The interaction of nonlinear hyperbolic waves

Nonlinearities in wave equations lead to focusing and defocusing of solutions. Focusing causes sharply defined wave fronts. The interaction of such sharply defined wave fronts and more generally of nonlinear hyperbolic waves is of fundamental importance and includes such phenomena as Mach triple point formation, shock wave diffraction patterns and the study of Riemann problems in one and higher dimensions. Recent progress in the study of nonlinear hyperbolic wave interactions has revealed a surprising range of new mathematical phenomena and structures. This mathematical theory should be useful in the design of improved computational algorithms and in part was motivated by such considerations. It is also of considerable interest for its own sake as new mathematical phenomena as well as in terms of the direct insight it provides into physical phenomena. Within the subject matter and point of view adopted here, we have attempted to present a broad and, we hope, a representative account of recent progress.     

Renormalisation du produit, Jacobiens et transformations de Riesz

The “correction algorithm”, applied in probability theory to the pointwise product of two martingales, has a natural analogue in the real-variable setting. It turns out that the corresponding bilinear operators obtained in this way provide us with a new “renormalization algorithm”, in the sense of Coifman, Dobyinski and Meyer. We give a few examples of applications, regarding multidimensional Hardy spaces and various nonlinear quantities.     

圆柱贮箱液体非线性晃动的多维模态分析方法

将Faltinsen等提出的多维模态理论应用到求解圆柱贮箱液体非线性晃动问题中．根据Narimanov-Moiseiev的三阶渐近假设关系,通过选取主导模态以及确定它们的阶次关系,将一般形式的无穷维模态系统降为五维渐近模态系统,即描述自由液面波高的广义坐标之间相互耦合的二阶非线性常微分方程组．通过对这个模态系统的数值积分,得到了与以前的理论分析和实验结果相吻合的非线性现象．研究结果表明,多维模态方法是用来求解液体非线性晃动动力学的一个很好的工具．在我们的下一步工作中,将继续发展这种方法,用来研究更为复杂的晃动问题．     

A new nonlinear interval programming method for uncertain problems with dependent interval variables

This paper proposes a new nonlinear interval programming method that can be used to handle uncertain optimization problems when there are dependencies among the interval variables. The uncertain domain is modeled using a multidimensional parallelepiped interval model. The model depicts single-variable uncertainty using a marginal interval and depicts the degree of dependencies among the interval variables using correlation angles and correlation coefficients. Based on the order relation of interval and the possibility degree of interval, the uncertain optimization problem is converted to a deterministic two-layer nesting optimization problem. The affine coordinate is then introduced to convert the uncertain domain of a multidimensional parallelepiped interval model to a standard interval uncertain domain. A highly efficient iterative algorithm is formulated to generate an efficient solution for the multi-layer nesting optimization problem after the conversion. Three computational examples are given to verify the effectiveness of the proposed method.     

多维标度法在亲属关系中的应用

简单地介绍了多维标度方法的原理及理论,并介绍了加权多维标度方法的理论及原理,对亲属关系亲密的程度采用多维标度法进行了分析,展示了15种亲属关系可分为五大类,并由此得到在人们心中亲属的分类情况,根据这些分类来解释一些亲属间的关系,理解人际关系中的一些社会现象,帮助缓和彼此之间的一些矛盾.     

A new method for the construction of solutions of nonlinear wave equations

We propose a simple new method for the construction of solutions of multidimensional nonlinear wave equations.     

On the Computation of Nonlinear Planetary Waves

A numerical method is developed to solve a class of nonlinear, nonlocal eigenvalue problems defined in an infinite strip, and is applied to compute solitary planetary waves in a sheared zonal current on the beta-plane. This method, an iterative procedure derived from the natural variational structure of these problems, is implemented in the physical case when the ambient parallel flow has a linear or a quadratic velocity profile. The results of the numerical experiments establish rigorous limits on the range of validity of the formal asymptotic theory of weakly nonlinear long waves, and also reveal some new phenomena involving strongly nonlinear waves. The iterative procedure is analyzed in a general setting, and is shown to be globally convergent without restriction on the wave amplitude.     

