0
votes
0answers
1 view

If $G$ be a p-group of order $p^n$, then $p^2 \le |G : G^\prime|$.

If $G$ be a p-group of order $p^n$, then $p^2 \le |G : G^\prime|$, where $G^\prime$ is the commutator subgroup of $G$.
0
votes
0answers
3 views

converting a equation to convex form which can be given to cvx solver to solve it.

Can anybody tell me how to convert this to quadratic programming format so that CVX could solve it...?? I am not asking the whole solution but need only conversion. objective is:- minimize {sum ( ...
0
votes
0answers
7 views

Another integral equation question

Suppose that $z = \int_{- \infty}^z f (y) d y$. If $f$ were continuous, we can differentiate both sides to get $f(y)=1$. But what if $f$ does not have to be continuous, is this still true or are there ...
0
votes
2answers
11 views

Area of the curve sin(cos(x))

Find the area of the region enclosed by the curves $y = \sin (\cos(x))$, $y = 0$ ,$x = π / 2$, and $x = −π / 2$. I am not able to integrate the function. How do I find this area?
0
votes
0answers
4 views

Artin-Rees Lemma for Semigroup

(Artin-Rees Lemma) Let S be a Noetherian semigroup and A,B be ideals of S. A∩B^İ=(A∩B^N)B^(İ-N) for each İ≥N where N is a natural number. Does anyone know its proof?
0
votes
1answer
12 views

Does matrix has a underlying basis?

Can I say a matrix (M) as a liner transformation and it operates on a vector? The vector must have a basis and the matrix M gave us a new vector. Now is there any basis associated with the matrix. ...
0
votes
0answers
4 views

Infinite subspaces for a vector space that cannot be spanned by a single element

If a vector space (over an infinite field) cannot be spanned solely by a single element, does it mean it has infinite subspaces? I couldn't find an example that contradicts this
0
votes
0answers
8 views

Taylor's expansion of vector valued functions

Apostol, Calculus, Vol 1 : Let $b$ be a given point in $\mathbb R^n$. Then, if $v$ be any given vector,my textbook defines the taylors expansion of $f$ as : $f(b+v) = f(b) + f~'(b)(v)+ ||~v~|| ...
0
votes
1answer
4 views

Rotation matrix and invariance of norm squared

I was wondering how the distance function $(\Delta s)^2 = (\Delta r)^2 + (r \Delta \theta)^2$ can be shown to be invariant under the rotation matrix $ \begin{pmatrix} cos\ \theta & - sin\ \theta ...
0
votes
2answers
11 views

If 'm' and 'n' women are standing toghter for photograph such that no men are woman are adjacent together what are the number of Permutations

suppose 'm' men and 'n' women from a single line for a photograph in such a way that no two men are next to each other and no women are next to each other how many lineup are possible ? Never solved ...
2
votes
0answers
12 views

Is <x,5> a maximal ideal in Z[x]?

Here $<x,5>$ is the ideal generated by $x$ and $5$ in $\mathbb Z[x]$ that is the polynomial ring in $\mathbb Z.$ How should I approach this question ?
3
votes
1answer
35 views

If $\frac{x-1}{e^x-1} = y$ then $x=?$

I have following equation: $$\frac{x-1}{e^x-1} = y$$ I want to solve this equation such that I have the value of $x$ in the term of $y.$ i.e. $x =$ something of $y$ , no matter how complicated it ...
2
votes
0answers
15 views

A compact $n-1$ dimesional manifold embedded in $\mathbb{R}^n$ has no boundary

Under what conditions is it true that a compact $n-1$ dimesional manifold embedded in $\mathbb{R}^n$ has no boundary (or more generally, when a manifold is embedded in some topological space)? For ...
0
votes
1answer
16 views

If a continuous function is strictly decreasing before a point and strictly increasing afterwards, is the point a global minimum?

I'm in the middle of a proof that a point on a function is a global minimum. Usually I'd just solve an inequality to prove by contradiction that there are no points less than the minimum. But I can't ...
0
votes
0answers
11 views

non-homogenous linear recurrence relation general questions

what happens if you have both repeated and non-repeated roots? i know there are different forms for both, so if given roots say 5, -3, -3, -3 would it then be $A(5)^n + Bn(-3)^n + Cn^2 (-3)^n + Dn^3 ...
1
vote
2answers
20 views

How to prove this recurrence

Been stuck on this problem for a good while. Not sure how to approach it any help would be great! It is problem 12.
0
votes
0answers
5 views

Prove the max and min for Herfindahl-Hirschman Index

HHI(w) = $\sigma w_i^2$ where $\sigma $ is the summation sign, sorry but it will be great if anyone could tell me how to print the capitalized Greek letter. $w_i $ is the weights for each of N assets ...
0
votes
0answers
10 views

Dijkstra's Algorithm for Negative Weights.

