Some new inequalities of Hermite-Hadamard's type

In this paper, we establish several new inequalities for some differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided

Positive Proportion of Small Gaps Between Consecutive Primes

We prove that a positive proportion of the gaps between consecutive primes are short gaps of length less than any fixed fraction of the average spacing between primes.Comment: 9 page

Collisional Damping of Giant Monopole and Quadrupole Resonances

Collisional damping widths of giant monopole and quadrupole excitations for $^{120}$Sn and $^{208}$Pb at zero and finite temperatures are calculated within Thomas-Fermi approximation by employing the microscopic in-medium cross-sections of Li and Machleidt and the phenomenological Skyrme and Gogny forces, and are compared with each other. The results for the collisional widths of giant monopole and quadrupole vibrations at zero temperature as a function of the mass number show that the collisional damping of giant monopole vibrations accounts for about 30-40% of the observed widths at zero temperature, while for giant quadrupole vibrations it accounts for only 20-30% of the observed widths of zero temperature.Comment: RevTex, 12 pages, 6 PS figure