关于Abel群上Cayley图的Hamilton圈分解

设Ｇ（Ｆ，Ｔ∩Ｔ＾－１）是有限Ａｂｅｌ群Ｆ上的Ｃａｙｌｅｙ图，Ｔ∩Ｔ＾－１只含２阶元，此文证明了当Ｔ是Ｆ的极小生成元集时，若ｄ（Ｇ）＝２ｋ，则Ｇ是ｋ个边不相交的Ｈａｍｉｌｔｏｎ圈的并，若ｄ（Ｇ）＝２ｋ＋１，则Ｇ是ｋ个边不相交的Ｈａｍｉｌｔｏｎ圈与一个１－因子的并。     

再论一类二次系统的无界双中心周期环域的POincare分支

本文再一次讨论了具有双曲线与赤道弧为边界的双中心周期环域的二次系统的Poincare分支，并构造出了此系统出现极限环的(0，3)分布或出现一个三重极限环的具体例子．     

Severi varieties on blow-ups of the symmetric square of an elliptic curve

We prove that certain Severi varieties of nodal curves of positive genus on general blow-ups of the twofold symmetric product of a general elliptic curve are nonempty and smooth of the expected dimension. This result, besides its intrinsic value, is an important preliminary step for the proof of nonemptiness of Severi varieties on general Enriques surfaces.     

Tocochromanols composition in kernels recovered from different apricot varieties: RP-HPLC/FLD and RP-UPLC-ESI/MSn study

Composition of tocochromanols in kernels recovered from 16 different apricot varieties (Prunus armeniaca L.) was studied. Three tocopherol (T) homologues, namely α, γ and δ, were quantified in all tested samples by an RP-HPLC/FLD method. The γ-T was the main tocopherol homologue identified in apricot kernels and constituted approximately 93% of total detected tocopherols. The RP-UPLC-ESI/MSⁿ method detected trace amounts of two tocotrienol homologues α and γ in the apricot kernels. The concentration of individual tocopherol homologues in kernels of different apricots varieties, expressed in mg/100 g dwb, was in the following range: 1.38–4.41 (α-T), 42.48–73.27 (γ-T) and 0.77–2.09 (δ-T). Moreover, the ratio between individual tocopherol homologues α:γ:δ was nearly constant in all varieties and amounted to approximately 2:39:1.     

On the Chow groups of certain cubic fourfolds

This note is about the Chow groups of a certain family of smooth cubic fourfolds. This family is characterized by the property that each cubic fourfold X in the family has an involution such that the induced involution on the Fano variety F of lines in X is symplectic and has a K3 surface S in the fixed locus. The main result establishes a relation between X and S on the level of Chow motives. As a consequence, we can prove finite-dimensionality of the motive of certain members of the family.     

A Factorization Theorem for Topological Abelian Groups

Using the nice properties of the w-divisible weight and the w-divisible groups, we prove a factorization theorem for compact abelian groups K; namely, K = K _tor  × K _d , where K _tor is a bounded torsion compact abelian group and K _d is a w-divisible compact abelian group. By Pontryagin duality this result is equivalent to the same factorization for discrete abelian groups proved in [9 Galindo , J. , Macario , S. ( 2011 ). Pseudocompact group topologies with no infinite compact subsets . J. Pure and Appl. Algebra 215 : 655 – 663 .[Crossref], [Web of Science ®] , [Google Scholar]].     

Geometric invariant theory and Einstein–Weyl geometry

In this article, we give a survey of geometric invariant theory for Toric Varieties, and present an application to the Einstein-Weyl geometry. We compute the image of the Minitwistor space of the Honda metrics as a categorical quotient according to the most efficient linearization. The result is the complex weighted projective space CP_1,1,2. We also find and classify all possible quotients.     

On the symplectic structure of instanton moduli spaces

We study the complex symplectic structure of the quiver varieties corresponding to the moduli spaces of SU(2) instantons on both commutative and non-commutative R⁴. We identify global Darboux coordinates and quadratic Hamiltonians on classical phase spaces for which these quiver varieties are natural completions. We also show that the group of non-commutative symplectomorphisms of the corresponding path algebra acts transitively on the moduli spaces of non-commutative instantons. This paper should be viewed as a step towards extending known results for Calogero–Moser spaces to the instanton moduli spaces.     

On the extendability of certain semi-Cayley graphs of finite abelian groups

A connected graph Γ with at least 2n+2 vertices is said to be n-extendable if every matching of size n in Γ can be extended to a perfect matching. The aim of this paper is to study the 1-extendability and 2-extendability of certain semi-Cayley graphs of finite abelian groups, and the classification of connected 2-extendable semi-Cayley graphs of finite abelian groups is given. Thus the 1-extendability and 2-extendability of Cayley graphs of non-abelian groups which can be realized as such semi-Cayley graphs of abelian groups can be deduced. In particular, the 1-extendability and 2-extendability of connected Cayley graphs of generalized dicyclic groups and generalized dihedral groups are characterized.