Now the problem states that their is a graph $ G = (V,E) $ where some of the edges have negative weights while some of the edges have positive edges. Now the question is why won't Dijkstra's algorithm ...
-1
votes
0answers
15 views

Conditional distribution of two binomials which both depend on a third

I have a question that I'm having some trouble with, but which I believe might have a fairly straightforward answer. I'd really appreciate it if someone could help point me in the right direction! ...
2
votes
2answers
33 views

Show that there exists a $3 × 3$ invertible matrix $M$ with entries in $\mathbb{Z}/2\mathbb{Z}$ such that $M^7 = I_3$.

Show that there exists a $3 × 3$ invertible matrix $M$ (which is not the identity matrix) with entries in the field $\mathbb{Z}/2\mathbb{Z}$ such that $M^7 = $Identity matrix. All I could do was use ...
-5
votes
0answers
25 views

what is the result of an infinity minus pi

what is $ \infty- \pi? $ Im doing some questions related to improper integral but then the final answer I got is $\tan^{-1} (\infty) - \tan^{-1} (\pi) .$ So what should I get as the final answer ?
-3
votes
2answers
14 views

Prove tautology by using boolean laws $\neg q \to \neg(q\wedge(p\to\neg q))$

$$\neg q \to \neg(q\wedge(p\to\neg q))$$ Please help me to prove if it's tautology or not by using the logic law.
-3
votes
2answers
27 views

Delta epsilon proof statement logic

In the delta epsilon proof, it says the following: For every $\delta > 0$ there is an $\epsilon > 0$ such that (some statement) What is the difference between the above statement and if we ...
1
vote
1answer
19 views

why is the domain of $\sec^{-1} x$, $\mathbb{R}- (-1 ,1)$? why can't $x$ take a values like 0.2, 0.3, etc?

Why is the domain of $\sec^{-1} x$, $\mathbb{R}- (-1 ,1)$? why can't $x$ take a values like $0.2, 0.3$ or $0$?
0
votes
0answers
16 views

Show that the relation R is reflexive on R(two)

Problem: Let $S$ be a relation on the set of $\mathbb R \times\mathbb R $ such that the relation is defined to be $(a,b)\ R\ (c,d)$ if $b = d.$ I am having issues showing that $S$ is reflexive. I ...
0
votes
0answers
11 views

Hyperbolic curves and elliptic curves

I am so sorry, if I am very wrong. I know some what hyperbolic functions/curves, and elliptic curves as well. Now my question is that; 'Is there hyperbolic elliptic curves?. If yes, what are the ...
1
vote
0answers
37 views

Application of the Fundamental Theorem of Calculus

I was wondering if someone could help me with a problem I'm having. I'm reading a paper 'Spatiotemporal dynamics of continuum neural fields' and on page 13 they authors derive a model for spatially ...
0
votes
0answers
11 views

A problem on finding the nearest points to the origin on the intersection of two surfaces

Suppose we are to find the points nearest to the origin on the curve of intersection of the two surfaces $g^{-1}_{1}\{ 0 \}$ and $g_{2}^{-1}\{ 0 \}$, where $g_{1}: (x, y, z) \mapsto x^{2} - xy + y^{2} ...
2
votes
0answers
16 views

Question related to the ballistic motion

A point mass will move in the gravitational field of the Earth according to the equation $$\ddot R =-\frac{GM_eR}{|R|^3},$$ where $R$ is the position vector of the point mass measured from the ...
0
votes
0answers
13 views

Marking Integers Using a Wheel

Suppose I had a wheel of diameter one meter and I was charged with marking every meter along an infinite stretch of a beach. The strategy is to insert pegs into the wheel so that every point that is a ...
1
vote
0answers
27 views

Let $a$, $b$, and $c$ be elements of a commutative ring, and suppose $a$ is a unit. Prove that $b$ divides $c$ if and only if $ab$ divides $c$.

Let $a$, $b$, and $c$ be elements of a commutative ring, and suppose $a$ is a unit. Prove that $b$ divides $c$ if and only if $ab$ divides $c$. Okay so here is the proof I came up with PLEASE be as ...
0
votes
0answers
7 views

What is the isotomic conjugate version of the six point circle of isogonal conjugates?

As it is well known, the pedal triangles of a pair of isogonal conjugates in a triangle share a circumcircle. This is a nice theorem, but is there an analogous version of it for a pair of isotomic ...
-4
votes
2answers
31 views

pls help to simpify

pls help to simpify: $\sqrt{\frac{1+cosx}{1-cosx}}$
0
votes
0answers
13 views

How to get more profit in stochastic process?

