Depth notions for orthogonal regression

Global depth, tangent depth and simplicial depths for classical and orthogonal regression are compared in examples, and properties that are useful for calculations are derived. The robustness of the maximum simplicial depth estimates is shown in examples. Algorithms for the calculation of depths for orthogonal regression are proposed, and tests for multiple regression are transferred to orthogonal regression. These tests are distribution free in the case of bivariate observations. For a particular test problem, the powers of tests that are based on simplicial depth and tangent depth are compared by simulations.     

Periodic and solitary-wave solutions of the Degasperis–Procesi equation

Travelling-wave solutions of the Degasperis–Procesi equation are investigated. The solutions are characterized by two parameters. For propagation in the positive x-direction, hump-like, inverted loop-like and coshoidal periodic-wave solutions are found; hump-like, inverted loop-like and peakon solitary-wave solutions are obtained as well. For propagation in the negative x-direction, there are solutions which are just the mirror image in the x-axis of the aforementioned solutions. A transformed version of the Degasperis–Procesi equation, which is a generalization of the Vakhnenko equation, is also considered. For propagation in the positive x-direction, hump-like, loop-like, inverted loop-like, bell-like and coshoidal periodic-wave solutions are found; loop-like, inverted loop-like and kink-like solitary-wave solutions are obtained as well. For propagation in the negative x-direction, well-like and inverted coshoidal periodic-wave solutions are found; well-like and inverted peakon solitary-wave solutions are obtained as well. In an appropriate limit, the previously known solutions of the Vakhnenko equation are recovered.     

State models and asymptotic behaviour of 2D positive systems

Homogeneous 2D positive systems are 2D state-space models whosevariables are alwalys nonnegative and, consequently, are describedby a pair of nonnegative square matrices (A, B). In the paper,the properties of these pairs are discussed both in the generalcase and under particular assumptions like finite memory, separability,and property L. Various aspects of the positive asymptotic dynamic are considered;in particular, sufficient conditions are provided guaranteeingthat the local states are eventually strictly positive. Finally,some results on the convergence of the states towards a constantasymptotic distribution are presented.     

近程空中目标航路研究

本文在等加速俯冲飞行假定下，分析了近程空中目标航路的特点，并据此提出了目标航路模型．经过投影变换，把目标航路模型转化为二次函数，从而使目标航路的滤波及预报问题得到简化．采用递推最小二乘（ＲＬＳ）原理，给出了目标航路的在线滤波器及预报器．最后，对本文方法进行了仿真，并对仿真结果进行了分析．     

秩为1矩阵的性质及应用

给出了秩1矩阵的结构,讨论了这类矩阵在矩阵运算、对角化、标准型等方面的性质,推广和改进了文[1]的一些相关结果,并指出了它的若干应用,重点讨论了一类矩阵,得到了有关结论和方法.     

MTL代数的特征定理

对于逻辑系统代数结构的研究,是一个十分重要的研究课题.近期提出的BL代数,R_0代数,MTL代数就是这个方向具有代表性的研究成果.本文讨论MTL代数的性质与结构,给出这种代数的几个特征定理,澄清这种代数与其它代数结构的关系.鉴于单位区间中由左连续t-范数诱导的剩余蕴涵与MTL代数的紧密联系,本文还考察了这种模糊蕴涵的特征性质.     

Some properties of singular integral operators over an open curve Dedicated to the 85th birthday of Prof. Lu Jianke

In this paper, the stability properties, the endpoint behavior and the invertible relations of Cauchy-type singular integral operators over an open curve are discussed. If the endpoints of the curve are not special, this type of operators are proved to be stable. At the endpoints, either the singularity or smoothness of the operators are exactly described. And the function sets or spaces on which the operators are invertible as well as the corresponding inverted operators are given. Meanwhile, some applications for the solution of Cauchy-type singular integral equations are illustrated.     

On the boundedness and unboundedness of external polyhedral estimates for reachable sets of linear differential systems

The boundedness and unboundedness properties of external polyhedral (paralle-lepiped-valued) estimates are investigated for reachable sets of linear differential systems with a stable matrix. Boundedness and unboundedness criteria on an infinite time interval are presented for two types of estimates (“touching” estimates, which were introduced earlier, and estimates with constant orientation matrix). Conditions for the system matrix and bounding sets are given under which there are bounded estimates among the estimates of the mentioned types, under which there are unbounded estimates, and under which all the estimates are bounded or all the estimates are unbounded. In terms of the exponents of the estimates, the possible rate of their growth is described. For two-dimensional systems, the classification and comparison of possible situations of the boundedness or unboundedness for estimates of both types are given and boundedness criteria for estimates with special (orthogonal and “quasi-orthogonal”) constant orientation matrices are found. Results of numerical modeling are presented.     

