Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 208

The minimizers of energy and length of a curve

Assume S is a regular surface with a Riemannian metric $g$. The energy of a curve $c: [0,a] to S$ is defined as : $$ E(c)...

Asked on 08/04/2020 by W. mu

1 answer

prove or give counter example, for every holomorphic function on the unit disc there is $f(z)=z$

let f be a holomorphic function on $D={zin mathbb C:|z|<1}$. and let $f$ be continuous on $cl(D)$ and $f[D]subseteq D$.Prove or give counter example,...

Asked on 08/04/2020 by hash man

1 answer

Is there an easier prime factorization method for the sum of a prime's powers?

I need to obtain prime factorizations of numbers of the type: $sum_{i=0}^n p^i$, for any prime number $p$ (not the same one each time). Do you know if...

Asked on 08/03/2020 by Ifn47

1 answer

How does the quotient ring $Bbb Z[x]/(x^2-x,4x+2)$ look like?

How does the quotient ring $Bbb Z[x]/(x^2-x,4x+2)$ look like?Normally to solve this you play around with generators until you get something you can work with. I was unsuccessful in...

Asked on 08/03/2020 by 2132123

2 answer

Calculus of Variations: Looking for theorem that ensures that a given variational problem has maxima and minima

Is there a theorem that garuantees that a variational problem $I[y] = int_a^bF(x,y,y')dx$ has local/ global maxima and minima? Perhaps similar to the extreme value theorem for continuous functions...

Asked on 08/03/2020 by user

1 answer

Primality testing using cyclotomic polynomials

Can you prove or disprove the following claim:Let $Phi_m(x)$ be the mth cyclotomic polynomial , and let $n$ be a natural number greater than one . If there...

Asked on 08/02/2020

1 answer

Sequence of integers $S_n$ where all elements that $n$ divides increment by one

Let $S_1$ denote the sequence of positive integers ${1,2,3,4,5,6,cdots}$ and define the sequence $S_{n+1}$ in terms of $S_n$ by adding 1 to those integers in ...

Asked on 07/31/2020 by twentyyears

1 answer

Compositeness testing using Jacobi polynomials

Can you prove or disprove the following claim:Let $P_n^{(alpha,beta)}(x)$ be Jacobi polynomial . If $p$ is a prime number such that $alpha , beta$...

Asked on 07/30/2020 by Peđa Terzić

1 answer

Branch cut of square root

I don't really understand how branch cuts work. Let's take the complex function $f(z) = sqrt{z}$. Apparently this function is not defined for $mathbb{R}^{-}$. But why? We defined...

Asked on 07/30/2020

2 answer

Nimber multiplication

In the question on nimbers, the original poster asks for the meaning of Nimber multiplication in the context of impartial games.Edit: As noted by Mark Fischler...

Asked on 07/30/2020 by yberman

2 answer

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