Suppose there is a system, for each step, I cost something but I didn't know how much I cost, and the system return to me something, which follow Guassian distribution and the expectation is what I ...
5
votes
2answers
22 views

Let $1 \leq p <\infty$ and $f \in L^p(\mathbb{R})$. Prove $\lim_{x \to \infty} \int_x^{x+1} f(t) dt = 0$.

(Jones, p. 246) Let $1 \leq p <\infty$ and $f \in L^p(\mathbb{R})$. Prove $\lim_{x \to \infty} \int_x^{x+1} f(t) dt = 0$. This seems pretty easy to prove in the following way: Let $g_j$ be a ...
0
votes
0answers
2 views

Gross Substitutes under continuous perturbations

Let $v_i(S)_{i \in [n], S \subseteq G}$ be a collection of Gross Substitute valuations. I am wondering if I can add a small perturbation to each valuation and still get Gross Substitute valuations. ...
0
votes
0answers
19 views

Generating sets of $Q_8$

Consider the matrices $$I=\left( {\begin{array}{ccc} 1 & 0 \\ 0 & 1 \\ \end{array} } \right), \qquad A=\left( {\begin{array}{ccc} i & 0 \\ 0 & i \\ \end{array} } ...
-10
votes
0answers
33 views

i want to know about cube root of unity [on hold]

Blockquotecomlex number cube root of unity origin of comlex numbers origin of cube root ofunity
0
votes
0answers
7 views

Book recommendation needed: asymptotic behavior of non-stationary Markov chain

Is there any stochastic process textbook which covers some standard results for non-stationary Markov chain? For my purpose, countable state space is enough. Thanks!
0
votes
1answer
17 views

a tax Deferred keogh account

Suppose you contribute $20,000 in an account at the end of the year.How much would you have at the end of 20 years if the account pays 8% annual interest.
0
votes
0answers
8 views

Degree of Multilinear interpolation

Supposing you want to interpolate an $n$-variate polynomial on $\{0,1\}^n$, we could take the polynomial to be linear in each coordinate. What is a good interpolation procedure for this that will give ...
0
votes
0answers
12 views

Deriving a formula for a confidence interval

Derive a formula for a $(1-\alpha)100\%$ C.I. for $\mu_x -\mu_y $ for data that has the following properties: A random sample $X_1,X_2...X_n \ are \ i.i.d ~N(\mu_x, \sigma^2 ) $ Another random ] ...
2
votes
1answer
27 views

Riemann Integral on $\mathbb{R}^2$

I have the following question. Find a function $f(x,y)$ that is integrable on rectangle $[0,1] \times [0,1]$, such that $g(y) = f(\frac{1}{2}, y)$ is not integrable for $y \in [0,1]$, or prove that ...
0
votes
3answers
15 views

How to prove expected value of uniform random variable?

I tried this: $$\int_a^b t~dt = \frac{t^2}{2}\Big]_a^b = \frac{b^2-a^2}{2} = \frac{(b+a)(b-a)}{2}$$ Isn't it supposed to be $\frac{b+a}{2}$ or something like that? Obviously if I multiply the ...
1
vote
1answer
14 views

Integration about x and y axes to find area

I have a problem statement that requires me to find area between the curves about x axis and about y axis. But my answers are not matching. Please find below my worked out solution - The ...
2
votes
1answer
9 views

parallelepiped change of variables

I can't figure out how to start this problem. Use a triple Integral to find the mass of a parallelepiped generated by the vectors $$<6,1,2>,\ <3,3,9>,\ {\rm and}\ <2,7,3>.$$ We are ...
0
votes
1answer
8 views

Is it possible to reconstruct signal using phase/magnitude only?

I am studying Fourier Transform and it's inverse. We get phase and magnitude from Fourier transform and reconstruct it back from both together My question is that is it possible to reconstruct given ...
2
votes
1answer
15 views

Level surface undefined

Can a level surface be undefined at some point, even if the original fuction is defined at the same point? example: $w(x,y,z) = xy+yz+xz$ is defined at $p=(1,-1,2).$ Its level surface at $p$ is ...
0
votes
1answer
18 views

laurent series expansion about $z=0$

using the Laurent expansion i got the answer to be $$-(z+1)\sum_{n=0}^\infty \frac{z^{n-1}}{2^{n+1}}$$ however, I've got a feeling I've made a mistake somewhere?
-3
votes
2answers
24 views

Explain why the following sums of a harmonic series is greater than or equal to 1/2.

The (non-geometric) series $\frac{1}{2} + \frac{1}{3}+ \frac{1}{4}+ \frac{1}{5}+ \cdots$ is called the harmonic series. a) Explain why each of the following sums is greater than or equal to 1/2. ...

15 30 50 per page