THE CONVERGENCE RATE OF PENALTY FUNCTION METHODS FOR OPTIMAL CONTROL PROBLEM

In this paper, we discuss the rate of convergence for applying a class of exponential penalty functions to solve the oplimal control problems, obtain the estimation of error of cost functional, and give some methods to estimate the convergence rate of trajectories for some systems.     

Shannon-type sampling for multivariate non-bandlimited signals

In this paper, starting from a function analytic in a neighborhood of the unit disk and based on Bessel functions, we construct a family of generalized multivariate sinc functions, which are radial and named radial Bessel-sinc (RBS) functions being time-frequency atoms with nonlinear phase. We obtain a recursive formula for the RBS functions in R d with d being odd. Based on the RBS function, a corresponding sampling theorem for a class of non-bandlimited signals is established. We investigate a class of radial functions and prove that each of these functions can be extended to become a monogenic function between two parallel planes, where the monogencity is taken to be of the Clifford analysis sense.     

A Unified Approach to Construct a Class of Daubechies Orthogonal Scaling Functions

We use Lorentz polynomials to give an efficient way to prove Daubechies’ results on the existence of spline type orthogonal scaling functions and to evaluate a class of Daubechies scaling functions in a unified approach.     

The uv-Decomposition on a Class of D.C. Functions and Optimality Conditions

In this paper,the UV-theory and P-differential calculus are employed to study second-order ex-pansion of a class of D.C.functions and minimization problems.Under certain conditions,some properties ofthe U-Lagrangian,the second-order expansion of this class of functions along some trajectories are formulated.Some first and second order optimality conditions for the class of D.C.optimization problems are given.     

FIXED/PREASSIGNED-TIME SYNCHRONIZATION OF QUATERNION-VALUED NEURAL NETWORKS INVOLVING DELAYS AND DISCONTINUOUS ACTIVATIONS: A DIRECT APPROACH

The fixed-time synchronization and preassigned-time synchronization are investigated for a class of quaternion-valued neural networks with time-varying delays and discontinuous activation functions. Unlike previous efforts that employed separation analysis and the real-valued control design, based on the quaternion-valued signum function and several related properties, a direct analytical method is proposed here and the quaternion-valued controllers are designed in order to discuss the fixed-tim...     

Analytic Functions Related with the Hyperbola

The author considers a new class SHm λμ(α) of normalized analytic functions defined by a diferential operator. Several basic properties and characteristics of the functions belonging to the class SHm λμ(α) are investigated. These include integral representations, coefcient bounds, the Fekete-Szego¨ problem, class-preserving operators and T δ-neighborhoods.     

由拟从属关系定义的P叶解析函数子类的Fekete-Szeg?问题（英文）

In this paper, a new certain class of р-valent analytic functions with quasisubordination is defined and the Fekete-Szeg? problems for functions belonging to the class are derived. The results presented here provide extensions of those given in some earlier works.     

A CLASS OF ENTIRE DIRICHLET SERIES AS AN FK-SPACE AND A FRECHET SPACE

In the present paper we consider a class of entire functions represented by Dirichlet series whose coefficients belong to a commutative Banach algebra and prove it to be a complex FK-space and a Frechet space.     

ON A CLASS OF ANALYTIC FUNCTIONS RELATED TO CONIC DOMAINS AND ASSOCIATED WITH CARLSON-SHAFFER OPERATOR

Making use of the Carlson-Shaffer convolution operator, we introduce and study a new class of analytic functions related to conic domains. The main object of this paper is to investigate inclusion relations, coefficient bound for this class. We also show that this class is closed under convolution with a convex function. Some applications are also discussed.     

Coefficient Estimates for Certain Subclasses of Bi-Univalent Ma-Minda Mocanu-Convex Functions

In this paper, we introduce and investigate a new subclass of the function class Σ of bi-univalent functions of the Mocanu-convex type defined in the open unit disk, satisfy Ma and Minda subordination conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients |a2| and |a3| for functions in the new subclass introduced here. Further Application of Hohlov operator to this class is obtained. Several(known or new) consequences of the results are also pointed out.     

