Notes on Noncommutative VNL-rings and GVNL-rings

In this note, a counterexample is given to show that a noncommutative VNL-ring need not be an SVNL-ring, answering an open question of Chen and Tong （Glasgow Math. J., 48（1）（2006）） negatively. Moreover, some new results about VNL-rings and GVNL-ringsare also given.     

Uniform Boundedness of Torsion Subgroups of Linear Groups

The torsion conjecture says： for any abelian variety A defined over a number field k, the order of the torsion subgroup of A（k） is bounded by a constant C（k,d） which depends only on the number field k and the dimension d of the abelian variety. The torsion conjecture remains open in general. However, in this paper, a short argument shows that the conjecture is true for more general fields if we consider linear groups instead of abelian varieties. If G is a connected linear algebraic group defined over a field k which is finitely generated over Q,Г is a torsion subgroup of G（k）. Then the order of Г is bounded by a constant C＇（k, d） which depends only on k and the dimension d of G.     

A Lower Bound for the Differences of Powers of Linear Operators

Let T be a bounded linear operator in a Banach space, with σ（T）={1}. In 1983, Esterle-Berkani＇ s conjecture was proposed for the decay of differences （I - T） T^n as follows： Eitheror lim inf （n→∞（n＋1）｜｜（I-T）T^n｜｜≥1/e or T = I. We prove this claim and discuss some of its consequences.     

Linear arboricity of regular digraphs

A linear directed forest is a directed graph in which every component is a directed path.The linear arboricity la(D) of a digraph D is the minimum number of linear directed forests in D whose union covers all arcs of D. For every d-regular digraph D, Nakayama and P′eroche conjecture that la(D) = d + 1. In this paper, we consider the linear arboricity for complete symmetric digraphs,regular digraphs with high directed girth and random regular digraphs and we improve some wellknown results. Moreover, we propose a more precise conjecture about the linear arboricity for regular digraphs.     

相应于Borcherds-Cartan矩阵的双参数弱Hopf代数

In this paper a class of two-parameter weak Hopf algebras wrτ,s（g） corresponding to Borcherds-Cartan matrix is constructed. This class consists of noncommutative and noncocommutative weak Hopf algebras but not Hopf algebras. It can be viewed as a generalized class of one-parameter weak Hopf algebras wUq（g）.     

Proof of Ding’s conjecture on maximal stable sets and maximal cliques in planar graphs

X. Deng et al. proved Chvātal＇s conjecture on maximal stable sets and maximal cliques in graphs. G. Ding made a conjecture to generalize Chvátal＇s conjecture. The purpose of this paper is to prove this conjecture in planar graphs and the complement of planar graphs.     

Permanence of Metric Sparsification Property under Finite Decomposition Complexity

The notions of metric sparsification property and finite decomposition com- plexity are recently introduced in metric geometry to study the coarse Novikov conjecture and the stable Borel conjecture. In this paper, it is proved that a metric space X has finite decomposition complexity with respect to metric sparsification property if and only if X itself has metric sparsification property. As a consequence, the authors obtain an alterna- tive proof of a very recent result by Guentner, Tessera and Yu that all countable linear groups have the metric sparsification property and hence the operator norm localization property.     

Classification of Lagrangian Surfaces of Curvature e in Non-flat Lorentzian Complex Space Form M12（4ε）

It is well known that a totally geodesic Lagrangian surface in a Lorentzian complex space form M12（4ε） of constant holomorphic sectional curvature 4s is of constant curvature 6. A natural question is ＂Besides totally geodesic ones how many Lagrangian surfaces of constant curvature εin M12（46） are there？＂ In an earlier paper an answer to this question was obtained for the case e = 0 by Chen and Fastenakels. In this paper we provide the answer to this question for the case ε≠0. Our main result states that there exist thirty-five families of Lagrangian surfaces of curvature ε in M12（4ε） with ε ≠ 0. Conversely, every Lagrangian surface of curvature ε≠0 in M12（4ε） is locally congruent to one of the Lagrangian surfaces given by the thirty-five families.     

