Extensions of modules over Weyl algebras

In this paper we calculate some groups of singular modules over the complex Weyl algebra . In particular we determine conditions under which is an infinite dimensional vector space when or .

     

抽象凸空间上的弱KKM映射, 相交定理和极大极小不等式

In this paper,we introduce the concept of weakly KKM map on an abstract convex space without any topology and linear structure,and obtain Fan＇s matching theorem and intersection theorem under very weak assumptions on abstract convex spaces.Finally,we give several minimax inequality theorems as applications.These results generalize and improve many known results in recent literature.     

On the correlations of directions in the Euclidean plane

Let denote the repartition of the -level correlation measure of the finite set of directions , where is the fixed point and is an integer lattice point in the square . We show that the average of the pair correlation repartition over in a fixed disc converges as . More precisely we prove, for every and , the estimate

We also prove that for each individual point , the -level correlation diverges at any point as , and we give an explicit lower bound for the rate of divergence.

     

Spaces of type and the Hankel convolution

In this paper we introduce new function spaces that are denoted by , -1/2$"> and and that are spaces of type where the Hankel convolution and the Hankel transformation are defined. The spaces will play the same role in the Hankel setting that the spaces play in the theory of Fourier transformation.     

关于${cal I}$-覆盖映射与1-${cal I}$-覆盖映射

In this paper,we introduce the concepts of I-covering mappings and 1-I-covering mappings,discuss the difference between sequence-covering and I-covering mappings by some examples.With those concepts,we get some interesting properties of I-covering(1-I-covering)mappings and some characterizations of I-covering(1-I-covering)and compact mapping images of metric spaces.     

A continuity property of multivariate Lagrange interpolation

Let be a sequence of interpolation schemes in of degree (i.e. for each one has unique interpolation by a polynomial of total degree and total order . Suppose that the points of tend to as and the Lagrange-Hermite interpolants, , satisfy for all monomials with . Theorem: for all functions of class in a neighborhood of . (Here denotes the Taylor series of at 0 to order .) Specific examples are given to show the optimality of this result.

     

共轭 A -调和张量的双权积分不等式

该文引进一类新的权函数 $-A^{\lambda_{3}}_{r}(\lambda_{1},\lambda-{2},\Omega)$ -权, 证明了共轭$\cal A$ -调和张量的局部加权积分不等式.作为局部结果的应用, 证明了在有界区域$\Omega$中共轭$\cal A$ -调和张量的整体加权积分不等式.这些结果可看成是经典结果的推广.最后, 给出了上述结果在拟正则映射理论中的应用.     

-adic -basis and regular local ring

We introduce the concept of -adic -basis as an extension of the concept of -basis. Let be a regular local ring of prime characteristic and a ring such that . Then we prove that is a regular local ring if and only if there exists an -adic -basis of and is Noetherian.

     

Some numerical invariants of local rings

Let be a formal power series ring over a field of characteristic zero and any ideal. The aim of this work is to introduce some numerical invariants of the local rings by using the theory of algebraic -modules. More precisely, we will prove that the multiplicities of the characteristic cycle of the local cohomology modules and , where is any prime ideal that contains , are invariants of .

     

-summand vectors in Banach spaces

The aim of this paper is to study the set of all -summand vectors of a real Banach space . We provide a characterization of -summand vectors in smooth real Banach spaces and a general decomposition theorem which shows that every real Banach space can be decomposed as an -sum of a Hilbert space and a Banach space without nontrivial -summand vectors. As a consequence, we generalize some results and we obtain intrinsic characterizations of real Hilbert spaces.

     

A note on the Hambleton-Taylor-Williams conjecture

I. Hambleton, L. Taylor and B. Williams conjectured a general formula in the spirit of H. Lenstra for the decomposition of $G_n(RG)$ for any finite group G and noetherian ring R. The conjectured decomposition was shown to hold for some large classes of finite groups. D. Webb and D. Yao discovered that the conjecture failed for the symmetric group $S_5$, but remarked that it still might be reasonable to expect the HTW-decomposition for solvable groups. In this paper we show that the solvable group $\mathrm{SL}(2,{\mathbb{F}}_3)$ is also a counterexample to the conjectured HTW-decomposition. Nevertheless, we prove that for any finite group G the rank of $G_1(\mathbb{Z}G)$ does not exceed the rank of the expression in the HTW-decomposition. We also show that the HTW-decomposition predicts correct torsion for $G_1(\mathbb{Z}G)$ for any finite group G. Furthermore, we prove that for any degree other than $n=1$ the conjecture gives a correct prediction for the rank of $G_n(\mathbb{Z}G)$.     

