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p-moment stability of stochastic impulsive differential equations and its application in impulsive control

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Science China(Technological sciences) 2009年第3期52卷 782-786页

作者： XU Wei NIU YuJun RONG HaiWu SUN ZhongKui Department of applied Math Northwestern Polytechnical UniversityXi’an 710072China Department of mathematics Fushan UniversityFushan 528000China

The exponential p-moment stability of stochastic impulsive differential equations is addressed. A new theorem to ensure the p-moment stability is established for the trivial solution of the stochastic impul- sive differential system. As an application of the theorem proposed, the problem of controlling chaos of Lorenz system which is excited by parameter white-noise excitation is considered using impulsive control method. Finally, numerical simulation results are given to verify the feasibility of our approach.

关键词： p-moment stability impulsive white-noise stochastic differential equations

Seizures dynamics in a neural field model of cortical-thalamic circuitry

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Science China(Technological sciences) 2017年第7期60卷 974-984页

作者： ZHANG HongHui ZHENG YanHong SU JianZhong XIAO PengCheng School of Natural and applied Science Northwestern Polytechnical University College of Mathematics and Computer Science Fujian Normal University Department of Mathematics the University of Texas at Arlington Department of Mathematics University of Evansville

The focus of this study is to explore the mechanisms during seizure behavior using a physiologically motivated by corticothalamic circuity. The model is based on the assumption that, the inhibitory projects from thalamus reticular nucleus(TRN) to specific relay nuclei(SRN) are mediated by GABAA and GABAB receptors which react different time scales in synaptic ***, we include the effects of slow modulation on the threshold current of TRN population that were found to generate bursting behavior. Our model can reproduce healthy and pathological dynamics including wake, spindle, deep sleep, and also seizure states. In addition, contour maps are used to explore the transition of different activity states. It is worthy to point out seizure duration is significantly affected by a time-varying delay as illustrated in our numerical simulation. Finally, a reduced model ignoring the cerebral cortex mass can also capture the feature of spike wave discharge as generated in the full network.

关键词： seizure spike wave neural field modeling corticothalamic

Visualizing diffusion tensor fields on streamsurfaces with merging ellipsoids

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applied Mathematics(A Journal of Chinese Universities) 2014年第4期29卷 399-409页

作者： SONG Wei-jie CHEN Wei CHEN Hai-dong ZHENG Hong-chan CUI Jun-zhi School of Science Northwestern Polytechnical University State Key Lab of CADCG Zhejiang University Academy of Mathematics and System sciences Chinese Academy of Sciences

Streamsurfaces in diffusion tensor fields are used to represent structures with pri- marily planar diffusion. So far, however, no effort has been made on the visualization of the anisotropy of diffusion on them, although this information is very important to identify the problematic regions of these structures. We propose two methods to display this anisotropy information. The first one employs a set of merging ellipsoids, which simultaneously character- ize the local tensor details - anisotropy - on them and portray the shape of the streamsurfaces. The weight between the streamsurfaces continuity and the discrete local tensors can be inter- actively adjusted by changing some given parameters. The second one generates a dense LIC （line integral convolution） texture of the two tangent eigenvector fields along the streamsurfaces firstly, and then blends in some color mapping indicating the anisotropy information. For high speed and high quality of texture images, we confine both the generation and the advection of the LIC texture in the image space. Merging ellipsoids method reveals the entire anisotropy information at discrete points by exploiting the geometric attribute of ellipsoids, and thus suits for local and detailed examination of the anisotropy; the texture-based method gives a global representation of the anisotropy on the whole streamsurfaces with texture and color attributes. To reveal the anisotropy information more efficiently, we integrate the two methods and use them at two different levels of details.

关键词： visualization anisotropy diffusion tensor field streamsurface merging ellipsoid LIC.

Global convergence of quasi-Newton methods for unconstrained optimization

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Chinese Science Bulletin 1996年第7期41卷 529-533页

作者：韩立兴刘光辉 Department of Mathematics and Institute of applied Mathematics Tianjin University Tianjin 300072 China. Department of Industrial Engineering and Management sciences Northwestern University Evanston IL 60208USA.

