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| 1 | Finite element method based on combination of 'saddle point' variational formulations显示文摘A modified mixed/hybrid finite element method, which is no longer required to satisfy the Babuska-Brezzi condition, is referred to as a stabilized method Based on the duality of vanational principles in solid mechanics, a new type of stabilized method, called the combinatorially stabilized mixed/hybrid finite element method, is presented by weight-averaging both the primal and the dual 'saddle-point' schemes. Through a general analysis of stability and convergence under an abstract framework, it is shown that for the methods only an inf-sup inequality much weaker than Babuska-Brezzi condition needs to be satisfied. As a concrete application, it is concluded that the combinatorially stabilized Raviart and Thomas mixed methods permit the C -elements to replace the H(div; Ω)-elements. | 周天孝 | 1997 | Science China(Technological Sciences)1997，40，3： | 16 |
| 2 | Boundary value problems of discrete generalized Emden-Fowler equation显示文摘By using the critical point theory, some sufficient conditions for the existence of the solutions to the boundary value problems of a discrete generalized Emden-Fowler equation are obtained. In a special case, a sharp condition is obtained for the existence of the boundary value problems of the above equation. For a linear case, by the discrete variational theory, a necessary and sufficient condition for the existence, uniqueness and multiplicity of the solutions is also established. | YU Jianshe GUO Zhiming | 2006 | Science China Mathematics2006，49，10： | 14 |
| 3 | THE MORSE INDEX OF A SADDLE POINT显示文摘This paper is devoted to clarifying the relationship between the classical Morse theory andthe Mountain Pass Lemma via the local linking concept.It is shown that for a C^1-function f with alocal linking,the m-thcritical group is nontrivial,where m is the Morse index.Combined with thebehavior of f at infinity,this result can be used to offer the existence of nontrivial critical points. | 刘嘉荃 | 1989 | Systems Science and Mathematical Sciences1989，2，1： | 7 |
| 4 | Analysis of the fusion hindrance in mass-symmetric heavy ion reactions显示文摘The fusion hindrance,which is also denominated by the term extra-push,is studied on mass-symmetric systems by the use of the liquid drop model with the two-center parameterization.Following the idea that the fusion hindrance exists only if the liquid drop barrier(saddle point) is located at the inner side of the contact point after overcoming the outer Coulomb barrier,the reactions in which two barriers are overlapped with each other are determined.It is shown that there are many systems where the fusion hindrance does not exist for the atomic number of projectile or target nucleus Z 43,while for Z> 43,all of the mass-symmetric reactions are fusion-hindered. | ABE Yasuhisa BOILLEY David | 2009 | Science China(Physics,Mechanics & Astronomy)2009，52，10： | 5 |
| 5 | Periodic Solutions for Second Order Systems at Resonance | Tang Chunlei, Department of Mathematics, Southwest Normal University, Chongqing 400715, China | 1998 | Acta Mathematica Sinica,English Series1998，14，4： | 4 |
| 6 | Dynamic modeling and parameter identification of a gun saddle ring显示文摘In this study,a theoretical nonlinear dynamic model was established for a saddle ring based on a dynamic force analysis of the launching process and the structure according to contact-impact theory.The ADAMS software was used to build a parameterized dynamic model of the saddle ring.A parameter identification method for the ring was proposed based on the particle swarm optimization algorithm.A loading test was designed and performed several times at different elevation angles.The response histories of the saddle ring with different loads were then obtained.The parameters of the saddle ring dynamic model were identified from statistics generated at a 500 elevation angle to verify the feasibility and accuracy of the proposed method.The actual loading history of the ring at a 70°elevation angle was taken as the model input.The response histories of the ring under these working conditions were obtained through a simulation.The simulation results agreed with the actual response.Thus,the effectiveness and applicability of the proposed dynamic model were verified,and it provides an effective method for modeling saddle rings. | Tong Lin Lin-fang Qian Qiang Yin Shi-yu Chen Tai-su Liu | 2020 | Defence Technology(防务技术)2020，16，2： | 3 |
