Novel high-order breathers and rogue waves in the Boussinesq equation via determinants

By virtue of the bilinear method and the Kadomtsev–Petviashvili (KP) hierarchy reduction technique, wider classes of high-order breather and semirational and rogue wave solutions to the Boussinesq equation are derived. These solutions are presented explicitly in terms of Gram determinants, whose matrix elements have simply algebraic expressions. The breather and rogue wave solutions are derived from two different types of tau functions of a bilinear equation in the single-component KP hierarchy. By taking a long wave limit of high-order breather solutions, a range of hybrid solutions consisting of solitons, breathers, and one fundamental rogue wave are generated. For the rational rogue waves, some typical patterns such as Peregrine-type, triple, and sextuple rogue waves are put forward by modifying the input parameters. Besides, a new rogue wave pattern of third-order rogue waves is found, which features a mixture of a triangular pattern of three fundamental rogue waves and a fundamental pattern of second-order rogue wave. These results may help understand the protean rogue wave manifestations in areas ranging from water waves to fluid dynamics.     

On some sets of dictionaries whose ω ‐powers have a given

A dictionary is a set of finite words over some finite alphabet X. The ω ‐power of a dictionary V is the set of infinite words obtained by infinite concatenation of words in V. Lecomte studied in [10] the complexity of the set of dictionaries whose associated ω ‐powers have a given complexity. In particular, he considered the sets ??( Σ ⁰k) (respectively, ??( Π ⁰_k), ??( Δ ¹₁)) of dictionaries V ? 2* whose ω ‐powers are Σ ⁰_k‐sets (respectively, Π ⁰_k‐sets, Borel sets). In this paper we first establish a new relation between the sets ??( Σ ⁰₂) and ??( Δ ¹₁), showing that the set ??( Δ ¹₁) is “more complex” than the set ??( Σ ⁰₂). As an application we improve the lower bound on the complexity of ??( Δ ¹₁) given by Lecomte, showing that ??( Δ ¹₁) is in Σ ¹ ₂(2^2*)\ Π ⁰₂. Then we prove that, for every integer k ≥ 2 (respectively, k ≥ 3), the set of dictionaries ??( Π ⁰_k+1) (respectively, ??( Σ ⁰_{k +1})) is “more complex” than the set of dictionaries ??( Π ⁰_k) (respectively, ??( Σ ⁰_k)) (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于灰色系统理论构建军队院校教学质量评估模型

根据军队院校教学工作的实际特点,构建了院校教学质量灰色关联评估模型.首先,通过实际调研确定影响教学质量的指标体系,并利用层次分析法确定各指标的权重.然后,计算某项指标与最优、最劣指标的综合关联度,利用优劣比来确定综合排序.最后,对各个指标进行关联分析得到指标体系中最敏感的指标.实例分析表明该评估模型能更准确的反映实际情况,能深层次挖掘内在隐藏的信息,从而可以为院校教学工作提供理论依据和决策支持.     

层次系统DEA模型的研究

经典的DEA模型视决策单元为黑匣子,不考虑内部结构.实际上,决策单元DMU可能具有各种各样的结构.对DMU进行效率评价时,尽管最初的输入和最终的输出相同,但考虑DMU结构与忽视DMU结构得到的效率不同.基于这样一种思想,提出了一种基于层次系统的DEA模型.     

基于模糊综合评判的航空公司战略联盟合作伙伴选择研究

航空公司战略联盟成功的关键是能否选择出理想的合作伙伴,这是一个复杂的决策问题.提出了一个比较新颖的算法.首先根据AHP方法确定模糊评价矩阵和权重向量,并针对航空联盟的敏捷性要求和特定的市场需求,提出了评价指标两两间的比较标度的修正方法,然后通过模糊运算对目标函数进行排序,实现对合作伙伴的最优选择.最后以实例表明本算法能有效的支持伙伴选择.     

重离子碰撞两体关联输运理Ⅳ.守恒定律

讨论了在物理截断下两体关联动力学中守恒定律保持与破坏的一般特点．数值计算表明：两体关联输运理论在不同的等级截断下均较好地保持了有关的守恒定律。     

建筑生产固有危险的评价研究

本指出对建筑生产安全状况应从两个层面即固有危险和安全管理来进行评价，并就固有危险的评价进行了专题研究；建立了建筑生产固有危险评价的层次结构模型，设计了有关的安全检查表，研究了具体的评价方法和评价模型。     

科技成果转让与收益分配率“β”科学计算的拓展

首先对科技成果转让中收益分配率确定的基本原则进行了分析 ,在此基础上 ,综合考虑合作伙伴的投资及所承担的风险 ,然后运用层次分析法和模糊综合评价法对科技成果转让中的风险进行了客观评价 ,提出了一种确定收益分配率科学计算方法 ,并进行实证分析说明其有效性 ,为科技成果转让的风险决策提供了具体、可行的依据 .     

Painlevé Hierarchies and the Painlevé Test

In a series of recent papers, we derived several new hierarchies of higher-order analogues of the six Painlevé equations. Here we consider one particular example of such a hierarchy, namely, a recently derived fourth Painlevé hierarchy. We use this hierarchy to illustrate how knowing the Hamiltonian structures and Miura maps can allow finding first integrals of the ordinary differential equations derived. We also consider the implications of the second member of this hierarchy for the Painlevé test. In particular, we find that the Ablowitz–Ramani–Segur algorithm cannot be applied to this equation. This represents a significant failing in what is now a standard test of singularity structure. We present a solution of this problem.     

A Decision support system integrating AHP and MDS to predict choice

A decision support system is proposed which uses the analytic hierarchy process along with integer programming to constrain the overall choice set. Two strategies for predicting choice are then presented. The first is a single step process which uses multi-dimensional scaling. The second strategy is an iterative process which uses both multi-dimensional scaling and the analytic hierarchy process. The latter strategy is discussed in detail and an illustrative example is provided.