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We will introduce the polynomial partitioning method which has wide applications in incidence geometry, geometric measure theory, and harmonic analysis. In the first course, we will present some basic...
Interferometric SAR is sensitive to earth surface undulation. The accuracy of interferometric parameters plays a significant role in precise digital elevation model (DEM). The interferometric calibrat...
The task of constructing higher-dimensional invariant manifolds for dynamical systems can be computationally expensive. We demonstrate that this problem can be locally reduced to solving a system of...
This paper introduces a novel approach for rapidly computing a very large number of geodesics on a smooth surface. The idea is to apply the recently developed phase flow method [15], an efficient and ...
The problem of electron scattering on the one-dimensional complexes is considered. We present a novel theoretical approach to solution of the transport problem for a quantum graph.
We prove that sufficiently regular solutions to the wave equation gK = 0 on the exterior of a sufficiently slowly rotating Kerr black hole obey the estimates ||  C(t)−3 2 + on a compact r...
This paper concerns developing a numerical method of the Newton type to solve systems of nonlinear equations described by nonsmooth continuous functions. We propose and justify a new generalized Newt...
The DGMRES method for solving Drazin-inverse solution of sin-gular linear systems is generally used with restarting. But the restarting often slows down the convergence and DGMRES often stagnates.
We use the Ulam method to study spectral properties of the Perron-Frobenius operators of dynamical maps in a chaotic regime. For maps with absorption we show that the spectrum is characterized by the ...
With dynamic mediums such as computer displays, we propose a new kind of visually dynamic presentation of proofs in plane geometry. In asingle diagram for the proof, when the proof text goes on step b...
In this paper, we discuss the finite volume element method of $P_1$-nonconforming quadrilateral element for elliptic problems and obtain optimal error estimates for general quadrilateral partition....
专著信息 书名 An efficient method for computing hyperbolic systems with geometrical source terms having concentrations, 语种 英文 撰写或编译 作者 S. Jin,X. Wen 第一作者单位 出版社 J. Computational Mathematics 22, 230-249, 2004...
A new method in Fano geometry     method  Fano geometry       2010/10/29
We give some bounds on the anticanonical degrees of Fano varieties with Picard number 1 and mild singularities, extending results of Koll\'ar et al. from the early 90's and improving them even in the ...
In this paper, methods of mechanical deriving of formulas from a set of di®erential polynomial equations and a set of di®erential polynomial inequations are presented. The methods have been ...

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