New cubic rational basis with tension shape parameters

By using the blossom approach, we construct four new cubic rational Bernsteinlike basis functions with two shape parameters, which form a normalized B-basis and include the cubic Bernstein basis and the cubic Said-Ball basis as special cases. Based on the new basis, we propose a class of C2 continuous cubic rational B-spline-like basis functions with two local shape parameters, which includes the cubic non-uniform B-spline basis as a special case.Their totally positive property is proved. In addition, we extend the cubic rational Bernsteinlike basis to a triangular domain which has three shape parameters and includes the cubic triangular Bernstein-B′ezier basis and the cubic triangular Said-Ball basis as special cases. The G1 continuous conditions are deduced for the joining of two patches. The shape parameters in the bases serve as tension parameters and play a foreseeable adjusting role on generating curves and patches.     

Weighted approximation by Bernstein quasiinterpolants for functions with singularities

We introduce a new type of modified Bernstein quasi-interpolants, which can be used to approximate functions with singularities. We establish direct, inverse, and equivalent theorems of the weighted approximation of this modified quasi-interpolants. Some classical results on approximation of continuous functions are generalized to the weighted approximation of functions with singularities.     

GENERALIZATIONS OF THE MEAN VALUES AND THEIR INEQUALITIES

Some generalizations of the classical Mean Values and their inequalities are presented inthis paper,using B-spline functions.The new generalized Means can be applied to nonlineardifference schemes for solving O.D.E.and P.D.E.with singularities([6,7,8]).     

ON GENERALIZED COMPLETE(p,q)-ELLIPTIC INTEGRALS

In this paper,we study the generalized complete(p,q)-elliptic integrals of the first and second kind as an application of generalized trigonometric functions with two parameters,and establish the monotonicity,generalized convexity and concavity of these functions.In particular,some Turán type inequalities are given.Finally,we also show some new series representations of these functions by applying Alzer and Richard's methods.     

Generalized Logan's Problem for Entire Functions of Exponential Type and Optimal Argument in Jackson's Inequality in L_2(R~3)

We study Jackson's inequality between the best approximation of a function f ∈ L_2(R~3) by entire functions of exponential spherical type and its generalized modulus of continuity.We prove Jackson's inequality with the exact constant and the optimal argument in the modulus of continuity.In particular,Jackson's inequality with the optimal parameters is obtained for classical modulus of continuity of order r and Thue–Morse modulus of continuity of order r ∈ N.These results are based on the solution of the generalized Logan problem for entire functions of exponential type.For it we construct a new quadrature formulas for entire functions of exponential type.     

On general Bernstein and Nikol’ski type inequalities

The goal of this paper is to establish the relations between general Bernstein and Nikol’ski type inequalities under some weak conditions. From these relations some known classical inequalities are implied. Also, a family of functions equipped with Bernstein type inequality which satisfies Nikol’ski type inequality is found.     

A moving average Cholesky factor model in joint mean-covariance modeling for longitudinal data

Modeling the mean and covariance simultaneously is a common strategy to efciently estimate the mean parameters when applying generalized estimating equation techniques to longitudinal data.In this article,using generalized estimation equation techniques,we propose a new kind of regression models for parameterizing covariance structures.Using a novel Cholesky factor,the entries in this decomposition have moving average and log innovation interpretation and are modeled as linear functions of covariates.The resulting estimators for the regression coefcients in both the mean and the covariance are shown to be consistent and asymptotically normally distributed.Simulation studies and a real data analysis show that the proposed approach yields highly efcient estimators for the parameters in the mean,and provides parsimonious estimation for the covariance structure.     

一类修正的和与积分混合型算子的$L_p$逼近

The generalized summation integral type operators with Beta basis functions are widely studied. At present, the investigations for the properties of these operators are only limited to the functions of bounded variation. Some authors studied the rate of point-wise rate of convergence, asymptotic formula of Voronovskaja type, and some direct results about these type of operators. The present paper considers the direct, inverse and equivalence theorems of modified summation integral type operators in the Lp spaces.     

UNIFYING REPRESENTATION OF BEZIERCURVE AND GENERALIZED BALL CURVES

Abstract. This paper presents two new families of the generalized Ball curves which include theI~zier curve, the generalized Ball curves defined by Wang and Said independently and some in-termediate curves. The relative degree elevation and reduction schemes, recursive algorithmsand the Bernstein-Bezier representation are also given.     

The Tricomi and Frankl problems for generalized Chaplygin equations in multiply connected domains

The present paper deals with Tricomi and Frankl problems for generalized Chaplygin equations in multiply connected domains. We first give the representation of solutions of the Tricomi problem for the equations, and then prove the uniqueness and existence of solutions for the problem by a new method, i.e. the complex functions in the elliptic domain and the hyperbolic complex functions in hyperbolic domain are used. Finally we discuss the Frankl problem for generalized Chaplygin equations in multiply connected domains.     

