Immanant positivity for Catalan-Stieltjes matrices

We give some sufficient conditions for the nonnegativity of immanants of square submatrices of Catalan-Stieltjes matrices and their corresponding Hankel matrices. To obtain these sufficient conditions, we construct new planar networks with a recursive nature for Catalan-Stieltjes matrices. As applications, we provide a unified way to produce inequalities for many combinatorial polynomials, such as the Eulerian polynomials, Schröder polynomials, and Narayana polynomials.     

On bandwidth sums of graphs

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Two-Arc Transitive Graphs and Twisted Wreath Products

The paper addresses a part of the problem of classifying all 2-arc transitive graphs: namely, that of finding all groups acting 2-arc transitively on finite connected graphs such that there exists a minimal normal subgroup that is nonabelian and regular on vertices. A construction is given for such groups, together with the associated graphs, in terms of the following ingredients: a nonabelian simple group T, a permutation group P acting 2-transitively on a set , and a map F : Tsuch that x = x ^–1 for all x F() and such that Tis generated by F(). Conversely we show that all such groups and graphs arise in this way. Necessary and sufficient conditions are found for the construction to yield groups that are permutation equivalent in their action on the vertices of the associated graphs (which are consequently isomorphic). The different types of groups arising are discussed and various examples given.     

Propagating transverse electric and transverse magnetic modes in liquid crystal-clad planar waveguides

ABSTRACT

In a planar dielectric waveguide, weak confinement of a propagating mode in a high index core leads to a measurable evanescent interaction with the cladding. In this work, we study the effect of a reorientable anisotropic cladding on the behaviour of Transverse Electric (TE) and Transverse Magnetic (TM) mode polarisations using a liquid crystal (LC)-clad waveguide architecture. The polarised evanescent field of a guided mode interacts with a voltage-tunable birefringent LC cladding to deflect an out-coupled beam. Experimental measurements are coupled with a theoretical framework and show good consistency with simulation results. We isolate the effect of mode confinement by changing the thickness of the high index core. Interactions between the LC index ellipsoid and the mode polarisation are probed by changing the initial alignment of the LC. Finally, we examine the difference in deflection between TE and TM modes, which incorporates both a change in mode confinement and a difference in LC index components.     

Isolated square planar metal complexes of carbon

Based on the group theory analysis and quantum chemical calculations within the framework of SW X _α method (in relativistic approximation for core electrons and non-relativistic for valence ones), the existence possibility of square planar complexes [M₄C] and [M₄C]^2? (M = Al, Ga, In, Tl, Sc, and Y) in gas phase has been shown. The extraction of Kt₂[M₄C] square planar complexes of carbon in the crystal state is possible too. A high stability of these complexes, in comparison with usual tetrahedral, is achieved due to the formation of five-and four-center bonds (bonds M-M and M-C).     

Estimations of subgraph positions in molecular graphs and their common subgraph peculiarities

Some questions emerged from electronic data processing of molecular structures (graphs) and its fragments have been considered in this work. Quantitative estimations of subgraph positions in molecular graphs are presented and some properties of their maximal common subgraphs are described.     

分子轨道图形理论中对称轴定理

本文试图以浅显明确的形式描述对称轴定理，使之能与对称面定理相媲美，并对对称轴定理作一定的扩展，给出分子轨道构造定理。     

Computer generation of chemical structures from known fragments

The interactive generation of chemical structures from given fragments is described and discussed. It is implemented as a part of our expert system CARBON, based on C-13 NMR spectra. As it is designed, this program can also be a useful tool in the structure elucidation process when information on parts of the structure is obtained by other means (IR, mass and other spectrometries, chemical analysis, other relevant information). The topological characteristics of candidate fragments are first chosen interactively and then the elements are connected in all topologically possible ways. In the following step, the topological building blocks are substituted by chemical structural fragments resulting in a set of all chemical structures consistent with the input information.     

Emanation thermal analysis study of a sol-gel precursor for silica-titania waveguides

Emanation Thermal Analysis (ETA) was demonstrated as a tool for the characterization of microstructure changes of a sol-gel precursor for silica-titania layers deposited on the glass plate to be used as planar waveguides. Temperature ranges of 280-330 and 380-500°C, respectively, in which the densification of the layers took place, were determined by ETA under in situ conditions of the sample heating. Results of thermogravimetry were compared with the ETA data. This revised version was published online in August 2006 with corrections to the Cover Date.     

Using three major criteria to evaluate aromaticity of five-member C-containing rings and their Si-, N-, and P-substituted aromatic heterocyclics

In this paper, we used bond-length equalization, aromatic stabilization energies (ASE) and nucleus-independent chemical shifts (NICS), calculated with (density functional theory) B3LYP levels at the 6-311+G^** basis set, to evaluate the aromaticity of a set of 38 five-member planar π-electron aromatic systems: sila-, aza- and phospha- derivatives and their parent systems. The result revealed statistically significant correlations among the above three criteria, and the order of aromaticity of the whole set was: Aza- derivatives rings > Phospha- derivatives rings > Sila- derivatives rings > Carbon-containing rings; NICS(0.6) and NICS(0.8) had the same results in evaluating the order of aromaticity in our case.