This paper gives the inner and outer limit value:Φ +(t)=(1-β(t)/S)φ(t)+∫ Ωφ(ζ)K(ζ,t) Φ -(t)=(-β(t)/S)φ(t)+∫ Ωφ(ζ)K(ζ,t)of the Cauchy_Fantappie type integral representation in domain DC n with piecewise smooth boundaries Ω are both belong to H(α,Ω), which generalizes a result by CHEN Shu_jin in 1994.

The new integral formula with weight factors for a strictly pseudoconvex polyhedron with non-smooth boundary;

We obtain a continuous solution of -equation for a strictly pseudoconvex domain with non-smooth boundary on Stein manifolds,which doesn t involve integral on boundary.

By meams of ΓK manifolds introduced by Laurent-Thiebaut,et al,we constructed extend B-M(Bochner-Matinelli) kernel to study extension formula of Koppelman-Leray-Norguet formula and obtained a continuous solutions of -equation on a strictly pseudoconvex domain with non-smooth boundary in Cn space.

A new method is obtained for a special nondifferentiable problem——piecewise smooth optimi- zation.

Defines bordered manifold and concordantly oriented concepts of smooth or piecewise smooth bordered manifold, thus proof“general Stokes formula by n-demensional E-G formula.

The paper aims to obtained a new method for a special nondifferentiable problem, Piecewise smooth optimization,and applys it to multiobjective programming to get a new minmax method.

The main purpose of this paper is to construct an abstract integral representation formula for smooth functions on bounded domains with piecewise smooth boundary in C~n.

In this paper, the author considers the discontinuous initial boundary value problem for the one-dimensional semilinear wave equation originated from semi-bounded string vibration, and proves the global existence theorem of piecewise smooth solutions to this problem by using the method of characteristic.