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OPTIMAL CONTROL OF MULTISOLUTION ORDINARY DIFFERENTIAL EQUATIONS IN THE ABSENCE OF CONVEXITY

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Journal of Systems Science & Complexity 2010年第2期23卷 321-333页

作者： Shu LUAN Hang GAO school of mathematics and Computation Science Zhanjiang Normal College Zhanjiang 524048 China. school of mathematics and statistics Northeast Normal University Changchun 130024 China.

In this paper,the authors study an optimal control problem governed by a class of multistateordinary differential equations in the absence of *** overcome the difficulty that thecorresponding approximate optimal control problem may have no solution,relaxed controls are *** the help of relaxation theory,Pontryagin's maximum principle for the optimal pairs ofthe original control problem is *** the end of this paper,the authors discuss the applicationof the maximum principle by an example.

关键词： Multisolution ODEs optimal control Pontryagin's maximum principle relaxed controls.

A general type of twisted anomaly cancellation formulas

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Science china.mathematics 2010年第7期53卷 1684-1695页

作者： WANG Yong school of mathematics and statistics, northeast normal university, changchun 130024, china 1. school of mathematics and statistics Northeast Normal University Changchun 130024 China

For even-dimensional manifolds, we prove some twisted anomaly cancellation formulas which generalize some well-known cancellation formulas. For odd dimensional manifolds, we obtain some modularly invariant characteris... 详细信息

关键词： modular invariance transgression cancellation formulas

The restricted EM algorithm under linear inequalities in a linear model with missing data

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Science china.mathematics 2005年第6期48卷 819-828页

作者： ZHENG Shurong, SHI Ningzhong & GUO Jianhua school of mathematics and statistics, northeast normal university, changchun 130024, china.Institute of mathematics, Jilin university, changchun 130012, china 1. school of mathematics and statistics Northeast Normal University 130024 Changchun China 2. Institute of mathematics Jilin University 130012 Changchun China

This paper discusses the maximum likelihood estimate of β under linear inequalities A0β≥ a in a linear model with missing data, proposes the restricted EM algo rithm and proves the convergence.

关键词： EM algorithm, linear model, maximum likelihood estimate, missing data.

Infinite-dimensional Hamiltonian Lie superalgebras

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Science china.mathematics 2010年第6期53卷 1625-1634页

作者： MU Qiang1,2 & ZHANG YongZheng1,1school of mathematics and statistics,northeast normal university,changchun 130024,china.2school of mathematics,Harbin normal university,Harbin 150025,china 1. school of mathematics and statistics Northeast Normal University Changchun 130024 China2. School of Mathematics Harbin Normal University Harbin 150025 China

The natural filtration of the infinite-dimensional Hamiltonian Lie superalgebra over a field of positive characteristic is proved to be invariant under automorphisms by characterizing ad-nilpotent *** are thereby able to obtain an intrinsic characterization of the Hamiltonian Lie superalgebra and establish a property of the automorphisms of the Lie superalgebra.

关键词： Hamiltonian superalgebra filtration automorphism

A PSTAIRE CDK-like protein localizes in nuclei and cytoplasm of Physarum polycephalum and functions in the mitosis

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Cell Research 2004年第2期14卷 169-175页

作者： Gui Ying LI~(1,2), Miao XING~(1,*), Bo HU~(1,3) ~1College of Life Science, Shenzhen Key Laboratory of Microbial Gene Engineering, Shenzhen university, Shenzhen 518060, china. ~2Department of Immunology, school of Basic Medical Sciences, Jilin university, changchun 130021, china.~3Institute of Genetics and Cytology, northeast normal university, changchun 130024, china. College of Life Science Shenzhen Key Laboratory of Microbial Gene Engineering Shenzhen University Shenzhen 518060 China.

CDKs play key roles in controlling cell cycle progression in all eukaryotes. In plants, multiple CDKs are present, among which the best characterized CDKs are PSTAIRE CDKs. In this study, we carried out Western blot, immunoelectron microscopy and antibody treatment with an anti-PSTAIRE monoclonal antibody to explore the subcellular localization and functions of PSTAIRE CDKs in Physarum polycephalum. The results of Western blot and immunoelectron microscopy showed that in P. polycephalum, a PSTAIRE CDK-like protein was 34 kD in molecular weight and located in both nuclei and cytoplasm. In nuclei, the protein was mainly associated with chromosomes and nucleoli. The expression of the PSTAIRE CDK-like protein in both the plasmodia and nuclei showed little fluctuation through the whole cell cycle. When treated with an anti-PSTAIRE monoclonal antibody at early S phase, the cells were arrested in S phase, and the mitotic onset of P. polycephalum was blocked for about 1 h when treated at early G2 phase. Our dat

关键词： PSTAIRE CDK-like protein Physarum polycephalum mitosis immunoelectron microscopy.

