椭圆截面圆环和扭圆环的转动惯量

首先建立了椭圆截面的圆环和扭圆环的数学模型,然后根据定义计算绕3个坐标轴的轴转动惯量和惯量积,其间充分利用截面图形的对称性对计算过程简化,得到一些有益的结论和结果.     

On the Well-Posedness of the Dissipative Kadomtsev–Petviashvili Equation

Mathematical Notes - The well-posedness of the initial-value problem associated with the dissipative Kadomtsev–Petviashvili equation in the case of two-dimensional space is studied. It is...     

Barrier Lyapunov functions-based fixed-time stabilization of nonholonomic systems with unmatched uncertainties and time-varying output constraints

The fixed-time stabilization problem is addressed in this paper for a kind of nonholonomic systems in chained form with unmatched uncertainties and time-varying output constraints. A novel tan-type barrier Lyapunov function is introduced to deal with time-varying output constraints. Under the unified framework of the considered system with and without output constraints, a state feedback controller is designed with the aid of adding a power integrator technique and switching control strategy. It is shown that the suggested controller ensures the states of closed-loop system to zero in a given fixed time without disobeying the constraints. Finally, simulation results are given to confirm the efficacy of the presented control scheme.

     

Stochastic exponential synchronization for delayed neural networks with semi-Markovian switchings: Saturated heterogeneous sampling communication

By implementing heterogeneous sampling communication mechanism, this article addresses the exponential synchronization issue of drive–response chaotic neural networks (CNNs) with interval time-varying delays by simultaneously taking into account the semi-Markovian switchings and saturating actuators. More specifically, a semi-Markovian jumping model whose transition rates (TRs) are not constant but depends on the sojourn time (ST) is introduced to characterize the stochastic changing among the interaction of CNNs, which makes the NNs model under consideration more suitable for some actual circumstances. More particularly, we assume that the sampling intervals are heterogeneous and time-varying, which may be more practical in real-life applications than homogeneous sampling policy. Additionally, by introducing some new terms, one novel time-dependent Lyapunov–Krasovskii function (LKF) is ingeniously constructed, which can fully capture the characteristic information of heterogeneous sampling pattern. Benefitting from the introduced relaxed free-weighting matrices (FWM) and resorting to the formed LKF, some sampling-interval-dependent sufficient conditions for controller design of the resulting semi-MJNNs error system are established and expressed by linear matrix inequalities (LMIs). These LMIs-based constraints can be effectively checked by utilizing the available software packages. Therein, the developed synchronization criteria dependent on both the lower and upper bounds of sampling periods, and the available information about the actual sampling pattern is fully considered. Ultimately, two numerical examples are provided to demonstrate the feasibility and practicability of our theoretical findings.     

Copper-catalyzed efficient dithiocyanation of styrenes: Synthesis of dithiocyanates

A novel Cu-catalyzed intermolecular chemoselectivity dithiocyanation of styrenes with ammonium thiocyanate has been developed under mild conditions. This reaction exhibits a wide range of functional-group tolerance in styrenes to afford various dithiocyanates. The reaction mechanism was primarily investigated and a radical process was proposed.     

Solvent Effect on the Assembly of Two Cadmium(II) Coordination Polymers Derived from 3,3′‐(Diazenediyl)dibenzoic Acid: Syntheses,Structures, Stabilities,and Photocatalytic Properties

Abstract. Two cadmium(II) coordination polymers, {CdL₂[(CH₃)₂NH₂]₂ · 2DMF}_n ( 1 ) and {[Cd₃L₄[(CH₃)₂NH₂]₂] · EtOH · 2DMF}_n ( 2 ) were synthesized from the solvothermal reactions of Cd(OAc)₂ · 2H₂O with 3,3′‐(diazenediyl)dibenzoic acid (H₂L) in different solvents. Both complexes were characterized by elemental analysis, IR spectroscopy, powder X‐ray diffraction, TG analysis, and single‐crystal X‐ray diffraction. In compound 1 , central cadmium(II) atoms were linked with the surrounding L ligands to generate an infinite 1D chain with repeated rings. Compound 2 displayed a 3D threefold interpenetrating framework based on cage‐like [Cd₃L₆]₈ species and exhibited a 4¹²6³ topological structure. The results demonstrated that the different solvents had significant effect on the construction of different coordination compounds from the same components. In addition, they exhibited excellent stability and good photocatalytic activity towards the degradation of methylene blue in aqueous solution under UV irradiation.     

An Organic‐Inorganic Hybrid Based on Keggin‐Type Polyoxometalate and Hypoxanthine: Synthesis,Structure, Stability,and Electrochemistry Properties

The organic‐inorganic hybrid H₅[Ag₂(hyp)₂]₂[BW₁₂O₄₀] · 9H₂O ( 1 ) (hpy = hypoxanthine), based on Keggin‐type polyoxometalate and hypoxanthine, was prepared by hydrothermal synthesis and characterized by single‐crystal and powder X‐ray diffraction, IR spectroscopy, elemental analysis, and thermogravimetry. The title compound has a two‐dimensional layer structure constructed by Keggin‐type [BW₁₂O₄₀]^5– anion, silver, and the biomolecule hyp. In addition, compound 1 exhibited excellent stability and superior activity in the electro‐catalytic oxidation of glucose.     

明清时期油脂炼硫法在医药与火药制造中的应用

硫磺自从汉代以来就是我国中医制药和炼丹术中所用的主要药物。唐代医家已用油煎法提纯雄黄,在宋代的医药界,油煎法已经应用于硫磺的提纯。明代医书中记载用油脂精炼硫磺的方法已经比较成熟。清代医家针对去除硫磺内的残留油脂,提出了精细的方案。宋代制造火药将硫磺与油脂混合,明代兵书中详细记载了利用油脂提炼硫磺的技术。明末清初西方人传入了独特的硫磺精炼法,西方人更加注重杂质的过滤以及硫磺中油分的去除。硫磺提纯是保障火药质量的关键步骤。     

固体潮相关的地球表面形变和涨落

在月球和太阳的引力作用下,地球的固体表面也发生与海水表面类似的周期性涨落,这种现象称为固体潮.固体潮的形成原因与海潮相同,但其计算问题远比后者复杂.本文用开尔文地球模型和比较简单的方法计算固体潮相关的地球表面方程和涨落幅度,并进行相关问题的讨论.     

Towards second order Lax pairs to discrete Painlevé equations of first degree

We investigate the question of finding discrete Lax pairs for the six discrete Painlevé equations (Pn). The choice we make is to discretize the pairs of Garnier, once converted to matrix form.