一类1 < α < 2非局部条件下的脉冲分数阶微分方程mild解的存在性

本文研究了一类1 < α < 2非局部条件下的脉冲分数阶偏微分方程mild解的存在性问题.利用解算子的相关性质及Krasnoselskii不动点理论的方法,获得了这类方程的mild解并予以证明,且得到了解的存在性结果.     

Bolzano's Theorems for Holomorphic Mappings

The existence of a zero for a holomorphic functions on a ball or on a rectangle under some sign conditions on the boundary generalizing Bolzano's ones for real functions on an interval is deduced in a very simple way from Cauchy's theorem for holomorphic functions.A more complicated proof,using Cauchy's argument principle,provides uniqueness of the zero,when the sign conditions on the boundary are strict.Applications are given to corresponding Brouwer fixed point theorems for holomorphic functions.Extensions to holomorphic mappings from Cn to Cn are obtained using Brouwer degree.     

抽象空间中非线性算子方程变号解的存在性研究

利用Banach空间中的锥理论和不动点定理讨论了非线性算子方程变号解的存在性,给出了E_u_0空间下非线性算子方程变号解至少有一个变号解、一个正解和一个负解的条件,并讨论了仅通过一个上解条件得出非线性算子方程变号解的存在性定理.     

2-距离空间中平方型压缩映象的一个新的耦合公共不动点定理

在2-距离空间的框架下, 利用映象对的ω-相容性条件, 建立了一类新的平方型压缩条件, 讨论了此类映象耦合公共不动点的存在性和唯一性.证明了一个新的耦合公共不动点定理, 也提供了一个有效的例子来支持该文的新结果.该文的结果改善了之前文献中的相关结果.     

基于随机微分博弈的动态投入产出问题研究

基于W Leontief提出的动态投入产出模型,讨论了考虑随机因素的离散时间下的最优策略设计问题.利用博弈论的思想,把动态投入产出系统抽象为离散时间的博弈模型,运用鞍点均衡策略设计出求解该投入产出问题的新方法,为宏观经济决策提供依据.     

一类奇异非线性多重调和方程存在正整解的充分必要条件

研究一类奇异非线性多重调和方程?~mu=f(|x|,u,|▽u|)u~(-β),给出了方程存在正的径向对称整体解的充分必要条件和解的性质.     

About the compatibility between ansatzes and constraints for a local formulation of orbital‐free density functional theory

Functional properties that are exact for the Hohenberg–Kohn functional may turn into mutually exclusive constraints at a given level of ansatz. This is exemplarily shown for the local density approximation. Nevertheless, it is possible to reach exactly the Kohn–Sham data from an orbital‐free density functional framework based on simple one‐point functionals by starting from the Levy–Perdew–Sahni formulation. The energy value is obtained from the density‐potential pair, and therefore does not refer to the functional dependence of the potential expression. Consequently, the potential expression can be obtained from any suitable model and is not required to follow proper scaling behavior.     

PVT properties of imidazolium-, phosphonium-, pyridinium- and pyrrolidinium-based ionic liquids using critical point constants

Song and Mason equation of state (EOS) with a simple modification has been extended to modelling PVT properties of ionic liquids (ILs). The considered ILs are [C₁mim][MeSO4], [C₁mim][CH₃OC₂H₅SO₄], [C₁mim][(CH₃)₂PO₄], [C₂mim][MeSO4], [C₂mim][BF₄], [C₂mim][SCN], [C₂eim][NTf₂], [C₄mim][C(CN)₃], [C₄mim][CF₃SO₃], [C₄mim][SCN], [C₅mim][NTf₂], [C₈mim][NTf₂], [(C₆H₁₃)₃P(C₁₄H₂₉)][Cl], [(C₆H₁₃)₃P(C₁₄H₂₉)][NTf₂], [(C₆H₁₃)₃P(C₁₄H₂₉)][Ac], [C₃mpyr][NTf₂], [C₄mpyr][NTf₂] and [Py][C₂H₅OC₂H₄SO₄]. Three temperature-dependent parameters in the proposed EOS have been scaled as functions of reduced temperature with the use of the law of corresponding states. It is shown that the knowledge of just critical temperature and critical density is sufficient to predict the PVT properties of these ILs. The overall average absolute deviation of calculated densities from literature values for 1347 data points of 18 ILs was found to be 0.58%. The predicted density of ILs from proposed EOS has been compared with those obtained by other literature work. Moreover, we indicate that the Zeno line regularity can well be predicted by proposed model for ILs.     

Determination of polybrominated diphenyl ethers in milk samples. Development of green extraction coupled techniques for sample preparation

Ultrasound‐assisted extraction (UAE), cloud point extraction (CPE), and ultrasound back‐extraction (UABE) techniques have been coupled for lixiviation, preconcentration, and cleanup of polybrominated diphenyl ethers (PBDEs) from milk samples for determination by gas chromatography‐electron capture detection (GC‐ECD). Physicochemical parameters that affect the efficiency of the extraction system were investigated using a design of experiments based on multivariate statistical tools, and considering the sample matrix along the development. The coupling of the leaching step, UAE, enhanced ca. 3.5 times the extraction efficiency of the former sample preparation methodology (CPE‐UABE) leading to cleaner sample extracts suitable for GC analysis. Under optimum conditions, the proposed methodology exhibits successful performance in terms of linearity and precision, with recoveries in the range of 68–70% and LODs within the range 0.05–0.5 ng/g dry weight (d.w.). The proposed sample preparation methodology coupled three green analytical techniques. It expands the application frontiers of CPE for the analysis of biological samples by GC. The optimized methodology was used for determination of PBDEs in powder milk samples, from both commercial and human sources.     

Equilibrium phase behavior of aqueous two-phase systems containing 17R4/L64 and citrates

The cloud points (CPs) of the copolymers 17R4 and L64 were first measured, and then the effects of salts ((NH₄)₃C₆H₅O₇, K₃C₆H₅O₇) on 17R4 and L64 were researched. After finishing the work described above, the temperature (278.15, 283.15, and 288.15) K of aqueous two-phase systems was determined, which consist of 17R4-(NH₄)₃C₆H₅O₇, 17R4-K₃C₆H₅O₇, L64-(NH₄)₃C₆H₅O₇, and L64-K₃C₆H₅O₇. Finally, the liquid–liquid equilibrium (LLE) data of binodal curve and the tie line for 17R4-(NH₄)₃C₆H₅O₇ aqueous two- phase systems (ATPSs) 17R4-K₃C₆H₅O₇ ATPSs, L64-(NH₄)₃C₆H₅O₇ ATPSs, and L64-K₃C₆H₅O₇ ATPSs were obtained. Nonlinear fitting of the empirical equation was used for making the diagram. The results showed that the change in the size of the two-phase areas increases with the increase of temperature. The capacity of the salts to induce phase segregation follows the Hofmeister series, that is, K₃C₆H₅O₇?>?(NH₄)₃C₆H₅O₇. In addition, the findings also showed that the phase separation ability of 17R4 is better than that of L64.