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On Rectifiable Curves in the Plane

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Acta Mathematica Sinica,English Series 2001年第2期17卷 327-332页

作者： Shi Pan LU department of mathematics, Teachers College, Jimei university, Xiamen 361021, P. R. China Cheng Ming LEE department of Mathematical, Sciences, university of wisconsin-milwaukee. milwaukee. wisconsin 53201, usa department of mathematics Jimei University Xiamen 361021 P. R. China department of Mathematical Sciences University of Wisconsin-Milwaukee Milwaukee USA

This paper gives a formula of integral for the rectifiable curves in the plane by the Hausdorff fractional derivation and integral.

关键词： Rectifiable curve Hausdorff measure Hausdorff fractional derivation

Littlewood-Paley operators with variable kernels

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Science China mathematics 2006年第5期49卷 639-650页

作者： CHEN Jiecheng, DING Yong & FAN Dashan department of mathematics, Zhejiang university (Xixi Campus), Hangzhou 310028, China School of Mathematical Sciences, Beijing Normal university, Beijing 100875, China department of mathematics, university of wisconsin-milwaukee. milwaukee.wi 53201, usa department of mathematics, Central China Normal university, Wuhan 430074, China department of mathematics Zhejiang University [Xixi Campus] Hangzhou 310028 China School of Mathematical Sciences Beijing Normal University Beijing 100875 China department of mathematics University of Wisconsin-Milwaukee Milwaukee WI 53201 USA department of mathematics Central China Normal University Wuhan 430074 China

In this paper we study a certain directional Hilbert transform and the boundedness on some mixed norm spaces. As one of applications, we prove the Lp-boundedness of the Littlewood-Paley operators with variable kernels... 详细信息

关键词： directional Hilbert transform, Sobolev spaces, Littlewood-Paley operator,variable kernel.

L^p-Boundedness of Marcinkiewicz Integrals with Hardy Space Function Kernels

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Acta Mathematica Sinica,English Series 2000年第4期16卷 593-600页

作者： Yong Ding department of mathematics, Beijing Normal university, Beijing 100875, P. R. China Dashan Fan department of mathematics, Anhui university and university of wisconsin-milwaukee. MW 53201 usa Yibiao Pan department of mathematics, university of Pittsburgh. Pittsburgh. Pennsylvania 15260. usa department of mathematics Beijing Normal University Beijing 100875 P. R. China department of mathematics Anhui University and University of Wisconsin-Milwaukee Wisconsin MW 53201 USA department of mathematics University of Pittsburgh Pittsburgh USA

We give the Lp-boundedness for a class of Marcinkiewicz integral operators μΩ, μΩ.λ and μΩ.S related to the Littlewood-Paley g-function, gλ-function and the area integral S, respectively. These operators have the kernel functions Ω∈H1(Sn-1), the Hardy space on Sn-1. The results in this paper substantially improve and extend the known results.

关键词： Marcinkiewicz integral g-function g_λ~*-function Area integral H^1 space Rough kernel

On an attack on RSA with small CRT-exponents

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Science China(Information Sciences) 2010年第8期53卷 1511-1518页

作者： HAN LiDong 1,2 , WANG XiaoYun 3 & XU GuangWu 3,4 1 Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong university, Jinan 250100, China 2 School of mathematics, Shandong university, Jinan 250100, China 3 Institute for Advanced Study, Tsinghua university, Beijing 100084, China 4 department of Electrical Engineering and Computer Science, university of wisconsin-milwaukee. milwaukee. wi 53201, usa 1. Key Laboratory of Cryptologic Technology and Information Security Ministry of Education Shandong University Jinan 250100 China2. School of Mathematics Shandong University Jinan 250100 China3. Institute for Advanced Study Tsinghua University Beijing 100084 China4. Department of Electrical Engineering and Computer Science University of Wisconsin-Milwaukee Milwaukee WI 53201 USA

This paper concerns the RSA system with private CRT-exponents. Since Chinese remainder representation provides efficiency in computation, such system is of some practical significance. In this paper, an existing attack to small private CRT-exponents is analyzed. It is indicated that this attack makes nice use of lattice in RSA analysis, but some argument does not hold in general. Several counterexamples are constructed. Refinements and more precise statements of the attack are given.