SUFFICIENT CONDITION FOR FUNCTIONS TO BE IN A CLASS OF MEROMORPHIC MULTIVALENT SAKAGUCHI TYPE SPIRAL-LIKE FUNCTIONS

In this article, we define a subclass of meromorphic multivalent Sakaguchi type functions and obtain certain sufficient conditions for functions to be in this class. The main result presented here includes a number of consequences as its special cases.     

Weak Form of Fuzzy Open Sets and Their Related Continuity

The aim of this paper is to give a new class of fuzzy open sets called fuzzy pre-γ-open sets in fuzzy topological spaces. Also,a new type of fuzzy continuous functions called,fuzzy pre-γ-continuous functions is introduced and studied.     

Fekete and Szeg problem in one and higher dimensions

In this paper, we establish the Fekete and Szeg inequality for a class of holomorphic functions in the unit disk, and then we extend this result to a class of holomorphic mappings on the unit ball in a complex Banach space or on the unit polydisk in C~n.     

A REMARK ON KOLMOGOROV'S COMPARISON THEOREM

In approximation theory the theorem of Kolmogorov concerning the comparison of derivatives of differentiable functions defined on the real line is well-known. It plays an important r le in establishing sharp inequalities between the norms of derivatives of a function. In this note we establish a comparison theorem of Kolmogorov type on a class of functions which are defined on the real line and can be continuated analytically in a stripped region containing the real llne. As a consequence we have derived an inequality of Landau-Kolmogorov type on this function class, and moreover, we have applied it to get the exact estimation for the Kolmogorov's N-widths of the analytic function class.     

非线性抛物型方程的二次元有限体积元方法

In this paper, a fully discrete finite volume element method for a class of second order nonlinear parabolic equations is given. Piecewise quadratic trial functions and piecewise constant test functions are used to obtain error estimates. A numerical example is given at, the end to show the feasibility of the method.     

On a Class of Generalized Sampling Functions

In this note, we discuss a class of so-called generalized sampling functions. These functions are defined to be the inverse Fourier transform of a family of piecewise constant functions that are either square integrable or Lebegue integrable on the real number line. They are in fact the generalization of the classic sinc function. Two approaches of constructing the generalized sampling functions are reviewed. Their properties such as cardinality, orthogonality, and decaying properties are discussed. The interactions of those functions and Hilbert transformer are also discussed.     

On S~i-quasinormal Subgroups

The objective of this paper is to invertigate the influence of maximal subgroups on the structure of a finite group.We introduce a concept of "normality" based on the permuting of certain subgroups.This concept leads to a generalization of Asaad and Shaalan's result.     

二元正交对称不可分尺度函数的参数化

Let I be the 2 × 2 identity matrix, and M a 2 × 2 dilation matrix with M2 = 2I. First, we present the correlation of the scaling functions with dilation matrix M and 2I. Then by relating the properties of scaling functions with dilation matrix 2I to the properties of scaling functions with dilation matrix M, we give a parameterization of a class of bivariate nonseparable orthogonal symmetric compactly supported scaling functions with dilation matrix M. Finally, a construction example of nonseparable orthogonal symmetric and compactly supported scaling functions is given.     

A CLASS OF STATIONARY MODELS OF SINGULAR STOCHASTIC CONTROL

A class of stationary models of singular stochastic control has been studied,in which the state is extended to solution of a class of S.D.E. from Wiener process. The existence of optimal control has been proved in all cases under some weaker conditions,and the structure of optimal control may be characterized.     

A REMARK ON KOLMOGOROVS COMPARISON THEOREM

In approximation theory the theorem of Kolmogorov concerning the comparison of derivatives of differentiable functions defined on the real line is well—known. It plays an important role in establishing sharp inequalities between the norms of derivatives of a function. In this note we establish a comparison theorem of Kolmogorov type on a class of functions which are defined on the real line and can be contlnuated analytically in a stripped region containing the real line. As a consequence we have derived an inequality of Landau-Kolmogorov type on this function class, and moreover, we have applied it to get the exact estimation for the Kolmogorov''s N-widths of the analytic function class.