无机不饱和类烯H~2NBLiF的构型及异构化反应的理论研究

用HF/D95^*^*解析梯度方法研究了无机不饱和类烯H~2NBLiF的结构,共得到4个平衡构型和3个异构化反应的过渡态构型。动力学分析表明,其中两种平衡构型是它们存在和参加化学反应的基本构型。分析了各平衡构型的结构特点及稳定性,给出了各构型的Mulliken集居数,并简单讨论了两种基本构型的化学活性。     

Spherical coxeter groups and hyperelliptic 3-manifolds

Reflection groups of Coxeter polyhedra in three-dimensional Thurston geometries are examined. For a wide class of Coxeter groups, the existence of subgroups of finite index that uniformize hyperelliptic 3-manifolds is established. Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 173–177, August, 1999.     

Proper partial geometries with Singer groups and pseudogeometric partial difference sets

A partial geometry admitting a Singer group G is equivalent to a partial difference set in G admitting a certain decomposition into cosets of line stabilizers. We develop methods for the classification of these objects, in particular, for the case of abelian Singer groups. As an application, we show that a proper partial geometry Π=pg(s+1,t+1,2) with an abelian Singer group G can only exist if t=2(s+2) and G is an elementary abelian 3-group of order ³(s+1) or Π is the Van Lint-Schrijver partial geometry. As part of the proof, we show that the Diophantine equation (m³−1)/2=(²rw−1)/(r²−1) has no solutions in integers m,r?1, w?2, settling a case of Goormaghtigh's equation.     

Geometry and electronic properties of Cu2(n≤9)

The equilibrium geometries and the atomization energies of Cu_n(n≤9) clusters have been calculated using the B3LYP/LANL2DZ method. It is shown that the clusters do not copy the bulk structures and undergo significant geometrical changes with size and the atomization energy per atom increases monotonically with size. By analysing the energy level distribution, the Fermi level, HOMO－LUMO gaps, the electron affinities and the ionization potentials are calculated and the results are in reasonable agreement with experiment. These electronic properties are found to be strongly structure dependent, which can be used to determine which of the low-lying structures is observed experimentally.     

Spreads in Strongly Regular Graphs

A spread of a strongly regular graph is a partitionof the vertex set into cliques that meet Delsarte's bound (alsocalled Hoffman's bound). Such spreads give rise to coloringsmeeting Hoffman's lower bound for the chromatic number and tocertain imprimitive three-class association schemes. These correspondenceslead to conditions for existence. Most examples come from spreadsand fans in (partial) geometries. We give other examples, includinga spread in the McLaughlin graph. For strongly regular graphsrelated to regular two-graphs, spreads give lower bounds forthe number of non-isomorphic strongly regular graphs in the switchingclass of the regular two-graph.     

Unexpected spin-off from quantum gravity

We propose a novel way of investigating the universal properties of spin systems by coupling them to an ensemble of causal dynamically triangulated lattices, instead of studying them on a fixed regular or random lattice. Somewhat surprisingly, graph-counting methods to extract high- or low-temperature series expansions can be adapted to this case. For the two-dimensional Ising model, we present evidence that this ameliorates the singularity structure of thermodynamic functions in the complex plane, and improves the convergence of the power series.     

3-Wise Exactly 1-Intersecting Families of Sets

Let f(l, t, n) be the maximal size of a family such that any l2 sets of have an exactly t1-element intersection. If l3, it trivially comes from [8] that the optimal families are trivially intersecting (there is a t-element core contained by all the members of the family). Hence it is easy to determine Let g(l,t,n) be the maximal size of an l-wise exaclty t-intersecting family that is not trivially t-intersecting. We give upper and lower bounds which only meet in the following case: g(3, 1, n) = n^2/3(1 + o(1)).     

Symplectic semifield planes and -linear codes

There are lovely connections between certain characteristic 2 semifields and their associated translation planes and orthogonal spreads on the one hand, and -linear Kerdock and Preparata codes on the other. These inter-relationships lead to the construction of large numbers of objects of each type. In the geometric context we construct and study large numbers of nonisomorphic affine planes coordinatized by semifields; or, equivalently, large numbers of non-isotopic semifields: their numbers are not bounded above by any polynomial in the order of the plane. In the coding theory context we construct and study large numbers of -linear Kerdock and Preparata codes. All of these are obtained using large numbers of orthogonal spreads of orthogonal spaces of maximal Witt index over finite fields of characteristic 2.

We also obtain large numbers of ``boring' affine planes in the sense that the full collineation group fixes the line at infinity pointwise, as well as large numbers of Kerdock codes ``boring' in the sense that each has as small an automorphism group as possible.

The connection with affine planes is a crucial tool used to prove inequivalence theorems concerning the orthogonal spreads and associated codes, and also to determine their full automorphism groups.

     

A limiting absorption principle for scattering problems with unbounded obstacles

A generalized mode matching method that applies to a wide class of scattering problems is developed in the time harmonic two‐dimensional Helmholtz case. This method leads by variational means to an integro‐differential formulation whose unknown is the trace of the field on an unbounded one‐dimensional interface. The well‐posedness is proved after a careful study of the rather original functional framework. Owing to a fundamental density result—based upon some properties of a singular integral operator similar to the Hilbert transform—the limiting absorption principle related to this original formulation is established. Finally, two other situations are emphasized. Copyright © 2001 John Wiley & Sons, Ltd.     

Veronese Varieties Over Finite Fields and Their Projections

Inthis paper Veronese varieties of degree d over aGalois field are studied. We also show that some of known capsembedded into classical varieties always are projections of Veronesevarieties.