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A class of mechanically decidable problems beyond Tarski's model

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Science china Mathematics 2007年第11期50卷 1611-1620页

作者： Lu YANG~(1,2) Yong FENG~(1+) Yong YAO~1 1 Laboratory for Automated Reasoning and Programming,Chengdu institute of Computer Applications,Chinese Academy of Sciences,Chengdu 610041,china 2.institute of theoretical computing,east china normal university,shanghai 2.0062.china Laboratory for Automated Reasoning Programming Chengdu Institute of Computer Applications Chinese Academy of Sciences Chengdu 610041 China institute of theoretical computing East China Normal University Shanghai 200062 China

By means of dimension-decreasing method and cell-decomposition,a practical algorithm is proposed to decide the positivity of a certain class of symmetric polynomials,the numbers of whose elements are *** is a class of mechanically decidable problems beyond Tarski *** implement the algorithm,a program nprove written in maple is developed which can decide the positivity of these polynomials rapidly.

关键词： symmetric polynomial inequality cell-decomposition Tarski's sentence Tarski's model mechanically decidable problem

computing rarity on uncertain data

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Science china(Information Sciences) 2011年第10期54卷 2028-2039页

作者： JIN CheQing,ZHOU MinQi & ZHOU AoYing shanghai Key Laboratory of Trustworthy computing,Software Engineering institute,east china normal university,shanghai 2.0062.china 1. shanghai Key Laboratory of Trustworthy computing Software Engineering Institute East China Normal University Shanghai 200062 China

The essence of uncertain data management has been well adopted since data uncertainty widely exists in lots of applications,such as Web,sensor networks,*** of the uncertain data models are based on the possible world *** the number of the possible worlds will blowup exponentially with the growth of the data set,it is much more challenging to handle uncertain data than deterministic *** this paper,we take the first attempt to study the rarity,an important statistic that describes the proportion of items with the same frequency,upon uncertain *** have proposed three novel solutions,including an exact method and an approximate method to compute the rarity of a given frequency respectively,and a method to find the frequency of the maximum *** in theorem and extensive experimental results demonstrate the effectiveness and efficiency of the proposed solutions.

关键词： rarity uncertain data possible world

Density functional theory study on the structural and electronic properties of Ag-adsorbed (MgO)_n clusters

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Science china(Physics,Mechanics & Astronomy) 2009年第5期52卷 734-741页

作者： GE GuiXian1, JING Qun1 & LUO YouHua2,3 1 Key Laboratory of Ecophysics and Department of Physics, normal College, Shihezi university, Shihezi 832003, china 2 School of Science, east china university of Science and Technology, shanghai 200237, china 3 institute for theoretical Physics, Henan university, Kaifeng 475004, china Key Laboratory of Ecophysics and Department of Physics Normal College Shihezi University Shihezi 832003 China School of Science East China University of Science and Technology Shanghai 200237 China institute for theoretical Physics Henan University Kaifeng 475004 China

Equilibrium geometries, charge distributions, stabilities and electronic properties of the Ag-adsorbed (MgO)n (n = 1-8) clusters have been investigated by density functional theory (DFT) with generalized gradient approximation (GGA) for exchange-correlation functional. The results show that hollow site is energetically preferred for n≥4, and the incoming Ag atoms tend to cluster on the existing Ag cluster. The Mulliken populations indicate that the interaction between the Ag atom and Magnesia clusters is mainly induced by a weak atomic polarization. The adsorbed Ag atom only causes charge redistributions of the atoms near itself. The effect of the adsorbed Ag atom on the bonding natures and structural features of Magnesia clusters is minor. Furthermore, the investigations on the first energy difference, fragmentation energies and electron affinities show that the Ag(MgO)4 and Ag(MgO)6 are the most stable among studied clusters.

关键词： Ag (MgO)_n clusters geometries electronic properties

ON NON-ISOTROPIC JACOBI PSEUDOSPECTRAL METHOD

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Journal of Computational Mathematics 2008年第4期26卷 511-535页

作者： Benyu Guo Keji Zhang Department of Mathematics,shanghai normal university,shanghai 200234,china Scientific computing Key Laboratory of shanghai Universities Division of Computational Science of E-institute of shanghai Universities Department of Mathematics Shanghai Normal University Shanghai 200234

In this paper, a non-isotropic Jacobi pseudospectral method is proposed and its appli- cations are considered. Some results on the multi-dimensional Jacobi-Gauss type interpolation and the related Bernstein-Jackson type inequalities are established, which play an important role in pseudospectral method. The pseudospectral method is applied to a twodimensional singular problem and a problem on axisymmetric domain. The convergence of proposed schemes is established. Numerical results demonstrate the efficiency of the proposed method.

