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More on Bounding Introspection in Modal Nonmonotonic Logics

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Acta Mathematica Sinica,English Series 2000年第4期16卷 555-564页

作者： Xishun Zhao Decheng Ding department of Mathematics. nanjing university. {2. 210093. P. R. china department of Mathematics Nanjing University Nanjing 210093 P. R. China

By L. we denote the set of all propositional fornmlas. Let C be the set of all clauses. Define C_n=C(Lη:η∈C}.In Sec. 2.of this paper. we prove that for normal modal logics S, the notions of (S. C_)-expansions and S-expansions coincide. In Sec. 3. we prove that if I consists of default clauses then the notions of S-expansions for I and (S.C)-expansions for I coincide. To this end. we first show. in Sec *** the notion of S-expansions for I is the same as that of (S.L)-expansions for I.

关键词： Modal nonmonotonic logic Expansion Bounding Introspection Default clause

Formation flying in elliptic orbits with the J_2.perturbation

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Research in Astronomy and Astrophysics 2012年第11期12卷 1563-1575页

作者： Xi-Yun Hou, Yu-Hui Zhao and Lin Liu School of Astronomy and Space Science, nanjing university, nanjing 210093. china Institute of Space Environment and Astrodynamics, nanjing university, nanjing 210093. china School of Astronomy and Space Science Nanjing University Institute of Space Environment and Astrodynamics Nanjing University

Relative dynamics between the chief satellite and the deputy ones in for- marion flying is crucial to maintaining the formation. A good choice of the forma- tion usually requires a lower control frequency or less control energy. For formation flying missions in highly elliptic orbits, the well-known C-W equation is not accu- rate enough. Instead, Lawden＇s equation is often used. First, the solution to Lawden＇s equation with a very simple form is deduced. Then the J2.perturbation is added. It is found that Lawden＇s solution is not necessarily valid when the J2.perturbation is con- sidered. Completely discarding Lawden＇s solution and borrowing the idea of mean orbit elements, two rules to initialize the formation are proposed. The deviation speed is greatly reduced. Different from previous studies on the J2.perturbation, except for the relatively simple expression for the semi-major axis, the tedious formulae of the long period terms and the short period terms of other orbital elements are not used. In addition, the deviation speed is further reduced by compensation of the nonlinear effects. Finally, a loose control strategy of the formation is proposed. To test the ro- bustness of this strategy, a third body perturbation is added in numerical simulations.

关键词： celestial mechanics

HIGH RESOLUTION SCB SCHEME FOR HYPERBOLIC SYSTEMS OF 2.D CONSERVATION LAWS

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Journal of Computational Mathematics 1998年第2期16卷 179-192页

作者： Ning Zhao (department of Aerodynamics, nanjing university of Aeronautics and Astronautics, {2. 2.0016, china) 南京航空航天大学空气动力学系江苏南京

In this paper, a new class of high resolution schemes satisfying the 'condition A' (SCA) and the 'condition B' (SCB) for hyperbolic systems of conservation laws in one and two dimensions are constructed. Moreover, the results of the numerical experiments by using these schemes are given for the system of Euler equations in one and two dimensions.

关键词： SCB scheme hyperbolic system conservation law

GLOBAL CONVERGENCE AND IMPLEMENTATION OF NGTN METHOD FOR SOLVING LARGE-SCALE SMARSE NONLINEAR PROGRAMMING PROBLEMS

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Journal of Computational Mathematics 2001年第4期19卷 337-346页

作者： Qin Ni (department of Mathematics, nanjing university of Aeronautics and Astronautics, {2. 2.0016, china) 南京航空航天大学江苏南京 210016

An NGTN method was proposed for solving large-scale sparse nonlinear programming (NLP) problems. This is a hybrid method of a truncated Newton direction and a modified negative gradient direction, which is suitable for handling sparse data structure and pos sesses Q-quadratic convergence rate. The global convergence of this new method is proved, the convergence rate is further analysed, and the detailed implementation is discussed in this paper. Some numerical tests for solving truss optimization and large sparse problems are reported. The theoretical and numerical results show that the new method is efficient for solving large-scale sparse NLP problems.

关键词： Nonlinear programming Large-scale problem Sparse.

