Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 167

Interchanging integral with real and imaginary operators?

$$ int sin(3x) cos(nx) dx to Re int sin(3x) e^{inx} dx$$ $$ sin(3x) to Im e^{i3x}$$ Hence, $$ Re left( Im int e^{i(3+n)x} dx right) $$ Or,...

Asked on 12/24/2020

2 answer

$f:X to Y$ is a continuous map. Suppose it induces an isomorphism $f_:H_(X) to H_*(Y)$. Does that imply $f:X to Y$ is a homotopy equivalence?

Suppose that $f:X to Y$ is a continuous map. Suppose it induces an isomorphism $f_*:H_*(X) to H_*(Y)$. Does that imply $f:X to Y$ is a homotopy equivalence?...

Asked on 12/24/2020 by zero2infinity

2 answer

Show that if $ gcd(|G|,|H|) = 1 $, then $ text{Aut}(G times H) cong text{Aut}(G) times text{Aut}(H) $.

Let $ G $ and $ H $ be finite groups. If $ gcd(|G|,|H|) = 1 $, then I want to show that$$text{Aut}(G times H) cong text{Aut}(G) times...

Asked on 12/24/2020 by La Rias

1 answer

Calculating the Fundamental Group of a CW Complex with Attaching Maps of Varying Degrees

I'm reviewing old homework questions for an upcoming topology exam, and I came across a question that I did not fully understand at the time. In the solution to this...

Asked on 12/24/2020

1 answer

prove the ratio of the line in the question

the book's solution uses $(a+b)/a= a/b$. I got my answer using b and c but want to understand the...

Asked on 12/24/2020 by sniperking

1 answer

prove the following inequality for integral

Let $eta$ be the smooth function supported in $B_1(0)$.such that $inteta = 1$ Let $u$ be a smooth function defined on an open set ...

Asked on 12/24/2020 by yi li

1 answer

Verify: Prove that $(A times B) cap (C times D) = (A cap C) times (B cap D)$

Prove that $(A times B) cap (C times D) = (A cap C) times (B cap D)$$x in (A times B) cap (C times D) Leftrightarrow xin (A...

Asked on 12/24/2020

0 answer

Standard Basis of $SU(2)$--where does the 1/2 come from?

The most common matrix representation of $SU(2)$ is given by$$begin{pmatrix}a & b\b^* & -a^*\end{pmatrix}$$where $a,binmathbb{C}$. If we denote real components by the subscript...

Asked on 12/24/2020 by JMJ

1 answer

Explicit function definition with the normal vector included

Integral of the upper hemisphere of a unit sphere at the origin: $$int^1_{-1} int^{sqrt{1-x^2}}_0 int^{sqrt{1-x^2 - y^2}}_0 F cdot n ; dz dy dx$$ $sqrt{1-x^2-y^2}$ should be the...

Asked on 12/24/2020 by user719062

2 answer

Nonlinear system for origin translation

the nonlinear system $$x'=a+bx+cx^2-x^3$$ by translating the origin, we can eliminate any second-degree terms, such that $$x'=mu_1+mu_2x-x^3$$ how to do this?...

Asked on 12/23/2020 by Toy

1 answer

Ask a Question

Get help from others!

Mathematics : Recent Questions and Answers (Page 167)

Ask a Question