Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 163

combinatorial numbers appearing in the topology of manifolds

This is a somewhat soft question. I would like to know examples when interesting numbers from combinatorics appear naturally or even unexpectedly in the study of manifolds and their topological...

Asked on 12/30/2020 by Nick L

1 answer

Understanding the SI units of the Euler–Lagrange equation terms

Page 88 of No-Nonsense Classical Mechanics states the Euler-Lagrange equation as follows:Questions: I'm having trouble understanding just what the statement means.Are...

Asked on 12/29/2020 by user1770201

1 answer

Line bundles on $S^2$ and $pi_2(mathbb{R}P^2)$

Real line bundles on $S^2$ are all trivial, but what about the following way to think about a line bundle: we view a line bundle on $S^2$...

Asked on 12/29/2020 by questions

1 answer

On the self-adjoint form for the general elliptic PDE

Under what conditions can a general elliptic PDE$$a_{ij}(x) frac{partial^2 u}{partial x_i partial x_j} + b_i(x) frac{partial u}{partial x_i} + c(x)u = f(x)label{a}tag{A}$$be reduced to a self-adjoint...

Asked on 12/29/2020 by Fizikus

1 answer

Given four real numbers $a,b,c,d$ so that $1leq aleq bleq cleq dleq 3$. Prove that $a^2+b^2+c^2+d^2leq ab+ac+ad+bc+bd+cd.$

Given four real numbers $a, b, c, d$ so that $1leq aleq bleq cleq dleq 3$. Prove that$$a^{2}+ b^{2}+ c^{2}+ d^{2}leq ab+ ac+ ad+ bc+ bd+...

Asked on 12/29/2020 by user818748

1 answer

Writing logic statements using quantifier

I was given two predicates $text{Prime}(x)$ and $text{Even}(x)$ and is required to write the following statements:For every odd natural number there is a different natural number such that...

Asked on 12/29/2020 by starry

1 answer

A probability question about choosing 6 shoes are chosen randomly from the 20 distinct pairs of shoes drawer.

$mathbf{Question:}$A drawer has 20 distinct pairs of shoes. 6 shoes are chosen randomly from the drawer. The drawer contain only one my favorite pair.(a) what is the...

Asked on 12/29/2020 by xxxxxx

1 answer

Given two complex numbers $z,w$ such that $ |z|=|w|=1$. Find the correct statement.

Given two complex numbers $z,w$ with unit modulus (i.e., $ |z|=|w|=1$), which of the following statements will always be correct? a.) $|z+w|ltsqrt2$ and $|z-w|ltsqrt2$ b.)...

Asked on 12/29/2020 by Broly-29

1 answer

The maximum value of the smaller root of given quadratic function

Consider the quadratic expression :$$ f(x) = x^2 +(a+2)x + (a^2 - a +2 ) $$ given is that $a , p, q , (p<q)$ are real...

Asked on 12/29/2020 by Mamta Kumari

1 answer

Showing $prod_{ngeq 1} (1+q^{2n}) = 1 + sum_{ngeq 1} frac{q^{n(n+1)}}{prod_{i=1}^n (1-q^{2i})}$

I want to show begin{align}prod_{ngeq 1} (1+q^{2n}) = 1 + sum_{ngeq 1} frac{q^{n(n+1)}}{prod_{i=1}^n (1-q^{2i})}end{align} I know one proof via self-conjugation of partition functions with Young Tableaux. ...

Asked on 12/29/2020 by phy_math

1 answer

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