近程空中目标航路研究

本文在等加速俯冲飞行假定下,分析了近程空中目标航路的特点,并据此提出了目标航路模型.经过投影变换,把目标航路模型转化为二次函数,从而使目标航路的滤波及预报问题得到简化,采用弟推最小二乘(RLS)原理,给出了目标航路的滤波器及预报器,最后,对本文方法进行了仿真,并对仿真结果进行了分析.     

Some properties of singular integral operators over an open curve Dedicated to the 85th birthday of Prof.Lu Jinake

In this paper, the stability properties, the endpoint behavior and the invertible relations of Cauchy-type singular integral operators over an open curve are discussed. If the endpoints of the curve are not special, this type of operators are proved to be stable. At the endpoints, either the singularity or smoothness of the operators are exactly described. And the function sets or spaces on which the operators are invertible as well as the corresponding inverted operators are given. Meanwhile, some applications for the solution of Cauchy-type singular integral equations are illustrated.     

Planes and processes

This article presented to Combinatorics 2006 is a survey of finite projective planes and the processes used to construct them. All non-translation planes are described, fundamental processes in translation planes are defined and some of these are used to connect semi-field flocks with symplectic spreads. Hermitian ovoids are connected to extensions of derivable nets, and three types of ‘lifting’ methods are discussed. Furthermore, hyperbolic fibrations and ‘regulus-inducing’ central collineation groups are connected to flocks of quadratic cones. Finally, hyper-reguli and multiple hyper-regulus replacement are considered.     

Stability of random impulsive coupled systems on networks with Markovian switching

Abstract

This article is intended to study global asymptotical stability in probability for random impulsive coupled systems on networks with Markovian switching. Two cases are considered. (1) Continuous dynamics are stable while impulses are unstable; (2) impulses are stable while continuous dynamics are unstable. To begin with, based on Lyapunov method as well as graph-theoretic technique, several new stability criteria in two cases are derived, that are, the Lyapunov-type criteria and the coefficients-type criteria. Then main results are used for a class of random impulsive coupled oscillators. Finally, the effectiveness of the obtained results is verified by numerical simulations.     

Three types of matrix stability

Three types of stability of real matrices are compared and necessary conditions are obtained in terms of the principal submatrices. For normal matrices and matrices whose off-diagonal elements are all positive, these conditions are sufficient, and the three types of stability are all equivalent. Necessary and sufficient conditions in terms of the elements of the matrix are proven for matrices of order 2 and 3.     

On Time Discretizations for Spectral Methods

New methods are introduced for the time integration of the Fourier and Chebyshev methods of solution for dynamic differential equations. These methods are unconditionally stable, even though no matrix inversions are required. Time steps are chosen by accuracy requirements alone. For the Fourier method both leapfrog and Runge-Kutta methods are considered. For the Chebyshev method only Runge-Kutta schemes are tested. Numerical calculations are presented to verify the analytic results. Applications to the shallow water equations are presented.     

广义泛函微分方程解的稳定性

本文首先给出广义泛函微分方程解的稳定性的概念,同时建立了有关稳定与不稳定的二个判据,然后作为例子,讨论二阶线性常系数广义微分差分程,得到了这类系统有关稳定与不稳定的若干结果,并发现了一些关于稳定性的分支或类似于分支的现象。     

Morse decompositions of nonautonomous dynamical systems

The global asymptotic behavior of dynamical systems on compact metric spaces can be described via Morse decompositions. Their components, the so-called Morse sets, are obtained as intersections of attractors and repellers of the system. In this paper, new notions of attractor and repeller for nonautonomous dynamical systems are introduced which are designed to establish nonautonomous generalizations of the Morse decomposition. The dynamical properties of these decompositions are discussed, and nonautonomous Lyapunov functions which are constant on the Morse sets are constructed explicitly. Moreover, Morse decompositions of one-dimensional and linear systems are studied.

     

QFS-Domains and their Lawson Compactness

In this paper, concepts of quasi-finitely separating maps and quasi-approximate identities are introduced. Based on these concepts, QFS-domains and quasicontinuous maps are defined. Properties and characterizations of QFS-domains are explored. Main results are: (1) finite products, nonempty Scott closed subsets and quasicontinuous projection images of QFS-domains, as well as FS-domains, are all QFS-domains; (2) QFS-domains are compact in the Lawson topology; (3) An L-domain is a QFS-domain iff it is an FS-domain, iff it is compact in the Lawson topology; (4) Bounded complete quasicontinuous domains, in particular quasicontinuous lattices, are all QFS-domains.     

局部双对角占优矩阵及应用

本文引进了局部双对角占优矩阵的概念，讨论了这类矩阵的性质，给出了局部双对角占优矩阵是广义严格对角占优矩阵的等价表征，得到了Ｍ－矩阵的新表征，推广了［１－１２］的相应结果。     

关于Bloch函数的性质

研究了Bloch函数族B中的两个子族Bα与B0,给出了它们的函数之间的关系;作为应用建立了Bα与B0中函数的偏差定理,从而刻画了Bα与B0中函数的有关性质.