Sieve methods and the twin prime conjecture

For $n \geq 3$ let $p_n$ denote the $n^{\rm th}$ prime number. Let $[ \; ]$ denote the floor or greatest integer function. For a positive integer $m,$ let $\pi_2(m),$ denote the number of twin primes not exceeding $m.$ The twin prime conjecture states that there are infinitely many prime numbers $p$ such that $p+2$ is also prime. In this paper we to show that for all integers $a>0$ there exists an integer $N_2(a)$ such that $$\left[\frac{ap^2_{n+1}}{2(n+1)} \right] \leq \pi_2\left(p^2_{n+1} \right)$$ for all $n \geq N_2(a)$ and thereby prove the twin prime conjecture.Comment: In the conclusion of the paper n_0 is depended on the given value of n and so is a function of n. This is not pointed out in the paper and this error means a conclusive proof is not achieve

Three-body analysis of incoherent η\eta-photoproduction on the deuteron in the near threshold region

A three-body calculation of the reaction $\gamma d\to\eta np$ in the energy region from threshold up to 30 MeV above has been performed. The primary goal of this study is to assess the importance of the three-body aspects in the hadronic sector of this reaction. Results are presented for the $\eta$-meson spectrum as well as for the total cross section. The three-body results differ significantly from those predicted by a simple rescattering model in which only first-order $\eta N$- and $NN$-interactions in the final state are considered. The major features of the experimental data are well reproduced although right at threshold the rather large total cross section could not be explained.Comment: 6 pages revtex including 3 figure

Investigation of the diffuse ultraviolet background using satellite data: Dynamics explorer guest investigator program

The imaging instrumentation for the Dynamics Explorer Mission was designed primarily to obtain global auroral images. The instrument, however, was also used successfully to study marine bioluminescence, the geocorona, and the global distribution of atmospheric ozone. The imager has considerable potential for the study of astronomical sources of ultraviolet radiation as well. The data produced by the imager is used to study the brightness and isotrophy of the diffuse ultraviolet background

Solution of the eta-4He problem with quasi-particle formalism

The Alt-Grassberger-Sandhas equations for the five-body eta-4N problem are solved for the case of the driving eta N and NN potentials limited to s-waves. The quasi-particle (Schmidt) method is employed to convert the equations into the effective two-body form. Numerical results are presented for the eta-4He scattering length.Comment: 8 pages, 5 figure

Investigation of the diffuse ultraviolet background with DE data

The imaging instrumentation on the Dynamics Explorer 1 satellite is used to measure the intensity of the diffused ultraviolet radiation on two great circles about the sky. It was found that the extragalactic component of the diffuse ultraviolet radiation has an intensity of 530 + or - 15 units (a unit is one photon/(sq cm s A sr) at a wavelength of 150 nm. The galactic component of the diffuse ultraviolet radiation has a dependence on galactic latitude which requires strongly forward scattering particles if it is produced by dust above the galactic plane