American Research Journal of Mathematics

YinYue Sha

 Every even integer greater than four can be expressed as a sum of two odd primes, and exists the formula as follows: Gp(N) ≥ INT{ Kpc×Ctwin×N/(Ln N)^2 }-1 ≥INT{ 0.66016×N/(Ln N)^2 }^1 ≥1

Rao Li

In this note, we present new sufficient conditions for Hamiltonian and traceable graphs. 

Мargarita A ZAEVA, 2Anatoly M. TSIRLIN

A generalization of the Filippov's velocity averaging method in the problem of determining the slip velocity of a dynamical system with discontinuous right-hand sides is proposed. It is shown that in the multidimensional case such an extension is reduced to the solution of the averaged nonlinear programming problem and the methods of averaged optimization can be used to calculate the slip velocity. Problems with various dimensions

Paul T E Cusack

Here we consider the Hodge’s Conjecture that expresses when a projective manifold coincides with a sum of algebraic cycles. More generally,