The finite difference method is employed to conduct five-point difference discreet for the two-dimension Helmholtz equation of Robbins boundary conditions and then with a large and sparse block tri-diagonal linear equation Au=b obtained.

This paper investigages the paley-type inequalities in the complete convergence, considers the more lower and upper bounds in the Hsu-Robbins-Erds law of large numbers, and discusses the question brought forward in [1].

Two new equivalent conditions of extensively subexponential densities;

Some equivalent conditions of one class of heavy-tailed distributions;

Equivalent condition of minimal square solution in Hilbert space and its application;

quasi_invex vector function, Ⅰ_strictly quasi_invex vector function and KT _Ⅰ_strictly quasi_invex vector function are defined, and then the equivalent conditions that every stationary point or Kuhn_Tucker point is an efficient point are obtained for multiobjective programming.

The present paper deals with the conditions of two-parameter σ-fields in the two-parameter martingales theory, and presents some equivalent conditions of (F5)-condition and G(F4′)-condition and their verification.