我国经济增长与产业结构演进关系的研究——基于面板数据模型的实证分析

本文运用面板数据模型,对我国各省1996-2005年人均GDP及三次产业产值比重的关系分别进行了模型拟合,结论认为:我国经济增长对产业结构变化的影响显著,而后者对前者的影响在统计上并不显著,我国经济增长模式是需求导向型的。其次,就各次产业与人均GDP的关系看,第一产业与人均GDP呈现负相关关系,而第二、三产业与人均GDP呈现正相关关系。     

Multiparticle correlations,entropy of partial distributions,and the direct variational method

In the classical statistical theory, multiparticle correlations are governed by a variational principle for a functional that becomes the thermodynamic potential on its extremal. We show that this functional contains a part that has the meaning of a sum of contributions from multiparticle entropies. We present a method for passing from the conditional variational problem for the thermodynamic potential to an unconditional one.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 143, No. 1, pp. 150–160, April, 2005.     

A Finite Element Formulation for the Nonlinear Analysis of Piezoelectric Three-Dimensional Beam Structures

A finite element formulation for a three-dimensional piezoelectric beam which includes geometrical and material nonlinearities is presented. To account for the piezoelectric effect, the coupling between the mechanical stress and the electrical displacement is considered. Based on the Timoshenko theory, an eccentric beam formulation is introduced which provides an efficient model to analyze piezoelectric structures. The geometrically nonlinear assumption allows the calculation of large deformations including buckling analysis. A quadratic approximation of the electric potential through the cross section of the beam ensures the fulfilment of the charge conservation law exactly. This assumption leads to a finite element formulation with six mechanical and five electrical degrees of freedom per node. To take into account the typical ferroelectric hysteresis phenomena, a nonlinear material model is essential. For this purpose, the phenomenological Preisach model is implemented into the beam formulation which provides an efficient determination of the remanent part of the polarization. The applicability of the introduced beam formulation is discussed with respect to available data from literature. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

作物品种多维物元分析法

运用可拓学理论,提出了一种用于作物品种区域试验分析的新方法—多维物元分析法,并利用2001—2002年度河南省小麦高肥冬水组区域试验资料(安阳点)的实例,介绍了这种分析方法的具体应用.在此基础上,讨论了这种方法的应用前景,指出,运用可拓学理论探讨作物品种综合评价方法,将是今后一个重要的研究方向.     

A new multiobjective allocator of capacitor banks and distributed generations using a new investigated differential evolution

This article has investigated a new multiobjective allocation of optimal sizing and sitting of distributed generation (DG) units and capacitor banks in simultaneous mode to improve reliability and reduce energy losses. The proposed method consists of four objectives, that is, cost of energy not supplied, system average interruption duration index, costs of energy loss and investment. A novel structure differential evolution has been suggested to solve this nonlinear complex problem and its results are compared with related values of genetic algorithm and simple differential evolutionary algorithm. In addition to the novel objective function, the other contribution of this article is proposing a new model for load and energy cost. Three types of DGs, that is, wind turbine, solar cell, and diesel generator have been used in placement process. To verify the comprehensiveness of the proposed function, three scenarios have been introduced: scenario i: first, placement of DGs, then capacitor banks, scenario ii: first, placement of capacitor banks, and then DGs, and scenario iii: simultaneous placement of DGs and capacitor banks. Simulations have been carried out on one part of practical distribution network in Metropolitan Tabriz in North West of Iran. The results of simulations have been discussed and analyzed using the five novel indices. The obtained simulation results using proposed function shows that the simultaneous placement of DGs and capacitor banks results in more reduction of the energy losses and increase improvements of reliability indices as well as voltage profile. © 2013 Wiley Periodicals, Inc. Complexity 19: 40–54, 2014     

Growth,Life Cycle and Dynamic Modelling

Growth and diffusion processes have received great interest from investigators in many disciplines, such as Biology, Demography or Economics. These processes are usually analyzed by means of sigmoidal curves that formalize the well-known theory of the life cycle. The characteristic stages in the biological life cycle of an organism are widely applicable to technology progress, sales of a new product or the evolution of economic sectors. In this paper a mathematical characterization of sigmoidal growth is presented that gives rise to a general methodology for modelling such processes, additionally allowing to establish a qualitative equivalence among sigmoidal growth-type phenomena.     

