rate of change of $f(x)= x^5-3x^4$ on the interval $[-2,4]$
0
votes
3answers
14 views

$X_n$ has limit $L$. Given a constant $C$ we have a new sequence $Y_n$ where for each $n,Y_n=X_n+C$. What is the limit of $Y_n$?

$X_n$ has limit $L$. Given a constant $C$ we have a new sequence $Y_n$ where for each $n$, $Y_n=Xn+C.$ What is limit of $Y_n$? I need help with this problem; I don't understand how to approach it.
0
votes
0answers
5 views

Value(s) of the parameter $a$ that give explicit formula's

For what value(s) of the parameter $a$ is it possible to find explicit formula's (without integrals) for the solutions to $$\frac{dy}{dt}= aty +4e^{-t^2}$$ The answer is $a=-2$. I don't know how to ...
1
vote
1answer
25 views

How do I solve the triangle?

Let $ABC$ be a given triangle, such that $AD=3$, $DE=5$, $EC=24$ and $∠ABE=90^\circ$, $∠DBC=90^\circ$, where $D$ and $E$ are points on $AC$ (and$ D$ is between $A$ and $E$). Then, find the length of ...
0
votes
1answer
14 views

How many lattice paths with step S and W are there that begin at (0,0), end at (-12,-12)

How many lattice paths with step $S$ and $W$ are there that begin at $(0,0)$, end at $(-12,-12)$ and do not go through any of the points $(-1,-4), \space (-5,-3), \space (-9,-11)$? I'm unsure of how ...
0
votes
1answer
15 views

Big Omega problem : is $n^2\in\Omega (2n^2)$?

Is $n^2\in\Omega (2n^2)$? If we find the limit we can see $\frac{1}{2}>0$, which means it is true, but I haven't learned the limit method. I need to figure out using this definition $\exists ...
0
votes
0answers
3 views

How to know the rate of convergence of a majorization - minimization algorithm?

The basic idea of majorization-minimization (MM) principlein optimization is to convert a hard problem (for example, non-smooth) into a sequence of simpler ones (for example smooth). To minimize ...
0
votes
0answers
13 views

Infinite product representation for the Sine Integral $\mathrm{Si}(z)$

The infinite series representation of the sine integral (http://en.wikipedia.org/wiki/Trigonometric_integral, previous m.se question: Is there any infinite series representation of the sine ...
1
vote
1answer
20 views

I need Sophie Germain primes in the 7-digit range

About a year ago some one asked if there was a list of ALL Sophie Germain primes. One answer pointed the questioner to: vaxasoftware.com/doc_eduen/mat/primsophie_en.pdf. That list only goes up to ...
0
votes
0answers
16 views

The largest $\sigma$-algebra generated by a subset

It is always possible to find a smallest $\sigma$-algebra that contains any subset $A$ of a given set $X$ (it is, by definition, the intersection of all the $\sigma$-algebras on $X$ that contain $A$). ...
0
votes
0answers
8 views

Is the stable homotopy group of sphere a commutative ring? If not, are there easy examples?

Is the stable homotopy group of spheres a commutative ring? If not, are there easy examples? In the Adams spectral sequence converging to the stable homotopy group of spheres, it seems that any page ...
1
vote
2answers
23 views

“Standard” proof that open disks in $\mathbb{R}^2$ are connected?

Homework for a complex analysis course asks me to prove as homework that open disks are connected. I do know a way to do this: open disks are convex, and an old exercise in Rudin's "Principles of ...
0
votes
1answer
19 views

Need help understanding onto function

Let function $g$ from $V = \{1,2,3,4\}$ into V be defined by: $g(n)=3$. I'm having trouble understanding why $g$ is not onto. I understand why it is not one-to-one but, since all the $y$ in $Y$, are ...
0
votes
1answer
19 views

Prove the following vectors are linearly independent

So I have these three vectors: [i, 2+i, 3]; [2, -i, 4-i}; [3, -1, 2] and I need to show they are linearly independent. This means that given scalars $x_1, x_2, x_3$ their scalar sum should equal 0. ...
-6
votes
1answer
23 views

How to show $ \ln \alpha $ is transcendental number if $ \alpha $ is a non negative algebraic number with $ \alpha \neq 1 $?

