Exploratory data analysis for planar tessellations: Structural analysis and point process methods

This paper presents methods for the exploratory analysis of particular geometrical data, namely planar tessellations. At first, two non-stochastic methods are suggested which may help to classify tessellations and to understand their structure. The first one consists of approximating a given tessellation by a Dirichlet tessellation. The other one uses the nodes of a given tessellation and tests the possibility of reconstructing it by a fixed rule of connecting nodes by edges. Furthermore, in order to obtain information on the spatial behaviour of a tessellation, we suggest the use of the methods of point process statistics. In particular, pair correlation and mark correlation functions describe spatial correlations in tessellations.     

Stability of interconnected impulsive systems with and without time delays,using Lyapunov methods

In this paper, we consider the input-to-state stability (ISS) of impulsive control systems with and without time delays. We prove that, if the time-delay system possesses an exponential Lyapunov–Razumikhin function or an exponential Lyapunov–Krasovskii functional, then the system is uniformly ISS provided that the average dwell-time condition is satisfied. Then, we consider large-scale networks of impulsive systems with and without time delays and prove that the whole network is uniformly ISS under the small-gain and the average dwell-time condition. Moreover, these theorems provide us with tools to construct a Lyapunov function (for time-delay systems, a Lyapunov–Krasovskii functional or a Lyapunov–Razumikhin function) and the corresponding gains of the whole system, using the Lyapunov functions of the subsystems and the internal gains, which are linear and satisfy the small-gain condition. We illustrate the application of the main results on examples.     

奇数维可压缩液晶流方程解的逐点估计

首先, 本文利用标准的能量估计方法得到高维(3 维及以上) 的液晶流方程组小初值经典解的整体存在性. 然后, 本文运用Green 函数方法, 得到奇数维情形(3 维及以上) 该解的逐点估计. 该结果表明, 密度ρ和动量m同Navier-Stokes 方程组一样满足一般Huygens 原理, 而单位向量场d则没有这种现象, 其有着与热方程的解类似的时空估计.     

Studying discrete dynamical systems through differential equations

In this paper we consider dynamical systems generated by a diffeomorphism F defined on U an open subset of Rn, and give conditions over F which imply that their dynamics can be understood by studying the flow of an associated differential equation, , also defined on U. In particular the case where F has n−1 functionally independent first integrals is considered. In this case X is constructed by imposing that it shares with F the same set of first integrals and that the functional equation μ(F(x))=det(DF(x))μ(x), x∈U, has some non-zero solution, μ. Several examples for n=2,3 are presented, most of them coming from several well-known difference equations.     

Explicit solutions of generalized Cauchy-Riemann systems using the transplant operator

In Kravchenko (2008) [8] it was shown that the tool introduced there and called the transplant operator transforms solutions of one Vekua equation into solutions of another Vekua equation, related to the first via a Schrödinger equation. In this paper we prove a fundamental property of this operator: it preserves the order of zeros and poles of generalized analytic functions and transforms formal powers of the first Vekua equation into formal powers of the same order for the second Vekua equation. This property allows us to obtain positive formal powers and a generating sequence of a “complicated” Vekua equation from positive formal powers and a generating sequence of a “simpler” Vekua equation. Similar results are obtained regarding the construction of Cauchy kernels. Elliptic and hyperbolic pseudoanalytic function theories are considered and examples are given to illustrate the procedure.     

Stabilization of nonlinear switched systems using control Lyapunov functions

In this paper, we study the stabilization of general nonlinear switched systems by using control Lyapunov functions. The concept of control Lyapunov function for nonlinear control systems is generalized to switched control systems. The first part of our contribution provides a necessary and sufficient condition of stabilization. The main idea is to use a common control Lyapunov function; this is achieved with the converse Lyapunov theorem dedicated to switched systems. In the second part, an explicit construction of a common control Lyapunov function is addressed with respect to a finite family of switched systems. The approach uses a family of control Lyapunov functions attached to the subsystems.     

Influence of nonmagnetic impurities on superconductivity in two-band systems with variable charge carrier densities

Two-band superconductors with a nonmagnetic impurity are considered in the framework of perturbation theory. Analytical expressions are obtained for the temperature of the superconductivity transition T_C and the order parameters Δ_n (n=1,2) at different values of the charge carrier density (chemical potential μ). An impurity introduced into the system can influence T_C and Δ_n in two ways: it can lead to a change in μ and can cause inter-band scattering by the impurity potential. These mechanisms can either cancel each other or destroy the superconductivity. Here a significant role is played by the occupation of the energy bands, by which superconductivity can be completely suppressed by the nonmagnetic impurity. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 111, No. 2, pp. 289–303, May, 1997.     

Unbiased identification of a class of multi-input single-output systems with correlated disturbances using bias compensation methods

This paper studies the modelling and identification problems for multi-input single-output (MISO) systems with colored noises. In order to obtain the unbiased recursive estimates of the systems, this paper presents a recursive least squares (RLS) identification algorithm based on bias compensation technique. The basic idea is to eliminate the estimation bias by adding a correction term in the least squares (LS) estimates, a set of stable digital prefilters are suitably designed to preprocess the input sampled data from multi-input channels for the purpose of getting the bias term arisen by colored noises in LS estimates, and further to derive a bias compensation based RLS algorithm. The performance of the developed method is both analyzed theoretically and shown by means of simulation results.     

