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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 Nanjing 210093 China Institute of Space Environment and Astrodynamics Nanjing University Nanjing 210093 China

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

Rank theorems of operators between Banach spaces

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science china Mathematics 2000年第1期43卷 1-5页

作者： MA JipuDepartment of Mathematics, nanjing university, nanjing 210093, china 1. Department of Mathematics Nanjing University 210093 Nanjing China

LetE andF be Banach spaces, andB(E,F) all of bounded linear operators onE intoF. LetT 0 ∈B( E,F) with an outer inverseT 0 # ∈B( F,E). Then a characteristic condition ofS=(I + T0 # (T-T0)-1 T0 # with T∈B(E, F) and ... 详细信息

关键词： rank theorem generalized inverse operator-value map.

A relative local variational principle for topological pressure

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science china Mathematics 2010年第6期53卷 1491-1506页

作者： MA XianFeng1,CHEN ErCai2,3,& ZHANG AiHua2,4 1Department of Mathematics,East china university of science and Technology,Shanghai 200237,china 2School of Mathematics and Computer science,nanjing Normal university,nanjing 210097,china 3.enter of nonlinear science,nanjing university,nanjing 210093.china 4College of Mathematics and Physics,nanjing university of Posts and Telecommunications,nanjing 210046,china 1. Department of Mathematics East China University of Science and Technology Shanghai 200237 China2. School of Mathematics and Computer Science Nanjing Normal University Nanjing 210097 China3. Center of Nonlinear Science Nanjing University Nanjing 210093 China4. College of Mathematics and Physics Nanjing University of Posts and Telecommunications Nanjing 210046 China

We define the relative local topological pressure for any given factor map and open cover,and prove the relative local variational principle of this *** precisely,for a given factor map π:(X,T)→(Y,S) between two topological dynamical systems,an open cover U of X,a continuous,real-valued function f on X and an S-invariant measure ν on Y,we show that the corresponding relative local pressure P(T,f,U,y) satisfies sup μ∈M(X,T){ hμ(T,U|Y)+∫X f(x)dμ(x) :πμ=ν}=∫Y P(T,f,U,y)dν(y),where M(X,T) denotes the family of all T-invariant measures on ***,the supremum can be attained by a T-invariant measure.

关键词： pressure conditional entropy relative local variational principle

QP-FREE,TRUNCATED HYBRID METHODS FOR LARGE-SCALE nonlinear CONSTRAINED OPTIMIZATION

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Journal of Computational Mathematics 1997年第1期15卷 36-54页

作者： Q. Ni(School of science, nanjing university of Aeronautics and Astronautics, nanjing, china) 南京航空航天大学研究生院江苏南京

In this paper, a truncated hybrid method is proposed and developed for solving sparse large-scale nonlinear programming problems. In the hybrid method, a symmetric system of linear equations, instead of the usual quadratic programming subproblems, is solved at iterative process. In order to ensure the global convergence, a method of multiplier is inserted in iterative process. A truncated solution is determined for the system of linear equations and the unconstrained subproblems are solved by the limited memory BFGS algorithm such that the hybrid algorithm is suitable to the large-scale problems. The local convergence of the hybrid algorithm is proved and some numerical tests for medium-sized truss problem are given.

关键词： QP-FREE,TRUNCATED HYBRID METHODS FOR LARGE-SCALE nonlinear CONSTRAINED OPTIMIZATION II

Quasi-periodic solutions with prescribed frequency in a nonlinear Schrdinger equation

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science china Mathematics 2010年第12期53卷 3067-3084页

作者： REN Xiu-Fang Department of Mathematics, nanjing university, nanjing 210093, china 1. Department of Mathematics Nanjing University Nanjing 210093 China

In this paper, one-dimensional (1D) nonlinear Schrdinger equation iut-uxx + Mσ u + f ( | u | 2 )u = 0, t, x ∈ R , subject to periodic boundary conditions is considered, where the nonlinearity f is a real analytic function near u = 0 with f (0) = 0, f (0) = 0, and the Floquet multiplier Mσ is defined as Mσe inx = σne inx , with σn = σ, when n 0, otherwise, σn = 0. It is proved that for each given 0 1, the above equation admits a Whitney smooth family of small-amplitude quasi-periodic solutions with b-dimensional Diophantine frequencies, corresponding to b-dimensional invariant tori of an associated infinite-dimensional Hamiltonian system. Moreover, these b-dimensional Diophantine frequencies are the small dilation of a prescribed Diophantine vector. The proof is based on a partial Birkhoff normal form reduction and an improved KAM method.