不完全信息多维Cournot模型及其分析

根据现实中的博弈现象,本文首先提出了多维博弈概念,然后描述了其特征、策略型式,并将Nash均衡扩展为多维Nash均衡．最后,讨论了两个企业关于具有一定替代性的两种产品的不完全信息静态多维Cournot多维博弈模型,并进一步分析得到两个企业对两种产品单独博弈的均衡策略劣于对两种产品多维博弈的均衡策略．     

Tensor Approximation of Generalized Correlated Diffusions and Functional Copula Operators

In this paper we develop a class of applied probabilistic continuous time but discretized state space decompositions of the characterization of a multivariate generalized diffusion process. This decomposition is novel and, in particular, it allows one to construct families of mimicking classes of processes for such continuous state and continuous time diffusions in the form of a discrete state space but continuous time Markov chain representation. Furthermore, we present this novel decomposition and study its discretization properties from several perspectives. This class of decomposition both brings insight into understanding locally in the state space the induced dependence structures from the generalized diffusion process as well as admitting computationally efficient representations in order to evaluate functionals of generalized multivariate diffusion processes, which is based on a simple rank one tensor approximation of the exact representation. In particular, we investigate aspects of semimartingale decompositions, approximation and the martingale representation for multidimensional correlated Markov processes. A new interpretation of the dependence among processes is given using the martingale approach. We show that it is possible to represent, in both continuous and discrete space, that a multidimensional correlated generalized diffusion is a linear combination of processes originated from the decomposition of the starting multidimensional semimartingale. This result not only reconciles with the existing theory of diffusion approximations and decompositions, but defines the general representation of infinitesimal generators for both multidimensional generalized diffusions and, as we will demonstrate, also for the specification of copula density dependence structures. This new result provides immediate representation of the approximate weak solution for correlated stochastic differential equations. Finally, we demonstrate desirable convergence results for the proposed multidimensional semimartingales decomposition approximations.     

Population models with diffusion, strong Allee effect, and nonlinear boundary conditions

We consider a population model with diffusion, a strong Allee effect per capita growth function, and constant yield harvesting. In particular, we focus our study on a population living in a patch, Ω⊆Rⁿ with n≥1, that satisfies a certain nonlinear boundary condition. We establish our existence results by the method of sub-supersolutions.     

非线性振动系统的异宿轨道分叉,次谐分叉和混沌

在参数激励与强迫激励联合作用下具有van der Pol阻尼的非线性振动系统,其动态行为是非常复杂的.本文利用Melnikov方法研究了这类系统的异宿轨道分叉、次谐分叉和混沌.对于各种不同的共振情况,系统将经过无限次奇阶次谐分叉产生Smale马蹄而进入混沌状态.最后我们利用数值计算方法研究了这类系统的混沌运动.所得结果揭示了一些新的现象.     

我国省际经济增长路径的收敛性检验

提出了强σ-收敛和弱σ-收敛等新的σ-收敛概念,并选择实际人均GDP自然对数标准差和实际人均GDP变异系数两个指标来度量σ-收敛性,运用DF-GLS单位根检验方法和ARFIMA模型,检验了强σ-收敛和弱σ-收敛在我国全国范围内以及东、中、西部地区的存在性.检验结论显示:所研究的四个区域都不存在强σ-收敛特征,但均表现出显著的弱σ-收敛特征.     

Measuring length of business cycles across countries using a new non‐stationary unit‐root cyclical approach

This article examines the length of the cycles in the gross domestic product (GDP) real per capita series of 15 countries by means of new statistical techniques based on unit root cycles. We propose tests for unit root cycles at each of the frequencies of the process. Using this approach, we are able to approximate the number of periods per cycle. The results show that the cycles have a periodicity of approximately six years when the disturbances are white noise. However, if we permit autocorrelation, they may also occur at smaller intervals of time. Copyright © 2006 John Wiley & Sons, Ltd.