HYPERCYCLIC OPERATORS ON QUASI-MAZUR SPACES

Modifying the method of Ansari, we give some criteria for hypercyclicity of quasi-Mazur spaces. They can be applied to judging hypercyclicity of non-complete and non-metrizable locally convex spaces. For some special locally convex spaces, for example, KSthe （LF）-sequence spaces and countable inductive limits of quasi-Mazur spaces, we investigate their hypercyclicity. As we see, bounded biorthogonal systems play an important role in the construction of Ansari. Moreover, we obtain characteristic conditions respectively for locally convex spaces having bounded sequences with dense linear spans and for locally convex spaces having bounded absorbing sets, which are useful in judging the existence of bounded biorthogonal systems.

Halton-type sequences from global function fields

For any prime power q and any dimension s≥1, a new construction of (t, s)-sequences in base q using global function fields is presented. The construction yields an analog of Halton sequences for global function fields. It is the first general construction of (t, s)-sequences that is not directly based on the digital method. The construction can also be put into the framework of the theory of (u, e, s)-sequences that was recently introduced by Tezuka and leads in this way to better discrepancy bounds for the constructed sequences.

ON(η,d)-CONTRACTIBLE ORBITS OF VECTOR FIELDS

Let ■ be the linear space of all C1 vector fields X on a compact n-dimensionalC∞ Riemann manifold（n≥2）,endowed with the C1 norm ‖X‖1.Write θ（X）for the numberof contractible periodic orbits of X∈（?）,which may be finite or infinite.Let （?）* be the set ofall X∈（?） possessing the property that X has a neighbourhood （?） such that every Y∈（?） hasonly a finite number of singularities and at most a countable number of periodic orbits.Inthis paper,it is shown that any given S∈（?） has a neighbourhood （?） in （?） together with anumber λ=λ（?）】0 such that θ（X）≤λfor all X∈（?）.

The Multiplier and Cohomology of Lie Superalgebras

Suppose that L is a Lie superalgebra over a field F of characteristic different from 2 and 3.In this paper,the so-called 5-sequence of cohomology for a central extension of L is constructed and is proved to be exact.Moreover,the multiplier of L is proved to be isomorphic to the second cohomology group with coefficients in the trivial module of L.Finally,an upper bound of the superdimension of the second cohomology group is given in the situation when L is nilpotent and finite-dimensional.

On Mixed Multiplicities of Good Filtrations

This paper interprets mixed multiplicities of good filtrations as Hilbert-Samuel multiplicities, and shows that （ε1,..., εm）-superficial sequences in [16] （2007） and superficial sequences in [15] （1973） are weak-（FC）-sequences in [19] （2000）. As consequences, we not only obtain generalized results for mixed multiplicities of ideals in [15, 16, 19] but also get an improvement of [19, Theorem 3.4] that seems to account well for the essence of [16, Theorem 1.4].

On the Multiplicity and the Cohen-Macaulayness of Fiber Cones of Graded Modules

Let(A,m)be a Noetherian local ring with maximal ideal m,I an ideal of A,J an m-primary ideal of A,N a finitely generated A-module,S=■n≥0 Sn a finitely generated standard graded algebra over A and M=■n≥0 Mn a finitely generated graded S-module.We characterize the multiplicity and the Cohen-Macaulayness of the fiber cone F(M)=■n≥0 Mn/JM_(n).As an application,we obtain some results on the multiplicity and the Cohen--Macaulayness of the fiber cone■n≥0 I^(n)N/JI^(n)N.