关键词： Schrdinger equation Hamiltonian system Birkhoff normal form quasi-periodic solution

nonlinear boundary value problems for discontinuous delayed differential equations

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Applied Mathematics(A Journal of Chinese Universities) 2010年第1期25卷 9-17页

作者： SUN Wu-jun Department of Finance & Insurance, Business School of nanjing university, nanjing 210093, china Department of Finance and Insurance Business School of Nanjing University Nanjing China

In this paper nonlinear boundary value problems for discontinuous delayed differen- tial equations are considered. Some existence and boundedness results of solutions are obtained via the method of upper and lower solutions, which may be discontinuous. Our analysis can be applied to those phenomena from physics and control theory which have been successfully described by delayed differential equations with discontinuous functions, such as electric, pneu- matic, and hydraulic networks. It is also an important step to precede the design of control signals when finite-time or practical stability control are concerned.

关键词： nonlinear boundary value problems upper and lower solutions discontinuous delayed differentialequations Carath^odory conditions existence of solutions.

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, nanjing 210016, 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.

QUASI-LOCAL CONJUGACY THEOREMS IN BANACH SPACES

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Chinese Annals of Mathematics 2005年第4期 64-71页

作者： ZHANG WEIRONG MA JIPU Department of Mathematics, nanjing university, nanjing 210093, china. Department of Mathematics, nanjing university, nanjing 210093, china. Department of Mathematics nanjing university nanjing 210093 china.

Let f : U(x0) (?) E→F be a. C1 map and f’(X0) be the Prechet derivative of /fat X0. In local analysis of nonlinear functional analysis, implicit function theorem, inverse function theorem, local surjectivity theorem, local injectivity theorem, and the local conjugacy theorem are well known. Those theorems are established by using the properties: f’(x0) is double splitting and R(f’(x))∩N(T0+) = nonlinear near X0. However, in infinite dimensional Banach spaces, f’(x0) is not always double splitting (i.e., the generalized inverse of f’(xo) does not always exist), but its bounded outer inverse of f’(x0) always exists. Only using the C1 map f and the outer inverse T0# of f’(x0), the authors obtain two quasi-local conjugacy theorems, which imply the local conjugacy theorem if X0 is a locally fine point of f. Hence the quasi-local conjugacy theorems generalize the local conjugacy theorem in Banach spaces.

关键词： Frediet derivative Quasi-local conjugacy theorems Outer inverse Local conjugacy theorem

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Progress in Natural science:Materials International 2005年第12期15卷 1110-1116页

作者： LIU Gang,LI Xin,JIANG Weimei and LI Min Department of Atmospheric sciences,nanjing university,nanjing 210093.china Beijing Municipal Environmental Protection Bureau,Beijing 100044,china Department of Atmospheric sciences Nanjing University Nanjing 210093 China. Beijing Municipal Environmental Protection Bureau Beijing 100044 China

The S-L (She and Leveque) scaling law,also named the hierarchical similarity theory,has been extensively tested for the turbulence made in the laboratory,but seldom been tested for the turbulence in the atmospheric boundary layer (ABL).In this paper, the S-L scaling law is applied to the turbulence in the ABL observed under unstably stratified conditions and over different types of underlying *** results of analyses show that over this type of homogeneous and flat underlying surface,such as the underlying surface in HUBEX (Huaihe River Basin Energy and Water Cycle Experiment),vertical speed and temperature fields well satisfy the S-L scaling *** the turbulence over the homogeneous but rather rough underlying surface of forest and under unstably stratified conditions in PFRD (Park Falls Ranger District of the Chequamegon National Forest,Wisconsin,USA),the analyses show that the vertical speed and temperature fields sometimes conform sometimes do not conform to the S-L scaling ***,at a time,either both of the vertical speed and temperature fields conform to the S-L scaling law,or both of them do *** speed fields in both of the field experiments do not satisfy the S-L scaling *** new explanation of the above-mentioned phenomena is given.

关键词： atmospheric turbulence Reynolds number S-L scaling law in the atmospheric turbulence boundary layer processes nonlinear dynamics