The initial value problems of first order impulsive differential equations in Banach spaces

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On euclidean domains

We consider Euclidean domains and their groups of units. Let K(a,b) be the set of remainders in the division of a by b. If Card K(a,b) = 1 for any a and b from a Euclidean domain R, then R is known to be isomorphic to the ring of polynomials over some field, see [4], [5]. On the other hand, the condition Card K(a,b) = 2 for any a and b implies that R is isomorphic to the ring Z of integers, see [2]. We give characterization of Euclidean domains and their groups of units under some other conditions on K(a,b).     

r×t阶Kirkman三连系构造的一种方法

发现了 6n+3的高阶 Kirkman三连系构造方法 .阐明了 r× t阶 Kirkman三连系构造的基本理论 .给出了完全三分图的定义 ,并证明了关于 Kirkman三连系构造的命题 .介绍了 1 3 5阶 Kirkman三连系的构造过程 .     

Oscillation of second-order forced functional dynamic equations with oscillatory potentials

Oscillation criteria are established for a second-order forced dynamic equation on time scales containing both delay and advance arguments. Moreover, the potentials are allowed to change sign. Several nontrivial examples from difference equations are provided to illustrate the easy application of the results. The theory can be applied to second-order dynamic equations regardless of the choice of delta or nabla derivatives.     

Effect of silver doping on the structure and phase separation of sulfur-rich As–S glasses: Raman and SEM studies

We report on the structural details and microphase separation of the bulk glasses Ag_x·(As₃₃S₆₇)_100-x for 0x25. Glass–glass phase separation occurs over a wide range of Ag content, i.e. 4x20. An off-resonant polarized Raman spectroscopic study has been carried out to elucidate structural aspects at the short- and medium-range structural order of the glasses. Analysis of Raman spectra revealed quantitative changes of the sulfur-rich microenvironments that reduce upon adding Ag. Scanning electron microscopy combined with X-rays microanalysis have been utilized to examine the type and extent of phase separation, and to provide quantitative details on the atomic concentrations in the Ag-poor and Ag-rich phases. It has been shown that at 7 at.% Ag the Ag-rich phase percolates through the structure; this effect can be associated with an ionic-to-superionic behavior of these glasses in accordance with similar studies on the stoichiometric arsenic sulfide glass; although the phase separation observed in the present glasses is qualitatively different.     

Fast chromatographic method for the determination of dyes in beverages by using high performance liquid chromatography—Diode array detection data and second order algorithms

A fast chromatographic methodology is presented for the analysis of three synthetic dyes in non-alcoholic beverages: amaranth (E123), sunset yellow FCF (E110) and tartrazine (E102). Seven soft drinks (purchased from a local supermarket) were homogenized, filtered and injected into the chromatographic system. Second order data were obtained by a rapid LC separation and DAD detection. A comparative study of the performance of two second order algorithms (MCR-ALS and U-PLS/RBL) applied to model the data, is presented. Interestingly, the data present time shift between different chromatograms and cannot be conveniently corrected to determine the above-mentioned dyes in beverage samples. This fact originates the lack of trilinearity that cannot be conveniently pre-processed and can hardly be modelled by using U-PLS/RBL algorithm. On the contrary, MCR-ALS has shown to be an excellent tool for modelling this kind of data allowing to reach acceptable figures of merit. Recovery values ranged between 97% and 105% when analyzing artificial and real samples were indicative of the good performance of the method. In contrast with the complete separation, which consumes 10 mL of methanol and 3 mL of 0.08 mol L⁻¹ ammonium acetate, the proposed fast chromatography method requires only 0.46 mL of methanol and 1.54 mL of 0.08 mol L⁻¹ ammonium acetate. Consequently, analysis time could be reduced up to 14.2% of the necessary time to perform the complete separation allowing saving both solvents and time, which are related to a reduction of both the costs per analysis and environmental impact.     

一类具有滞的二阶非线性系统的定性分析

考虑具有滞的二阶非线性系统x‘‘(t)f(x(t),x‘(t)) g(x(t),x‘(t)ψ(x(t-τ））＝p(t),借助李雅普诺夫函数方法,得到了其零解稳定性,解的有界性,周期解的在性和平衡振荡的存在唯一性。     

一类一阶常微分方程初值问题的无穷多解性

应用分离变量法,得到了一类一阶微分方程初值问题u′(t)=b(t)f(u(t)),t0,u(0)=0存在无穷多个解的充分必要条件.并给出了全部解.     

Loading‐Dependent Structural Model of Polymeric Micelles Encapsulating Curcumin by Solid‐State NMR Spectroscopy

Detailed insight into the internal structure of drug‐loaded polymeric micelles is scarce, but important for developing optimized delivery systems. We observed that an increase in the curcumin loading of triblock copolymers based on poly(2‐oxazolines) and poly(2‐oxazines) results in poorer dissolution properties. Using solid‐state NMR spectroscopy and complementary tools we propose a loading‐dependent structural model on the molecular level that provides an explanation for these pronounced differences. Changes in the chemical shifts and cross‐peaks in 2D NMR experiments give evidence for the involvement of the hydrophobic polymer block in the curcumin coordination at low loadings, while at higher loadings an increase in the interaction with the hydrophilic polymer blocks is observed. The involvement of the hydrophilic compartment may be critical for ultrahigh‐loaded polymer micelles and can help to rationalize specific polymer modifications to improve the performance of similar drug delivery systems.