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why $2pi= c$ and $c=pi ?$

Let $T:Vrightarrow V$ be the linear transformation defined as follows: If $fin V, g=T(f)$means that $$g(x)=int_{-pi}^{pi}{1+cos(x-t)}f(t)~dt$$Find all real $c neq 0$ and all nonzero ...

Mathematics Asked on 2 years ago

Unspecified Constraint

In the following question-Let a, b, c be positive real numbers. Prove that $$sum_{cyc} {a^3over a^3+b^3+abc} ge 1.$$In here, there is no constraint given.But in the solution, the...

Mathematics Asked on 2 years ago

equality of subobjects

Suppose A $xrightarrow{f}$ B $xrightarrow{g}$ C is exact in an abelian category. f and g has factorization f = me and g = m'e' where m and m'...

Mathematics Asked by gerrard on 2 years ago

Numerical differentation - discrete data

I was analyzing my data in Origin and I did the numerical differentation. I wanted to find the maximum of $frac {dM}{dT}$. The black curve corresponds to $frac...

Mathematics Asked on 2 years ago

What is the equation of the quadratic function whose vertex of the graph is on the $x$-axis and passes through the two points $(1,4)$ and $(2,8)$?

What is the equation of the quadratic function whose vertex of the graph is on the $x$-axis and passes through the two points $(1,4)$ and $(2,8)$? Here...

Mathematics Asked on 2 years ago

Lebesgue measure of boundary of an open set.

Let $g$ be a continuous function on $mathbb{R}^n$ and $$O={xin mathbb{R}^n:g(x)neq 0}.$$Is it true that Lebesgue measure of Boundary of $O$ always zero?...

Mathematics Asked by Santanu Debnath on 2 years ago

Chinese Remainder Theorem for moduli that are not necessarily pairwise coprime

Assume that ${n_1},cdots ,{n_k}$ is a finite set of $k$ positive integers. We are not assuming that these integers are pairwise coprime. Consider the homomorphism of additive groups...

Mathematics Asked on 2 years ago

Prove that $x^m$ is a generator of the cyclic group $G$ of order $n$ if and only if $(m,n) = 1$

I want to check my proof of the statement. First, i'll state the following theorem: Theorem 1.Let $o(x)$ be the order of $x in G$. If ...

Mathematics Asked by Morganuz on 2 years ago

Must a local homomorphism from a Noetherian local ring to an artinian local ring factor through a power of its maximal ideal

Let $f : Brightarrow A$ be a local homomorphism of Noetherian local rings where $A$ is moreover Artinian. Must $f$ factor through $B/m_B^n$ for some ...

Mathematics Asked on 2 years ago

If Mu is a projection matrix, how can I show that Mu^2=Mu by direct computation?

The definition of Mu, or the projection matrix, I am working with is Mu(a)=Pu(a). Let's say that a set of vectors (v1, v2.....vm) is an orthonormal basis of U. Then,...

Mathematics Asked by johnathan on 2 years ago

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