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PRELIMINARY GROUP CLASSIFICATION OF EQUATION v_t=f(x, v_x)v_(xx)+g(x, v_x)

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Acta Mathematica Scientia 1997年第3期17卷 255-261页

作者：屈长征 department of mathematics Northwest University Xi'an 710069 China

Using the method of preliminary group classification introduced by Ibragimov et al[***.32,2988(1991)], we give a classification of equations vt= f(x, vx)vxx+g(x, vx) which admitting an extension by one of the principal Lie algebra of the equation. The result of this paper is a table of nonequivalent equations possessing an additional symmetry.

关键词： SYMMETRY CLASSES COEFFICIENT

Thermal decomposition of Pr[（C5H8NS2）3(C12H8N2)]

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Science china Chemistry 2005年第S1期48卷 83-87页

作者： GUO Pengjiang,JIAO Baojuan,CHEN Sanping,HU Rongzu,GAO Shengli & SHI Qizhen department of Chemistry,northwest university Shaanxi Key Laboratory of Physico-lnorganic Chemistry,xi'an 710069,china department of mathematics,northwest university,xi'an 710069,china xi'an Modern Chemistry Research Institute,xi'an 710065,china Shaanxi Key Laboratory of Physico-inorganic Chemistry Department of Chemistry Northwest University Xi'an 710069 China department of mathematics Northwest University Xi'an 710069 China xi'an Modern Chemistry Research Institute Xi'an 710065 China

The thermal behavior of the complex Pr[(C5H8NS2)3(C12H8N2)] in a dry nitrogen flow was examined by TG-DTG analysis. The TG-DTG investigations indicated that Pr[(C5H8NS2)3-(C12H8N2)] was decomposed into Pr2S3 and deposited carbon in one step where Pr2S3 predominated in the final products. The results of non-isothermal kinetic calculations showed that the decomposition stage was the random nucleation and subsequent growth mechanism (n = 2/3), the corresponding apparent activation energy ?was 115.89 kJ·mol-1 and the pre-expo-nential constant ln[A/s] was 7.8697. The empirical kinetics model equation was proposed as/(α) =3/2(1-α)[-ln(1-α)]1/*** X-ray powder diffraction patterns of the thermal decomposition products at 800℃under N2 atmosphere show that the product can be indexed to the cubic Pr2S3 phase. The transmission electron microscopy (TEM) of the final product reveals the particle appearance of a diameter within 40 nm. The experimental results show that the praseodymium sulfide nanocrystal can be prepared from thermal decomposition of Pr[(C5H8NS2)3(C12H8N2)].

关键词： Pr[(C5H8NS2)3(C12H8N2)] thermal analysis kinetics noncrystal characteristics

Classification and Functional Separable Solutions to Extended Nonlinear Wave Equations

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Communications in Theoretical Physics 2005年第10期44卷 589-596页

作者： ZHANG Shun--Li LOU Sen--Yue QU Chang--Zheng YUE Rui--Hong Institute of Modern Physics, northwest university, xi'an 710069, china department of mathematics, northwest university, xi'an 710069, china Center of Nonlinear Science, Ningbo university, Ningbo 315211, china department of Physics, Shanghai Jiao Tong university, Shanghai 200030, china Institute of Modern Physics Northwest University Xi'an 710069 China department of mathematics Northwest University Xi'an 710069 China Center of Nonlinear Science Ningbo University Ningbo 315211 China department of Physics Shanghai Jiao Tong University Shanghai 200030 China

The generalized conditional Symmetry approach is applied to study the variable separation of the extendedwave equations. Complete classification of those equations admitting functional separable solutions is obtained ... 详细信息

关键词： nonlinear wave equations functional separable solutions generalized conditional symmetry

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L1/2 regularization

Science china(Information Sciences) 2010年第6期53卷 1159-1169页

作者： XU ZongBen 1 , ZHANG Hai 1,2 , WANG Yao 1 , CHANG xiangYu 1 & LIANG Yong 3 1 Institute of Information and System Science, xi'an Jiaotong university, xi'an 710049, china 2 department of mathematics, northwest university, xi'an 710069, china 3 university of Science and Technology, Macau 999078, china Institute of Information and System Science Xi’an Jiaotong University Xi’an China department of mathematics Northwest University Xi’an China university of Science and Technology Macau China

In this paper we propose an L1 /2 regularizer which has a nonconvex *** L 1/2 regularizer is shown to have many promising properties such as unbiasedness, sparsity and oracle properties.A reweighed iterative algorithm is proposed so that the solution of the L 1/2 regularizer can be solved through transforming it into the solution of a series of L 1 *** solution of the L 1/2 regularizer is more sparse than that of the L 1 regularizer, while solving the L 1/2 regularizer is much simpler than solving the L 0 *** experiments show that the L 1/2 regularizer is very useful and efficient, and can be taken as a representative of the Lp(0 < p < 1) regularizer.

