A Superlinearly Convergent SSLE Algorithm for Optimization Problems with Linear Complementarity Constraints

In this paper we study a special kind of optimization problems with linear complementarity constraints. First, by a generalized complementarity function and perturbed technique, the discussed problem is transformed into a family of general nonlinear optimization problems containing parameters. And then, using a special penalty function as a merit function, we establish a sequential systems of linear equations (SSLE) algorithm. Three systems of equations solved at each iteration have the same coefficients. Under some suitable conditions, the algorithm is proved to possess not only global convergence, but also strong and superlinear convergence. At the end of the paper, some preliminary numerical experiments are reported.     

Explicit and Implicit Continuation Algorithms for Strongly Monotone Variational Inequalities with Box Constraints

In this paper we discuss the variational inequality problems VIP(X, F), where F is assumed to be a strongly monotone mapping from ⁿ to ⁿ, and the feasible set X = [l, u] has the form of box constraints. Based on the Chen-Harker-Kanzow smoothing functions, first we present an explicit continuation algorithm (ECA) for solving VIP(X, F). The ECA possesses main features as follows: (a) at each iteration, it yields a new iterative point by solving a system of equations in ^{(n + s)} with a parameter and nonsingular Jacobian matrix, where s = |{j: - < l _j < u _j < +}|, (b) it generates a sequence of iterative points in the interior of the feasible set X. Secondly we give an implicit continuation algorithm (ICA) for solving VIP(X,F), the prime character of the ICA is that it solves only one, rather than a series of, system of nonlinear equations to obtain a solution of VIP(X,F). The two proposed algorithms are shown to possess strongly global convergence. Finally, some preliminary numerical results of the two algorithms are reported.     

A Luminescent Dicyanodistyrylbenzene-based Liquid Crystal Polymer Network for Photochemically Patterned Photonic Composite Film

A novel photonic composite film based on a luminescent dicyanodistyrylbenzene-based liquid crystal polymer network (LCN)was fabricated by using a silica colloidal crystal as a template.The upper part of inverse opal structure and the luminescence characteristics of dicyanodistyrylbenzene-based moiety endowed the resulting bilayer photonic film with structural color arising from coherent Bragg reflection and fluorescence properties,respectively.A fluorescence enhancement phenomenon was observed in the photonic film due to the overlap between the reflection band and emission band of the fluorescent LCN.More importantly,the photo-induced irreversible Z/E photoisomerization of dicyanodistyrylbenzene-based moiety in the photonic film led to both a reflection spectral shift and an observable fluorescence variation.On the basis of this effective phototuning process,microscopic patterning ofphotonic film was developed under both fluorescence mode and reflection mode.The work demonstrated here provides a new route to construct photo-responsive photonic film.     

Palladium-Catalyzed Tunable Carbonylative Synthesis of Enones and Benzofulvenes

A palladium-catalyzed four-component carbonylative coupling reaction involving aryl halides, internal alkynes, arylboronic acids, and CO has been developed for the first time. All-carbon substituted α-unsaturated ketones and benzofulvenes can be selectively obtained in a highly regio- and stereocontrolled manner. Using Cu(TFA)₂ as the additive, a series of tetrasubstituted α-unsaturated ketones were prepared in moderate to high yields. Using more acidic Lewis acid Cu(OTf)₂ as the additive, multisubstituted benzofluvenes were synthesized in moderate yields. This efficient methodology involved the formation of three new C−C bonds, and provided a divergent method for the quick construction of multisubstituted α-unsaturated ketones and benzofulvenes from easily available starting materials.     

Two modified nonlinear conjugate gradient methods with disturbance factors for unconstrained optimization

The nonlinear conjugate gradient method (CGM) is a very effective iterative method for solving large-scale optimal problems. In this paper, based on a variant of Polak–Ribière–Polyak method, two modified CGMs with disturbance factors are proposed. By the disturbance factors, the two proposed methods not only generate sufficient descent direction at each iteration but also converge globally for nonconvex minimization if the strong Wolfe line search is used. Finally, elementary numerical experiment results are reported, which show that the proposed methods are promising.     

An ε-generalized gradient projection method for nonlinear minimax problems

In this paper, combining the techniques of ε-generalized gradient projection and Armjio’s line search, we present a new algorithm for the nonlinear minimax problems. At each iteration, the improved search direction is generated by an ε-generalized gradient projection explicit formula. Under some mild assumptions, the algorithm possesses global and strong convergence. Finally, some preliminary numerical results show that the proposed algorithm performs efficiently.     

电子等离子体波动方程的摄动分析

该文采用减缩摄动法，将电子等离子体的非线性耦合方程组变换为非线性Ｓｃｈｒ¨ｏｄｉｎｇｅｒ方程．     

Borylation of aryldiazonium salts at room temperature in an aqueous solution under catalyst-free conditions

A general and convenient borylation reaction of aryldiazonium tetrafluoroborate salts with B₂pin₂ has been developed. In this catalytic system, no catalyst, additional ligands or additives were required. The reaction proceeded smoothly in an aqueous solution, and a variety of arylboronates were isolated in moderate to excellent yields under mild reaction conditions.     

Third-order Stokes wave solutions for interfacial internalwaves in three-layer dendity-stratified fluid

<正>Interfacial internal waves in a three-layer density-stratified fluid are investigated using a singular perturbation method,and third-order asymptotic solutions of the velocity potentials and third-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory.As expected,the third-order solutions describe the third-order nonlinear modification and the third-order nonlinear interactions between the interfacial waves.The wave velocity depends on not only the wave number and the depth of each layer but also on the wave amplitude.     

A kind of extended Korteweg——de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system

This paper considers interfacial waves propagating along the interface between a two-dimensional two-fluid with a flat bottom and a rigid upper boundary. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. It just focuses on the weakly non-linear small amplitude waves by introducing two small independent parameters: the nonlinearity ratio $\varepsilon $, represented by the ratio of amplitude to depth, and the dispersion ratio $\mu $, represented by the square of the ratio of depth to wave length, which quantify the relative importance of nonlinearity and dispersion. It derives an extended KdV equation of the interfacial waves using the method adopted by Dullin {\it et al} in the study of the surface waves when considering the order up to $O(\mu ^2)$. As expected, the equation derived from the present work includes, as special cases, those obtained by Dullin {\it et al} for surface waves when the surface tension is neglected. The equation derived using an alternative method here is the same as the equation presented by Choi and Camassa. Also it solves the equation by borrowing the method presented by Marchant used for surface waves, and obtains its asymptotic solitary wave solutions when the weakly nonlinear and weakly dispersive terms are balanced in the extended KdV equation.