A Crowning Moment for Wiener Indices

The Wiener (Sum of All Distances) Index for three out of the four classes of hexagonal models or regular planar hex-patterns used to model graphite and similar structures have been known for a few years. In this paper we find the Wiener Index for the Crown or Beehive hexagonal model.     

Spectral Domain Analysis of Coaxial Cavities

Coaxial cavities are used in high power gyrotrons as the beam-wave interaction structure. Much research has been devoted to their mode selective properties. A coaxial cavity lacks a sharp boundary at its open end, so it has some physical features that can only be observed using a spectral model, such as frequency-dependent field profiles and mode overlapping effects. These properties are important since cold tests are usually conducted in the frequency domain. This study applies the incident/reflected wave boundary condition to the wave equation of a weakly irregular coaxial waveguide. The resistivity of the wall is considered in the analysis. Calculations reveal that the fixed-position spectrum yields an uncertain resonant frequency and quality factor. Although the maximum-field spectrum can uniquely determine the properties of the coaxial cavity, the resonant frequency obtained using the maximum-field spectral model is inconsistent with that obtained using the temporal model. The field-energy spectrum explains the low Q nature of the coaxial cavity. Moreover, resonant frequencies evaluated using the field-energy spectrum agree precisely with those evaluated using the temporal model.     

Synthesis,and Antimycobacterial and Cytotoxic Evaluation of Certain Fluoroquinolone Derivatives

Certain 1‐ethyl‐ and 1‐aryl‐6‐fluoro‐1,4‐dihydroquinol‐4‐one derivatives were synthesized and evaluated for antimycobacterial and cytotoxic activities. Preliminary results indicated that, for 1‐aryl‐6‐fluoroquinolones, both 7‐(piperazin‐1‐yl)‐ and 7‐(4‐methylpiperazin‐1‐yl) derivatives, 9b and 11a , are able to completely inhibit the growth of M. tuberculosis at a concentration of 6.25 μg/ml, while the 7‐[4‐(2‐oxo‐2‐phenylethyl)piperazin‐1‐yl] derivative 13 exhibits only 31% growth inhibition at the same concentration. For 1‐ethyl‐6‐fluoroquinolones, both 7‐[4‐(2‐oxopropyl)piperazin‐1‐yl]‐ and 7‐[4‐(2‐oxo‐2‐phenylethyl)piperazin‐1‐yl]‐derivatives, 2a and 2b , respectively, show complete inhibition, while their 2‐iminoethyl and substituted phenyl counterparts 3a and 2c are less active. In addition, the 6,8‐difluoro derivative was a more‐favorable inhibitor than its 6‐fluoro counterpart ( 2b vs. 2d ). These results deserve full attention especially because 2a, 2b, 9b , and 11a are non‐cytotoxic at a concentration of 100 μM . Furthermore, compound 9b proved to be a potent anti‐TB agent with selective index (SI)>40 and an EC₉₀ value of 5.75 μg/ml.     

On eigenvalues and eigenvectors of graphs

It is known that there exists an equivalence relation between the adjacency matrix of graph theory and the Hückel matrix of Hückel molecular orbital theory. This paper presents some useful methods which allow us to systematically find eigenvalues and eigenvectors of various classes of graphs without calculating characteristic polynomials. Results obtained from this study give insight into the topological studies of molecular orbitals.Dedicated to Professor Frank Harary on the occasion of his 70th birthday.     

复合载荷下圆底扁球壳非线性稳定性

本文采用半解析方法研究在中心分布载荷及中心集中力联合作用下,圆底扁球壳的非线性稳定性问题.避免了求近似解析解时繁重的人工计算,而p-W_m特征关系仍可由显式表达.     

Vinyl copolymers containing pendant 1,4‐distyrylbenzene and 1,3,4‐oxadiazole chromophores: Preparation and optoelectronic properties

We prepared two vinyl copolymers P1 and P2 containing pendant distyrylbenzene and aromatic 1,3,4‐oxadiazole derivatives, respectively, from their precursor poly(styrene‐ran‐4‐vinylbenzyl chloride) (M_w = 11,400, PDI = 1.18), which had been prepared by the controlled radical polymerization (RAFT). Two main chain polymers containing similar isolated distyrylbenzene ( P3) and aromatic 1,3,4‐oxadiazole ( P4 ) chromophores were also synthesized for comparative study. The resulted copolymers ( P1 – P4 ) are soluble in common organic solvents and are basically amorphous materials with 5% weight‐loss temperature higher than 360 °C. The PL spectral results reveal that the architecture of P1 prevents the formation of inter‐ or intramolecular interaction. The HOMO and LUMO levels of P2 , estimated from cyclic voltammetric data, are ?5.96 and ?3.81 eV, respectively, which are much lower than those of P1 (?5.12 and ?3.11 eV). The emission of blend from P1 and P2 are contributed mainly from distyrylbenzene fluorophore (～450 nm) owing to efficient energy transfer. Moreover, the blend exhibits three kinds of redox behavior depending on their weight ratios. The luminance and current efficiency of the EL device lpar;ITO/PEDOT/ MEH ‐ PPV + P2 /Al) are 503 cd/m² and 0.11 cd/A, which can be improved to 1285 cd/m² and 0.44 cd/A, respectively, as the weight ratio of P2 increases from 0 to 20%. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5362–5377, 2006     

Radiation Effects on Concentrated Potassium Hexacyanoferrate(III) Solutions

The neutron irradiated potassium hexacyanoferrate(III) solutions were analyzed for Fe(CN)₆^4?, Fe(CN)₆^3?, and Prussian blue. The retention values (1.1%) were constant throughout the pH and concentration ranges studied, and did not change with the length of irradiation. The complex behavior of the radiochemical yield of the Fe(CN)₆^4? and Prussian blue was attributed to the competition of the various reactions involved in the irradiation.     

Partitioning Boolean lattices into chains of subsets

We prove that the Boolean lattice of all subsets of an n-set can be partitioned into chains of size four if and only if n9.Research supported in part by N.S.F. grant DMS-8401281.Research supported in part by N.S.F. grant DMS-8406451.     

Topological analysis of some special classes of graphs. II. steps,ladders, cylinders

A general strategy is proposed for generating the eigenvectors and the eigenvalues of some special classes of graphs from the well-known chemical graphs such as lines and cycles which are isomorphic to the hydrogen-suppressed linear and cyclic polyenes. This method is applied to step graphs, ladders, cylinders, etc. Net sign analyses are then performed for all these special classes of graphs.     

A Study of the Sydnone Compounds: Bromination and Chlorination(III)

A convenient method for the bromination or chlorination of 4-unsubstituted sydnone with NBS or NCS in DMF solution was carefully investigated. Tweleve bromo-compounds (yield 74-96%) and seven chloro-compounds (yield 75-93%) were obtained.