有限时滞微分系统依照双测度的实际稳定性

本文对具有有限时滞的泛函微分方程建立了关于依照两种测度的实际稳定性的Razumikhin型判定定理，其中未采用通常的辅助函数，且可运用多个含有状态变量x的部分变元的Lyapunov函数，得出部分变远实际稳定性的判定定理，从而改进了已有的结果。     

Vibrational EELS and DFT study of propionic acid and pyruvic acid on Ni(1 0 0): Effects of keto group substitution on room-temperature adsorption and thermal chemistry

The room-temperature adsorption and thermally induced processes of propionic acid and pyruvic acid on Ni(1 0 0) have been investigated by electron energy loss spectroscopy (EELS). Computational vibrational analysis of the optimized bidentate structures for acid-Ni model complexes (involving the organic acid and a Ni atom) has been performed by using the two-layer ONIOM method with the Density Functional Theory and used to interpret the vibrational EELS data. Dehydrogenation of the hydroxyl group is found to result in bonding of the carboxylate group in the propionate and pyruvate adspecies to either a single Ni surface atom in a bidentate configuration or two neighbouring Ni atoms in a bridge configuration. Given the similarities in the total energies and related vibrational frequencies obtained by the calculations in the case of pyruvate adspecies, it is difficult to differentiate the alternate adsorption structure, in which the keto O and hydroxyl O atoms are bonded to a Ni atom in a five-member chelate ring configuration. Furthermore, temperature-dependent EELS studies show that both the propionate and pyruvate adspecies could decompose upon annealing to above 400 K and further dissociate to CO adspecies above 550 K and to C and/or O above 600 K.     

An invariance of geometric mean with respect to Lagrangian means

The invariance of the geometric mean G with respect to the Lagrangian mean-type mapping (Lf,Lg), i.e. the equation G○(Lf,Lg)=G, is considered. We show that the functions f and g must be of high class regularity. This fact allows to reduce the problem to a differential equation and determine the second derivatives of the generators f and g.     

Nonlinear second-order equations with functional implicit impulses and nonlinear functional boundary conditions

In this paper we deal with nonlinear second-order boundary value problems with impulses. The impulsive functions depend implicitly on the different considered variables and the boundary value conditions are nonlinear. In both cases functional dependence on the solution is allowed. The existence results follow from the existence of a pair of well-ordered lower and upper solutions.     

具功能反应的三种群捕食者——食饵系统数学模型稳定性的研究

[1]中提出了具有功能反应的三种群捕食者——食饵系统的两种模型(Ⅰ)、(Ⅱ),并给出了局部渐近稳定的条件。本文研究了另外两种模型(Ⅲ)和(Ⅳ)的局部渐近稳定的条件。     

微分脉冲溶出伏安法同时测定食品中的锌铁锰

在1％乙二胺-0．1mol／L酒石酸钠-pH11．82 Britton—Robinson缓冲溶液体系中用微分脉冲溶出伏安法同时测定锌、铁、锰三种微量元素。它们的峰电位分别为-1184，-1392和-1456mV(vs．Ag/AgCl)；线性范围分别为：0.001—0.015，0．005—0．05和0．04—0．7μg／mL，最低检出浓度分别为0．0007，0．0014和0．0193μg／mL。本法操作简便、准确、灵敏度较高，用于食品中这三种元素的分析，结果令人满意。     

On the Hyers-Ulam-Rassias stability of functional equations in n-variables

In this paper we investigate a generalization of the Hyers-Ulam-Rassias stability for a functional equation of the form f(φ(X))=?(X)f(X)+ψ(X) and the stability in the sense of Ger for the functional equation of the form f(φ(X))=?(X)f(X), where X lie in n-variables. As a consequence, we obtain a stability result in the sense of Hyers-Ulam-Rassias, Gǎvruta, and Ger for some well-known equations such as the gamma, beta, and G-function type's equations.     

HILBERTIAN INVARIANCE PRINCIPLE FOR EMPIRICAL PROCESS ASSOCIATED WITH A MARKOV PROCESS

The authors establish the Hilbertian invariance principle for the empirical process of a stationary Markov process, by extending the forward-backward martingale decomposition of Lyons-Meyer-Zheng to the Hilbert space valued additive functionals associated with general non-reversible Markov processes.     

The Maximal Closed Classes of Unary Functions in p-Valued Logic

In many-valued logic the decision of functional completeness is a basic and important problem, and the thorough solution to this problem depends on determining all maximal closed sets in the set of many-valued logic functions. It includes three famous problems, i.e., to determine all maximal closed sets in the set of the total, of the partial and of the unary many-valued logic functions, respectively. The first two problems have been completely solved ([1], [2], [8]), and the solution to the third problem boils down to determining all maximal subgroups in the k-degree symmetric group S_k, which is an open problem in the finite group theory. In this paper, all maximal closed sets in the set of unary p-valued logic functions are determined, where p is a prime. Mathematics Subject Classification: 03B50, 20B35.     

Hydrogel nanonetworks with functional core-shell structure

Nanohydrogel particles of poly(acrylonitrile-co-N-isopropylacrylamide (p(AN-c-NIPAM)) were synthesized using a microemulsion polymerization technique. Highly monodisperse nanohydrogel particles e.g. 50-150 nm, and various morphology such as core-shell and connected beads were obtained. It was shown that the shell thickness and the size of particles can be tuned by the monomer concentrations and their ratios as well as by the utilization of different crosslinkers. The hydrophobic core monomer, AN was converted to amidoxime groups to increase the hydrophilicity of the nanogels which provide more hydrophilic character and impart new functionality to the nanonetwork. Transmission electron microscopy (TEM), and dynamic light scattering (DLS) techniques were employed for the particle size characterizations. The amidoximation reaction was confirmed by FT-IR spectroscopy.