Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 104

Is it possible to justify these approximations about prime numbers?

A recently closed question asked for a possible closed form of the infinite summation$$f(a)=sum _{i=1}^{infty } a^{-p_i}$$ for which I already proposed a first simple but totally...

Asked on 11/01/2021 by Claude Leibovici

3 answer

Impossible to pack Circles without gaps

It is intuitively apparent that circles cannot be packed without any gaps. I thought this is easy to prove, but it turns out not to me. I have $2$...

Asked on 11/01/2021

1 answer

Is there a generalization of the helix from $mathbb{R}^3$ to $mathbb{R}^4$?

The helix is a curve $x(t) in mathbb{R}^3$ defined by: $$x(t) = begin{bmatrix}sin(t) \cos(t) \tend{bmatrix}$$ and it takes the classic shape: ...

Asked on 11/01/2021 by kdbanman

2 answer

How to solve this problem using set theory?

$36$ students took English and Math test. $25$ passed English, and $28$ passed Math. $20$ passed both subjects. a. How many students failed both subject?b. How many students passed...

Asked on 11/01/2021 by hugseirvak

3 answer

Column Space vs Span and minimum size of a set of vectors to guarantee a vector is in span?

Given a set A of vectors, is there a minimum number of vectors in A to guarantee that a particular vector b is in span(A)? If we have a m...

Asked on 11/01/2021 by Hazim

2 answer

Rational number and irrational number

There are 197 different non-zero real numbers, and the sum of any two distinct numbers is a rational number or the product is a rational number. Prove that: 197 numbers,...

Asked on 11/01/2021 by user579861

2 answer

"Periodicity" of the Wiener integral?

Let $(B_t)_{tge 0}$ be the standard Brownian motion.I am thinking about "translation" in Wiener integral. For exemple we have, for a non random constant $c$,$s,tin...

Asked on 11/01/2021 by TTL

1 answer

{$v,f(v),f^2(v),ldots,f^{n-1}(v)$} is a basis of $V$ if the minimal polynomial of $f$ is equal to the characteristic polynomial of $f$

I want to prove the following statemaent.Let $V$ be a $n$-demensional vector space on field $K$ and $f:Vrightarrow V$ be a linear operator.There exists ...

Asked on 11/01/2021 by kufs

1 answer

Proving the Strong Markov property on the whole paths using monotone class theorem

Let $(X_t)_{tge 0}$ be an $mathscr{F}_t$ adapted, $d$-dimensional stochastic process with (right-)continuous paths and $sigma$ be a stopping time. The usual Markov process is the following...

Asked on 11/01/2021 by nomadicmathematician

1 answer

If a non-constant function is continuous wrt two different topologies, can anything be said about how these two topologies are related?

I apologize in advance for my gross mathematical ignorance. Let $X$ and $Y$ be sets, let $fcolon Xto Y$ be a non-constant function, and let $T_y$...

Asked on 11/01/2021

1 answer

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