关键词： Jacobi pseudospectral method in multiple dimensions Jacobi-Gauss type inter-polation Bernstein-Jackson type inequalities Singular problem Problem on axisymmetricdomain.

A computational investigation of boron-doped chromium and chromium clusters by density functional theory

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Science china(Physics,Mechanics & Astronomy) 2010年第5期53卷 812-817页

作者： GE GuiXian1,JING Qun1 & LUO YouHua2,3 1 Key Laboratory of Ecophysics and Department of Physics,normal College,Shihezi university,Xinjiang 832003,china 2 School of Science,east china university of Science and Technology,shanghai 200237,china 3 institute of theoretical Physics,School of Physics and Information Optoelectronics,Henan university,Kaifeng 475004,china 1. Key Laboratory of Ecophysics and Department of Physics Normal College Shihezi University Xinjiang 832003 China2. School of Science East China University of Science and Technology Shanghai 200237 China3. Institute of Theoretical Physics School of Physics and Information Optoelectronics Henan University Kaifeng 475004 China

The geometries,stabilities and electronic properties of Crn and CrnB(n=2-9) clusters have been systematically investigated by density functional *** results suggest that the lowest energy structures for CrnB clusters can be obtained by substituting one Cr atom in Crn+1 clusters with B *** geometries of CrnB clusters are similar to that of Crn+1 clusters except for local structural *** second-order difference and fragmentation energy show Cr4,Cr6,Cr8,Cr3B,Cr5B and Cr8B cluster are the most stable among these studied *** impurity B increases the stabilities of chromium *** B is doped on the Crn clusters,cluster geometry does dominate positive role in enhancing their *** doped B atom does not change the coupling way of the Cr site in Crn clusters,but breaks the symmetry and the Cr atoms are no longer *** doped B atom increases the total magnetic moments of Crn in most cases.

关键词： Crn and CrnB clusters geometries electronic properties

The stochastic semantics and verification for periodic control systems

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Science china(Information Sciences) 2012年第12期55卷 2675-2693页

作者： YANG MengFei 3,WANG Zheng 1,2,PU GeGuang 1,Qin ShengChao 4,GU Bin 2 & HE JiFeng 1 1 shanghai Key Laboratory of Trustworthy computing,east china normal university,shanghai 2.0062.china 2 Beijing institute of Control Engineering,Beijing 100190,china 3 china Academy of Space Technology,Beijing 100049,china 4 university of Teesside,TS1 3BA,UK 3. china Academy of Space Technology Beijing 100049 China1. Shanghai Key Laboratory of Trustworthy Computing East China Normal University Shanghai 200062 China2. Beijing Institute of Control Engineering Beijing 100190 China4. University of Teesside TS13BA Teesside UK

Periodic control systems(PCS) are widely used in the embedded industry like aerospace and *** systems usually run periodic tasks and respond to the external *** on our previous work on Mode diagram modeling(MDM) notations for specifying the periodic control system,we present the stochastic semantics for MDM in this *** stochastic semantics of MDM is based on the Markov *** semantics proposed here provides the basis for the satisfaction of formulae of the interval temporal logic(ITL) based specification language that is aimed to specify the properties of *** verify whether the system satisfies the ITL-based properties,we apply the statistical model checking technique to efficiently estimate the probability of the system satisfying the given property with a desired level of *** empirical experiments show that our approach is both effective and efficient.

关键词： periodic control system stochastic semantics statistical model checking

Virtual multi-dimensional internal bonds model and its application in simulation of rock mass

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Science china(Technological Sciences) 2008年第2期51卷 192-201页

作者： ZHANG ZhenNan1,2 & GE XiuRun3,4 1 Department of Civil Engineering,shanghai university,shanghai 200072,china 2 shanghai institute of Applied Mathematics and Mechanics,shanghai university,shanghai 200072, china 3 institute of Geotechnical Engineering,shanghai Jiao Tong university,shanghai 200030,china 4 institute of Rock and Soil Mechanics,Chinese Academy of Sciences,Wuhan 430071,china 1. Department of Civil Engineering Shanghai University Shanghai 200072 China 2. shanghai institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 China 3. institute of Geotechnical Engineering Shanghai Jiao Tong University Shanghai 200030 China 4. institute of Rock and Soil Mechanics Chinese Academy of Sciences Wuhan 430071 China

