Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 177

Prove that T is transitive if and only if the score of the $k^{th}$ vertex ($s_k$) = '$k-1$' for $k =1,2,ldots. n $

There is a transitive tournament (T) with $n > 1$ vertices and the score sequence is defined as $s_1, s_2, ldots,s_n$ Prove that T is transitive if and...

Asked on 12/14/2020 by user146215

1 answer

Continuous $f$ has $≥2$ roots if $int_{-1}^{1} f(x)sqrt {1 - x^2} mathrm{d}x = int_{-1}^{1} xf(x) mathrm{d}x = 0$?

Let $f$ be a continuous function on $[-1, 1]$ such that $$int_{-1}^{1} f(x)sqrt {1 - x^2} mathrm{d}x = 0 = int_{-1}^{1} xf(x) mathrm{d}x .$$ Prove that the...

Asked on 12/14/2020

2 answer

Does this lead to a contradiction within ZF?

Let the following be an axiom (which I will denote P):If $x,y$ are sets and $f:yto x$ is a surjection, then the existence of an injection $f:xto...

Asked on 12/14/2020 by quanticbolt

1 answer

Finding the probability of $Y>1/4$ when conditioned on $X=x$.

I am trying to find:$$Pr(Y>1/4 mid X = x) $$where $X$ and $Y$ are two jointly continuous random variables with the following joint PDF:...

Asked on 12/14/2020 by RexWilliamson

2 answer

$arctan(z)$ and Riemann Surfaces

How do I link the complex trigonometric function arctan(z) and it's branch cuts and branch points with Riemann surfaces? I have seen the picture of the function's Riemann surface but...

Asked on 12/14/2020 by Elene

0 answer

How does $A$ relate to $B$ if $A - lfloor A/B rfloor - lceil A/B rceil leq lfloor A/B rfloor times (B+1)$?

For $A geq B$, both are strictly positive integers, what is the relationship between $A$ and $B$ such that the following is true?$$A - lfloor...

Asked on 12/14/2020 by Nicholas

2 answer

multiplicity of functions

I'm reading Forster's riemann surfaces book and l have problem with the meaning of multiplicity, can someone give an example to show how we can compute multiplicity of any functions,not...

Asked on 12/14/2020 by MathH

0 answer

If $x_n = (prod_{k=0}^n binom{n}{k})^frac{2}{n(n+1)}$ then $lim_{n to infty} x_n = e$

I try to prove the following:$$x_n = left(prod_{k=0}^n binom{n}{k}right)^frac{2}{n(n+1)}$$$$lim_{n to infty} x_n = e$$I want to use double sided theorem, so I've proven that$$x_n ge frac{n}{sqrt[n]{n!}}$$...

Asked on 12/13/2020 by perlik

2 answer

Find the angle that lets you make a bendy pipe

I have a pipe with $n$ segments of equal length. I move the farthest end nearer than the combined length to make the pipe bend. How do I find...

Asked on 12/13/2020 by John Porter

1 answer

How beneficial are Gröbner bases for solving systems of equations

So I have understood that Gröbner bases are a pretty big deal and have variety of applications. Namely, if you can represent something with a system of polynomial equations you...

Asked on 12/13/2020 by Qwaster

1 answer

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