Deterministic relief dielectric structures to realize phase modulation of surface-plasmon polaritons

We propose a modified effective-refractive-index model for the design of relief dielectric structures on a metal surface to realize phase modulation of surface-plasmon polaritons (SPPs). In this model, the length of the dielectric structure is optimized to reach phase shifting between the SPP waves transmitted through dielectric structure and those directly propagated with the consideration of SPP losses. Specifically, a one-dimensional dielectric Fresnel zone plate is designed by employing the proposed model to demonstrate phase modulation of SPPs for the highest focusing efficiency.     

Linear Convergence Rates for Variants of the Alternating Direction Method of Multipliers in Smooth Cases

In the present paper, we propose a novel convergence analysis of the alternating direction method of multipliers, based on its equivalence with the overrelaxed primal–dual hybrid gradient algorithm. We consider the smooth case, where the objective function can be decomposed into one differentiable with Lipschitz continuous gradient part and one strongly convex part. Under these hypotheses, a convergence proof with an optimal parameter choice is given for the primal–dual method, which leads to convergence results for the alternating direction method of multipliers. An accelerated variant of the latter, based on a parameter relaxation, is also proposed, which is shown to converge linearly with same asymptotic rate as the primal–dual algorithm.     

企业雇佣下残疾人就业行为研究——基于就业促进政策的演化博弈分析

融合就业是残疾人可持续发展的关键途径。基于演化博弈理论和残疾人就业促进政策,建立残疾人与用人单位(企业)行为交互过程的动态演化模型,用数值实验展示了初始条件改变和决策变量不同取值对系统演化结果的影响。研究发现,残疾人就业行为路径演化系统收敛于良好状态和“锁定”状态两种模式;调控模型中的参数收敛于不同模式的概率发生显著变化或变化不明显,揭示了现实中残疾人就业治理效果不理想的深层次原因;通过提高残疾人的工资待遇、心理收益、为企业创造的价值,减少残疾人的社会补助与就业付出的人力和社会资本,增加残疾人就业法定比例、企业雇佣残疾人的声誉收益、增值税退税优惠(企业符合退税条件)与雇佣残疾人数量,减少企业支持残疾人的就业投入等均能使系统演化到良好状态的概率增加。这为制定灵活有效的残疾人就业制度、政策与措施提供了较大的操作空间,多元主体协同治理,利益共享,良性互动,以跳出不良“锁定”状态,实现残疾人就业行为良序发展,破解就业难题。     

Accelerated projection-based forward-backward splitting algorithms for monotone inclusion problems

In this paper, based on inertial and Tseng''s ideas, we propose two projection-based algorithms to solve a monotone inclusion problem in infinite dimensional Hilbert spaces. Solution theorems of strong convergence are obtained under the certain conditions. Some numerical experiments are presented to illustrate that our algorithms are efficient than the existing results.     

A two-step modulus-based multisplitting iteration method for the nonlinear complementarity problem

In this paper, we construct a two-step modulus-based multisplitting iteration method based on multiple splittings of the system matrix for the nonlinear complementarity problem. And we prove its convergence when the system matrix is an $H$-matrix with positive diagonal elements. Numerical experiments show that the proposed method is efficient.     

Pricing VIX options in a 3/2 plus jumps model

This paper proposes and makes a study of a new model (called the 3/2 plus jumps model) for VIX option pricing. The model allows the mean-reversion speed and volatility of volatility to be highly sensitive to the actual level of VIX. In particular, the positive volatility skew is addressed by the 3/2 plus jumps model. Daily calibration is used to prove that the proposed model preserves its validity and reliability for both in-sample and out-of-sample tests. The results show that the models are capable of fitting the market price while generating positive volatility skew.     

COM-negative binomial distribution: modeling overdispersion and ultrahigh zero-inflated count data

We focus on the COM-type negative binomial distribution with three parameters, which belongs to COM-type (a, b, 0) class distributions and family of equilibrium distributions of arbitrary birth-death process. Besides, we show abundant distributional properties such as overdispersion and underdispersion, log-concavity, log-convexity (infinite divisibility), pseudo compound Poisson, stochastic ordering, and asymptotic approximation. Some characterizations including sum of equicorrelated geometrically distributed random variables, conditional distribution, limit distribution of COM-negative hypergeometric distribution, and Stein’s identity are given for theoretical properties. COM-negative binomial distribution was applied to overdispersion and ultrahigh zero-inflated data sets. With the aid of ratio regression, we employ maximum likelihood method to estimate the parameters and the goodness-of-fit are evaluated by the discrete Kolmogorov-Smirnov test.     

Bijective linear maps on semimodules spanned by Boolean matrices of fixed rank

Let M_m,n(B) be the semimodule of all m×n Boolean matrices where B is the Boolean algebra with two elements. Let k be a positive integer such that 2?k?min(m,n). Let B(m,n,k) denote the subsemimodule of M_m,n(B) spanned by the set of all rank k matrices. We show that if T is a bijective linear mapping on B(m,n,k), then there exist permutation matrices P and Q such that T(A)=PAQ for all A∈B(m,n,k) or m=n and T(A)=PA^tQ for all A∈B(m,n,k). This result follows from a more general theorem we prove concerning the structure of linear mappings on B(m,n,k) that preserve both the weight of each matrix and rank one matrices of weight k². Here the weight of a Boolean matrix is the number of its nonzero entries.     

Coalition formation in the presence of continuing conflict

This paper studies endogenous coalition formation in a rivalry environment where continuing conflict exists. A group of heterogeneous players compete for a prize with the probability of winning for a player depending on his strength as well as the distribution of strengths among his rivals. Players can pool their strengths together to increase their probabilities of winning as a group through coalition formation. The players in the winning coalition will compete further until one individual winner is left. We show that in any equilibrium there are only two coalitions in the initial stage of the contest. In the case of three players, the equilibrium often has a coalition of the two weaker players against the strongest. The equilibrium coalition structure with four players mainly takes one of the two forms: a coalition of the three weaker players against the strongest or a coalition of the weakest and strongest players against a coalition of the remaining two. Our findings imply that the rivalry with the possibility of coalition formation in our model exhibits a pattern of two-sidedness and a balance of power. We further study the impact of binding agreements by coalition members on equilibrium coalition structures. Our analysis sheds some light on problems of temporary cooperation among individuals who are rivals by nature.     

The (signless) Laplacian spectral radius of unicyclic and bicyclic graphs with <Emphasis Type="Italic">n</Emphasis> vertices and <Emphasis Type="Italic">k</Emphasis> pendant vertices

In this paper, the effects on the signless Laplacian spectral radius of a graph are studied when some operations, such as edge moving, edge subdividing, are applied to the graph. Moreover, the largest signless Laplacian spectral radius among the all unicyclic graphs with n vertices and k pendant vertices is identified. Furthermore, we determine the graphs with the largest Laplacian spectral radii among the all unicyclic graphs and bicyclic graphs with n vertices and k pendant vertices, respectively.