Deduction of Semi-Optimal Mollifier for Obtaining Lower Bound for N(0)(T) for Riemann's Zeta-Function.

An effective optimization algorithm for locally nonconvex Lipschitz functions based on mollifier subgradients

On the Zeros of the Riemann Zeta Function

We describe extensive computations which show that Riemann's zeta function f(s) has exactly 200,000,001 zeros of the form a + it in the region 0 < t < 81,702,130.19; all these zeros are simple and he on the line a = j. (This extends a similar result for the first 81,000,001 zeros, established by Brent in Math. Comp., v. 33, 1979, pp. 1361-1372.) Counts of the numbers of Gram blocks of various t...

Cold standby redundancy optimization for nonrepairable series-parallel systems: Erlang time to failure distribution

In modeling a cold standby redundancy allocation problem (RAP) with imperfect switching mechanism, deriving a closed form version of a system reliability is too difficult. A convenient lower bound on system reliability is proposed and this approximation is widely used as a part of objective function for a system reliability maximization problem in the literature. Considering this lower bound do...

Probability laws related to the

This paper reviews known results which connect Riemann's integral representations of his zeta function, involving Jacobi's theta function and its derivatives, to some particular probability laws governing sums of independent exponential variables. These laws are related to one-dimensional Brownian motion and to higher dimensional Bessel processes. We present some characterizations of these prob...

Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions

This paper reviews known results which connect Riemann's integral representations of his zeta function, involving Jacobi's theta function and its derivatives, to some particular probability laws governing sums of independent exponential variables. These laws are related to one-dimensional Brownian motion and to higher dimensional Bessel processes. We present some characterizations of these prob...