Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 201

Edge contraction-like graph operation

Given a simple graph $G=(V,E)$ and an edge $uvin E$, the contraction of $uv$ refers to the replacement of the vertices $u$ and $v$ with...

Asked on 10/05/2020 by Emre Yolcu

0 answer

Numerically approximating the second order derivative at the end points of a closed interval

I have approximate the second order derivative of some function $f(x)$ on some interval $[a,b]$. Let $ h =frac{b-a}{n}$ for some positive integer $n$, the discretization...

Asked on 10/05/2020 by Aulwmate

0 answer

How are those vectors linearly independent?

I presume we can call a set of vectors a basis if it spans some subspace and are linearly independent. Is this matrix $$ begin{bmatrix} ...

Asked on 10/05/2020 by user378298

1 answer

Computing the variance of hypergeometric distribution using indicator functions

I want to compute the variance of a random variable $X$ which has hypergeometric distribution $mathrm{Hyp}(n,r,b)$, where $n$ is the total number of balls in the urn and $r$ and...

Asked on 10/05/2020 by xxx

3 answer

KF Riley problem 13.7

Find the Fourier transform of the unit rectangular distributionf(t)=1 |t|<10 otherwiseDetermine the convolution of f with itself and, without further integration, deduce its transform.Deduce thatmathint_{-inf}^{inf}...

Asked on 10/04/2020 by user215736

0 answer

Critical values of the evaluation map for rational curves in toric surface

I'm looking at rational curves in a toric surface. Such curves have a parametrization of the form$$tdashrightarrow chi prod_{j=1}^m (t-alpha_j)^{n_j} in (mathbb{C}^*)^2 ,$$for some scalars $alpha_i$,...

Asked on 10/03/2020 by Blm

0 answer

Monoid, where $2+2 = 2$

Let's consider the set $S subset Bbb N$, consisting of all prime numbers. We can introduce a binary "addition" ($+$) operation on the power set $Bbb P(S)$,...

Asked on 10/03/2020 by HEKTO

0 answer

Can a non-inner automorphism map every subgroup to its conjugate?

Let $G$ be a finite non-cyclic group. Can a non-inner automorphism map every subgroup to its conjugate? Namely, can there be a non-inner automorphism $alpha$ that, for every...

Asked on 10/03/2020 by Benjamin

1 answer

Solving a system of nonlinear equations: show uniqueness or multiplicity of solutions

Consider this system of $12$ equations$$left{begin{array}{rcrclr}alpha^{2}p_{i} & + &left(1 - alpharight)^{2}left(1 - p_{i}right) & = & c_{i}, & forall i =1,2,3,4\[1mm]alphaleft(1...

Asked on 10/02/2020 by STF

1 answer

Is there a symbol or notation for collinearity?

Let's say points $a$, $b$ and $c$ are collinear. Is there some way to express this using a symbol instead of writing out a sentence. Note I'm...

Asked on 10/02/2020 by Kantura

2 answer

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