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CONVERGENCE OF CASCADE ALGORITHMS AND SMOOTHNESS OF REFINABLE DISTRIBUTIONS

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Chinese Annals of mathematics,Series B 2003年第3期24卷 367-386页

作者： SUN QIYU department of mathematics, university of houston, houston, tx 77204, usa. department of mathematics, National university of Singapore, 10 Kent Ridge Crescent, 119260, Singapore. Univ houston Dept Math Houston TX 77204 USA Natl Univ Singapore Dept Math Singapore 119260 Singapore

In this paper, the author at first develops a method to study convergence of the cascadealgorithm in a Banach space without stable assumption on the initial (see Theorem 2.1), andthen applies the previous result on the convergence to characterizing compactly supportedrefinable distributions in fractional Sobolev spaces and Holder continuous spaces (see Theorems3.1, 3.3, and 3.4). Finally the author applies the above characterization to choosing appropriateinitial to guarantee the convergence of the cascade algorithm (see Theorem 4.2).

关键词： Cascade algorithm Cascade operator Refinable distribution Shift-invariant space Linear independent shifts Stable shifts Fractional Sobolev space

Flatness of CR submanifolds in a sphere

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Science China mathematics 2010年第3期53卷 701-718页

作者： JI ShanYu 1, & YUAN Yuan 2 1 department of mathematics, university of houston, houston, tx 77204, usa 2 department of mathematics, Rutgers university, Piscataway, NJ 08854, usa 1. department of mathematics University of Houston Houston TX 77204 USA2. Department of Mathematics Rutgers University Piscataway NJ 08854 USA

In Euclidean geometry, for a real submanifold M in E n+a , M is a piece of E n if and only if its second fundamental form is identically zero. In projective geometry, for a complex submanifold M in CP n+a , M is a piece of CP n if and only if its projective second fundamental form is identically zero. In CR geometry, we prove the CR analogue of this fact in this paper.

关键词： CR submanifolds sphere CR second fundamental form proper holomorphic mappings between balls

Classification of rational holomorphic maps from B^2 into B^N with degree 2

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Science China mathematics 2009年第12期52卷 2647-2667页

作者： JI ShanYu 1 & ZHANG Yuan 2 1 department of mathematics, university of houston, houston, tx 77204, usa 2 department of mathematics, university of California at San Diego, La Jolla, CA 92093, usa department of mathematics University of Houston Houston USA department of mathematics Rutgers University New Brunswick USA

Rational proper holomorphic maps from the unit ball in C 2 into the unit ball C N with degree 2 are classified, up to automorphisms of balls.

关键词： rational holomorphic maps between balls classification maps with degree 2

The truncated Second Main Theorem and uniqueness theorems

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Science China mathematics 2010年第3期53卷 605-616页

作者： CHEN ZhiHua 1 , RU Min 2, & YAN QiMing 1 1 department of mathematics, Tongji university, Shanghai 200092, China 2 department of mathematics, university of houston, houston, tx 77204, usa 1. department of mathematics Tongji University Shanghai 200092 China2. Department of Mathematics University of Houston Houston TX 77204 USA

In this paper, we first establish a truncated Second Main Theorem for algebraically nondegenerate holomorphic mappings from the complex plane into a complex projective variety V intersecting hypersurfaces. We then prove some uniqueness results for meromorphic mappings. The result of Demailly about a partial solution to the Fujita’s conjecture is used.

关键词： value distribution theory uniqueness theorem meromorphic mappings Fujita’s conjecture

Oligo(ethylene glycol)-terminated monolayers on silicon surfaces and their nanopatterning with a conductive atomic force microscope

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Science China Chemistry 2010年第1期53卷 36-44页

作者： QIN GuoTing & CAI ChengZhi department of Chemistry,university of houston,houston,Texas 77204,usa 1. department of Chemistry University of Houston Houston Texas 77204 USA

Functionalization of silicon substrate surfaces with a stable monolayer for resisting non-specific adsorption of proteins has attracted great interest,since it is directly relevant to the development of miniature,silicon-based biosensors and implantable microdevices,such as silicon-neuron *** brief review summarizes our contribution to the development of robust monolayers grown by surface hydrosilylation on atomically flat,hydrogen-terminated silicon *** review also outlines our strategy and progress on the fabrication of single molecule patterns on such monolayer platforms.

关键词： protein-resistant monolayers surface hydrosilylation conductive atomic force microscope nanopatterning

Non-Recursive Base Conversion Using a Deterministic Markov Process

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Journal of Applied mathematics and Physics 2024年第6期12卷 2112-2118页

作者： Louis M. houston department of Innovation and Research The University of Louisiana at Lafayette Lafayette LA USA

We prove that non-recursive base conversion can always be implemented by using a deterministic Markov process. Our paper discusses the pros and cons of recursive and non-recursive methods, in general. And we include a comparison between non-recursion and a deterministic Markov process, proving that the Markov process is twice as efficient.

关键词： Base Conversion Recursion Euclidean Division Geometric Series Markov Process

Uniqueness theorem for algebraic curves on compact Riemann surfaces

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Science China mathematics 2007年第5期50卷 683-688页

作者： Yan XU & Min RU department of mathematics, Nanjing Normal university, Nanjing 210097, China department of mathematics, university of houston, houston, tx 77401, usa 1. department of mathematics Nanjing Normal University Nanjing 210097 China 2. department of mathematics University of Houston Houston TX 77401 USA

In this paper, we prove a uniqueness theorem for algebraic curves from a compact Riemann surface into complex projective spaces.

关键词： uniqueness theorem algebraic curves Riemann surfaces Nevanlinna theory 32H30

Oxides for High Temperature Superconductivity and Beyond

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Tsinghua Science and Technology 1998年第1期3卷 57-78页

作者： Ching Wu Chu department of Physics and Texas Center for Superconductivity, university of houston, houston, tx 77204, usa department of Physics and Texas Center for Superconductivity University of Houston TX 77204 USA

In this paper, I shall briefly summarize the present state of high temperature superconductivity research and development together with an assessment of the prospect of yet a higher transition temperature and an outline of challenges facing today's practitioners of high temperature super conductivity science and technology. The extensive knowledge acquired in the last decade in high temperature superconducting science and materials may usher in a new era of material engineering, which I would like to call mesomaterial engineering for the fabrication of perovskite and related oxide superlattices, a new class of materials for science and technology. Therefore, I shall also present the rationale behind this effort and the promises of the new materials, together with a list of several preliminary successful examples.

关键词： high temperature superconductivity oxide mesomaterial engineering

WHAT DOES CHAOS HAVE TO DO WITH SYSTEMS AND CONTROL ENGINEERING?

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Journal of Systems Science & Complexity 2001年第1期14卷 31-39页

作者： CHEN Guanrong (department of Electrical and Computer Engineering, university of houston, houston, Texas 77204, usa department of Electronic Engineering, City university of Hong Kong, Kowloon, Hong Kong SAR, China) university of houston 美国 77204

Chaos as a very special type of complex dynamical behaviors has been studied for about four decades. Yet the traditional trend of analyzing and understanding chaos has evolved to controlling and utilizing chaos today. Research in the field of chaos modeling, control, and synchronization includes not only ordering chaos, which means to weaken or completely suppress chaos when it is harmful, but also chaotification, which refers to enhancing existing Chaos or creating chaos purposely when it is useful, by any means of control technology. This article offers a brief overview about the potential impact of controlled chaos on beneficial applications in science and engineering, and introduces some recent progress in chaotification via feedback control methods.

关键词： Chaos chaos control chaotification complexity feedback.