Cycles in Circuit Graphs of Matroids

Let G be the circuit graph of any connected matroid. We prove that G is edge-pancyclic if it has at least three vertices. This work is supported by the National Natural Science Foundation(60673047) and the Doctoral Program Foundation of Education Ministry (20040422004) of China.     

Linear Maps Preserving Idempotence on Nest Algebras

In this paper, we discuss the rank-l-preserving linear maps on nest algebras of Hilbertspace operators. We obtain several characterizations of such linear maps and apply them to show that a weakly continuous linear hijection on an atomic nest algebra is idempotent preserving if and only if it is a Jordan homomorphism, and in turn, if and only if it is an automorphism or an anti-automorphism.     

Sharp threshold of global existence for the Klein-Gordon equations with critical nonlinearity

In this paper, we present a cross-constrained variational method to study the Cauchy problem of the nonlinear Klein-Gordon equations with critical nonlinearity in two space dimensions. By constructing a type of cross-constrained variational problem and establishing so-called cross-invariant manifolds of the evolution flow, we establish a sharp threshold of global existence and blowup of it. Furthermore, we answer the question： How small are the initial data if the solution exists globally.     

Heteroclinic cycles in lattice dynamical systems

A criterion of spatial chaos occurring in lattice dynamical systems—heteroclinic cycle—is discussed It is proved that if the system has asymptotically stable heteroclinic cycle, then it has asymptotically stable homoclinic point which implies spatial chaos. Project supported by the National Natural Science Foundation of China.     

Tracial Limit of C^＊-algebras

A new limit of C^*-algebras, the tracial limit, is introduced in this paper. We show that a separable simple C^*-algebra A is a tracial limit of C^*-algebras in Z-(k) if and only if A has tracial topological rank no more than k. We present several known results using the notion of tracial limits.     

Growth theorem of convex mappings on bounded convex circular domains

The growth theorem and the 1/2-covering theorem are obtained for the class of normalized biholomorphic convex mappings on bounded convex circular domains, which extend the corresponding results of Sufridge, Thomas, Liu, Gong, Yu, and Wang. The approach is new, which does not appeal to the automorphisms of the domains; and the domains discussed are rather general on which convex mappings can be studied, since the domain may not have a convex mapping if it is not convex. Project supported by the National Natural Science Foundation of China and the State Education Commission Doctoral Foundation.     

Dynamics of the Overdamped Coupled Josephson Junctions with an Interference Term

Employing the monotonicity approach and the theory of orientation preserving circle homeomorphisms, we provide a rigorous analysis on the IV characteristics of the coupled Josephson junctions including an interference term in a specified parameters region. In particular, when the system is driven by a dc-current, we show that there exist either globally stable single-wave-form solutions if and only if the average voltage is nonzero, or equilibria if and only if the average voltage vanishes. Supported by National Natural Science Foundation of China (10771155, 10571131) and Natural Science Foundation of Jiangsu Province (BK 2006046).     

On connected factors inK 1,3-free graphs

A graph is said to beK _1,3-free if it contains noK _1,3 as an induced subgraph. It is shown in this paper that every 2-connectedK _1,3-free graph contains a connected [2,3]-factor. We also obtain that every connectedK _1,3-free graph has a spanning tree with maximum degree at most 3. This research is partially supported by the National Natural Sciences Foundation of China and by the Natural Sciences Foundation of Shandong Province of China.     

On Varieties Generated by Minimal Complex Semigroups

A semigroup is complex if it generates a variety the subvariety lattice of which contains an isomorphic copy of every finite lattice. It is known that a complex semigroup has at least four elements and that up to isomorphism and anti-isomorphism, there are four complex semigroups of order four. Subvarieties of the varieties generated by two of these four minimal complex semigroups have previously been described. To complete the study, we describe subvarieties of the varieties generated by the remaining two semigroups. This research was partially supported by the National Natural Science Foundation of China (No.10571077) and the Natural Science Foundation of Gansu Province (No.3ZS052-A25-017)     

A Result On the Probability Measures Dominated by g-Expectation

It is proved that a probability measure is dominated by g-expectation ε_μ[·] if and only if it can begenerated by Girsanov transformation via a process which is uniformly bounded by μ.     

Relative local control and the block source algebras

The local control of pointed groups is generalized to the concept of relative local control, and it is proved that there exists a lifting for a covering of a block source algebra if the relative local control holds. As an application, a result is proved on the source algebras of blocks, whose defect groups are direct products of a normal subgroup and a subgroup that gives a relative local control. Project supported by the National Natural Science Foundation of China.     

