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.     

非线性互补约束规划问题的一个新的QP-free算法

本文研究了非线性互补约束均衡问题.利用互补函数以及光滑近似法,把非线性互补约束均衡问题转化为一个光滑非线性规划问题,得到了超线性收敛速度,数值实验结果表明本文提出的算法是可行的.     

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     

On the structure of split Leibniz triple systems

We study the structure of arbitrary split Leibniz triple systems with a coherent 0-root space. By developing techniques of connections of roots for this kind of triple systems, under certain conditions, in the case of T being of maximal length, the simplicity of the Leibniz triple systems is characterized.     

The long‐term extreme price risk measure of portfolio in inventory financing: An application to dynamic impawn rate interval

Different from the short‐term risk measure for traditional financial assets (stocks, bonds, etc.), the key to illiquid inventory portfolio traded in the over‐the‐counter markets is to estimate the long‐term extreme price risk with time varying volatility. In this article, a new long‐term extreme price risk (value at risk and conditional value at risk) measure method for inventory portfolio and an application to dynamic impawn rate interval are proposed. To realize this, we first establish AutoRegressive Moving Average‐Exponential Generalized Autoregressive Conditional Heteroskedasticity‐Extreme Value Theory model and multivariatet‐Copula to depict the autocorrelation, fat tails, and volatility clustering of returns of inventories and the nonlinear dependence structure of inventories. Furthermore, we obtain the long‐term extreme price risk with time varying volatility via Monte Carlo simulation instead of square‐root‐of time rule. The results show that, first, benefits from risk diversification is significant; second, long‐term extreme price risk measure of inventory portfolio via Monte Carlo method outperforms the square‐root‐of time rule; the last is that the dynamic rate interval based on the long‐term price risk is superior to the crude rules of thumb in terms of reducing efficiency loss and improving risk coverage. In summary, this article provides a new quantitative framework for managing the risk of portfolio in inventory financing practice for banks constrained by risk limitation. © 2014 Wiley Periodicals, Inc. Complexity 20: 17–34, 2015     

Analysis of an aggregation‐based algebraic two‐grid method for a rotated anisotropic diffusion problem

A two‐grid convergence analysis based on the paper [Algebraic analysis of aggregation‐based multigrid, by A. Napov and Y. Notay, Numer. Lin. Alg. Appl. 18 (2011), pp. 539–564] is derived for various aggregation schemes applied to a finite element discretization of a rotated anisotropic diffusion equation. As expected, it is shown that the best aggregation scheme is one in which aggregates are aligned with the anisotropy. In practice, however, this is not what automatic aggregation procedures do. We suggest approaches for determining appropriate aggregates based on eigenvectors associated with small eigenvalues of a block splitting matrix or based on minimizing a quantity related to the spectral radius of the iteration matrix. Copyright © 2015 John Wiley & Sons, Ltd.     

Ionic liquid 1-ethyl-3-methylimidazolium acetate: an attractive solvent for native chemical ligation of peptides

The ionic liquid 1-ethyl-3-methylimidazolium acetate ([C₂mim][OAc]) was successfully used as alternative solvent for native chemical ligation of peptide fragments to produce model peptide LYRAXCRANK (X = G, A, L, N, Q, K, and F). The commonly used buffer system including thiol additives such as thiophenol and benzyl mercaptan can be replaced by the nontoxic ionic liquid [C₂mim][OAc]. In addition to improving the solubility of the peptides in [C₂mim][OAc], yields and rates of the ligation reactions were found to be efficiently enhanced.     

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.     

Palladium‐Catalyzed C?S Activation/Aryne Insertion/Coupling Sequence: Synthesis of Functionalized 2‐Quinolinones

The insertion of an aryne into a C S bond can suppress the addition of an S nucleophile to the aryne in the presence of palladium. Catalyzed by Pd(OAc)₂, a wide range of α‐carbamoyl ketene dithioacetals readily react with arynes to selectively afford functionalized 2‐quinolinones in high yields under neutral reaction conditions by a C S activation/aryne insertion/intramolecular coupling sequence. The attractive feature of the new strategy also lies in the versatile transformations of the alkythio‐substituted quinolinone products.