Coverings of Abelian groups and vector spaces

We study the question how many subgroups, cosets or subspaces are needed to cover a finite Abelian group or a vector space if we have some natural restrictions on the structure of the covering system. For example we determine, how many cosets we need, if we want to cover all but one element of an Abelian group. This result is a group theoretical extension of the theorem of Brouwer, Jamison and Schrijver about the blocking number of an affine space. We show that these covering problems are closely related to combinatorial problems, including the so-called additive basis conjecture, the three-flow conjecture, and a conjecture of Alon, Jaeger and Tarsi about nowhere zero vectors.     

Horizontal Connection and Horizontal Mean Curvature in Carnot Groups

In this paper we give a geometric interpretation of the notion of the horizontal mean curvature which is introduced by Danielli Garofalo-Nhieu and Pauls who recently introduced sub- Riemannian minimal surfaces in Carnot groups. This will be done by introducing a natural nonholonomic connection which is the restriction （projection） of the natural Riemannian connection on the horizontal bundle. For this nonholonomic connection and （intrinsic） regular hypersurfaces we introduce the notions of the horizontal second fundamental form and the horizontal shape operator. It turns out that the horizontal mean curvature is the trace of the horizontal shape operator.     

COMPLETENESS OF THE PARABOLIC SUBGROUPS OF PROJECTIVE ORTHOGONAL GROUPS

All parabolic subgroups and Borel subgroups of PΩ(2m 1, F) over a linear-able field F of characteristic 0 are shown to be complete groups, provided m > 3.     

Lefschetz Formulae for p -Adic Groups

Abstract In this paper, Lefschetz formulae for torus actions on p-adic groups are proven. These are similar to comparable formulae for real Lie groups. Applications lie in the realm of dynamical zeta functions.     

模糊概念格与模糊推理

基于伽罗瓦连接,分别在交换伴随对与对合剩余格条件下,讨论了模糊概念格的四种定义形式。并证明了在对合剩余格上,对偶性成立,四种模糊算子将具有与经典意义下一致的相互关系。最后我们提出了一种基于模糊概念格的模糊推理规则,并证明了其还原性。     

Derived Lengths of Solvable Groups Having Five Irreducible Character Degrees II

Let G be a solvable group with five character degrees. Suppose that there is some prime p so that G/O ^p (G) is not Abelian. Also, assume that cd(G) contains a degree that is not divisible by p. Under these hypotheses, we show that the derived length of G is at most 4.     

Molecular programming of organogelators which can accept [60]fullerene by encapsulation

New porphyrin-based gelators bearing eight hydrogen-bond-forming amide groups at their periphery were synthesized. They acted as versatile gelators for aromatic solvents. SEM and TEM observations and X-ray crystallographic analysis established that they tend to aggregate into a two-dimensional sheet-like structure utilizing the intermolecular hydrogen-bonding interaction. In this structure the porphyrin-porphyrin π-π stacking interaction is not involved because of the energetically-predominant hydrogen-bonding interactions, keeping the space distance of 12.9 Å. Very interestingly, when C₆₀ was added, the morphology was transformed to a one-dimensional fibrous structure, which can enjoy a porphyrin-C₆₀-porphyrin interaction. This multicapsular structure having porphyrin-based compartments for hosting C₆₀ was further characterized by XRD, EPR of a Cu(II) analogue, and the theoretical calculation. Thus, this paper presents a new concept, ‘molecular recognition in gel’, which is effective for the weak host-guest interaction.     

Integrated Groups and Smooth Distribution Groups

In this paper, we prove directly that α-times integrated groups define algebra homomorphisms. We also give a theorem of equivalence between smooth distribution groups and α-times integrated groups.     

Rigidity of Branch Groups Acting on Rooted Trees

Automorphisms of groups acting faithfully on rooted trees are studied. We find conditions under which every automorphism of such a group is induced by a conjugation from the full automorphism group of the rooted tree. These results are applied to known examples such as Grigorchuk groups, Gupta–Sidki group, etc.     

一些部分差集和相对差集的构造

In this paper, we give a construction of RDS in Galois ring by using some bent function, and obtain the equivalent relationship between RDS and a kind of bent function. At the same time, its existence is demonstrated.