Scaling properties of ℤ k- 1 actions on the circle

We derive universal scaling properties for ^k–1 actions on the circle whose generators have rotation numbers algebraic of degreek. As fork=2 these properties can be explained for arbitraryk in terms of a renormalization group transformation. It has at least one trivial fixed point corresponding to an action whose generators are pure rotations. The spectrum of the linearized transformation in this fixed point is analyzed completely. The fixed point is hyperbolic with a (k–1)-dimensional unstable manifold. In the casek=2 the known results are therefore recovered.     

Topological degree of a family of convex functions and localization of nash equilibrium points

We define the degree of a family of convex functionsf _x, wherex , and prove that, if this degree is different from zero, one has at least one Nash equilibrium point in . This is a criterion of localization of such equilibrium points.     

Influence of extractions on physicochemical characterization and bioactivity of Piper nigrum oils: Study on the non-isothermal decomposition kinetic

Black pepper oils have been investigated frequently in the recent years. However, there is a significant variation in physicochemical properties and bioactivity of oils depended on extraction techniques. In this study, the systemic investigation of four various extraction methods was performed to evaluate the physicochemical characterizations, antioxidant and antibacterial activity. The investigation of ¹H NMR, FTIR and UV–Vis spectra confirmed presence of non-volatile components in oils extracted through supercritical CO₂ and hexane-soaking extractions which induced their typical thermal properties. The isothermal behaviour of extracted oils related to evaporation was within range of 3.2–7.3% (w/w) at 27 °C. The SEM images of the black pepper confirmed different operation manners of mechanism between extractions using the solvents and heating process. The lowest MIC for both essential oils from conventional hidrodistillation and microwave-assisted hidrodistillation against two bacteria including E. coli and B. subtilis were found to be 137 µg mL⁻¹. The non-isothermal decomposition kinetics were investigated on the essential oil of microwave-assisted hydrodistillation extraction. The activation energies and pre-exponent factors of non-isothermal decomposition were found to be in range of 36.5–73.7 KJ mol⁻¹ and 4.98 × 10³–1.97 × 10⁸ s⁻¹, respectively, dependent on conversional fractions of the oil. The results revealed that chemical components, physicochemical properties and bioactivity of black pepper essential oils depended on the extraction techniques.     

Optimized POCl3-assisted synthesis of 2-amino-1,3,4-thiadiazole/1,3,4-oxadiazole derivatives as anti-influenza agents

Although recent decades have witnessed the synthesis of 1,3,4-thiadiazoles via phosphorus POCl₃-promoted cyclization reaction, simultaneous access to 2-amino-1,3,4-thiadiazole and 2-amino-1,3,4-oxadiazole analogs remains unexpected and elusive. Herein, a detailed regiocontrolled synthesis of 2-amino-1,3,4-thiadiazoles in good to high yields with good regioselectivities from readily available thiosemicarbazides using POCl₃ was disclosed. Meantime, to establish a comprehensive structure–activity relationship, 2-amino-1,3,4-oxadiazole derivatives as single regioisomers were prepared via EDCI·HCl-triggered cyclization of the thiosemicarbazide intermediates. The in vitro anti-influenza assays proved that the selected compounds with the pyrazine/pyridine ring exhibited certain inhibitory activities against influenza A virus strains A/HK/68 (H3N2) and A/PR/8/34 (H1N1) in MDCK cells. Among them, N-(adamantan-1-yl)-5-(5-(azepan-1-yl)pyrazin-2-yl)-1,3,4-thiadiazol-2-amine (4j) was the most active compound, and exhibited favorable activity with EC₅₀ values of 3.5 μM and 7.5 μM, respectively. In addition, the molecular docking results explained the reason why compound 4j had dual inhibitory activity and revealed the reasonable binding mode of this compound with the M2-S31N and M2-WT ion channels. This compound had the potential to be further developed as an anti-influenza drug.     

A convergence result for a sequence of distributed-parameter optimal control problems

In this paper, we consider a sequence of abstract optimal control problems by allowing the cost integrand, the partial differential operator, and the control constraint set all to vary simultaneously. Using the notions of -convergence of functions,G-convergence of operators, and Kuratowski-Mosco convergence of sets, we show that the values of the approximating problems converge to that of the limit problem. Also we show that a convergent sequence of optimal pairs for the approximating problems has a limit which is optimal for the limit problem. A concrete example of parabolic optimal control problems is worked out in detail.This research was supported by NSF Grant No. DMS-88-02688.     

Existence of maximal points with respect to ordered bipreference relations

The maximality of a point with respect to an ordered pair of arbitrary preference relations is introduced. Necessary and sufficient conditions for the existence of maximal points are given.The authors are grateful for the referee's comments which led to an improved presentation of the paper.     

Optimal monotone hysteretic Markov policies in anM/M/1 queueing model with switching costs and finite time horizon

In anM/M/1 queueing model, a decision maker can choosem pairs of arrival- and service rates. He can change his action at any time epoch, a switch of action costs an amount depending on the size of the switch. Besides that there are continuously incurring costs. Over a finite time horizon, there exists an optimal monotone hysteretic Markov policy. This is shown essentially by the technique of time discretization.The work producing this article was done during a half year stay at the University of Leiden, The Netherlands, with Prof. Arie Hordijk. A technical report (a more detailled version of this article) was written there [6]. The opportunity for this stay was given by the University of Bonn, Germany, where the author, at that time, worked as scientific assistant of Prof. M. Schäl.     

有限群极大子群的θ-子群偶

N.P.Mukherjee和 P.Bhattacharya在“On theta pairs for a maximal sub-group”(Proc.Amer.Math.Soc,Vl09N3(1990))一文中定义了有限群的极大子群的θ-子群偶概念,研究了极大子群的极大θ-子群偶对群结构的影响,得到了一系列结果.本文在进一步探究θ-子群偶性质的基础上,对该文中一系列主要结果作出了本质性的改进,并给出了可解性、幂零性的一些新刻划.     

Extended radial epiderivatives of non-convex vector-valued maps and parametric quasiconvex programming

In this paper, we consider extended vector-valued mappings defined on a normed linear space. Based on the recent semicontinuous regularizations related to hypographical and/or epigraphical profile mappings of the considered function introduced, we define semicontinuous radial epiderivatives. We, then, demonstrate that the properties of these epiderivatives amount to properties of hypographical and/or epigraphical profile mappings of the corresponding difference quotient of the underlying function, which simplify fairly well the proofs in the radial epiderivative formulaes. In particular, we stress the impact of semicontinuity, hence, we characterize with new arguments the radial epiderivatives in terms of the suprema and/or infima of the interiorly radial cone of the hypograph and/or epigraph of the considered function. Finally, we obtain optimality conditions for general non-convex constrained vector optimization problems. We apply thereafter the obtained pattern to a parametric quasiconvex programming problem for which we derive necessary and sufficient optimality conditions that are not sensitive to perturbation at the nominal level, yielding henceforth more – and strong at least under asymptotically regular constraints – information than the recent stability results obtained under additional conditions on the regularity of the normal cone to the adjusted sublevel sets of the underlying function.