Suppose $ \alpha $ is a non negative algebraic number with $ \alpha \neq 1 $. Show that $ \ln \alpha $ is transcendental number. Thanks.
1
vote
1answer
22 views

Ideals of formal power series ring

I need help understanding the following solution for the given problem. The problem is as follows: Given a field $F$, the set of all formal power series $p(t)=a_0+a_1 t+a_2 t^2 + \ldots$ with $a_i ...
-2
votes
0answers
14 views

Min. color $N$ if every $4$ vertex subgraph has a $3$ degree vertex [duplicate]

If a graph has $N$ vertices and every $4$ vertex subgraph has a $3$ degree vertex then prove there is a vertex with degree $N-1$.
1
vote
1answer
11 views

Asymptotic formula for sums related to primes

Suppose $0 < \alpha < 1$. What is the asymptotic formula for the sum $$\displaystyle \sum_{p \leq x} \frac{\log p}{p^\alpha}?$$ Thanks for any insights.
0
votes
0answers
3 views

Order of Dilated horizontally and translated horizontally

I have a parent function $f(x) = x^2$, and $g(x) = (6[x-2]))^2$ is a transformation from $f(x)$. The question is: $g(x)$ is from $f(x)$ by Dilated horizontally by a factor of 1/6, then translated ...
0
votes
0answers
19 views

What are some interesting and useful math “tricks” or manipulations that are great for competitions and difficult questions in general [on hold]

An example of a "clever" trick includes componendo dividendo. The "tip" should be applicable for amc 10 type questions and more difficult contest type questions.
-2
votes
0answers
11 views

Prove that $C_c(X)^c=C_0(X)$ if $X$ is locally compact $T_2$

Prove that $C_c(X)^c=C_0(X)$ if $X$ is locally compact $T_2$ So in genarel $C_c(X)$ is not complete wr.t . Supnorm.
0
votes
1answer
23 views

Computing $\mathrm{lcm}(2,3,6)$

I have the following question: I will earn money if I share it with 2, 3 and 6 people. The money I am about to earn is less than $100,000 (USD). How much money will I earn if the condition is met? ...
0
votes
1answer
9 views

Find the standard matrix of T given T is a linear transformation

$T:\mathbb{R}^2\to \mathbb{R}^2$ first performs a horizontal sheer that transforms $e_2$ into $e_2 + 2e_1$ (leaving $e_1$ unchanged) and then reflects points through the line $x_2 = -x_1.$ I am ...
3
votes
3answers
83 views

Surprising applications of topology

Today in class we got to see how to use the Brouwer Fixed Point theorem for $D^2$ to prove that a $3 \times 3$ matrix $M$ with positive real entries has an eigenvector with a positive eigenvalue. The ...
0
votes
0answers
16 views

Logic - Is it safe to state the following?

say that ∀x∃y in all possible integers (negative integers, 0 and positive integers) is x*y = x is it safe to say that ∃y∀x is also true. If not can someone explain why its not true. The way I'm ...
-1
votes
2answers
18 views

how many jelly beans did each girl have at first?

Martha and Mary had $375$ jelly beans in all. After Mary ate $24$ jelly beans and Martha ate $\frac 17$ of her jelly beans, they each had the same number of jelly beans left. How many jelly beans did ...
-1
votes
0answers
5 views

Need Help with this conical container word problem [on hold]

A conical container (r= 7 ft, h = 28 ft) is filled to (h=24 ft) of a liquid weighing 62.4 ft/lb^3. How much work will it take to pump the contents to the rim? r = radius h = height

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