Functional Central Limit Theorems for Triangular Arrays of Function-Indexed Processes under Uniformly Integrable Entropy Conditions

Functional central limit theorems for triangular arrays of rowwise independent stochastic processes are established by a method replacing tail probabilities by expectations throughout. The main tool is a maximal inequality based on a preliminary version proved by P. Gaenssler and Th. Schlumprecht. Its essential refinement used here is achieved by an additional inequality due to M. Ledoux and M. Talagrand. The entropy condition emerging in our theorems was introduced by K. S. Alexander, whose functional central limit theorem for so-calledmeasure-like processeswill be also regained. Applications concern, in particular, so-calledrandom measure processeswhich include function-indexed empirical processes and partial-sum processes (with random or fixed locations). In this context, we obtain generalizations of results due to K. S. Alexander, M. A. Arcones, P. Gaenssler, and K. Ziegler. Further examples include nonparametric regression and intensity estimation for spatial Poisson processes.     

A note on the weighted norm inequality for the one-sided maximal operator

Let be the one-sided maximal function. In this note we obtain some necessary and sufficient conditions in order that the weighted weak type inequality holds for . Meanwhile, some necessary or sufficient conditions for the weighted inequality for are given.

     

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.     

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.     

光子晶体光纤在熔接夹具中的受力分析

运用接触力学和圆环压溃强度理论对由V型槽固定的光子晶体光纤进行了受力分析。分别考虑了两种极限情况,以推导光纤中的应力分布。第一种情况假设光纤是完全由纯石英材料制成的内部均匀的实芯圆柱体;第二种情况是把光纤假设成一个空芯圆柱体。根据这两种极限情况推导出了光子晶体光纤受力后光纤内部的最大应力点位于平行于接触面的外层空气孔的附近。采用有限元方法验证了此结论,计算出了光子晶体光纤可能承受的最大压力,并给出了光子晶体光纤在V型槽中的应力分布和变形情况。     

振荡型积分对极大函数的估计

首先将2维KaKeya型的极大函数通过Fourier变换转化成振荡型积分的形式,对此振荡型积分作相应的估计。通过Littlewood—Paley方法将此振荡型积分分解成不同的算子,在估计极大算子时,通过Newton—Leibnig公式,将其转化为相应的积分形式,最后通过经典的振荡型积分的估计,得到最后的结果,本方法强调振荡型积分的方法和以前几何测度论的方法不同。     

基于失效情景的应急设施选址问题

非常规突发事件巨大的破坏力以及发生时间、地点和规模的不确定性,使应急系统内设施有可能被破坏而失效,因此选址时必须考虑设施失效情景的发生.给出以最大限度覆盖用户需求为目标,基于失效设施数目具有不确定性情景的设施选址双层随机规划模型;通过计算模型上下界,给出减小规模的等价模型,降低了双层规划求解难度;最后实验验证了模型的合理性,并给出新增选址方案.     

A note on the paper “characterization of all optimal solutions and parametric maximal flows in networks” of G. Ruhe (optimization 16 (1985) 1, 51-61)

First it is shown that the implementation of the algorithm proposed in the considered paper may cause some problems if no further specification is made as to one of its steps. Secondly, such a specification is suggested.