in the civil procedure act, local inquiry is explained in a chapter separate from testimony, but for similarity of these two proofs, connection of them and criterion of separating them is disputable. in this article, we will study in one portion the role of witness and testimony conditions and in other portion, the role of number, sexuality, locality and ceremonies in separating of these proofs...

where t is a large real parameter. For enlightening accounts on this topic, the reader is referred to E. Krätzel’s monographs [14] and [15], to a recent survey article by A. Ivić, E. Krätzel, M. Kühleitner, and W.G. Nowak [10], and to M. Huxley’s book [7] where he exposed his breakthrough in the planar case (”Discrete Hardy-Littlewood method”). For the case that ∂B is of bounded nonzero Gaussia...

where the summation runs over primes, a is a fixed non-zero integer and r(n) is the number of representations of n as a sum of two squares. This implies the first unconditional proof that there are infinitely many primes of the form p = m+n+1. Huxley and Iwaniec [1] considered primes of the formm+n+1 with (m,n) = 1 in the short interval (x, x+x]. They proved that for θ = 99/100 this interval co...

A stochastic probing problem consists of a set of elements whose values are independent random variables. The algorithm knows the distributions of these variables, but not the actual outcomes. The only way to learn the actual outcomes is to probe these elements. However, there are constraints on which set of elements may be probed. (E.g., we may have to travel in some metric to probe elements b...