The construction of generalized B-spline low-pass filters related to possibility density

Starting from piecewise constant functions, a novel family of generalized symmetric B-splines, with realizable ideal low-pass filters, are constructed. The first order generalized B-spline low-pass filter is closely related to functions analytic in a neighborhood of the unit disc and the generalized sinc functions. The properties of this kind of low-pass filters are investigated. The behavior of the generalized B-spline low-pass filter related to normalized Gaussian distribution is considered.     

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.     

Julia''''s lemma and Bloch constants

The classical Julia's lemma is improved, branch points of Bloch functions are investigated, and new lower bounds of Bloch constants for functions with branch points are obtained.     

Asymptotics on Semiparametric Analysis of Multivariate Failure Time Data Under the Additive Hazards Model

Many survival studies record the times to two or more distinct failures on each subject. The failures may be events of different natures or may be repetitions of the same kind of event. In this article, we consider the regression analysis of such multivariate failure time data under the additive hazards model. Simple weighted estimating functions for the regression parameters are proposed, and asymptotic distribution theory of the resulting estimators are derived. In addition, a class of generalized Wald and generalized score statistics for hypothesis testing and model selection are presented, and the asymptotic properties of these statistics are examined.     

POINTWISE CONVERGENCE FOR EXPANSIONS IN SPHERICAL MONOGENICS

We offer a new approach to deal with the pointwise convergence of FourierLaplace series on the unit sphere of even-dimensional Euclidean spaces. By using spherical monogenics defined through the generalized Cauchy-Riemann operator, we obtain the spherical monogenic expansions of square integrable functions on the unit sphere. Based on the generalization of Fueter＇s theorem inducing monogenic functions from holomorphic functions in the complex plane and the classical Carleson＇s theorem, a pointwise convergence theorem on the new expansion is proved. The result is a generalization of Carleson＇s theorem to the higher dimensional Euclidean spaces. The approach is simpler than those by using special functions, which may have the advantage to induce the singular integral approach for pointwise convergence problems on the spheres.     

A REGULARIZED CONJUGATE GRADIENT METHOD FOR SYMMETRIC POSITIVE DEFINITE SYSTEM OF LINEAR EQUATIONS

AbstractA class of regularized conjugate gradient methods is presented for solving the large sparse system of linear equations of which the coefficient matrix is an ill-conditioned symmetric positive definite matrix. The convergence properties of these methods are discussed in depth, and the best possible choices of the parameters involved in the new methods are investigated in detail. Numerical computations show that the new methods are more efficient and robust than both classical relaxation methods and classical conjugate direction methods.     

GLOBAL EXISTENCE OF SOLUTIONS OF CAUCHY PROBLEM FOR GENERALIZED BBM-BURGERS EQUATION

In this paper, the existence and the uniqueness of the local generalized solution and the local classical solution of the Cauchy problem for the generalized BBM-Burgers equationare proved. The existence and the uniqueness of the global generalized solution and the global classical solution for the Cauchy problem of equation （1） are proved when n = 3, 2, 1. Moreover, the decay property of the solution is discussed.     

UNIFORM APPROXIMATION OF ENTIRE FUNCTIONS OF SLOW GROWTH ON COMPACT SETS

In the present paper,we study the polynomial approximation of entire functions of several complex variables.The characterizations of generalized order and generalized type of entire functions of slow growth are obtained in terms of approximation and interpolation errors.     

A NEW WAY TO ESTIMATE THE PARAMETERS IN THE PROGRESSIVE STRESS ACCELERATED LIFE TESTING

Among the three types of accelerated life testing, that is, the constant stress accelerated life testing, the step stress accelerated life testing, and the progressive stress accelerated life testing, the last one is the most effective and economical way to get the failure times of products in a short period of time. In this artiele a deficiency inthe classical approach is pointed out and a new method for the statisticul analysis of lifedata, especially for electronic products, under progressive stress (voltage) V(t)=Kt is given. Using the Bayesian method, for certain choices of the prior distribution, several forms of estimators of the parameters in the noraml stress We|bull distribution and the htverse power law model are derived. In particular, when the new shape parameter computers. The formulations are given for the general case and are illustrated for a special sitnpio case. comparison with the classical approach using pseudorandom dataas well as real data on solid tantatum electrolytic capacitors shows that the proposed method is better and more effective.     

Some Generalized q-Bessel Type Wavelets and Associated Transforms

In this paper wavelet functions are introduced in the context of q-theory.We precisely extend the case of Bessel and q-Bessel wavelets to the generalized q-Bessel wavelets.Starting from the(q,v)-extension(v =(α,β)) of the q-case,associated generalized q-wavelets and generalized q-wavelet transforms are developed for the new context.Reconstruction and Placherel type formulas are proved.