Dimension and measure theoretic entropy of a subshift in symbolic space

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Chinese Science Bulletin 1997年第14期42卷 1193-1196页

作者： CHEN Ercai and XIONG Jincheng1. department of Astronomy, nanjing university, Nangjing {2. china 2. department of Mathematics, South china Normal university, Guangzhou 510631, china department of Astronomy Nanjing University Nangjing China department of Mathematics South China Normal University Guangzhou China

1 Definitions and resultsWITH the development of the theory of dynamical systems and fractal geometry, one provedthat symbolic dynamics is a powerful tool to study chaos and fractals. It is useful to study thefractal characteristics of symbolic dynamics. In the present note we shall point out the relationbetween the dimension and measure theoretic entropy of any subshift in symbolic space. Weprove here that the Bowen’s formula for Hausdorff dimension holds without Markov struc-ture. A variational principle for dimension is obtained.

关键词： symbolic space subshift measure theoretic entropy dimension.

Study on the Relationship between Lamellar Spacing and Growth Rate inthe Regular Eutectic Growthby Monte-Carlo Simulation

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Journal of Materials Science & Technology 2002年第4期18卷 322-324页

作者： Weimin WANG, Junming LIU and Zhiguo LIULaboratory of Solid State Microstructures, nanjing university, nanjing 210093. china Lab. of Solid State Microstructures Nanjing Univ. Nanjing 210093 China

A modified Monte-Carlo(MC) method to simulate the regular growth of binary eutectic alloys is presented. It is found that the growth rate has a linear dependence on the chemical potential difference between the solid and liquid; the relation between the lamellar spacing A and growth rate R accords well with the prediction of Jackson-Hunt(JH) theory unless the growth rate is very low.

关键词： Eutectic Monte-Carlo simulation Growth

MEASUREMENT OF NUMBER AVERAGE MOLECULAR WEIGHT OF STYRENE OLIGOMER BY ^(13)C-NMR METHOD

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Chinese Journal of Polymer Science 1999年第2期17卷 135-140页

作者： Song Wang Xiao-hu Yan Rong-shi Cheng department of Polymer Science and Engineering, nanjing university,{2. department of Polymer Science and Engineering Nanjing University Nanjing 210093 China

^(13)C-NMR ~1H-decoupled spectra of styrene polymers were assigned by comparison with modelcompounds, then used in measurements of number average molecular weights. The higher limit of an exactdetermination of the end group signal is less than a molecular weight of 10~4. For polymer samples withM_n<10~3, the results obtained from ^(13)C-NMR spectra of saturated carbon region are in excellent agreementwith the values determined by ~1H-NMR, SEC, and VPO methods, while the results from ^(13)C-NMR spectra ofphenyl C-1 carbon region are somewhat higher than the values determined by other methods.

关键词： Molecular weight measurement Styrene oligomer ^(13)C-NMR spectra

Maschke-type theorem and Morita context over weak Hopf algebras

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Science china Mathematics 2006年第5期49卷 587-598页

作者： ZHANG Liangyun College of Science, nanjing Agricultural university, nanjing 2.0095, china department of Mathematics, nanjing university, nanjing 2.0008, china College of Science Nanjing Agricultural University Nanjing China department of Mathematics Nanjing University Nanjing China

This paper gives a Maschke-type theorem over semisimple weak Hopf algebras,extends the well-known Maschke-type theorem given by Cohen and Fishman and constructs a Morita context over weak Hopf algebras.

关键词： weak Hopf algebra, smash product, Maschke-type theorem, Morita context.

Global dimension and left derived functors of Hom

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Science china Mathematics 2007年第6期50卷 887-898页

作者： Li-xin MAO & Nan-qing DING Institute of Mathematics, nanjing Institute of Technology, nanjing 2.1167, {2. department of Mathematics, nanjing university, nanjing 210093. china Institute of Mathematics Nanjing Institute of Technology Nanjing China department of Mathematics Nanjing University Nanjing China

It is well known that the right global dimension of a ring R is usually computed by the right derived functors of Hom and the left projective resolutions of right R-modules. In this paper, for a left coherent and right perfect ring R, we characterize the right global dimension of R, from another point of view, using the left derived functors of Hom and the right projective resolutions of right R-modules. It is shown that rD(R) ? n (n ? 2. if and only if the gl right Proj-dim M R ? n?2.if and only if Ext n?1(N,M) = 0 for all right R-modules N and M if and only if every (n?2.th Projcosyzygy of a right R-module has a projective envelope with the unique mapping property. It is also proved that rD(R) ? n (n ? 1) if and only if every (n?1)th Proj-cosyzygy of a right R-module has an epic projective envelope if and only if every nth Proj-cosyzygy of a right R-module is projective. As corollaries, the right hereditary rings and the rings R with rD(R) ? 2.are characterized.

关键词： global dimension projective resolution envelope 16E10 16E30 16E05