关键词： RSA CRT cryptanalysis continued fraction lattice reduction

A Discrete Singular Integral Operator(In Memory of Professor Long Ruilin)

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Acta Mathematica Sinica,English Series 1998年第2期14卷 235-244页

作者： Fan Dashan (department of Mathematical Sciences,university of wisconsin-milwaukee.milwaukee.wi 53201,usa)(Email:fan@alpha1.csd.uwm.edu)Lu Shanzhen (department of mathematics,Beijing Normal university,Beijing 100875,China)(Email:lusz@***)Pan Yibiao (department of mathematics and Statistics,university of Pittsburgh,Pittsburgh,PA 15260,usa)(Email:yibiao@tomato.math.pitt.edu) university of wisconsin-milwaukee 美国北京师范大学数学系北京 Pittsburgh大学美国

Suppose that {αk}k∞=-∞ is a Lacunary sequence of positive numbers satisfying infαk+1/αk=α>1 and that Ω（y’）is a function in the Besov space B10,1(Sn-1)where Sn-1 is the unit sphere on Rn（n≥2）.We prove that if ∫Sn-1Ω（y’）dσ（y’）=0 then the discrete singular integral operator TΩf（x）=∫(Sn-1)f（x-αky’）Ω（y’）dσ（y’） and the associated maximal operator TΩf（x）=∫Sn-1f（x-αky’）Ω（y’）dσ（y’） are both bounded in the space L2（Rn）. The theorems in this paper improve a result by Duoandikoetxea and Rubio de Francia in the L2 case.

关键词： Singular integral Besov space Rough kernel

Computational Equivalence Between the Problems of Sorting and Monotone Reconstruction for Random Permutations

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Journal of Mathematical Research with Applications 1991年第1期 1-8页

作者： Kequan Ding(department of mathematics, university of wisconsin-Madison Madison, wi 53706, usa)

In this note,it is shown that the monotone reconstruction problem is equi-valent to that of sorting,in the sense of computational *** particularfrom any given sorting al gorithm A,an algorithm B for the monotone reconstruc-tion problem can be developed with at most O(m)time and O(m)space cost morethan that used in A,and vice *** a consequence of this result,it is obtai-ned that the time complexity of the monotone reconstruction problem of n-ele-ment random perm utations is O(nlogn).

关键词： Computational Equivalence Between the Problems of Sorting and Monotone Reconstruction for Random Permutations

GENE THERAPY (continued) Ⅱ. TECHNIQUES FOR GENE THERAPY

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中国实验血液学杂志 1994年第2期2卷 115-124页

作者： Lifen Ren(department of Physiology, Medical College of wisconsin, milwaukee. usa)

An essential prerequisite of any genetherapy technique is the efficient and stable de-livery of transferred DNA into the target *** of techniques are available for directly in-troducing DNA into eukaryotic cells,includingcoprecipitation with calcium phosphate,electroporation and microinjection. The efficien-cy of most of these physical transfection tech-niques is less than one in ten thousand, and

关键词： DNA livery continued transfection prerequisite eukaryotic thousand GENE THERAPY dystrophin packaging

DISCONTINUOUS SOLUTIONS IN L~∞ FOR HAMILTON-JACOBI EQUATIONS

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Chinese Annals of mathematics,Series B 2000年第2期21卷 165-186页

作者： CHENGUIQIANG SUBo ：departmentofmathematics NorthwesternUniversity2033SheridanRoadEvanstonIL60208-2730USA departmentofmathematics UniversityofWisconsinatMadisonMadisonWI53706-1380USA.

An approach is introduced to construct global discontinuous solutions in L~∞ for HamiltonJacobi equations. This approach allows the initial data only in L~∞ and applies to the equations with nonconvex Hamiltonians. The profit functions are introduced to formulate the notion of discoatinuous solutions in L~∞. The existence of global discontinuous solutions in L~∞ is established. These solutions in L~∞ coincide with the viscosity solutions and the minimax solutions, provided that the initial data are continuous. A prototypical equation is analyzed to examine the L~∞ stability of our L~∞ solutions. The analysis also shows that global discontinuous solutions are determined by the topology in which the initial data are approximated.

关键词： Hamilton-Jacobi equations Discontinuous solutions Profit functions Viscosity solutions Madman solutions Stability

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GENE THERAPY

中国实验血液学杂志 1994年第1期2卷 17-24页

作者： Lifen Ren(department of Physiology, Medical College of wisconsin, milwaukee. wi, usa)

本综述包括了1994年1月及1993年9月两次有关基因治疗国际会议上的新资料,内容新,且系统扼要地介绍了基因治疗的新概念、新进展及新的技术。本文分两部分发表;第Ⅱ部分有关基因转导新技术及参考文献等将于下一期发表。

关键词：新概念新技术基因治疗国际会议基因转导新资料新进展综述参考文献血液学