Maximal 2-Local Geometries for the Symmetric Groups

Abstract

The set 𝒩_max (G, T) consisting of all maximal 2-local subgroups of G = Sym(n) which contain T, a Sylow 2-subgroup of G, is investigated. In addition to determining the structure of the subgroups in 𝒩_max (G, T), the simplicial sets of maximal rank are classified.     

Modified finite volume method applied to radiative transfer in 2D complex geometries and graded index media

A modified finite volume method with unstructured triangular meshes is proposed to solve the RTE in 2D complex geometries and for graded index media. In such media, the RTE has an additional term corresponding to “angular redistribution”. This term is due to the change in the orientation of the direction of propagation for the radiation along curved optical paths. Some benchmark cases applied to a slab (1D) and a square cavity (2D) with linear and nonlinear refractive graded index are used to validate the new method. New results are presented for a disk with radial graded index.     

Minimum Weight and Dimension Formulas for Some Geometric Codes

The geometric codes are the duals of the codes defined by the designs associated with finite geometries. The latter are generalized Reed–Muller codes, but the geometric codes are, in general, not. We obtain values for the minimum weight of these codes in the binary case, using geometric constructions in the associated geometries, and the BCH bound from coding theory. Using Hamada's formula, we also show that the dimension of the dual of the code of a projective geometry design is a polynomial function in the dimension of the geometry.     

Inclusion of exact exchange for self-interaction corrected H3 density functional potential energy surface

The effect of the inclusion of the exact exchange into self-interaction corrected generalized gradient approximation density functional theory (GGA-DFT) for the simplest hydrogen abstraction reaction, H + H₂ → H₃ → H₂ + H, is presented using a triple-zeta augmented 6-311++G(d,3pd) basis set. The introduction of the self-interaction correction has a considerably larger effect on molecular geometry and vibrational frequencies than the inclusion of the exact exchange. We investigate the influence of the self-interaction error on the shape of the potential energy surface around the transition state of the hydrogen abstraction reaction. The decomposition of the self-interaction error into correlation and exchange parts shows that the exchange self-interaction error is the main component of the energy barrier error. The best agreements with the experimental barrier height were achieved by self-interaction corrected B3LYP, B-LYP and B3PW functionals with errors of 1.5, 2.9 and 3.0 kcal/mol, respectively. Received: 13 August 1997 / Accepted: 14 November 1997     

Simultaneous determination of elastic and optical properties of polymers by high performance Brillouin spectroscopy using different scattering geometries

General aspects of high performance Brillouin spectroscopy in polymers using special scattering geometries such as 90A-scattenng geometry are discussed. Technical improvements are reported resulting in absolute accuracies up to 0.05 % for sound velocity determination. A method of data analysis is presented delivering simultaneously the complete set of elastic stiffness constants. The influence of birefringence on the Brillouin line shifts in anisotropic polymeric systems is estimated and techniques to reduce this influence are proposed. The determination of the principal refractive indices by Brillouin spectroscopy is discussed. Furthermore, a quantityD ^X , which is sensitive to hypersonic relaxation processes, is introduced.Dedicated to Prof. Dr. H.-G. Kilian on the occasion of his 60th birthday.     

A family of 2-weight codes related to BCH-codes

For every prime-power q and every pair of natural numbers m ≤ n′, we construct a q-ary linear code of length q^m (q^n′ − 1)(q^n′ − q^n′−m + 1)/(q − 1) and dimension 3n′, whose only nonzero weights are and . These code parameters and those of the corresponding family of strongly regular graphs are new in odd characteristic. © 1997 John Wiley & Sons, Inc. J Combin Designs 5: 391–396, 1997     

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。