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The approximation theorem of Convolution Operator in △~p Set-valued Function Space

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Acta Mathematicae Applicatae Sinica 2002年第3期18卷 495-500页

作者： Pei-xin YeInstitute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Science, Beijing Institute of Mathematics Academy of Mathematics and System Sciences Chinese Academy of Science Beijing 100080 China

The paper is a contribution to the problem of approximating random set with values in a separable Banach space. This class of set-valued function is widely used in many *** investigate the properties of p-bounded integrable random set. Based on this we endow it with △p metric which can be viewed as a integral type hausdorff metric and present some approximation theorem of a class of convolution operators with respect to △p metric. Moreover we also can establish analogous theorem for other integral type operator in △p space.

关键词： Set-valued function random set convolution operator △~p space approximation theorem

approximation BY GENERALIZED MKZ-OPERATORS IN POLYNOMIAL WEIGHTED SPACES

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Analysis in Theory and Applications 2007年第1期23卷 64-75页

作者： Lucyna Rempulska Mariola Skorupka Poznan University of Technology

We prove some approximation properties of generalized Meyer-Konig and Zeller operators for differentiable functions in polynomial weighted spaces. The results extend some results proved in [1-3,7-16].

关键词： Meyer-Konig and Zeller operator polynomial weighted space approximation theorem

approximation BY SOME OPERATORS OF SZASZ-MIRAKYAN TYPE

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Analysis in Theory and Applications 2004年第1期20卷 1-15页

作者： L.Rempulska Z.Walczak Poznan University of Technology PolandPoznan University of Technology Poland

In this paper we give theorems on the degree of approximation of functions of one and two variables by certain operators of the Szasz-Mirakyan type.

关键词： Szasz-Mirakyan operator approximation theorem polynomial weighted space

Why neural networks apply to scientific computing?

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Theoretical & Applied Mechanics Letters 2021年第3期11卷 125-129页

作者： Shaoqiang Tang Yang Yang HEDPS and LTCS College of EngineeringPeking UniversityBeijing 100871China

In recent years,neural networks have become an increasingly powerful tool in scientific *** universal approximation theorem asserts that a neural network may be constructed to approximate any given continuous function at desired *** backpropagation algorithm further allows efficient optimization of the parameters in training a neural *** by GPU’s,effective computations for scientific and engineering problems are thereby *** addition,we show that finite element shape functions may also be approximated by neural networks.

关键词： Neural networks Universal approximation theorem Backpropagation algorithm

On the Injectivity of Bers Map β

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Acta Mathematica Sinica,English Series 1986年第3期2卷 207-211页

作者：陈怀惠 Department of Mathematics Nanjing Normal University

we know that the Bers map β~* is injective for q = 2, or for a group with quotient consisting ofsurfaces of finite type, and then for a finitely generated group. But it is unknown that whether themap β~* is injective for an integer q>2 and an infinitely generated group ([1]). Now we give apartial solution of this problem by proving that for a group with simply connected region ofdiscontinuity the map β~* is injective for any q≥2.

关键词： Finite Type approximation theorem Automorphic Form Kleinian Group Connected Region