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Generalized gradient projection neural networks for nonsmooth optimization problems

Science china(Information Sciences) 2010年第5期53卷 990-1005页

作者： LI GuoCheng 1 , SONG ShiJi 2 ? & WU Cheng 2 1 department of Mathematics, Beijing Information Science and Technology university, Beijing 100192, china 2 department of Automation, Tsinghua university, Beijing 100084, china 1. department of Mathematics Beijing Information Science and Technology University Beijing 100192 China2. Department of Automation Tsinghua University Beijing 100084 China

Generalized gradient projection neural network models are proposed to solve nonsmooth convex and nonconvex nonlinear programming problems over a closed convex subset of R n . By using Clarke’s generalized gradient, the neural network modeled by a differential inclusion is developed, and its dynamical behavior and optimization capabilities both for convex and nonconvex problems are rigorously analyzed in the framework of nonsmooth analysis and the differential inclusion theory. First for nonconvex optimization problems, the quasi convergence results similar to those achieved by previous work are proved. For convex optimization problems, the global convergence results are proved, i.e. any trajectory of the neural network converges to an asymptotically stable equilibrium point, which is an optimal solution of the primal problem whenever it exists. This result remains valid even if the initial condition is chosen outside the feasible set. In addition, an asymptotic control result involving a Tykhonov like regularization shows that any trajectory of the revised neural network can be forced to converge toward a particular optimal solution of the primal problem. Finally, two simulation optimization algorithms for solving the optimization and control problems are designed respectively, and three typical simulation experiments are illustrated to present the accuracy and efficiency of theoretical convergence results of this paper.

关键词： nonsmooth optimization problem generalized gradient projection networks differential inclu sions convergence

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APPLICATIONS OF THE DIVISION PROBLEM IN SPACES OF ENTIRE FUNCTIONS

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Systems Science and Systems Engineering 2003年第3期12卷 307-313页

作者： Guang WANGdepartment of Mathematics shanxi university, taiyuan 030006, P.R.china shanxi university Department of Mathematics Taiyuan (GRID:grid.163032.5) (ISNI:***)

Based on the results of (Wang 2001), we give some applications of division problem in spaces of entire functions of finite type. Especially, when p = 1 and H is the support functions of a bounded convex domain of C , ... 详细信息

关键词： Entire function plurisubharmonic function weight system division problem

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Biorthogonal multiple wavelets generated by vector refinement equation

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Science china Mathematics 2007年第7期50卷 1015-1025页

作者： Song LI~(1+) Jun XIAN~2 1 department of Mathematics,Zhejiang university,Hangzhou 310027,china 2 department of Mathematics,Sun Yat-Sen university,Guangzhou 510275,china 1. department of Mathematics Zhejiang University Hangzhou 310027 China 2. department of Mathematics Sun Yat-Sen University Guangzhou 510275 China

Biorthogonal multiple wavelets are generated from refinable function vectors by using the multiresolution analysis. In this paper we provide a general method for the construction of compactly supported biorthogonal multiple wavelets by refinable function vectors which are the solutions of vector refinement equations of the form $$\varphi (x) = \sum\limits_{\alpha \in \mathbb{Z}^s } {a(\alpha )\varphi (Mx - \alpha ), x \in \mathbb{R}^s } ,$$ where the vector of functions ? = (? 1, …, ? r)T is in $(L_2 (\mathbb{R}^s ))^r ,a = :(a(\alpha ))_{\alpha \in \mathbb{Z}^s } $ is a finitely supported sequence of r × r matrices called the refinement mask, and M is an s × s integer matrix such that lim n→∞ M ?n = 0. Our characterizations are in the general setting and the main results of this paper are the real extensions of some known results.

关键词： refinement equation biorthogonal multiple wavelets refinable function vector 42C40 41A10 41A15 41A25

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Variational construction of unbounded orbits in Lagrangian systems

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Science china Mathematics 2010年第3期53卷 617-624页

作者： CHENG Chong-Qing 1, & LI Xia 2 1 department of Mathematics, Nanjing university, Nanjing 210093, china 2 department of Mathematics, Suzhou university of Science and Technology, Suzhou 215001, china 1. department of Mathematics Nanjing University Nanjing 210093 China2. Department of Mathematics Suzhou University of Science and Technology Suzhou 215001 China

We show the existence of unbounded orbits in perturbations of generic geodesic flow in T2 by a generic periodic potential. Different from previous work such as in Mather (1997), the initial values of the orbits obtain... 详细信息

关键词： positive definite Lagrangian variational method unbounded orbit

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Gene Expression Profiling of Human Colorectal Adenocarcinoma,Adenoma and Normal Tissues

Gene Expression Profiling of Human Colorectal Adenocarcinoma...

