Exponential stability of discrete-time systems with slowly time-varying delays

Slowly time-varying delays are seldom, but do need to be, considered in the context of discrete-time systems. This paper addresses the exponential stability issue of discrete-time systems with slowly time-varying delays. The basic idea is to transform, by utilizing the switching transformation approach, the original system with slowly time-varying delays into an equivalent switched system with special switching signal. Different types of delays correspond to different types of switching signals, and the stability issue of the original system is converted into that of a switched system. It is the first time that the method of switched homogeneous polynomial Lyapunov function is applied to general delayed systems. Some sufficient exponential stability conditions for the original system are proposed in several situations. It is numerically shown that the conservativeness of the proposed conditions reduces as the degree of the switched homogeneous polynomial Lyapunov function increases.     

Curvature invariants, differential operators and local homogeneity

We first prove that a Riemannian manifold with globally constant additive Weyl invariants is locally homogeneous. Then we use this result to show that a manifold whose Laplacian commutes with all invariant differential operators is a locally homogeneous space.

     

原位氧化还原沉淀水热合成法制备LixMn2O4尖晶石

Li xMn2O4尖晶石是新一代的锂离子二次电池正极材料 [1], 其合成方法对材料的电化学性质影响很大[2].常规合成大多采用高温固相反应法, 此法具有反应温度高, 反应时间长, 容易产生缺陷和产物不纯净等缺点, 导致所合成的锂离子二次电池正极材料的性能较差. 目前用水热合成法制备电池正极材料Li xMn2O4尖晶石尚未见文献报道. 本文在常规水热合成法的基础上采用原位氧化还原沉淀水热合成法 [3]制备前驱物, 该法合成条件更温和, 而且使材料的综合性能得到了改善和提高.      

Mechanism of Reppe's nickel-catalyzed ethyne tetramerization to cyclooctatetraene: a DFT study

In this B3 LYP model study, homoleptic nickel(0) ethyne complexes have been predicted as the catalyst resting state for the title reaction. Ethyne ligand coupling of Ni(C(2)H(2))(3) yields monoethyne nickelacyclopentadiene in the rate-determining step. Ethyne coordination is followed by insertion of an ethyne ligand into the Ni--C sigma bond. A highly strained monoethyne trans-nickelacycloheptatriene is formed. This trans intermediate is unable to reductively eliminate benzene without prior isomerization to a cis-structure. Instead, it rapidly collapses to a nickelacyclononatetraene. Ethyne coordination induces reductive elimination to the cyclooctatetraene complex Ni(eta(2)-C(2)H(2))(eta(2)-C(8)H(8)), followed by facile ligand exchange. Other ethyne coupling pathways have been computed to be less favored. The cyclooctatetraene ligand binds significantly weaker to nickel(0) than ethyne, both for mononuclear, and for dinuclear species. For this reason, C--C bond formation steps at Ni(2)(micro-cot) fragments have been predicted to feature prohibitively high overall reaction barriers.     

关于Liesegang环形成机理的研究

本文研究了Ｌｉｅｓｅｇａｎｇ环的形成，受到两扩散电解质溶液的浓度比、离子浓度积及光照等条件影响。侧重对成环的微观汇聚过程进行了探讨。     

搅拌釜中制备草酸铈的团聚尺寸模型研究

以硝酸铈和草酸铵反应生成草酸铈沉淀为研究对象，探讨了搅拌釜中输入功率、溶液过饱和度与产物团聚尺寸之间的变化关系并在团聚和破碎动力学的基础上建立了团聚尺寸模型。根据草酸铈沉淀实验中得到的实验结果求得了一定反应体系浓度下的模型K1，K2和K3值，最后通过－↑LtE,max的模型计算值与实验值，ε--↑LtE的模型曲线与实验曲线的比较初步证明了该模型的实际适用性。     

Effect of molecular orientation distribution and crystallinity on the measurement of the crystal lattice modulus of nylon 6 by x-ray diffraction

The crystal lattice modulus of nylon 6 (-type) was measured by x-ray diffraction using nylon 6 films drawn up to five times. The measured crystal lattice modulus was 173–175 GPa for all specimens whose crystallinity and the Young's modulus were beyond 46% and 3.75 GPa, respectively. These results indicate that a state of homogenous stress can be achieved. In contrast, the values were scattered for the speciments whose crystallinity and Young's modulus are less than the above values. To study the origin, a numerical calculation of the crystal lattice modulus, as measured by x-ray diffraction, was carried out by considering effects on the orientation factors of molecular chains and crystallinity. In this calculation, a previously introduced model was employed, in which oriented crystalline layers are surrounded by oriented amorphous phases so that the strains of the two phases at the boundary are identical. The theoretical results calculated by the introduced model indicated that the crystal lattice modulus by x-ray diffraction is almost equal to the intrinsic crystal modulus if the morphology of the test specimen can be represented as a series model. In contrast, if a parallel model is more appropriate, the difference between the measured modulus and the intrinsic value can be pronounced. Such morphological dependence was found to be less pronounced with increasing high degree of molecular orientation and crystallinity.     

Transition metal-catalyzed olefin arylation via C–H bond activation of arenes

In this article, two kinds of our transition metal-catalyzed olefin arylations are summarized and discussed. The first one is Ir-catalyzed novel anti-Markovnikov hydroarylation of olefins with benzene. Using this reaction catalyzed by [Ir(μ-acac-O,O′,C₃)(acac-O,O′)(acac-C₃)]₂ (acac = acetylacetonato), 1, straight-chain alkylarenes, which were not obtainable by the conventional Friedel-Crafts aromatic alkylation with olefins, were able to be successfully synthesized directly from arenes and olefins with the higher selectivity than that of branched alkylarenes. This is the first efficient catalyst which shows the desirable high regioselectivity. The reaction of benzene with propylene gave n-propylbenzene and cumene in 61% and 39% selectivities, respectively, and the reaction of benzene and styrene afforded 1,2-diphenylethane in 98% selectivity. The reaction of alkylarene and olefin showed meta and para orientations. A wide range of olefins and arenes can be employed for the synthesis of alkylarenes. The mechanism of the reaction involves C–H bond activation of benzene by Ir center to form Ir–phenyl species. The second reaction is Rh-catalyzed oxidative arylation of ethylene with benzene to directly produce styrene, namely one-step synthesis of styrene. The reaction of benzene with ethylene catalyzed by Rh(ppy)₂(OAc) (ppyH = 2-phenylpyridine, OAc = acetate), 3 with Cu oxidizing agent gave styrene and vinyl acetate in 77% and 23% selectivities, respectively, in contrast to those by Pd(OAc)₂, 47% of styrene and 53% of vinyl acetate. The mechanism of the reaction involves Rh-mediated C–H bond activation of benzene, which appears to be a rate-determining step. Furthermore, Rh complexes in a Rh(I) oxidation state at the beginning of the reaction work as catalysts for the reaction by addition of acacH and O₂ without any oxidizing agent, like Cu salt.     

微圆盘电极上耦合—级均相反应的稳态电流

在电极袭面反应物浓度均匀的近似假设下,得到了微圆盘电极上暂态可逆反应的一般解.然后利用该一般解得到了微圆盘电极上耦合一级均相反应的可逆电极反应CE、EC、EC′和ECE 的稳态电流计算公式.