# All Questions

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### 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 $G$.
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### 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 ( ...
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### 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 ...
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### 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?
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### 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?
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### 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. ...
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### 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
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### 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 ...
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### 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 ?
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### pls help to simpify

pls help to simpify: $\sqrt{\frac{1+cosx}{1-cosx}}$
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### 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 ...
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### 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 ...
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### 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. ...
Consider the matrices $$I=\left( {\begin{array}{ccc} 1 & 0 \\ 0 & 1 \\ \end{array} } \right), \qquad A=\left( {\begin{array}{ccc} i & 0 \\ 0 & i \\ \end{array} } ... 0answers 33 views ### i want to know about cube root of unity [on hold] Blockquotecomlex number cube root of unity origin of comlex numbers origin of cube root ofunity 0answers 7 views ### Book recommendation needed: asymptotic behavior of non-stationary Markov chain Is there any stochastic process textbook which covers some standard results for non-stationary Markov chain? For my purpose, countable state space is enough. Thanks! 1answer 17 views ### a tax Deferred keogh account Suppose you contribute 20,000 in an account at the end of the year.How much would you have at the end of 20 years if the account pays 8% annual interest. 0answers 8 views ### Degree of Multilinear interpolation Supposing you want to interpolate an n-variate polynomial on \{0,1\}^n, we could take the polynomial to be linear in each coordinate. What is a good interpolation procedure for this that will give ... 0answers 12 views ### Deriving a formula for a confidence interval Derive a formula for a (1-\alpha)100\% C.I. for \mu_x -\mu_y  for data that has the following properties: A random sample X_1,X_2...X_n \ are \ i.i.d ~N(\mu_x, \sigma^2 )  Another random ] ... 1answer 27 views ### Riemann Integral on \mathbb{R}^2 I have the following question. Find a function f(x,y) that is integrable on rectangle [0,1] \times [0,1], such that g(y) = f(\frac{1}{2}, y) is not integrable for y \in [0,1], or prove that ... 3answers 15 views ### How to prove expected value of uniform random variable? I tried this:$$\int_a^b t~dt = \frac{t^2}{2}\Big]_a^b = \frac{b^2-a^2}{2} = \frac{(b+a)(b-a)}{2}$$Isn't it supposed to be \frac{b+a}{2} or something like that? Obviously if I multiply the ... 1answer 14 views ### Integration about x and y axes to find area I have a problem statement that requires me to find area between the curves about x axis and about y axis. But my answers are not matching. Please find below my worked out solution - The ... 1answer 9 views ### parallelepiped change of variables I can't figure out how to start this problem. Use a triple Integral to find the mass of a parallelepiped generated by the vectors$$<6,1,2>,\ <3,3,9>,\ {\rm and}\ <2,7,3>.$$We are ... 1answer 8 views ### Is it possible to reconstruct signal using phase/magnitude only? I am studying Fourier Transform and it's inverse. We get phase and magnitude from Fourier transform and reconstruct it back from both together My question is that is it possible to reconstruct given ... 1answer 15 views ### Level surface undefined Can a level surface be undefined at some point, even if the original fuction is defined at the same point? example: w(x,y,z) = xy+yz+xz is defined at p=(1,-1,2). Its level surface at p is ... 1answer 18 views ### laurent series expansion about z=0 using the Laurent expansion i got the answer to be$$-(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?
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. ...