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2008年全国生物化学与分子生物学学术大会

作者： Zhi-rong Liu Niu-liang Cheng (department of Biochemistry and Molecular Biology,shanxi medical university,taiyuan 030001,china.)

Objective:To profile tissue specific gene expression in colorectal adenoma,adenocarcinoma and normal tissues. Methods:The U133plus2.0 gene chips were used to analyze gene expression profiles of colorectal ad- enoma,ad...

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THE PHYSICAL ENTROPY OF SINGLE CONSERVATION LAWS

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Journal of Computational Mathematics 1998年第5期16卷 437-444页

作者： (department of Mathematics, Peking university, Beijing 100871, china) Beijing Univ Dept Math Beijing 100871 Peoples R China

By means of the comparisons with the formulas in statistical mechanics and thermodynamics, in this paper it is demonstrated that for the single conservation law partial derivative(t)u + partial derivative(x)f(u) = 0, if the flux function f(u) is convex (or concave), then, the physical entropy is S = -f(u); Furthermore, if we assume this result can be generalized to any f(u) with two order continuous derivative, from the thermodynamical principle that the local entropy production must be non-negative, one entropy inequality is derived, by which the O.A. Olejnik's famous E- condition can be explained successfully in physics.

关键词： conservation laws entropy entropy production

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Prophylaxis and Therapy of Isaria felina on Acute Renal Failure Induced by Glycerin in Rats

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Chinese Herbal Medicines 2012年第4期4卷 319-323页

作者： YANG Xi-hua2,3,ZHANG Sheng-wan1,REN Lian-sheng3,BAI Xi-hua3 1.College of Life Science,shanxi university,taiyuan 030006,china 2.College of Chemistry and Chemical Engineering,shanxi university,taiyuan 030006,china 3.department of Comparative Medicine,shanxi Cancer Institute,taiyuan 030013,china [a] College of Life Science Shanxi University Taiyuan 030006 China [b] College of Chemistry and Chemical Engineering Shanxi University Taiyuan 030006 China [c] department of Comparative Medicine Shanxi Cancer Institute Taiyuan 030013 China

Objective To evaluate the prophylaxis and therapy of Isaria felina(IF) on glycerin-induced acute renal failure(ARF) in *** Forty male Wistar rats were divided into control,model,Uremic Clearance Granule(UCG,positive control),high-and low-dose IF *** in the high-and low-dose IF groups were ig administered with 200 and 100 mg/kg IF,respectively,while rats were ig administered with 3.6 g/kg UCG successively for 7 d to establish UCG *** rats in model,control,and drug-treated groups were im injected with 8 mL/kg 50% glycerin after drinking was quitted for 24 h to induce ARF in *** drugs were continued to give *** level of blood urea nitrogen(BUN) and serum creatinine(SCr) were determined 24 and 72 h after the injection of glycerin,also the kidney was dissected for pathology *** Im injection with 8 mL/kg 50% glycerin could successfully induce ARF in *** dose of 200 mg/kg IF could reduce the high levels of BUN and SCr,and ameliorate the pathological damage of the *** IF has good protective and therapeutic effects on ARF and it is a potential and valuable Chinese herb for ARF.

关键词： acute renal failure blood urea nitrogen glycerin Isaria felina serum creatinine

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Effect of active immunization with peptides corresponding to the second extracellular loop of alpha1-adrenoceptor on vascular function in rats

Effect of active immunization with peptides corresponding to...

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中国生理学会第23届全国会员代表大会暨生理学学术大会

作者： Li YAN~1,Zhong-Hua DAI~1,Guang-Zhao YANG~2,Su-Li ZHANG~2,Hui-Rong LIU~(2,3),Ji-Min CAO~1 1 department of physiology and Pathophysiology,Institute of Basic medical Sciences,Chinese Academy of medical Sciences,School of Basic Medicine,Peking Union medical College,Beijing 100005,china 2 department of physiology,shanxi medical university, taiyuan,shanxi,china 3 department of Pathophysiology,School of Basic medical Sciences,Capital medical university,Beijing, 100069,china