VMIB (virtual multi-dimensional internal bonds) is a multiscale mechanical model developed from the VIB (virtual internal bond) theory. In VIB theory,the solid mate-rial is considered to consist of random-distributed material particles in microscale. These particles are connected with normal bonds. The macro constitutive relation is derived from the cohesive law between particles. However,in VMIB,the micro particles are connected with both normal and shear bonds. The macro constitutive relation is derived in terms of bond stiffness coefficients. It has been theoretically certified that there exists a corresponding relationship between the two bond stiffness coefficients and the two macro material constants,i.e. the Young’s modulus and Poisson ratio. This corresponding relationship suggests that it should be necessary and sufficient to simultaneously account for the normal and shear interactions between particles. Due to the fact that the fracture criterion is directly incorporated into the constitutive relation,both VIB and VMIB present many advantages in simulating fractures of materials. In the damage model of rock mass,a damage tensor is usually defined to describe the distribution of cracks. The damage value in one direction determines the relative stiffness of rock mass in this direction. In VMIB solid,the relative distribution density of micro bonds in one direction determines the relative macro stiffness of the material in this direction. The effects of the damage value and the relative distribution density of bonds are consistent. To simulate the failure behavior of rock mass with VMIB,the presented paper sets up a quantitative relationship between the damage tensor and the rela-tive distribution density of bonds. Comparison of the theoretical and the experi-mental results shows that VMIB model can represent the effect of distributed cracks on rock mass with this relationship. The presented work provides a founda-tion for further simulating fracture behavior

关键词： VMIB (virtual multi-dimensional internal bonds) rock mass VIB (virtual internal bonds) multi-cracked body numerical simulation

Mechanical decision for a class of integral inequalities

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Science china(Information Sciences) 2010年第9期53卷 1800-1815页

作者： YANG Lu1,3,YU WenSheng1,2* & YUAN RuYi2 1shanghai Key Laboratory of Trustworthy computing,Software Engineering institute,east china normal university,shanghai 2.0062.china 2The Key Laboratory of Complex Systems and Intelligence Science,institute of Automation,Chinese Academy of Sciences,Beijing 100190,china 3Laboratory for Automated Reasoning and Programming,Chengdu institute of Computer Applications,Chinese Academy of Sciences,Chengdu 610041,china 1. shanghai Key Laboratory of Trustworthy computing Software Engineering Institute East China Normal University Shanghai 200062 China3. Laboratory for Automated Reasoning and Programming Chengdu Institute of Computer Applications Chinese Academy of Sciences Chengdu 610041 China2. The Key Laboratory of Complex Systems and Intelligence Science Institute of Automation Chinese Academy of Sciences Beijing 100190 China

A class of integral inequalities is transformed into homogeneous symmetric polynomial inequalities beyond Tarski model,where the number of elements of the polynomial,say n,is also a variable and the coefficients are functions of *** is closely associated with some open problems formulated recently by Yang et *** Timofte's dimension-decreasing method for symmetric polynomial inequalities,combined with the inequality-proving package BOTTEMA and a program of implementing the method known as successive difference substitution,we provide a procedure for deciding the nonnegativity of the corresponding polynomial inequality such that the original integral inequality is mechanically decidable;otherwise,a counterexample will be *** effectiveness of the algorithm is illustrated by some more examples.

关键词： integral inequality symmetric polynomial inequality Timofte’s dimension-decreasing method successive difference substitution mechanical decision inequality-proving package BOTTEMA

Finite Symmetry Transformation Groups and Some Exact Solutions to(2+1)-Dimensional Cubic Nonlinear Schrdinger Equantion

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Communications in theoretical Physics 2009年第5期51卷 773-776页

作者： LI Biao~(1,3,+) LI Yu-Qi~(1,3) CHEN Yong~(1,2)1 Nonlinear Science Center,Ningbo university,Ningbo 315211,china2.institute of theoretical computing,east china normal university,shanghai 2.0062.china3 Key Laboratory of Mathematics Mechanization,Chinese Academy of Sciences,Beijing 100080,china Nonlinear Science Center Ningbo University Ningbo 315211 China institute of theoretical computing East China Normal University Shanghai 200062 China Key Laboratory of Mathematics Mechanization Chinese Academy of Sciences Beijing 100080 China

Making use of the direct method proposed by Lou et al. and symbolic computation, finite symmetry trans-formation groups for a (2+1)-dimensional cubic nonlinear Schrdinger (NLS) equation and its corresponding cylindricalNLS equations are presented. Nine related linear independent infinitesimal generators can be obtained from the finitesymmetry transformation groups by restricting the arbitrary constants in infinitesimal forms. Some exact solutions arederived from a simple travelling wave solution.

关键词： symmetry groups cubic NLS equation exact solution