A Langevin equation is suggested to describe a system driven by correlated Gaussian white noise as well as with positive and negative damping demarcated by a critical velocity. The equation can be transformed into the Fokker-Planck equation by the Kr...

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Based on Harnack's inequality and convex analysis we show that each plurisubharmonic function is locally BUO (bounded upper oscillation) with respect to polydiscs of finite type but not for arbitrary polydiscs. We also show that each function in the ...

In this paper, we establish the global $C^{2,\alpha}$ and $W^{2,p}$ regularity for the Monge-Amp\`ere equation subject to a natural boundary condition arising in optimal transportation and many other applications.

The concept of cutting is first explicitly introduced. By the concept, a convex expansion for finite distributive lattices is considered. Thus, a more general method for drawing the Hasse diagram is given, and the rank generating function of a finite...

In this article we are interested in the differential geometric properties of certain higher direct images of exterior powers of the sheaf of relative differentials twisted with a line bundle. We obtain explicit curvature formulas, especially in case...

We start from a finite dimensional Higgs bundle description of a result of Burns on negative curvature property of the space of complex structures, then we apply the corresponding infinite dimensional Higgs bundle picture and obtain a precise curvatu...

We shall give a definition of the curvature operator for a family of weighted Bergman spaces {H-t} associated to a smooth family of smoothly bounded strongly pseudoconvex domains {D-t}. In order to study the "boundary term" in the curvature operator,...

This paper is concerned with the mathematical analysis of the inverse random source problem for the time fractional diffusion equation, where the source is assumed to be driven by a fractional Brownian motion. Given the random source, the direct prob...