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Mathematics : Recent Questions and Answers (Page 87)

Find answers to your questions about Mathematics or help others by answering their Mathematics questions.

Show that $sup_{k geq 1 }inf_{n geq k} a_n = inf_{k geq 1} sup_{n geq k} a_n$ for an alternating sequence

The question I'm having trouble with is the following: Let $a_n$ be defined for all $n in mathbb{N}$ by $a_n = frac{1}{n^3}$ if $n$ is even,...

Asked on 11/12/2021 by FratSourced

1 answer

How to prove that $-|z| le Re (z) le |z|$ and $-|z| le Im (z) le |z|$?

I am reading Ahlfors' "Complex Analysis". Early in the book, he uses the fact that for $z in mathbb{C}$ we have$$ -lVert zrVert le Re (z)...

Asked on 11/12/2021

2 answer

Does $g(v_n) longrightarrow g(0)$ for all $v_n text{s.t.} ||v_{n+1}|| leq ||v_n||$ imply $g$ continuos at $0$?

The question is pretty much summed up in the title: Let $V,W$ be normed vector spaces and $$ g: V to W$$. Suppose g fulfills $$g(v_n) longrightarrow...

Asked on 11/12/2021 by a_student

2 answer

Your favorite way to think of $k[x_1,ldots,x_n]$ modulo some graded ideal?

I was looking at Graded Syzygies by Peeva, and on page 3 she says "throughout this book, $R=S/I$ and is standard graded." Here, $S=k[x_1,ldots,x_n]$ and $I$ is...

Asked on 11/12/2021

0 answer

Why are the probability and mean number of edges between two nodes in a network equal for large networks?

Slide 18 in this lecture goes:What is the probability of an edge between nodes $i$ and $j$?There are $k_i$ stubs at node $i$ and $k_j$ at ...

Asked on 11/12/2021

1 answer

Geometric proof for the half angle tangent

Using the fact that the angle bisector of the below triangle splits the opposite side in the same proportion as the adjacents sides, I need to give a geometric proof...

Asked on 11/12/2021 by brazilian_student

3 answer

What are the relations between eigenvectors of $A$ and its adjoint $A^*$?

Everywhere I can read that a matrix and its adjoint have pretty much the same eigenvalues ( only complex conjugation is the difference between them). Now I was wondering whether...

Asked on 11/12/2021 by user66906

3 answer

Skyscrapers sheaf's global sections

I'm reading a book written by Serre and, even though he's one of the best math writer ever, there's a step I don't understand. This may imply that I'm one...

Asked on 11/12/2021 by Abramo

2 answer

Constructibility of the 17-gon

Comment: I greatly shortened and simplified the question. As a drawback, some comments/answers might not make any sense anymore. Assume we are using this set of axioms...

Asked on 11/12/2021

2 answer

Building palisade with Lego bricks

I have problem solving the following questions:I have infinite amount of Lego bricks with 6 and 8 studs in length. I want to build a palisade that has the length...

Asked on 11/12/2021

1 answer

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