The Functor Amin⁡A^{\min} for (p−1)(p-1)-cell Complexes and \EHP Sequences

Let $X$ be a co-$H$-space of $(p-1)$-cell complex with all cells in even dimensions. Then the loop space $\Omega X$ admits a retract $\bar A^{\min}(X)$ that is the evaluation of the functor $\bar A^{\min}$ on $X$. In this paper, we determine the homology $H_*(\bar A^{\min}(X))$ and give the \EHP sequence for the spaces $\bar A^{\min}(X)$.Comment: 32 page

Chen's double sieve, Goldbach's conjecture and the twin prime problem

We give a more comrehensive treatment of Chen's double sieve and improve related constants in Goldbach's conjecture and the twin prime problem

Operators on random hypergraphs and random simplicial complexes

Random hypergraphs and random simplicial complexes have potential applications in computer science and engineering. Various models of random hypergraphs and random simplicial complexes on n-points have been studied. Let L be a simplicial complex. In this paper, we study random sub-hypergraphs and random sub-complexes of L. By considering the minimal complex that a sub-hypergraph can be embedded in and the maximal complex that can be embedded in a sub-hypergraph, we define some operators on the space of probability functions on sub-hypergraphs of L. We study the compositions of these operators as well as their actions on the space of probability functions. As applications in computer science, we give algorithms generating large sparse random hypergraphs and large sparse random simplicial complexes.Comment: 22 page