On sums of sets of primes with positive relative density

On sums of sets of primes with positive relative density

on direct sums of baer modules

the notion of baer modules was defined recently

Sums of Positive Density Subsets of the Primes

We show that if A and B are subsets of the primes with positive relative lower densities α and β, then the lower density of A+B in the natural numbers is at least (1 − o(1))α/(eγ log log(1/β)) which is asymptotically best possible. This improves results of Ramaré and Ruzsa and of Chipeniuk and Hamel. As in the latter work the problem is reduced to a similar problem for subsets of Zm using techn...

The ternary Goldbach problem with primes in positive density sets

Let P denote the set of all primes. P1, P2, P3 are three subsets of P . Let δ(Pi) (i = 1, 2, 3) denote the lower density of Pi in P , respectively. It is proved that if δ(P1) > 5/8, δ(P2) ≥ 5/8, and δ(P3) ≥ 5/8, then for every sufficiently large odd integer n, there exist pi ∈ Pi such that n = p1 + p2 + p3. The condition is the best possible.

construction of vector fields with positive lyapunov exponents

in this thesis our aim is to construct vector field in r3 for which the corresponding one-dimensional maps have certain discontinuities. two kinds of vector fields are considered, the first the lorenz vector field, and the second originally introced here. the latter have chaotic behavior and motivate a class of one-parameter families of maps which have positive lyapunov exponents for an open in...