The convergence of quasi-Newton methods for unconstrained optimization has at-tracted much attention. Powell proved a global convergence result for the BFGS algorithmusing inexact linesearch which satisfies the Wolfe conditions. Byrd, Nocedal and Yuanextended this result to the convex Broyden class of quasi-Newton methods except the DFPmethod. However, the global convergence of the DFP method, the first quasi-Newtonmethod, using the same linesearch strategy, is still an open question (see ref. [2]).

关键词： quasi-Newton methods unconstrained optimization DFP algorithm global convergence.

Latent ancestral graph of structure vector autoregressive models

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Journal of Systems Engineering and Electronics 2010年第2期21卷 233-238页

作者： Wei Gao1,2and Zheng Tian2,3 1.School of Statistics,Xi’an university of Finance&Economics,Xi’an 710061,P.R.China 2.Department of applied Mathematics,northwestern Polytechnical university,Xi’an 710072,P.R.China 3.State Key Laboratory of Remote Sensing Science,Institute of Remote Sensing Applications,Chinese Academy of sciences,Beijing 100101,P.R.China School of Statistics Xi'an University of Finance & Economics Xi'an 710061 P. R. China Department of applied Mathematics Northwestern Polytechnical University Xi'an 710072 P. R. China Department of applied Mathematics Northwestern Polytechnical University Xi'an 710072 P. R. China State Key Laboratory of Remote Sensing Science Institute of Remote Sensing Applications Chinese Academy of Sciences Beijing 100101 P. R. China

A class of latent ancestral graph for modelling the dependence structure of structural vector autoregressive （VAR） model affected by latent variables is proposed. The graphs are mixed graphs with possibly two kind of edges, namely directed and bidirected edges. The vertex set denotes random variables at dif- ferent times. In Gaussian case, the latent ancestral graph leads to a simple parameterization model. A modified iterative conditional fitting algorithm is presented to obtain maximum likelihood esti- mation of the parameters. Furthermore, a log-likelihood criterion is used to select the most appropriate models. Simulations are performed using illustrative examples and results are provided to demonstrate the validity of the methods.

关键词： multivariate time series latent ancestral graph itera- tive conditional fitting.

Rate-dependent tipping-delay phenomenon in a thermoacoustic system with colored noise

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Science China(Technological sciences) 2020年第11期63卷 2315-2327页

作者： ZHANG XiaoYu XU Yong LIU Qi KURTHS Jurgen Department of applied Mathematics Northwestern Polytechnical UniversityXi’an 710072China MIIT Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical UniversityXi’an 710072China Potsdam Institute for Climate Impact Research Potsdam 14412Germany

Tipping is a phenomenon in multistable systems where small changes in inputs cause huge changes in *** the parameter varies within a certain time scale,the rate will affect the tipping *** behaviors are undesirable in thermoacoustic systems,which are widely used in aviation,power generation and other ***,this paper aims at considering the tipping behaviors of the thermoacoustic system with the time-varying parameters and the combined excitations of additive and multiplicative colored *** dynamical behaviors for the proposed thermoacoustic model are implemented through the reduced Fokker-Planck-Kolmogorov equation derived by a standard stochastic averaging ***,the tipping problems of the rate-dependent thermoacoustic systems with random fluctuations are studied by virtue of the obtained probability density *** results show that the rate delays the value of the tipping parameter compared to the one with the quasi-steady assumption,which is called as a rate-dependent tipping-delay ***,the influences of the initial values,the rate,the changing time of the parameters,and the correlation time of the noises on the rate-dependent tipping-delay phenomenon are analyzed in *** results are of great significance for research in related fields such as aviation and land gas turbines.