| 7 | THE THEORETICAL STUDIES OF PRODUCT ALIGNMENT OF THE REACTIONS OF Na,F WITH CH_3I显示文摘The NaI and IF product rotational alignment of the reactionsof Na,F+CH3I has been theoretically studied in a LEPS PES.Theproduct alignment versus the relative translational energy of the reactantshas been obtained. | Ke Li HAN Guo Zhong HE Nan Quan LOU State Key Laboratory of Molecular Reaction Dynamics,Dalian Institute of Chemical Physics,CAS,Dalian 116012,China | 1993 | Chinese Chemical Letters1993，4，6： | 3 |
| 8 | Coherence-Resonance-Induced Neuronal Firing near a Saddle-Node and Homoclinic Bifurcation Corresponding to Type-I Excitability显示文摘Excitability is an essential characteristic of excitable media such as nervous and cardiac systems.Different types of neuronal excitability are related to different bifurcation structures.We simulate the coherence resonance effect near a saddle-node and homoclinic bifurcation corresponding to type-I excitability in a theoretical neuron model,and recognize the obvious features of the corresponding firing pattern.Similar firing patterns are discovered in rat hippocampal CA1 pyramidal neurons.The results are not only helpful for understanding the dynamics of the saddle-node bifurcation and type-I excitability in a realistic nervous system,but also provide a practical indicator to identify types of excitability and bifurcation. | 贾冰 古华光 李玉叶 | 2011 | Chinese Physics Letters2011，28，9： | 3 |
| 9 | A LIMIT CYCLE OF THE SYSTEM WITH NONLINEAR DAMPING AND SOFT SPRING AND AN APPLICATION TO MECHANICAL VIBRATIONS显示文摘where 0<λ<1, μ>1>γ,β>0. The system (1.1) is an actual model in many fields of engineering. For β= 0, 1 + λ + μ<2, a qualitative analysis has been considered. One concrete example of (1.1) has been discussed by an isocline method. With regard to (1.1) for a=0 or b=0 there are problems of limit | 李继彬 | 1983 | Chinese Science Bulletin1983，28，4： | 2 |
| 10 | Existence of periodic solutions for second-order Hamiltonian systems with asymptotically linear conditions显示文摘We consider a class of asymptotically linear nonautonomous second- order Hamiltonian systems.Using the Saddle Point Theorem,we obtain the existence result,which extends some previously known results. | Xingfan CHEN Fei GUO Peng LIU | 2018 | Frontiers of Mathematics in China2018，13，6： | 2 |
| 11 | 集值B-H-S变分不等式及其应用显示文摘本文在Danach空间中,研究了集值B-H-S变分不等式问题和相补问题.将有限维空间、单值映象的若干结果改进并推广到无穷维空间.利用本文获得的结果.我们解决了无穷维空间中的鞍点问题和两类规划问题. | 张从军 | 1995 | 大学数学1995，16，4： | 2 |
| 12 | AN APPLICATION OF TOPOLOGICAL ANALYSIS TO STUDYING THE THREE-DIMENSIONAL FLOW IN CASCADES;PART I—TOPOLOGICAL RULES FOR SKIN-FRICTION LINES AND SECTION STREAMLINES显示文摘Based on the working of Lighthill and Hunt et al.,in the present paper the author hasestablished the topological rules adapting to analysing the skin-friction lines and the sectionstreamlines in cascades.These rules are(1)for a rotor cascade without shroud band,thetotal number of nodal points equals that the saddle points on the skin-friction line vectorfields in eachpitch range;(2)for an annular or straight cascade with no-clearances at bladeends,the total number of saddle points is two more than that of nodal points on the skin-friction line fields in a pitch;(3)the total number of saddles in the secondary flow fields oncross-sections in cascade is one less than that of nodes;(4)in the section streamline vectorfields on a meridian surface penetrating a flow passage,and on leading and trailing edgesections,the total number of nodes is equal to that of saddles;(5)on the streamline vectorfields of a blade-to-blade surface,the total number of nodes is one less than that of saddles. | 康顺 | 1990 | Applied Mathematics and Mechanics(English Edition)1990，11，5： | 2 |
| 13 | PROPER EFFICIENCY OF NONCONVEX VECTOR OPTIMIZATION PROBLEMS显示文摘In topological vector spaces, we estalish a Lagrange Multiplier Theorem forproper efficiency of nonconvex vector opti mization problems. The saddle point theoremsfor the scalar-valued Lagrangian fonction are derived. A new duality form is introducedand the duality theorems are established. | RONG Weidong (Department oI Mothematics, Inner Mongolio Uuiversitg, Hohhot O10021, China) | 1998 | Systems Science and Mathematical Sciences1998，11，1： | 2 |