On The Research of Foreign and Domestic Human Capital Theory

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Chinese Journal of Population,Resources and Environment 2005年第4期3卷 61-65页

作者： Li Fuzhu school of Urban and Environmental Science, northeast normal university, changchun 130024, china

Human Capital Theory came into being in the middle and later periods of the 20th century. A lot of achievements have been made on the research in its connotation, measures of the value, investment and income, function mechanism and so on, by foreign scholars. In recent 10 years of the new Millennium alternation, the "steal business effect" and the structure of human capital on the mechanism of economic rise has become the two emphasis in current foreign Human Capital Theory’s research. On the basis of foreign researches and Chinese situations, domestic scholars have enriched and developed it, but there are many disparities in its methods, aspects and levels between foreign and domestic researches.

关键词： Human Capital Theory (HCT) research western developed countries china

Split-plot designs with general minimum lower-order confounding

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Science china.mathematics 2010年第4期53卷 939-952页

作者： WEI JiaLin 1,4,YANG JianFeng 1,LI Peng 3 & ZHANG RunChu 1,2,1 school of Mathematical Sciences and LPMC,Nankai university,Tianjin 300071,china.2 KLAS and school of mathematics and statistics,northeast normal university,changchun 130024,china.3 school of Mathematical Sciences,Capital normal university,Beijing 100037,china.4 school of Sciences,Tianjin university of Commerce,Tianjin 300134,china 1. school of Mathematical Sciences and LPMC Nankai University Tianjin 300071 China4. School of Sciences Tianjin University of Commerce Tianjin 300134 China3. School of Mathematical Sciences Capital Normal University Beijing 100037 China2. KLAS and School of Mathematics and Statistics Northeast Normal University Changchun 130024 China

Split-plot designs have been widely used in industrial *** to now,most methods for choosing this kind of designs are based on the minimum aberration (MA) ***,by introducing a new pattern,called aliased effect-number pattern (AENP),Zhang et *** a general minimum lowerorder confounding (denoted by GMC for short) criterion and established a general minimum confounding (also denoted by GMC for saving notations) *** is proved that,the GMC criterion selects optimal designs in a more elaborate manner than the existing ones,and when an experimenter has a prior about the importance ordering of factors in experiments the GMC designs are better than other optimal *** this paper we extend the GMC criterion to the split-plot design case and give a GMC-FFSP criterion for ranking split-plot *** comparisons of the new criterion with the MA-MSA-FFSP criterion are given,and the optimal 32-run split-plot designs up to 14 factors under the two criteria are tabulated for comparison and application.

关键词： fractional factorial design GMC criterion minimum aberration split-plot

A theorem of Fong's type for graded algebras

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Science china.mathematics 2005年第5期48卷 577-582页

作者： FAN Yun & ZHU Ping school of mathematics and statistics, Central china.normal university, Wuhan 430079, china.school of Mathematical Science, Nankai university, Tianjin 300071, china 1. school of mathematics and statistics Central China Normal University 430079 Wuhan China 2. school of Mathematical Science Nankai University 300071 Tianjin China

Let G be a finite p-solvable group and k be an algebraic closed field of characteristic p. It is proved that any projective indecomposable module of a G-graded k-algebra is an induced module of a module of the subalgebra graded by a Hall p′-subgroup. A necessary and sufficient condition for the indecomposability of an induced module from a Hall p′-subgroup is obtained.

关键词： group graded algebra indecomposable induced module primitive idempotent.

BIFURCATIONS OF PERIODIC ORBITS IN THREE-WELL DUFFING SYSTEM WITH A PHASE SHIFT

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Journal of Systems Science & Complexity 2011年第3期24卷 519-531页

作者： Jicai HUANG Han ZHANG school of mathematics and statistics Central China Normal University Wuhan 430079 China College of Information Technical Science Nankai University Tianjin 300071 China.

Bifurcations of periodic orbits of three-well Duffing system with a phase shift are investigated in detail. The conditions of the existence and bifurcations for harmonics, subharmonics （2-order, 3- order and m-order） and superharmonics under small perturbations are given by using second-order averaging method and Melnikov＇s method. The influence of the phase shift on the dynamics is also obtained.

关键词： Bifurcations Melnikov's method periodic orbits second-order averaging three-well Duffing system.