LIMIT CYCLES BIFURCATED FROM THE ORIGIN AND EQUATOR FOR A CLASS OF FIFTH SYSTEM

For a class of real fifth system, the first 8 singular point quantities of the origin and the first 6 singular point quantities of the equator are obtained, and at the same time, the two highest-order cases are proved respectively. Moreover, the problems of stability and limit cycle bifurcated from the origin and the equator are studied comparatively, then some better results are obtained.     

Strongly Gauduchon Spaces

The authors define strongly Gauduchon spaces and the class■■, which are generalization of strongly Gauduchon manifolds in complex spaces. Comparing with the case of Kahlerian, the strongly Gauduchon space and the class■are similar to the Kahler space and the Fujiki class■■ respectively. Some properties about these complex spaces are obtained. Moreover, the relations between the strongly Gauduchon spaces and the class■■ are studied.     

SPHERICAL SYMMETRIC SOLUTIONS FOR THE MOTION OF RELATIVISTIC MEMBRANES AND NULL MEMBRANES IN THE REISSNER-NORDSTROM SPACE-TIME

In this article, we concern the motion of relativistic membranes and null mem- branes in the Reissner-Nordstrom space-time. The equation of relativistic membranes moving in the Reissner-Nordstrom space-time is derived and some properties are discussed. Spherical symmetric solutions for the motion are illustrated and some interesting physical phenomena are discovered. The equations of the null membranes are derived and the exact solutions are also given. Spherical symmetric solutions for null membranes are just the two horizons of Reissner-NordstrSm space-time.     

SPHERICAL SYMMETRIC SOLUTIONS FOR THE MOTION OF RELATIVISTIC MEMBRANES AND NULL MEMBRANES IN THE REISSNER-NORDSTRM SPACE-TIME

In this article, we concern the motion of relativistic membranes and null membranes in the Reissner-Nordstrm space-time. The equation of relativistic membranes moving in the Reissner-Nordstrm space-time is derived and some properties are discussed. Spherical symmetric solutions for the motion are illustrated and some interesting physical phenomena are discovered. The equations of the null membranes are derived and the exact solutions are also given. Spherical symmetric solutions for null membranes are just the two horizons of Reissner-Nordstrm space-time.     

Fekete-Szeg? Functional Problems for Certain Subclasses of Bi-Univalent Functions Involving the Hohlov Operator

In the paper the new subclasses ■ and ■ of the function class ∑ of bi-univalent functions involving the Hohlov operator are introduced and investigated.Then, the corresponding Fekete-Szeg functional inequalities as well as the bound estimates of the coefficients a_2 and a_3 are obtained. Furthermore, several consequences and connections to some of the earlier known results also are given.     

卷入Hohlov 算子的双单值函数某些子类的Fekete-Szeg\"o泛函问题

In the paper the new subclasses■and■of the function class∑of bi-univalent functions involving the Hohlov operator are introduced and investigated.Then,the corresponding Fekete-Szeg functional inequalities as well as the bound estimates of the coefficients a2 and a3 are obtained.Furthermore,several consequences and connections to some of the earlier known results also are given.     

The blue and minque in Gauss-Markoff model with linear transformation of the observable variables

For a singular linear model A = (y, Xβ, σ2 V) and its transformed model AF = (Fy, FXβ, σ2FVF'), where V is nonnegative definite and X can be rank-deficient,the expressions for the differences of the estimates for the vector of FXβ and the variance factor σ2 are given. Moreover, the necessary and sufficient conditions for the equalities of the estimates for the vector of FXβ and the variance factor σ2 are also established. In the meantime, works in Baksalary and Kala (1981) are strengthened and consequences in Puntanen and Nurhonen (1992), and Puntanen (1996) are extended.     

GEOMETRY OF EXPONENTIAL TYPE REGRESSION MODELS AND ITS ASYMPTOTIC INFERENCE

In this paper,exponential type regression modeis are considered from geometric point of view.The stochastic expansions relsting to the estimate are derived and are used to study several asymptotic inference problems.The biases and the covariances relating to the estimate may be calculated based on the expansions.The information loss of the estimate and a limit theorem connected with the observed and expected Fisher informations are obtained in terms of the curvatures.     

关于矩阵Γα-群逆和Γα序

The Γα-group inverse and the Γα-sharp ordering in matrix set are introduced.Some characterizations and properties of the Γα-sharp ordering are given.The relations between the Γα-sharp ordering and the Γα-mantis ordering are discussed.     

Optimality conditions and duality for a class of nondifferentiable multiobjective generalized fractional programming problems

This paper studies a class of multiobjective generalized fractional programming problems, where the numerators of objective functions are the sum of differentiable function and convex function, while the denominators are the difference of differentiable function and convex function. Under the assumption of Calmness Constraint Qualification the Kuhn-Tucker type necessary conditions for efficient solution are given, and the Kuhn-Tucker type sufficient conditions for efficient solution are presented under the assumptions of （F, α, ρ, d）-V-convexity. Subsequently, the optimality conditions for two kinds of duality models are formulated and duality theorems are proved.     

Numerical methods for Hamilton Jacobi functional differential equations

Initial and initial boundary value problems for first order partial functional differential equations are considered. Explicit difference schemes of the Euler type and implicit difference methods are investigated. The following theoretical aspects of the methods are presented. Sufficient conditions for the convergence of approximate solutions are given and comparisons of the methods are presented. It is proved that assumptions on the regularity of given functions are the same for both the methods. It is shown that conditions on the mesh for explicit difference schemes are more restrictive than suitable assumptions for implicit methods. There are implicit difference schemes which are convergent and corresponding explicit difference methods are not convergent. Error estimates for both the methods are construted.     

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.     

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.     

Estimating a survival function with incomplete cause-of-death data

We propose a random censorship model which permits uncertainty in the cause of death assessments for a subset of the subjects in a survival experiment. A nonparametric maximum likelihood approach and a “self-consistency” approach are considered. The solution sets corresponding to both approaches are found. They are infinite and identical. Only some of the solutions are consistent; i.e., the MLEs and self-consistent estimators are not consistent in general. Two estimates are thus proposed and their asymptotic properties are studied. It is shown that both estimates are strongly consistent and converge to Gaussian processes. The covariance structures of these Gaussian processes are derived.     

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.     

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.     

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.     

Enumeration of point-determining graphs

Point-determining graphs are graphs in which no two vertices have the same neighborhoods, co-point-determining graphs are those whose complements are point-determining, and bi-point-determining graphs are those both point-determining and co-point-determining. Bicolored point-determining graphs are point-determining graphs whose vertices are properly colored with white and black. We use the combinatorial theory of species to enumerate these graphs as well as the connected cases.     

Economic design of screening procedures when the rejected items are reprocessed

In a screening inspection, all of the items are subject to acceptance inspection. If an item fails to meet the predetermined specifications, it is rejected. In this paper, economic screening procedures are considered when the rejected items are reprocessed. It is assumed that the reprocessed and nonreprocessed items are produced by the same manufacturing process and therefore their quality characteristics are identically and independently distributed. Screening procedures based on the performance variable of interest and a variable which is correlated with the performance variable are considered. Cost models are constructed which involve the cost incurred by imperfect quality, reprocessing cost, and inspection cost. Methods of finding the optimal screening procedures are presented and an example is given.     

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.