Hydrothermal preparation and photoluminescence of bundle-like structure of ZnWO4 nanorods

ZnWO₄ nanorods with a bundle-like structure were synthesized at 180°C for 12 h by a hydrothermal technology from Na₂WO₄⋅2H₂O and ZnSO₄⋅7H₂O in the presence of sodium dodecyl sulfate (SDS). The as-synthesized bundle-like structure of ZnWO₄ nanorods was characterized by various techniques: TEM, XRD and EDS. The luminescence properties of the bundle-like structure of the ZnWO₄ nanorods were investigated by photoluminescence (PL) spectroscopy.     

Infinite horizon H_2/H_\infty optimal control for discrete-time Markov jump systems with (x,u,v)-dependent noise

In this paper, an infinite horizon $H_2/H_\infty $ control problem is addressed for a broad class of discrete-time Markov jump systems with ( $x,u,v$ )-dependent noises. First of all, under the condition of exact detectability, the stochastic Popov–Belevich–Hautus (PBH) criterion is utilized to establish an extended Lyapunov theorem for a generalized Lyapunov equation. Further, a necessary and sufficient condition is presented for the existence of state-feedback $H_2/H_\infty $ optimal controller on the basis of two coupled matrix Riccati equations, which may be solved by a backward iterative algorithm. A numerical example with simulations is supplied to illustrate the proposed theoretical results.     

Nonlinear Saturation Amplitude in Classical Planar Richtmyer–Meshkov Instability

The classical planar Richtmyer–Meshkov instability(RMI) at a fluid interface supported by a constant pressure is investigated by a formal perturbation expansion up to the third order,and then according to definition of nonlinear saturation amplitude(NSA) in Rayleigh–Taylor instability(RTI),the NSA in planar RMI is obtained explicitly.It is found that the NSA in planar RMI is affected by the initial perturbation wavelength and the initial amplitude of the interface,while the effect of the initial amplitude of the interface on the NSA is less than that of the initial perturbation wavelength.Without marginal influence of the initial amplitude,the NSA increases linearly with wavelength.The NSA normalized by the wavelength in planar RMI is about 0.11,larger than that corresponding to RTI.     

Global periodicity and complete integrability of discrete dynamical systems

Consider the discrete dynamical system generated by a map F. It is said that it is globally periodic if there exists a natural number p such that F ^p (x)=x for all x in the phase space. On the other hand, it is called completely integrable if it has as many functionally independent first integrals as the dimension of the phase space. In this paper, we relate both concepts. We also give a large list of globally periodic dynamical systems together with a complete set of their first integrals, emphasizing the ones coming from difference equations.     

Existence of positive periodic solutions for second-order functional differential equations

In this paper, we show the existence of positive $T$ -periodic solutions of second-order functional differential equations $u^{\prime \prime }(t)-\rho ^2u(t)+\lambda g(t)f(u(t-\tau (t)))=0,\ \ t\in \mathbb R , $ where $\rho >0$ is a constant, $g\in C(\mathbb R ,[0,\infty ))$ , $\tau \in C(\mathbb R ,\mathbb R )$ are $T$ -periodic functions, $f\in C([0,\infty ),[0,\infty ))$ and $\lambda $ is a positive parameter. Our approach based on global bifurcation theorem.     

Cost estimation algorithm and decision-making model for curriculum modification in educational organization

The decision about curriculum modification usually takes place at the knowledge level, mainly with consideration of individual academic staff competences and qualifications. However, traditional approaches to cost estimation of curriculum modification are focused on material resources only. In this paper we present a cost estimation method and decision model for curriculum modification in educational organizations. The proposed method works at the knowledge level and employs competence sets as knowledge representation models in educational organizations. Authors used the theory of hierarchical, multilevel systems in order to define the model of the decision-making process of curriculum modification and its dimension. Basing on this and also using a fuzzy competence model the cost estimation algorithm in the form of a group competences expansion algorithm is proposed. The algorithm focuses on the cost of staff competence expansion caused by the knowledge development process.     

Efficient glycosylation with glycosyl ortho-allylbenzoates as donors

Glycosylation reactions are significant as they provide access to model compounds that are useful for elucidating biochemical pathways. Herein, we describe the development of glycosyl ortho-alkynylbenzoates as novel, bench-top stable, and readily available glycosyl donors. Glycosylation is promoted by inexpensive trimethylsilyl triflate (TMSOTf) in combination with N-iodosuccinimide (NIS) under mild reaction conditions; hence, the novel glycosyl donors are promising reagents for the synthesis of glycosides.     

One-pot diastereoselective synthesis of tetrahydroepimino-benzo[b]azocines through sequential [3+2]-cycloaddition and Staudinger-aza-Wittig reactions

The one-pot synthesis of tetrahydro-epiminobenzo[b]azocines through a sequential 1,3-dipolar cycloaddition and intramolecular Staudinger-aza-Wittig reaction sequence is reported. This methodology provides a new and efficient approach for medium-sized and bridged nitrogen heterocyclic molecules.     

Efficient Synthesis of Spirooxindole Pyrrolones by a Rhodium(III)‐Catalyzed C−H Activation/Carbene Insertion/Lossen Rearrangement Sequence

A rhodium(III)‐catalyzed domino annulation of simple olefins with diazo oxindoles to give spirooxindole pyrrolone products is described. This reaction can be formally viewed as the result of an anomalous tandem C?H activation, carbene insertion, Lossen rearrangement, and a nucleophilic addition process. The potential utility of this reaction was further demonstrated by the late‐stage diversification of drug molecules.