Backgroud:Autoantibody against the second extracellular loop ofα-adrenoceptor(α-AA) which had been found in hypertensive patients possess agonist-like activity as phenylephrine evidenced by previous studies, however,long-term stimulation ofα-AA did not modify the mean arterial pressure in spite of the occurrence of cardiac and vascular remodeling,and the mechanism was not fully ***:In this study,the effect of acuteα-AA administration on mean arterial blood pressure was observed;the models with antibodies against theα-adrenoceptor were established by immunizing Wistar rats with the synthesized peptide corresponding to the second extracellular loop ofα-adrenoceptor(α-AR-EC).The age-matched male Wistar rats received a mixture of saline and immunological adjuvant as sham immunized *** the rats were raised for 8 *** blood pressure and heart rate were measured every *** reactivity experiments were performed in segments of thoracic ***-1(ET-1) concentration and iNOS expression were determined by ELISA and immunochemistry ***:The mean arterial pressure significantly increased after the administration ofα- AA in *** the systolic blood pressure of immunized rats having no difference with sham group,the isolated thoracic arteries showed hyperresponsiveness to phenylephrine and decreased endothelium-dependent relaxation at 6 and 8 months after initial ***,the plasma endothelin-1(ET-1) concentration and iNOS expression in vascular endothelium from the thoracic aorta increased,indicating that the long-term stimulation might contribute to endothelium injury,which plays an important role in the vasomotor dysfunction and enhanced pressor ***:The results demonstrated thatα-AA could contribute to vasomotor dysfunction in rats by vascular endothelial damage and increase iNOS expression,and might play a particular role in the pathological changes of hypertension.

关键词： receptor,adrenergic,alpha1 autoantibody vascular dysfunction hypertension

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A Characterization of Homomorphisms Between Banach Algebras

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Acta Mathematicae Applicatae Sinica 2004年第4期 761-768页

作者： Jian Lian CUI department of Mathematical Sciences,Tsinghua university,Beijing 100084 P.R.china and department of Mathematics,shanxi Teachers university,Linfen 041004,P.R.china Jin Chuan HOU department of Mathematics,shanxi Teachers university,Linfen 041004,P.R.china and department of Mathematics,shanxi university,taiyuan 030000,P.R.china

We show that every unital invertibility preserving linear map from a yon Neumann algebraonto a semi-simple Banach algebra is a Jordan homomorphism;this gives an affirmative answer to aproblem of Kaplansky for all von Neumann *** a unital linear map Φ from a semi-simplecomplex Banach algebra onto another,we also show that the following statements are equivalent:(1)Φ is an homomorphism;(2)Φ is completely invertibihty preserving;(3)Φ is 2-invertibility preserving.

关键词： Banach algebras Homomorphisms Jordan homomorphisms

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Frequent ventricular premature beats increase blood pressure variability in rats

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Acta Pharmacologica Sinica 2004年第5期25卷 3-11页

作者： Chao-yu MIAO2, Li-ping XU, Jian-guo LIU, He-hui XIE, Wen-jun YUAN, Ding-feng SU2department of Pharmacology, Second Military medical university, Shanghai 200433, china department of Pharmacology Second Military Medical University

AIM: The present study was designed to test a hypothesis that nonfatal ventricular arrhythmia such as ventricularpremature beats (VPB) is a contributing factor in the elevation of blood pressure variability (BPV). METHODS:Blood pressure (BP) and electrocardiogram were continuously recorded. The relation between VPB and BPV wasobserved under conscious state in chronic myocardial infarction (MI) rats one month after ligation of the leftcoronary artery, and further verified under anesthetized state in rat model of ventricular arrhythmia produced byacute intravenous infusion of aconitine. RESULTS: MI rats exhibited a big difference in the count and pattern ofVPB, and were divided into no VPB, occasional VPB, and frequent VPB groups. Among the three groups, therewere no differences in BP, heart period (HP), and MI size. However, BPV was markedly higher in frequent notoccasional VPB rats, and HP variability (HPV) was larger in both frequent and occasional VPB rats, when comparedwith no VPB rats. In the whole population of MI rats, BPV was positively correlated with VPB and HPV, not withBP, HP and MI size. Infusion of aconitine had no effect on BP, HP, BPV, and HPV during the period without *** VPB after several minutes of aconitine infusion induced significant increase in BPV and HPV with nochange in BP and HP. BPV was also positively correlated with VPB and HPV, not with BP and HP. Hemodynamicsin aconitine-evoked ventricular tachycardia was characterized as lower BP, higher BPV, and higher ***: High BPV can be caused by frequent not occasional VPB in rats.

关键词： arrhythmia blood pressure variability heart period variability

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