QUARTIC CONVEX TYPE PIECEWISE POLYNOMIAL

In the present paper we consider quartic piecewise polynomial for approximation to the function f ∈ C 2 [0, 1]. A convex type condition has been imposed in the partition so that the matrix involved for the computation of pp functions is of lower band. This reduces the computation for constructions of the pp functions for the approximation.     

A bivariate INAR(1) time series model with geometric marginals

In this paper we introduce a simple bivariate integer-valued time series model with positively correlated geometric marginals based on the negative binomial thinning mechanism. Some properties of the model are considered. The unknown parameters of the model are estimated using the modified conditional least squares method.     

Modified nodal cubic spline collocation for elliptic equations

We consider the modified nodal cubic spline collocation method for a general, variable coefficient, second order partial differential equation in the unit square with the solution subject to the homogeneous Dirichlet boundary conditions. The bicubic spline approximate solution satisfies both the Dirichlet boundary conditions and a perturbed partial differential equation at the nodes of a uniform partition of the square. We prove existence and uniqueness of the approximate solution and derive an optimal fourth order maximum norm error bound. The resulting linear system is solved efficiently by a preconditioned iterative method. Numerical results confirm the expected convergence rates. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2011     

A Revisit on the Derivation of the Particular Solution for the Differential Operator ∆2 ± λ2

In this paper, we applied the polyharmonic splines as the basis functions to derive particular solutions for the differential operator ∆² ± λ². Similar to the derivation of fundamental solutions, it is non-trivial to derive particular solutions for higher order differential operators. In this paper, we provide a simple algebraic factorization approach to derive particular solutions for these types of differential operators in 2D and 3D. The main focus of this paper is its simplicity in the sense that minimal mathematical background is required for numerically solving higher order partial differential equations such as thin plate vibration. Three numerical examples in both 2D and 3D are given to validate particular solutions we derived.     

Approximation by Discrete GB-Splines

This paper addresses the definition and the study of discrete generalized splines. Discrete generalized splines are continuous piecewise defined functions which meet some smoothness conditions for the first and second divided differences at the knots. They provide a generalization both of smooth generalized splines and of the classical discrete cubic splines. Completely general configurations for steps in divided differences are considered. Direct algorithms are proposed for constructing discrete generalized splines and discrete generalized B-splines (discrete GB-splines for short). Explicit formulae and recurrence relations are obtained for discrete GB-splines. Properties of discrete GB-splines and their series are studied. It is shown that discrete GB-splines form weak Chebyshev systems and that series of discrete GB-splines have a variation diminishing property.     

强度为MOBVE分布时并联结构系统可靠度的估计

设系统A由两个结构单元A1和A2并联组成.A1和A2的强度(Y1,Y 2)服从由Marshall和Olkin提出的MOBVE分布,其联合可靠度函数为R(y1,y2)=exp[-λ1y1-λ2y2-λ12max(y1,y2)].I[y1>0,y2>0],其中λ1>0,λ2>0,λ12≥0均未知.系统A所承受的应力服从指数分布(参数未知).本文给出了系统A的可靠度PA的两种估计(^P)A和(～P)A以及两种渐近置信下限L(^PA)和L(～PA),讨论了(^P)A和(～P)A的统计性质,最后还进行了模拟计算.     

A sampling theorem on homogeneous manifolds

We consider a generalization of entire functions of spherical exponential type and Lagrangian splines on manifolds. An analog of the Paley-Wiener theorem is given. We also show that every spectral entire function on a manifold is uniquely determined by its values on some discrete sets of points.

The main result of the paper is a formula for reconstruction of spectral entire functions from their values on discrete sets using Lagrangian splines.

     

BIVARIATE FRACTAL INTERPOLATION FUNCTIONS ON RECTANGULAR DOMAINS

AbstractNon-tensor product bivariate fractal interpolation functions defined on gridded rectangular domains are constructed. Linear spaces consisting of these functions are introduced. The relevant Lagrange interpolation problem is discussed. A negative result about the existence of affine fractal interpolation functions defined on such domains is obtained.     

A logarithmic complexity floating frame of reference formulation with interpolating splines for articulated multi-flexible-body dynamics

An interpolating spline-based approach is presented for modeling multi-flexible-body systems in the divide-and-conquer (DCA) scheme. This algorithm uses the floating frame of reference formulation and piecewise spline functions to construct and solve the non-linear equations of motion of the multi-flexible-body system undergoing large rotations and translations. The new approach is compared with the flexible DCA (FDCA) that uses the assumed modes method [1]. The FDCA, in many cases, must resort to sub-structuring to accurately model the deformation of the system. We demonstrate, through numerical examples, that the interpolating spline-based approach is comparable in accuracy and superior in efficiency to the FDCA. The present approach is appropriate for modeling flexible mechanisms with thin 1D bodies undergoing large rotations and translations, including those with irregular shapes. As such, the present approach extends the current capability of the DCA to model deformable systems. The algorithm retains the theoretical logarithmic complexity inherent in the DCA when implemented in parallel.     

带有二元连接函数的半参数模型

提出了一种新的带有二元连接函数的广义半参数模型,即二元连接模型(简称为BLM).使用轮廓似然方法估计模型的参数和非参数部分,并给出了计算算法.证明了所得的未知参数的估计量为n~(1/2)-相合,渐近正态且具有渐近最小方差,给出了实际数据分析和模拟研究,最终采用局部功效方法来检验非参数部分的线性性.