In this paper we consider spline function of general degree m which has the same area as the function does in each partition of the sub-intervals. The existence and uniqueness in general of spline functions also been studied and obtained the result. : In this paper we consider spline function of general degree, i.e.,of degree m, m=2,3,.... We first give definitions and notations. We take 0 =x 0...

An interaction integral method for evaluating mixed-mode stress intensity factors (SIFs) for two dimensional crack problems using NURBS-based isogeometric analysis method is investigated. The interaction integral method is based on the path independent J-integral. By introducing a known auxiliary field solution, the mixed-mode SIFs are calculated simultaneously. Among features of B-spline basis...

the present study was carried out to compare different random regression models to estimate variance components of lamb's average birth weight per lambing (abwll) in mehraban sheep. the data were 5,559 abwll records of 2,244 mehraban ewes. the random regression models consisted of namely, flock-year-season of lambing as fixed effect, a fixed regression to fit average trajectory of the popu...

Uniform cubic B-spline functions have been used for mapping functions in various areas such as image warping and morphing, 3D deformation, and volume morphing. The injectivity (one-to-one property) of a mapping function is crucial to obtain desirable results in these areas. This paper considers the injectivity conditions of 2D and 3D uniform cubic B-spline functions. We propose a geometric inte...

For spline smoothing one can rewrite the smooth estimation as a linear mixed model (LMM) where the smoothing parameter appears as the variance of spline basis coefficients. Smoothing methods that use basis functions with penalization can utilize maximum likelihood (ML) theory in LMM framework ([8]). We introduce the minimum description length (MDL) model selection criterion in LMM and propose a...

A flexible nonparametric regression model is considered in which the response depends linearly on some covariates, with regression coefficients as additive functions of other covariates. Polynomial spline estimators are proposed for the unknown coefficient functions, with optimal univariate mean square convergence rate under geometric mixing condition. Consistent model selection method is also ...

In this paper we derive optimal subspaces for Kolmogorov n-widths in the L2 norm with respect to sets of functions defined by kernels. This enables us to prove the existence of optimal spline subspaces of arbitrarily high degree for certain classes of functions in Sobolev spaces of importance in finite element methods. We construct these spline spaces explicitly in special cases. Math Subject C...

We present a data reduction scheme for efficient surface storage, by introducing a coefficient–based least squares spline operator that does not require any pointwise evaluation to approximate (in a lower dimension spline space) a given bivariate B–spline function. In order to define an accurate approximation of the target spline with a significant reduction of the space dimension, this operato...

In this paper, the Bagley-Torvik equation is constructed. A model approach based on non-polynomial numerical methods spline interpolation is developed to solve some problems. We show that the approximate solutions of such problems obtained by the numerical algorithm developed using non-polynomial spline interpolation functions are better than those produced by other numerical methods. The aim o...

This paper discusses the dimension of spline spaces S(m,n,m−1, n−1,T ) over certain type of hierarchical T-meshes. The major step is to set up a bijection between the spline space S(m,n,m− 1, n− 1,T ) and a univariate spline space whose definition depends on the l-edges of the extended T-mesh. We decompose the univariate spline space into direct sums in the sense of isomorphism using the theory...