A general two-function minimax theorem

A two-function minimax theorem is proved. In this result, the concavity-convexity conditions of both functions involve monotone transforms and mixing of functional values, and the ＂w- upwardness/w-downwardness＂ conditions; both spaces are required to be compact topological spaces but without linear structure. By this result, an open question proposed by Forgo and Joo in 1998 is answered.     

On subnormal solutions of second order linear periodic differential equations

In this paper, we investigate the existence and the form of subnormal solution for a class of second order periodic linear differential equations, estimate the growth properties of all solutions, and answer the question raised by Gundersen and Steinbart.     

POISSON ALGEBRA STRUCTURES ON sp2l（^～CQ） WITH NULLITY m

Noncommutative Poisson algebras are the algebras having both an associative algebra structure and a Lie algebra structure together with the Leibniz law. In this article,the noncommutative Poisson algebra structures on sp2l（^～CQ） are determined.     

Three-Dimensional Finite Element Superconvergent Gradient Recovery on Par6 Patterns

<正>In this paper,we present a theoretical analysis for linear finite element superconvergent gradient recovery on Par6 mesh,the dual of which is centroidal Voronoi tessellations with the lowest energy per unit volume and is the congruent cell predicted by the three-dimensional Gersho's conjecture.We show that the linear finite element solution u_h and the linear interpolation u_1 have superclose gradient on Par6 meshes. Consequently,the gradient recovered from the finite element solution by using the superconvergence patch recovery method is superconvergent to▽u.A numerical example is presented to verify the theoretical result.     

Testing for random effects in linear mixed models for longitudinal data under moment conditions

In this paper, we consider whether the random effect exists in linear mixed models （LMMs） when only moment conditions are assumed. Based on the estimators of parameters and their asymptotic properties, a Wald-type test is constructed. It is consistent against global alternatives and is sensitive to the local alternatives converging to the null hypothesis at parametric rates, a fastest possibly rate for goodness-of-fit testing. Moreover, a simulation study shows the performance of the test is good. The procedure also applies to a real data.     

Estimation of the Bezout number for piecewise algebraic curve

A piecewise algebraic curve is a curve determined by the zero set of a bivariate spline function.In this paper.a coniecture on trianguation is confirmed The relation between the piecewise linear algebraiccurve and four-color conjecture is also presented.By Morgan-Scott triangulation, we will show the instabilityof Bezout number of piecewise algebraic curves. By using the combinatorial optimization method,an upper     

FURTHER RESULTS ON CORRELATION FUNCTIONS OF DE BRUIJN SEQUENCES

In this paper we develop some bounds for the correlation functions of sequences with perfod 2~nand specific linear complexities.These bounds are also applicable to the correlation functions of deBruijn sequences with span n and specific linear complexities.It is interesting that a conjecture of Chan,Games and Key's for the case of n=2~m can be proved easily by using the results developed here.Theirconjecture asserts that there are no de Bruijn sequences with span n and linear complexity 2~(n-1)+n+1.The comjecture was proved by Games by a different method.     

A note on the maximum genus of 3-edge-connected nonsimple graphs

Let G be a 3-edge-connected graph (possibly with multiple edges or loops), and let γM(G) and β(G) be the maximum genus and the Betti number of G, respectively. Then γM(G)≥β(G)/3 can be proved and this answers a question posed by Chen, et al. in 1996.     

Some Notes on Normality Criteria of Meromorphic Functions

In this paper, we study the normality of families of meromorohic functions related to a Hayman conjecture. We prove that the conditions in Hayman conjecture and in other criterions can be relaxed. The results in this paper improve some previous results.     

ψ-bounded Solutions for a System of Difference Equations on Z

In this work we discuss the existence of ψ-bounded solutions for linear difference equations. We present a necessary and sufficient condition for the existence of ψ--bounded solutions for the linear nonhomogeneous difference equation x（n＋1）=A（n）x（n）＋f（n） for every ψ-bounded sequence f（n）.     

Unitary Bases and Noncommutative Wavelets

In this paper, we construct new unitary bases in noncommutative wavelets.