| 14 | ON FIRST-ORDER STRUCTURALLY STABLE SYSTEMS ON 2-MANIFOLDS显示文摘Let (?) be the space of C’ vector fields defined on a 2-dimensional closed differentiable manifold M2 endowed with the C’ topology. Let ∑’ denote the set of all structurally stable vector fields. The complement (?)1=(?)’-∑’, is called the bifurcation set. In order to study (?)1, in [1] Andronov and Leontovitch first introduced Definition 1 below and studied the properties of dynamical systems of | 余澍祥 | 1984 | Chinese Science Bulletin1984，29，1： | 1 |
| 15 | NECESSARY AND SUFFICIENT CONDITIONS OF EXISTENCE AND UNIQUENESS OF LIMIT CYCLES FOR A CLASS OF POLYNOMIAL SYSTEM显示文摘In this paper, we discuss the limit cycles of the systemdx/dt=y·[1+(A(x)]oy/dt=(-x+δy+α1x2+α2xy+α5x2y)[1+B(x)] (1)where A(x)=sum form i=1 to n(aix), B(x)=sum form j=1 to m(βjxj) and 1+B(x)>0. We prove that (1) possesses at most one limit cycle and give out the necessary and sufficient conditions of existence and uniqueness of limit cycles. | 刘德明 | 1991 | Acta Mathematica Scientia1991，11，1： | 1 |
| 16 | ON VECTOR OPTIMIZATION WHEN THE ORDERING CONE HAS AN EMPTY INTERIOR显示文摘1.IntroductionLetXbeavectorspace,Ybeatopologicalvectorspace,Zbealocallyconvexspace,andletthetopologicaldualspacesofYandZbedenotedbyY*andZ*,respectively.LetCbeapointedconvexconeinYandKbeaclosedconvexpointedconeinZ.ThedualconesofCandKaredefinedasrespec... | GONG Xun hua (Department of Mathematics, Nanchang University, Nanchang 330047, China) | 2000 | Systems Science and Mathematical Sciences2000，13，1： | 1 |
| 17 | Lagrangian duality and saddle points for sparse linear programming显示文摘The sparse linear programming(SLP) is a linear programming problem equipped with a sparsity constraint, which is nonconvex, discontinuous and generally NP-hard due to the combinatorial property involved.In this paper, by rewriting the sparsity constraint into a disjunctive form, we present an explicit formula of the Lagrangian dual problem for the SLP, in terms of an unconstrained piecewise-linear convex programming problem which admits a strong duality under bi-dual sparsity consistency. Furthermore, we show a saddle point theorem based on the strong duality and analyze two classes of stationary points for the saddle point problem. At last,we extend these results to SLP with the lower bound zero replaced by a certain negative constant. | Chen Zhao Ziyan Luo Weiyue Li Houduo Qi Naihua Xiu | 2019 | Science China Mathematics2019，62，10： | 1 |
| 18 | An Effective Numerical Procedure to Determine Saddle-Type Unstable Invariant Limit Sets in Nonlinear Systems显示文摘A new technique that can efficiently approximate the attracting set of a nonlinear dynamical system is proposed under the framework of point mapping with the cell reference method.With the aid of the approximated attracting set,the difficulties encountered by the PIM-triple method and bisection procedure in finding trajectories on the stable manifolds of chaotic saddles in basins of attraction and on basin boundaries can be overcome well.On the basis of this development,an effective method to determine saddle-type invariant limit sets of nonlinear dynamical systems can be devised.Examples are presented for the purposes of illustration and to demonstrate the capabilities of the proposed method. | 江俊 | 2012 | Chinese Physics Letters2012，29，5： | 1 |
| 19 | GLOBAL BIFURCATIONS IN A DISTURBED HAMILTONIAN VECTOR FIELD APPROACHING A 3:1 RESONANT POINCAR MAP (Ⅰ)显示文摘In this paper, we use a qualitative method to study global and local bifurcations in a disturbedHamiltonian vector field approaching a Poincare map in the 3:1 resonant case. We give explicitcalculation formulas to determine bifurcation parameters and draw various bifurcations and phaseportraits in the phase plane. | 李继彬 万世栋 | 1991 | Acta Mathematicae Applicatae Sinica1991，7，1： | 1 |
| 20 | EXTENSION OF MOUNTAIN PASS LEMMA显示文摘In 1973, A. Ambrosetti and P. H. Rabinowitz proved Mountain Pass Lemma as follows: Lemma 1. Let E be a real Banach space, f: E→R^1 be a C^2 functional. | 戚桂杰 | 1987 | Chinese Science Bulletin1987，32，12： | 1 |
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