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3
votes
1answer
47 views

Complete classification of complexity classes / infinite approaching sequences

http://en.wikipedia.org/wiki/Time_complexity#Table_of_common_time_complexities For complexity as seen in the above link, complexity classes can be log, polynomial, exp, or composition of any of these ...
2
votes
1answer
118 views

Is there a dense rational sequence of positive separation?

Let us consider the set $\ell_\neq$ of bounded sequences of unequal real terms. We use the following descriptions. A sequence $x=(x_0,x_1,...)\in\ell_\neq$ is dense if, for all $\varepsilon>0$, ...
0
votes
1answer
162 views

Lemma about infinite sequences we are hoping is true [closed]

Given N infinite sequences of non-negative integers, some of which diverge to infinity, must there exist two steps i, j in which $x_i \leq x_j$ for all sequences x?
1
vote
0answers
88 views

Bound a sum of a serie defined by a recursive integer function

I'm using a recursive function $f: \mathbb{N} \rightarrow \mathbb{N}$, that is defined as \begin{equation} f(n)=\lceil \log(f(n-1)) \rceil +f(n-1) \end{equation} where $f(1)=F\in \mathbb{N}$, and ...
2
votes
1answer
127 views

Iterated projections in Hilbert spaces

Let $E$ be an Hilbert space and $F, G$ two subspaces such that $F \cap G =\{0\}$. Let $(x_n)$ be the sequence of iterated orthogonal projections: $x_0 \in F$, $x_1$ is the orthogonal projection of ...
0
votes
0answers
163 views

Greedy sequences without k-term arithmetic progressions

If $S_k$ is the greedy sequence with no length-k arithmetic subsequence, (ie $S_3$ = A003278 , $S_4$ = A005837 , $S_5$ = A020655 ), is it guaranteed that any other sequence $a$ with no length-k ...
0
votes
2answers
182 views

sequence, such that sum of any combinations in the sequence does not equal another [closed]

Hi, Is there any known sequence such that the sum of a combination of one subsequence never equals another subsequence sum. The subsequences should have elements only from the parent sequence. ...
-2
votes
1answer
193 views

How to work with infinite random graph(s) ?

Hi, In the case where we are dealing with an infinite random graph (RG with infinite nodes). How do we model/work with notions like degrees, degree distribution ? How are they defined ? Thanks!
1
vote
2answers
294 views

sum of infinite series

Given the complex variable $x$, complex constant $c$, and integer number $r$. I want to solve the equation: $\sum_{k=1}^{\infty}\frac{e^{kx}}{k^r}=c$. I was thinking that if there is a formula or ...
1
vote
2answers
319 views

Is it necessary that gcd > 1 of an infinite set? [closed]

Consider an infinite set $S$, of positive integers. If all the finite subsets of $S$ have GCD $>$ $1$, is it necessary that the GCD of $S$ is greater than $1$ as well?
2
votes
2answers
405 views

References for the result that $\sqrt{n}$ is equidistributed mod 1

It is not difficult to show (even without Weyl criterion) that the sequence $\sqrt{n}$, $n=1,2,\ldots$ is equidistributed mod 1. However, I need a reference to this result. Can you help me? Thanks.
0
votes
0answers
326 views

In a network with N nodes, what is the general formula for computing the propagation of a set of numbers?

I am creating a circular neural network with N nodes. Each node is connected via a send pathway to every other node, and the connection between two nodes has a weight. Any number sent over the ...
12
votes
1answer
812 views

Self-avoiding walk on $\mathbb{Z}$

This one is an unanswered question in Math.SE. I've posted it here because I think it deserves more attention. How many sequences $\{a_n\}$ exist satisfying: a) $a_1=0$ b) $\forall k\ge1 $ ...
4
votes
2answers
385 views

Ends of topological spaces. Why independent of choice of ascending sequence of compact subsets?

Quoting from http://en.wikipedia.org/wiki/End_(topology): "Let X be a topological space, and suppose that K1 ⊂ K2 ⊂ K3 ⊂ · · · is an ascending sequence of compact ...
6
votes
1answer
470 views

Magic square on an infinite lattice

This question came to me while reading the discussion of magic square in the complex plane with equal integrals along every horizontal, vertical and diagonal "magic square in the complex plane with ...
0
votes
4answers
2k views

Does Cauchy continuity imply uniform continuity? [No.] [closed]

It is well known that if $X$ is a first countable topological space and $Y$ is a topological space, then $f : X \rightarrow Y$ is continuous iff $$\forall x \in {\rm map}(\mathbb{N},X),\forall p \in X ...