An appraisal of computational complexity for operations researchers

We review recent developments in the theory and practice of computational complexity, in order to highlight some of the basic concepts and ideas that have come out of this area. The discussion centers around the progress on twelve important open problems listed in 1979 by M.R. Garey and D.S. Johnson, the introduction of probabilistic elements in the analysis and design of algorithms, the problem classes around P and RP, and the P ≠ RP conjecture.     

Synthesis of zeolite IM-5 under rotating and static conditions and the catalytic performance of Mo/H-IM-5 catalyst in methane non-oxidative aromatization

The hydrothermal crystallization of zeolite IM-5 was investigated under rotating (denoted as IM-5-R) and static (denoted as IM-5-S) synthesis conditions. Mo-modified catalysts (Mo-IM-5-R and Mo-IM-5-S) were prepared for the methane non-oxidative aromatization. The physical properties and acidities of the samples were characterized by XRD, SEM, BET and IR spectroscopy. Compared with Mo-IM-5-S, the Mo-IM-5-R catalyst showed both a higher conversion of methane and higher selectivity to benzene in methane aromatization. A higher catalytic activity of Mo-IM-5-R may be attributed to the preferable textural properties and acidities of zeolite IM-5-R. Moreover, the catalyst prepared by the physical mixing method exhibited lower initial activity, but better stability for methane aromatization than that prepared by the impregnation method.     

Mesomorphic properties of 4-(polyfluoroalkoxycarbonyl)phenyl 4-(4-n-heptoxy-2,3,5,6-tetrafluorophenyl)benzoates

A series of 4-(polyfluoroalkoxycarbonyl)phenyl 4-(4-n-heptoxy-2,3,5,6-tetrafluorophenyl)benzoates were synthesized and observed using DSC and optical polarizing microscopy. The results show that they are not mesogens. Their mesomorphic properties were compared with similar compounds containing no aromatic fluorine substituents.     

Synthesis and mesomorphic properties of steroidal liquid crystals containing perfluoroalkoxycarbonylphenyl units

Two cholesteryl esters liquid crystals containing perfluoroalkoxy terminal chains, and benzoate and carbonate moieties, have been synthesized. Their mesomorphic properties were observed and measured by optical polarizing microscopy and differential scanning calorimetry. The results show that the two liquid crystals exhibit smectic A and B phases. No chiral tilted smectic phase was observed.     

A new assignment technique of 2D‐NMR spectra by spin‐lock sequence to a tripeptide containing tryptophan in water

We developed a new assignment technique of tryptophan residues using pulsed field gradient TOCSY–ROESY (PFG‐TORO) and pulsed field gradient TOCSY–ROESY–TOCSY (PFG‐TOROTO) techniques in water. Connectivity from βH to ζ2H (H‐7) via ε1H (H‐1) and δ1H (H‐2) in the TORO spectrum and from βH to ζ3H (H‐5) and η2H (H‐6) via ε1H (H‐1) and δ1H (H‐2) in the TOROTO spectrum could be able to assign each of the protons of the indole rings. Copyright © 2010 John Wiley & Sons, Ltd.     

The Cycloaddition Reactions of Furan with Cyanoacetylenes

The temperature-dependent adduct formation has been reported on the cycloaddition reactions of furan and dimethylacatyledicarboxylate as symmetrically substituted acetylene, in which the kinetically controlled products I and II are formed at room temperature, whereas the thermodynamically controlled ones, III, IV, and V, are obtained at elevated temperature.¹     

Chemical oscillation of vanadium complexes: Simple and aperiodic systems

An oscillatory chemical reaction is an intriguing phenomenon subject to various and often uncontrollable factors. Many oscillatory systems consist of a strong acid, metal ion and an additional species with accessible oxidation states, and restrictive temperature conditions. Thus, an oscillatory system in which all the factors are understood would be useful. In this paper, we describe the first such system based on vanadium chemistry. The V(IV) complex (pale green color) turns dark orange with the production of a V(V) complex. This reaction is affected by many factors such as oxygen, ultraviolet (UV) irradiation, visible irradiation, and aldehyde addition. This oscillation reaction occurs only in a dichloromethane solution, suggesting that the solvent intervenes in the reaction. Examination of the gas phase during the oscillation reaction revealed the formation of carbon monoxide, carbon dioxide, hydrogen chloride, and phosgene. Based on these observations, we propose a plausible oscillation reaction mechanism.The results of this study contribute to the field of nonlinear dynamics. Additionally, this work offers new insights into vanadium chemistry because this oscillation phenomenon is strongly correlated with the electron transfer reaction of the vanadium complex. Moreover, studies using vanadium complexes may help in understanding vanadium-mediated electron transfer systems in vivo, such as vanadium accumulation and storage observed in marine organisms.     

Almost sure state estimation for nonlinear stochastic systems with Markovian switching

In this paper, the almost sure asymptotic stability is investigated for the state estimation problem of a general class of nonlinear stochastic systems with Markovian switching. A nonlinear state estimator with Markovian switching is first proposed, and then, a sufficient condition is given, which guarantees the almost sure asymptotic stability of the dynamics of the estimation error. Based on this condition, some simplified criteria are deduced by taking special forms of Lyapunov functions. Subsequently, an easy-to-verify procedure is put forward for the state estimation problem of the linear stochastic system with Markovian switching. Finally, two numerical examples are used to illustrate the effectiveness of the main results.     

K3-free图的线图的哈密顿性

设G是一个简单图，Gi G，G1在G中的度定义为d（Gt）=∑v∈v（c）d（v），其中d（v）为v在G中的度数。本文的主要结果是：设G是n≥2阶几乎无桥的简单连通K3-free图，且G≌k1,n-1、Q1和Q2，若对G中任何同构于四个顶点路的导出子图I有d（I）≥n＋2，则G有一个D-闭迹，从而G的线图L（G）是哈密顿图。