In the paper some new upper bounds with parameters were obtained for the classical Ramsey numbers R(m,n,l) and R(m,n,l,s) . By using the upper bounds, it was proved that R (4,4,4)≤236.
In this paper, Wittmann type strong laws of large numbers for blockwise mnegatively associated random variables are established which extend and improve the related known works in the literature.
This paper is a review, a thesis, of some interesting results that have been obtained in various research concerning the “brane collisions in string and M-theory” (Cyclic Universe), p-adic inflation and p-adic cosmo...This paper is a review, a thesis, of some interesting results that have been obtained in various research concerning the “brane collisions in string and M-theory” (Cyclic Universe), p-adic inflation and p-adic cosmology. In Section 2, we have described some equations concerning cosmic evolution in a Cyclic Universe. In Section 3, we have described some equations concerning the cosmological perturbations in a Big Crunch/Big Bang space-time, the M-theory model of a Big Crunch/Big Bang transition and some equations concerning the solution of a braneworld Big Crunch/Big Bang Cosmology. In Section 4, we have described some equations concerning the generating ekpyrotic curvature perturbations before the Big Bang, some equations concerning the effective five-dimensional theory of the strongly coupled heterotic string as a gauged version of N=1five-dimensional supergravity with four-dimensional boundaries, and some equations concerning the colliding branes and the origin of the Hot Big Bang. In Section 5, we have described some equations regarding the “null energy condition” violation concerning the inflationary models and some equations concerning the evolution to a smooth universe in an ekpyrotic contracting phase with w>1. In Section 6, we have described some equations concerning the approximate inflationary solutions rolling away from the unstable maximum of p-adic string theory. In Section 7, we have described various equations concerning the p-adic minisuperspace model, zeta strings, zeta nonlocal scalar fields and p-adic and adelic quantum cosmology. In Section 8, we have shown various and interesting mathematical connections between some equations concerning the p-adic inflation, the p-adic quantum cosmology, the zeta strings and the brane collisions in string and M-theory. Furthermore, in each section, we have shown the mathematical connections with various sectors of Number Theory, principally the Ramanujan’s modular equations, the Aurea Ratio and the Fibonacci’s numbers.展开更多
文摘In the paper some new upper bounds with parameters were obtained for the classical Ramsey numbers R(m,n,l) and R(m,n,l,s) . By using the upper bounds, it was proved that R (4,4,4)≤236.
基金Supported by the National Natural Science Foundation of China(Grant No.11271161)
文摘In this paper, Wittmann type strong laws of large numbers for blockwise mnegatively associated random variables are established which extend and improve the related known works in the literature.
文摘This paper is a review, a thesis, of some interesting results that have been obtained in various research concerning the “brane collisions in string and M-theory” (Cyclic Universe), p-adic inflation and p-adic cosmology. In Section 2, we have described some equations concerning cosmic evolution in a Cyclic Universe. In Section 3, we have described some equations concerning the cosmological perturbations in a Big Crunch/Big Bang space-time, the M-theory model of a Big Crunch/Big Bang transition and some equations concerning the solution of a braneworld Big Crunch/Big Bang Cosmology. In Section 4, we have described some equations concerning the generating ekpyrotic curvature perturbations before the Big Bang, some equations concerning the effective five-dimensional theory of the strongly coupled heterotic string as a gauged version of N=1five-dimensional supergravity with four-dimensional boundaries, and some equations concerning the colliding branes and the origin of the Hot Big Bang. In Section 5, we have described some equations regarding the “null energy condition” violation concerning the inflationary models and some equations concerning the evolution to a smooth universe in an ekpyrotic contracting phase with w>1. In Section 6, we have described some equations concerning the approximate inflationary solutions rolling away from the unstable maximum of p-adic string theory. In Section 7, we have described various equations concerning the p-adic minisuperspace model, zeta strings, zeta nonlocal scalar fields and p-adic and adelic quantum cosmology. In Section 8, we have shown various and interesting mathematical connections between some equations concerning the p-adic inflation, the p-adic quantum cosmology, the zeta strings and the brane collisions in string and M-theory. Furthermore, in each section, we have shown the mathematical connections with various sectors of Number Theory, principally the Ramanujan’s modular equations, the Aurea Ratio and the Fibonacci’s numbers.