关键词： thermoacoustic system colored noise rate-dependent tipping-delay phenomenon stochastic averaging method

Recent advances in crystalline and amorphous particulate protein formulations for controlled delivery

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Asian Journal of Pharmaceutical sciences 2016年第4期11卷 469-477页

作者： Sebastian Puhl Lorenz Meinel Oliver Germershaus Institute for Pharmacy and Food Chemistry University of WuerzburgAm Hubland97074 WuerzburgGermany Institute for Pharma Technology University of Applied Sciences Northwestern SwitzerlandGruendenstrasse 404132 MuttenzSwitzerland

The number of particulate delivery systems for biologics is negligible compared to liquid dosage forms, signifying the complications associated with development of solid protein delivery systems. Particulate protein delivery systems can improve stability, reduce viscosity of suspensions at high protein concentration and allow for controlled drug release. This review discusses current advances in controlled delivery of particulate protein formulations. While the focus lies on protein crystals and delivery systems employing protein crystals,amorphous protein particles will also be addressed. Crystallization and precipitations methods and modifications allowing controlled delivery with and without encapsulation are summarized and discussed.

关键词： Protein crystals Protein particles Protein delivery Controlled release

Microstructure evolution of single crystal copper wires in cold drawing

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Science China(Technological sciences) 2007年第6期50卷 736-748页

作者： CHEN Jian1,2, YAN Wen1,2, WANG XueYan2 & FAN XinHui2 1 Department of applied Physics, northwestern Polytechnical university, Xi’an 710072, China 2 School of Material Science and Chemical Engineering, Xi’an Technological university, Xi’an 710032, China Department of applied Physics Northwestern Polytechnical University Xi’an China School of Material Science and Chemical Engineering Xi’an Technological University Xi’an China

The deformation microstructure evolution of single crystal copper wires produced by OCC method has been studied with the help of TEM, EBSD; OM. The results show that there are a small number of dendrites; twins in the undeformed single crystal copper wires. However, it is difficult to observe these dendrites in deformed single crystal copper wires. The structure evolution of deformed single crystal copper wires during drawing process can be divided into three stages. When the true strain is lower than 0.94, macroscopic subdivision of grains is not evident,; the microscopic evolution of deformed structure is that the cells are formed; elongated in drawn direction. When the true strain is between 0.94; 1.96, macroscopic subdivision of grains takes place,; the number of microbands located on {111}; cell blocks is much more than that with the true strain lower than 0.94. When the true strain is larger than 1.96, the macroscopic subdivision of grains becomes more evident than that with the true strain between 0.94; 1.96,; S-bands structure; lamellar boundaries will be formed. From EBSD analysis, it is found that part of 100 texture resulting from solidifying is transformed into 111; 112 due to shear deformation, but 100 texture component is still kept in majority. When the true strain is 0.94, the misorientation angle of dislocation boundaries resulting from deformation is lower than 14°. However, when the true strain arrives at 1.96, the misorientation angle of some boundaries will be greater than 50°,; the peak of misorientation angle distribution produced by texture evolution is located in the range between 25°; 30°.

关键词： single crystal copper wires, deformation structure, electron backscattering diffraction, transmission electron microscopy

TWO FUNDAMENTAL CONVERGENCE THEOREMS FOR NONLINEAR CONJUGATE GRADIENT METHODS AND THEIR APPLICATIONS

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Acta Mathematicae Applicatae Sinica 2001年第1期17卷 38-46页

作者：韩继业刘光辉孙德锋尹红霞 The Academy of Mathematics and Systems sciences Institute of Applied Mathematics Beijing China he Chinese Academy of sciences Institute of Applied Mathematics Beijing China Department of Industrial Engineering and Management sciences Northwestern University Evanston USA School of Mathematics University of New York Wales Sydney Australia Hua Luo-keng Institute for applied Mathematics and Information Science the Chinese Academy of Sciences Beijing China

Two fundamental convergence theorems are given for nonlinear conjugate gradient methods only under the descent condition. As a result, methods related to the Fletcher-Reeves algorithm still converge for parameters in a slightly wider range, in particular, for a parameter in its upper bound. For methods related to the Polak-Ribiere algorithm, it is shown that some negative values of the conjugate parameter do not prevent convergence. If the objective function is convex, some convergence results hold for the Hestenes-Stiefel algorithm.

关键词： Conjugate gradient method descent condition global convergence