A Smoothing-Type Algorithm for Solving Linear Complementarity Problems with Strong Convergence Properties

In this paper, we construct an augmented system of the standard monotone linear complementarity problem (LCP), and establish the relations between the augmented system and the LCP. We present a smoothing-type algorithm for solving the augmented system. The algorithm is shown to be globally convergent without assuming any prior knowledge of feasibility/infeasibility of the problem. In particular, if the LCP has a solution, then the algorithm either generates a maximal complementary solution of the LCP or detects correctly solvability of the LCP, and in the latter case, an existing smoothing-type algorithm can be directly applied to solve the LCP without any additional assumption and it generates a maximal complementary solution of the LCP; and that if the LCP is infeasible, then the algorithm detect correctly infeasibility of the LCP. To the best of our knowledge, such properties have not appeared in the existing literature for smoothing-type algorithms. This work was partially supported by the National Natural Science Foundation of China (Grant No. 10571134), the Natural Science Foundation of Tianjin (Grant No. 07JCYBJC05200), and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.     

Finite p-Groups Whose Abelian Subgroups Have a Trivial Intersection

A subgroup H of a finite group G is called a TI-subgroup if H ∩ H^x = 1 or H for all x ∈ G. In this paper, a complete classification for finite p-groups, in which all abelian subgroups are TI-subgroups, is given.     

Two-sided approximation to periodic solutions of ordinary differential equations

Summary A two-sided approximation to the periodic orbit of an autonomous ordinary differential equation system is considered. First some results about variational equation systems for periodic solutions are obtained in Sect. 2. Then it is proved that if the periodic orbit is convex and stable, the explicit difference solution approximates the periodic orbit from the outer part and the implicit one from the inner part respectively. Finally a numerical example is given to illustrate our result and to point out that the numerical solution no longer has a one-sided approximation property, if the periodic orbit is not convex.The Work is supported by the National Natural Science Foundation of China     

Convergence of one-leg methods for nonlinear neutral delay integro-differential equations

Some convergence results of one-leg methods for nonlinear neutral delay integro-differential equations (NDIDEs) are obtained. It is proved that a one-leg method is E (or EB) -convergent of order p for nonlinear NDIDEs if and only if it is A-stable and consistent of order p in classical sense for ODEs, where p = 1, 2. A numerical example that confirms the theoretical results is given in the end of this paper. This work was supported by National Natural Science Foundation of China (Grant No. 10871164), the Natural Science Foundation of Hunan Province (Grant No. 08JJ6002), and the Scientific Research Fund of Changsha University of Science and Technology (Grant No. 1004259)     

Cutset Condition for Geometric Lattices

In this paper we prove that an atomistic lattice L of finite length is geometric if it has the nontrivial modular cutset condition, that is, every maximal chain of L contains a modular element which is different from the minimum element and the maximum element of L. The first author is partially supported by the National Natural Science Foundation of China (Grant no. 10471016).     

Orbits connecting singular points in the plane

This paper concerns the global structure of planar systems. It is shown that if a positively bounded system with two singular points has no closed orbits, the set of all bounded solutions is compact and simply connected. Also it is shown that for such a system the existence of connecting orbits is tightly related to the behavior of homoclinic orbits. A necessary and sufficient condition for the existence of connecting orbits is given. The number of connecting orbits is also discussed.Supported by the National Science Foundation of China Grant No. 10461003.     

A homological spectral sequence of group products

In this paper the “residual complex” is defined when a group and its subgroups act on a complex. With its aid a homological spectral sequence of group products is given. And the author makes a concentrated study of the structure of the residual complex and proves that it becomes a clear “step complex” if the group can be expressed as an amalgamated free product of its subgroups. Project supported by the National Natural Science Foundation of China     

Study of interfering nuclear reactions in determination of platinum group elements by neutron activation analysis

Eighteen interfering nuclear reactions that likely occur in neutron activation analysis of platinum group elements are studied. Their degrees are calculated by the basic principle of activation analysis. The calculation results indicate that most of the nuclear interferences become significant only if the interfering elements exist in major amount and the elements of interest in trace amount. However, the second-order interference to platinum analysis from gold and the fission interference to analysis of ruthenium and palladium from uranium cannot be neglected even if the gold and uranium exist as trace constituents in samples. Project supported by the National Natural Science Foundation of China (Grant No. 19392100) and the China Postdoctoral Science Foundation.     

The Schwarzian derivative in several complex variables (III)

In the point view of Lie group, the cross ratio and Schwarzian derivative in Cⁿ are defined and discussed, especially the Schwarzian derivative of holomorphic mappings on the domains in matrix space C^{m x n} is defined and discussed. It is proved that it is invariant up to similarity under the group of holomorphic automorphism of the Grassmann manifold CG(m, n). And it is also proved that the Schwarzian derivative equals zero if and only if the mapping is liaearly fractional. Project supported by the National Natural Science Foundation of China.