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A predict-correct projection method for monotone variant variational inequalities

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Chinese Science Bulletin 1998年第15期43卷 1264-1267页

作者： HAN Qiaoming 1 and HE Bingsheng 2 1. Institute of Applied mathematics, Chinese Academy of Sciences, Beijing 100080, China 2. department of mathematics, Nanjing University, Nanjing 210093, China Institute of Applied mathematics Chinese Academy of Sciences Beijing China department of mathematics Nanjing University Nanjing China

A predict_correct projection method is presented for solving monotone variant variational inequalities, which could exploit the advantages and overcome the difficulties of both explicit and implicit projection methods.

关键词： variant variational inequality explicit projection method implicit projection method predict_correct projection method.

Nonsingularity in second-order cone programming via the smoothing metric projector

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Science China mathematics 2010年第4期53卷 1025-1038页

作者： WANG Yun 1,& ZHANG LiWei 2 1 College of Information Sciences and Engineering,Shandong Agricultural University,Tai’an 271018,China 2 department of Applied mathematics,Dalian University of Technology,Dalian 116024,China College of Information Sciences and Engineering Shandong Agricultural University Tai’an China department of Applied mathematics Dalian University of Technology Dalian China

Based on the differential properties of the smoothing metric projector onto the second-order cone,we prove that,for a locally optimal solution to a nonlinear second-order cone programming problem,the nonsingularity of the Clarke's generalized Jacobian of the smoothing Karush-Kuhn-Tucker system,constructed by the smoothing metric projector,is equivalent to the strong second-order sufficient condition and constraint nondegeneracy,which is in turn equivalent to the strong regularity of the Karush-Kuhn-Tucker ***,this nonsingularity property guarantees the quadratic convergence of the corresponding smoothing Newton method for solving a Karush-Kuhn-Tucker ***,the analysis does not need the strict complementarity condition.

关键词： second-order cone programming problem smoothing metric projector B-subdifferential Clarke’s generalized Jacobian smoothing Newton method

Admissibilities of linear estimator in a class of linear models with a multivariate t error variable

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Science China mathematics 2010年第8期53卷 2011-2019页

作者： YANG GuoQing 1 & WU QiGuang 2 1 department of mathematics,Tongji University,Shanghai 200092,China 2 Institute of Systems Science,Academy of mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China department of mathematics Tongji University Shanghai China Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

This paper discusses admissibilities of estimators in a class of linear models,which include the following common models:the univariate and multivariate linear models,the growth curve model,the extended growth curve model,the seemingly unrelated regression equations,the variance components model,and so *** is proved that admissible estimators of functions of the regression coefficient β in the class of linear models with multivariate t error terms,called as Model II,are also ones in the case that error terms have multivariate normal distribution under a strictly convex loss function or a matrix loss *** is also proved under Model II that the usual estimators of β are admissible for p 2 with a quadratic loss function,and are admissible for any p with a matrix loss function,where p is the dimension of β.

关键词： multivariate t distribution convex loss quadratic loss matrix loss admissible estimator

Integral spinor norms in dyadic local fields Ⅲ

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Science China mathematics 2010年第9期53卷 2425-2446页

作者： L JianRui1 & XU Fei2,1department of mathematics,Jinan University,Guangzhou 510632,China 2School of mathematics,Capital Normal University,Beijing 100048,China department of mathematics Jinan University Guangzhou China School of mathematics Capital Normal University Beijing China

In this paper we give an alternative computation of integral spinor norms over dyadic local fields by using the Jordan decomposition of *** particular,we emphasize the striking similarity between the theory over dyadi... 详细信息

关键词： integral lattice spinor norm Jordan decomposition

FLOATING QUANTIZATION EFFECTS ON MULTIRATE SAMPLED-DATA NONLINEAR CONTROL SYSTEMS

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Acta Mathematica Scientia 2007年第3期27卷 635-644页

作者：余宏旺汪志鸣 department of mathematics East China Normal University

In this article, floating quantization effects on multirate sampled-data control systems are studied. It shows that the solutions of multirate digital feedback control systems with nonlinear plant and with floating quantization in the controller are uniformly ultimately bounded if the associated linear systems consisting of linearization of the plant and controller with no quantization are Schur stable. Moreover, it also shows that the difference between the response of multirate digital controllers without quantizers and the same plant with floating quantization in the controllers can be made as small as desired by selecting proper quantization level.

