分数阶微分方程m点边值共振问题解的存在性

利用Mawhin延拓定理考察了一类分数阶微分方程m点边值共振问题解的存在性.得到了解的存在性的一个充分性条件,并且举出实例用以说明主要结果.     

Standing waves for 4‐superlinear Schrödinger‐Kirchhoff equations

We consider standing waves for 4‐superlinear Schrödinger–Kirchhoff equations in with potential indefinite in sign. The nonlinearity considered in this study satisfies a condition that is much weaker than the classical Ambrosetti–Rabinowitz condition. We obtain a nontrivial solution and, in the case of odd nonlinearity, an unbounded sequence of solutions via the Morse theory and the fountain theorem, respectively. Copyright © 2014 John Wiley & Sons, Ltd.     

Periodic solutions for fourth-order nonlinear functional difference equations

By using the critical point method, some new criteria are obtained for the existence and multiplicity of periodic solutions for fourth-order nonlinear functional difference equations. The proof is based on the linking theorem in combination with variational technique. Recent results in the literature are generalized and significantly improved. Copyright © 2013 John Wiley & Sons, Ltd.     

广义sine-Gordon方程高精度隐式紧致差分方法

本文研究一类二维非线性的广义sine-Gordon(简称SG)方程的有限差分格式.首先构造三层时间的紧致交替方向隐式差分格式,并用能量分析法证明格式具有二阶时间精度和四阶空间精度.然后应用改进的Richardson外推算法将时间精度提高到四阶.最后,数值算例证实改进后的算法在空间和时间上均达到四阶精度.     

Matching energy of unicyclic and bicyclic graphs with a given diameter

Gutman and Wagner proposed the concept of matching energy (ME) and pointed out that the chemical applications of ME go back to the 1970s. Let G be a simple graph of order n and be the roots of its matching polynomial. The ME of G is defined to be the sum of the absolute values of . In this article, we characterize the graphs with minimal ME among all unicyclic and bicyclic graphs with a given diameter d. © 2014 Wiley Periodicals, Inc. Complexity 21: 224–238, 2015     

Additive hazards regression with random effects for clustered failure times

Additive hazards model with random effects is proposed for modelling the correlated failure time data when focus is on comparing the failure times within clusters and on estimating the correlation between failure times from the same cluster, as well as the marginal regression parameters. Our model features that, when marginalized over the random effect variable, it still enjoys the structure of the additive hazards model. We develop the estimating equations for inferring the regression parameters. The proposed estimators are shown to be consistent and asymptotically normal under appropriate regularity conditions. Furthermore, the estimator of the baseline hazards function is proposed and its asymptotic properties are also established. We propose a class of diagnostic methods to assess the overall fitting adequacy of the additive hazards model with random effects. We conduct simulation studies to evaluate the finite sample behaviors of the proposed estimators in various scenarios. Analysis of the Diabetic Retinopathy Study is provided as an illustration for the proposed method.     

Synthesis and application of moisture-stable methallylsilanated phosphorylcholine as a surface modifier

New methallylsilanated phosphorylcholine (MASPCs) were synthesized via a copper-catalyzed ‘click’ reaction and demonstrated excellent moisture stability. Hydroxylated silicon compounds, silanol, and silica were grafted or modified by MASPCs in the presence of triflic acid (TfOH) and they possessed a good grafting efficiency and high loading rate.     

Amicoumacins from the marine-derived bacterium Bacillus sp. with the inhibition of NO production

Chemical examination of the fermentation broth of the marine-derived bacterium Bacillus sp. resulted in the isolation of seven new amicoumacin-type isocoumarin derivatives, namely bacillcoumacins A–G (1–7), together with four known analogues. Their structures were elucidated on the basis of extensive spectroscopic analysis, while the absolute configurations of the new compounds were determined by CD, Mosher’s method, and chemical conversion. Compounds 7 and 9 showed inhibitory effects against the NO production induced by lipopolysaccharide (LPS) in mouse macrophage RAW 264.7 cells.     

C?H Functionalization/Asymmetric Michael Addition Cascade Enabled by Relay Catalysis: Metal Carbenoid Used for C?C Bond Formation

A combination of either ruthenium(II) or rhodium(II) complexes and quinine‐derived squaramide enables 3‐diazooxindoles, indoles, and nitroalkenes to undergo highly efficient asymmetric three‐component reactions, thus affording optically active 3,3′‐bis(indole)s through a consecutive C C bond‐forming sequence, which turned out to be applicable to the facile total synthesis of (−)‐folicanthine.