Studying an overload system using rotation

1. IntroductionThe motivation of writing this paper was from calculating the blocking probability foran overloaded finite system. Our numerical experiments suggested that this probability canbe approximated efficiently by rotating the transition matrix by 180". Some preliminaryresults were obtained and can be found in [11 and [2]. Rotating the transition matrix definesa new Markov chain, which is often called the dual process in the literature, for example,[3--7]. For a finite Markov chain, …     

Identification of MIMO systems using radial basis function networks with hybrid learning algorithm

When a radial basis function network (RBFN) is used for identification of a nonlinear multi-input multi-output (MIMO) system, the number of hidden layer nodes, the initial parameters of the kernel, and the initial weights of the network must be determined first. For this purpose, a systematic way that integrates the support vector regression (SVR) and the least squares regression (LSR) is proposed to construct the initial structure of the RBFN. The first step of the proposed method is to determine the number of hidden layer nodes and the initial parameters of the kernel by the SVR method. Then the weights of the RBFN are determined by solving a simple minimization problem based on the concept of LSR. After initialization, an annealing robust learning algorithm (ARLA) is then applied to train the RBFN. With the proposed initialization approach, one can find that the designed RBFN has few hidden layer nodes while maintaining good performance. To show the feasibility and superiority of the annealing robust radial basis function networks (ARRBFNs) for identification of MIMO systems, several illustrative examples are included.     

Differential systems with semi-stable equilibria and numerical methods

Summary. In this paper the (long time) stability of numerical methods for a class of nonlinear autonomous differential systems possessing a semi-stable equilibrium, is considered. The local dynamics of the class under the H-assumptions is reviewed. Some interesting differential systems of stiff type are seen to belong to this class. It is also shown that the Implicit Euler method is the only one of practical interest which is unconditionally stable. Mathematics Subject Classification (2000):65L20, 47H10, 37G05     

Stabilization methods for systems with two linear delays

In this paper we obtain stabilization methods for some systems with two linear delays. We present a numerical example which illustrates the effectiveness of one of stabilization methods.     

统计相关性分析方法的进展

系统综述了自19世纪开始且至今常用统计相关性的方法,例如Pearson和Spearman相关系数,CorGc和CovGc 相关性及距离相关性方法。重点介绍了2011年提出的MIC方法以及由此引发的毁誉参半的大量评述,旨在揭示这一热点领域研究面貌。该领域不仅受到统计学家的关注,而且受到了分析大样本和异质数据的应用研究领域的学者们的追捧,例如基因组生物学家和网络信息研究者。这些研究者期望在众多已有方法的理解和剖析中更恰当地付诸应用,并提出新的应用问题来推动新的分析方法的创造。     

GLOBAL EXISTENCE AND LONG-TIME BEHAVIOR FOR THE STRONG SOLUTIONS IN H2 TO THE 3D COMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOWS

In this paper, we investigate the global existence and long time behavior of strong solutions for compressible nematic liquid crystal flows in three-dimensional whole space. The global existence of strong solutions is obtained by the standard energy method under the condition that the initial datas are close to the constant equilibrium state in H²-framework. If the initial datas in L¹-norm are finite additionally, the optimal time decay rates of strong solutions are established. With the help of Fourier splitting method, one also establishes optimal time decay rates for the higher order spatial derivatives of director.     

The Three-Dimensional ℤ2 Electrodynamics and the Two-Dimensional Ising Model

We calculate the correlation functions for the three-dimensional ₂ electrodynamics for particular values of the interaction energies and with free boundary conditions.     

Dissipativity of Runge-Kutta methods for dynamical systems with delays

This paper is concerned with the numerical solution of dissipativeinitial value problems with delays by Runge-Kutta methods. Asufficient condition for the dissipativity of the systems isgiven. The concepts of D(l)-dissipativity and GD(l)-dissipativityare introduced. We investigate the dissipativity propertiesof (k,l)-algebraically stable Runge-Kutta methods with piecewiseconstant or linear interpolation procedures for finite-dimensionaland infinite-dimensional dynamical systems with delays.     

Bias compensation methods for stochastic systems with colored noise

For ARX-like systems, this paper derives a bias compensation based recursive least squares identification algorithm by means of the prefilter idea and bias compensation principle. The proposed algorithm can give the unbiased estimates of the system model parameters in the presence of colored noises, and can be on-line implemented. Finally, the advantages of the proposed bias compensation recursive least squares algorithm are shown by simulation tests.     

Economic dynamics with computer algebra systems

The aim of this work is to analyse some possibilities offered by computer algebra systems as a tool for studying economic dynamics. Not only do they enable the solving of problems of considerable difficulty with undergraduate levels of mathematical knowledge but they also allow the approach to the problem itself to be transformed. In this context, the paper illustrates the strategies for studying the Shinkai two-sector model using Maple V®.     

A-stability of Runge-Kutta methods for systems with additive noise

Numerical stability of both explicit and implicit Runge-Kutta methods for solving ordinary differential equations with an additive noise term is studied. The concept of numerical stability of deterministic schemes is extended to the stochastic case, and a stochastic analogue of Dahlquist'sA-stability is proposed. It is shown that the discretization of the drift term alone controls theA-stability of the whole scheme. The quantitative effect of implicitness uponA-stability is also investigated, and stability regions are given for a family of implicit Runge-Kutta methods with optimal order of convergence.This author was partially supported by the Italian Consiglio Nazionale delle Ricerche.