Irregular hypergeometric systems associated with a singular monomial curve

In this paper we study irregular hypergeometric systems defined by one row. Specifically, we calculate slopes of such systems. In the case of reduced semigroups, we generalize the case studied by Castro and Takayama. In all the cases we find that there always exists a slope with respect to a hyperplane of this system. Only in the case of an irregular system defined by a integer matrix we might need a change of coordinates to study slopes at infinity. In the other cases slopes are always at the origin, defined with respect to a hyperplane. We also compute all the -characteristic varieties of the system, so we have a section of the Gröbner fan of the module defined by the hypergeometric system.

     

BEM with linear complexity for the classical boundary integral operators

Alternative representations of boundary integral operators corresponding to elliptic boundary value problems are developed as a starting point for numerical approximations as, e.g., Galerkin boundary elements including numerical quadrature and panel-clustering. These representations have the advantage that the integrands of the integral operators have a reduced singular behaviour allowing one to choose the order of the numerical approximations much lower than for the classical formulations. Low-order discretisations for the single layer integral equations as well as for the classical double layer potential and the hypersingular integral equation are considered. We will present fully discrete Galerkin boundary element methods where the storage amount and the CPU time grow only linearly with respect to the number of unknowns.

     

$\mathcal{F}$-Perfect Rings and Modules

Let $R$ be a ring, and let $(\mathcal{F}, C)$ be a cotorsion theory. In this article, the notion of $\mathcal{F}$-perfect rings is introduced as a nontrial generalization of perfect rings and A-perfect rings. A ring $R$ is said to be right $\mathcal{F}$-perfect if $F$ is projective relative to $R$ for any $F ∈ \mathcal{F}$. We give some characterizations of $\mathcal{F}$-perfect rings. For example, we show that a ring $R$ is right $\mathcal{F}$-perfect if and only if $\mathcal{F}$-covers of finitely generated modules are projective. Moreover, we define $\mathcal{F}$-perfect modules and investigate some properties of them.     

The universal central extension of the three-point loop algebra

We consider the three-point loop algebra,

where denotes a field of characteristic 0 and is an indeterminate. The universal central extension of was determined by Bremner. In this note, we give a presentation for via generators and relations, which highlights a certain symmetry over the alternating group . To obtain our presentation of , we use the realization of as the tetrahedron Lie algebra.

     

A note on a conjecture of Ryser

A special case of a conjecture of Ryser states that if a 3-partite 3-uniform hypergraph has at mostv pairwise disjoint edges then there is a set of vertices of cardinality at most 2v meeting all edges of the hypergraph. The best known upper bound for the size of such a set is (8/3)v, given by Tuza [7]. In this note we improve this to (5/2)v.     

一致空间的理想导集映射

本文介绍一致空间的理想导集映射,并对这些映射的像展开研究.同时,介绍I-Hurewicz有界性的概念,研究I-Hurewicz有界性的基础拓扑运算性质.最后,得到一致空间中I-Hurewicz有界性的一个等价刻画.     

2-极大子群的$F_s$-拟正规性

$F$是一个群系. $G$的子群$H$在$G$中称为$F_s$-拟正规的,如果存在$G$的正规子群$T$,使得$HT$在$G$中是$s$-置换的并且$(H\cap T)H_G/H_G$包含在$G/H_G$的$F$超中心$Z^F_\infty(G/H_G)$中.本文利用$F_s$-拟正规子群研究了有限群的结构.获得了某些新的结果.     

Singularities of the hypergeometric system associated with a monomial curve

We compute, using -module restrictions, the slopes of the irregular hypergeometric system associated with a monomial curve. We also study rational solutions and reducibility of such systems.