Thisstudy considered the Ruin problem with an income process stationaryindependent increments. The characterization is obtained which general forthe probability of r(y), that asset a firm will never bezero whenever initial level y. aim this studyis also to determine r(y) = P{T < ¥ | Y(0)= y}, If we let T inf{t ≥ 0; Y(t)< 0}, A condition necessary and sufficient studied for adistribution one – d...

In [K. Gokhberg, V. Vysotskiy, L. S. Cederbaum, L. Storchi, F. Tarantelli, and V. Averbukh, J. Chem. Phys. 130, 064104 (2009)] we introduced a new L(2) ab initio method for the calculation of total molecular photoionization cross-sections. The method is based on the ab initio description of discretized photoionized molecular states within the many-electron Green's function approach, known as al...

This paper is concerned with some general theorems on the distributional Stieltjes transformation. Some Abelian theorems are proved. Throughout the paper, r will denote a positive continuous function on an interval (X,=), X > 0, such that the limit lim r(pt) r(t) exists for' every p > 0. Such functions are called regularly varying fu.Lc-tions (r.v.f.) at infinity and it is well known ([ 7] that...

Many combinatorial numbers can be placed in the following generalized triangular array [ T n , k ] ? 0 satisfying recurrence relation: = ? ( a + 1 2 ) ? b d with and unless ? for suitable . For denote by q generating function of -th row. In this paper, we develop various criteria x -Stieltjes moment property 3- -log-convexity based on Jacobi continued fraction expression ? t where is set indete...