关键词： Multirate sampled-data control systems quantization Schur stable uniformly ultimately bounded

Stability of a Neutral Stochastic Functional Differential Equations

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Wuhan University Journal of Natural Sciences 2005年第6期10卷 957-960页

作者： LI Bi-wen~1,21. department of mathematics, Hubei Normal University, Huangshi 435002, Hubei, China 2. department of mathematics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China department of mathematics Hubei Normal University Huangshi Hubei China department of mathematics Huazhong University of Science and Technology Wuhan Hubei China

Sufficient condition for stochastic unifrom stability of a neutral stochastic functional differential equation is given, especially, new techniques are developed to cope with the neutral delay case, we obtained the sufficient condition for asymptotic stability of neutral stochastic differential delay equations. Due to the new techniques developed in this paper, the results obtained arc very general and useful. The theory developed here gives a unified treatment for various asymptotic estimates e.g. exponential and polynomial bounds.

关键词： Lyapunov function D operator It's formula stochastic unifrom stabillty asymptotic stability

λ-fold indecomposable large sets of Steiner triple systems

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Science China mathematics 2010年第11期53卷 2877-2888页

作者： JI LiJun1, TIAN ZiHong2, & KANG QingDe2 1department of mathematics, Suzhou University, Suzhou 215006, China 2College of mathematics and Information Science, Hebei Normal University, Shijiazhuang 050016, China department of mathematics Suzhou University Suzhou China College of mathematics and Information Science Hebei Normal University Shijiazhuang China

A family (X, B1), (X, B2), . . . , (X, Bq) of q STS(v)s is a λ-fold large set of STS(v) and denoted by LSTSλ(v) if every 3-subset of X is contained in exactly λ STS(v)s of the collection. It is indecomposable and denoted by IDLSTSλ(v) if there exists no LSTSλ (v) contained in the collection for any λ 1 and orders v ≡ 1, 3 (mod 6) do there exist IDLSTSλ(v)? In this paper, we use partitionable candelabra systems (PCSs) and holey λ-fold large set of STS(v) (HLSTSλ(v)) as auxiliary designs to establish a recursive construction for IDLSTSλ(v) and show that there exists an IDLSTSλ(v) for λ = 2, 3, 4 and v ≡ 1, 3 (mod 6).

关键词： Steiner triple system large set candelabra system indecomposable

A conjecture on k-factor-critical and 3-γ-critical graphs

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Science China mathematics 2010年第5期53卷 348-354页

作者： WANG Tao1&YU QingLin2 1Institute of Applied mathematics,College of mathematics and Information Science,Henan University,Kaifeng 475001,China 2department of mathematics and Statistics,Thompson Rivers University,Kamloops,BC V2C5N3,Canada Institute of Applied mathematics College of Mathematics and Information Science Henan University Kaifeng China department of mathematics and Statistics Thompson Rivers University Kamloops Canada

For a graph G =(V,E),a subset VS is a dominating set if every vertex in V is either in S or is adjacent to a vertex in *** domination number γ(G) of G is the minimum order of a dominating set in G.A graph G is said to be domination vertex critical,if γ(G-v) 2 and k≡|V|(mod 2).If G is 3-γ-edge-critical and claw-free,then G is *** this paper we present a proof to this conjecture,and we also discuss the properties such as connectivity and bicriticality in 3-γ-vertex-critical claw-free graph.

关键词： domination critical graph factor critical bicritical

Necessary and sufficient condition of C^0 flows on closed surfaces with isolated singular points having the pseudo-orbit tracing property

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Chinese Science Bulletin 1997年第3期42卷 259-260页

作者： MAI Jiehua and GU Rongbao1.Institute of mathematics, Shantou University, Shantou 515063, China 2. department of mathematics, Anhui University, Hefei 230039, China Institute of mathematics Shantou University Shantou China department of mathematics Anhui University Hefei China

IN this letter we discuss the necessary and sufficient condition of C^0 flows on closed surfaces with isolated singular points having the pseudo-orbit tracing property. According to ref. [1], on a closed surface, every minimal set of a C^r(r≥2) flow is trivial, but it is possible for a C^0 flow to contain non-trivial minimal sets. Thus C^0 flows on closed surfaces are more complicated than C^r(r≥2) flows.

关键词： Necessary and sufficient condition of C^0 flows on closed surfaces with isolated singular points having the pseudo-orbit tracing property