A condition guaranteeing the absence of the blow-up phenomenon for the generalized Burgers equation

The initial boundary value problem for the generalized Burgers equation with nonlinear sources is considered. We formulate a condition guaranteeing the absence of the blow-up of a solution and discuss the optimality of this condition.     

Synthesis of CdSpillared K2La2Ti3Olo Catalyst via a Microwave Assisted Process and Its Photocatalytic Property

采用微波辅助通过酸交换、胺柱撑、离子交换等步骤制备了CdS插层的K2La2Ti3010（ia做CdS-K2La2Ti3010）复合光催化剂．利用x射线粉末衍射（xgo）,场发射扫描电子显微镜（SEM）,紫外一可见漫反射吸收光谱（UV-Vis）和光致发光光谱（PL）等对产物进行表征,考察了CdS．KzLa2Ti3010在紫外光及可见光下催化制氢活性．结果表明,微波辅助法与传统法制备的插层复合催化剂晶型结构相似,同时大大减少了离子交换反应时间,减少了对层间结构的破坏,拓展了催化剂的可见光吸收范围．微波辅助制备的催化剂在紫外光和可见光照射3h后的产氢量分别为221．53mmol／（gcat．）和3．23mmol／（gcat．）,并对光催化机理进行了分析．     

An accurate determination of the K‐shell X‐ray fluorescence yield of silicon

A measurement of the K‐shell fluorescence yield of silicon is undertaken in which identified sources of systematic errors in previous measurements are reduced or eliminated. This enables a stringent test of the only two sets of theoretical predictions available for atomic numbers less than 18. Our result ω_K = 0.0495 ± 0.0015 is very slightly lower than the non‐relativistic Hartree‐Fock‐Slater (HFS) prediction of 0.0514. This stringent test of the HFS predictions helps to refine the fundamental parameter database of the X‐ray fluorescence analysis technique, whose importance for light elements is increasing. Our work indicates the need for new theoretical calculations of K‐shell fluorescence yields for these elements. Copyright © 2012 John Wiley & Sons, Ltd.     

Increasing directionally convex orderings of random vectors having the same copula, and their use in comparing ordered data

In this paper, we establish some results for the increasing convex comparisons of generalized order statistics. First, we prove that if the minimum of two sets of generalized order statistics are ordered in the increasing convex order, then the remaining generalized order statistics are also ordered in the increasing convex order. This result is extended to the increasing directionally convex comparisons of random vectors of generalized order statistics. For establishing this general result, we first prove a new result in that two random vectors with a common conditionally increasing copula are ordered in the increasing directionally convex order if the marginals are ordered in the increasing convex order. This latter result is, of course, of interest in its own right.     

About a numerical method of successive interpolations for functional Hammerstein integral equations

A new and robust numerical method for Hammerstein functional integral equations is proposed. The convergence and the numerical stability of the method are mathematically proved and tested on some examples.     

A mountain pass algorithm with projector

In this paper, we present an enhanced version of the minimax algorithm of Chen, Ni, and Zhou that offers the additional guarantee that the solution found is a fix-point of a projector on a cone. Positivity, negativity, and monotonicity can be expressed in this way. The convergence of the algorithm is proved by means of a “computational deformation lemma” instead of the usual deformation lemma used in the calculus of variations.     

A full-Newton step non-interior continuation algorithm for a class of complementarity problems

In this paper, we investigate a class of nonlinear complementarity problems arising from the discretization of the free boundary problem, which was recently studied by Sun and Zeng [Z. Sun, J. Zeng, A monotone semismooth Newton type method for a class of complementarity problems, J. Comput. Appl. Math. 235 (5) (2011) 1261–1274]. We propose a new non-interior continuation algorithm for solving this class of problems, where the full-Newton step is used in each iteration. We show that the algorithm is globally convergent, where the iteration sequence of the variable converges monotonically. We also prove that the algorithm is globally linearly and locally superlinearly convergent without any additional assumption, and locally quadratically convergent under suitable assumptions. The preliminary numerical results demonstrate the effectiveness of the proposed algorithm.     

Lipschitz gradients for global optimization in a one-point-based partitioning scheme

A global optimization problem is studied where the objective function f(x)$f\left(x\right)$ is a multidimensional black-box function and its gradient f^′(x)$f^{\prime }\left(x\right)$ satisfies the Lipschitz condition over a hyperinterval with an unknown Lipschitz constant K$K$. Different methods for solving this problem by using an a priori given estimate of K$K$, its adaptive estimates, and adaptive estimates of local Lipschitz constants are known in the literature. Recently, the authors have proposed a one-dimensional algorithm working with multiple estimates of the Lipschitz constant for f^′(x)$f^{\prime }\left(x\right)$ (the existence of such an algorithm was a challenge for 15 years). In this paper, a new multidimensional geometric method evolving the ideas of this one-dimensional scheme and using an efficient one-point-based partitioning strategy is proposed. Numerical experiments executed on 800 multidimensional test functions demonstrate quite a promising performance in comparison with popular DIRECT-based methods.     

Maximal K3's and Hamiltonicity of 4‐connected claw‐free graphs

Let cl(G) denote Ryjá?ek's closure of a claw‐free graph G. In this article, we prove the following result. Let G be a 4‐connected claw‐free graph. Assume that G[N_G(T)] is cyclically 3‐connected if T is a maximal K₃ in G which is also maximal in cl(G). Then G is hamiltonian. This result is a common generalization of Kaiser et al.'s theorem [J Graph Theory 48(4) (2005), 267–276] and Pfender's theorem [J Graph Theory 49(4) (2005), 262–272]. © 2011 Wiley Periodicals, Inc. J Graph Theory     

Solutions to the seepage face model for dual porosity flows with hysteresis

This paper is concerned with theoretical analysis of the initial-boundary value problem for the dual porosity model of Darcian flows with the Preisach hysteresis operator. Due to the presence of the so-called unilateral boundary condition, the problem comes as an evolution variational inequality. We apply the penalty method to prove the global-in-time existence of the variational solution by constructing approximate solutions satisfying suitable energy type estimates.