关键词： machine learning variable selection regularizer compressed sensing

The essential ability of sparse reconstruction of different compressive sensing strategies

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Science china(Information Sciences) 2012年第11期55卷 2582-2589页

作者： ZHANG Hai1,2,LIANG Yong3,GOU HaiLiang1 & XU ZongBen1 1 Institute for Information and System Science,xi'an Jiaotong university,xi'an 710049,china 2department of mathematics,northwest university,xi'an 710069,china 3university of Science and Technology,Macau 999078,china Institute for Information and System Science Xi’an Jiaotong University Xi’an China department of mathematics Northwest University Xi’an China university of Science and Technology Macau China

We show the essential ability of sparse signal reconstruction of different compressive sensing strategies,which include the L1 regularization,the L0 regularization(thresholding iteration algorithm and OMP algorithm),the Lq(0 < q ≤ 1) regularizations,the Log regularization and the SCAD *** phase diagram as the basic tool for analysis,we find that(i) the solutions of the L0 regularization using hard thresholding algorithm and OMP algorithm are similar to those of the L1 regularization;(ii) the Lq regularization with the decreasing value of q,the Log regularization and the SCAD regularization can attain sparser solutions than the L1 regularization;(iii) the L1/2 regularization can be taken as a representative of the Lq(0 < q < 1) *** 1/2 < q < 1,the L1/2 regularization always yields the sparsest solutions and when 0 < q < 1/2 the performance of the regularizations takes no significant *** results of this paper provide experimental evidence for our previous work.

关键词： compressive sensing regularization sparsity L1/2 regularization

Thermal decomposition of Pr[(C_(5)H_(8)NS_(2))_(3)(C_(12)H_(8)N_(2))]

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Science china Chemistry 2005年第Z1期48卷 83-87页

关键词： Pr[(C5H8NS2)3(C12H8N2)], thermal analysis, kinetics, noncrystal, characteristics.

A New Method Based on the Non-isothermal Kinetic Equation to Estimate the Critical Temperature of Thermal Explosion for Energetic Materials Using Non-isothermal DSC

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Journal of Shanghai Jiaotong university(Science) 2011年第2期16卷 247-251页

作者：张海胡俊英胡荣祖赵凤起高红旭 department of mathematics Northwest University Institute of System and Information Science Xi'an Jiaotong University xi'an Modern Chemistry Research Institute

A method for estimating the critical temperature of thermal explosion for energetic materials using differential scanning calorimetry (DSC) measurement is derived from the Semenov's thermal explosion theory and the non-isothermal kinetic equation based on Harcourt-Esson's kinetic *** result obtained from this method coincides completely with that of the Hu-Yang-Liang-Wu method.

关键词： critical temperature thermal explosion differential scanning calorimetry (DSC) non-isothermal

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苏云金芽孢杆菌发酵实验参数的分析

生物数学学报 2002年第4期17卷 471-475页

作者：窦霁虹李博海孙珺西北大学数学系陕西西安710069 西北大学化工系陕西西安710069

采用最小二乘法对苏云金芽孢杆菌发酵实验测试数据进行回归分析,得到了还原糖含量、PH值及溶氧值随时间的变化规律,并对其进行误差分析.为苏云金芽孢杆菌发酵实验过程的参数设计和控制提供了可靠的理论依据.

关键词：苏云金芽孢杆菌发酵实验参数回归分析复相关系数决定性指标

An Efficient Algorithm for the Calculation of NURBS Curves and All Their Derivatives

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Computer Aided Drafting,Design and Manufacturing 1998年第2期8卷 22-28页

作者： Zhang xiaopeng Wu Enhua (Computer Science Lab, Institute of Software, The Chinese Academia Sinica, Beijing 100080)Kang Baosheng (department of mathematics, northwest university, xi’an 710069, china)

Through a precise recursion of B-spline bases, this paper presents an efficient algorithm for the calculation of NURBS curves and all their derivatives. The algorithm requires less storage and is proved to be stable.

关键词： NURBS B-spline de Boor algorithm