we study the notion of harmonicity in the sense of symplectic geometry, and investigate the geometric properties of harmonic thom forms and distributional thom currents, dual to different types of submanifolds. we show that the harmonic thom form associated to a symplectic submanifold is nowhere vanishing. we also construct symplectic smoothing operators which preserve the harmonicity of distri...

In this paper, we study several radial basis function approximation schemes in Sobolev spaces. We obtain an optional error estimate by using a class of smoothing operators. We also discussed sufficient conditions for the smoothing operators to attain the desired approximation order. We then construct the smoothing operators by some compactly supported radial kernels, and use them to approximate...

Tikhonov regularization of linear discrete ill-posed problems often is applied with a finite difference regularization operator that approximates a low-order derivative. These operators generally are represented by banded rectangular matrices with fewer rows than columns. They therefore cannot be applied in iterative methods that are based on the Arnoldi process, which requires the regularizati...

This thesis presents a family of discrete differential operators. Since these operators are derived taking into account the continuous notions of differential geometry, they possess many similar properties. This family consists of firstand second-order properties, both geometric and parametric. These operators are then analyzed and their practical use is tested in several example applications. ...

In this paper we focus on the validity of some fundamental estimates for time-degenerate Schr\"{o}dinger-type operators. On one hand derive global homogeneous smoothing operators any order by means suitable comparison principles (that shall obtain here). other hand, prove weighted Strichartz-type Scrh\"{o}dinger and apply them to local well-posedness semilinear Cauchy problem. Most our results ...