氢负离子H^-关联能的Bsplines计算

对用Ｂｓｐｌｉｎｅｓ构造有限正交基矢集的方法进行了讨论，并计算了氢负离子Ｈ－的关联能，使得在合理的计算量范围内，总能量可以达到很高的精度，比常用的Ｓｌａｔｅｒ基计算结果提高了一个数量级。结果表明：Ｂｓｐｌｉｎｅｓ方法可以有效用于电子关联能的计算。

一维四势阱能谱和波函数的B splines计算

用B splines函数基研究一维四势阶模型的能谱和波函数,讨论能谱和波函数随着势阶形状变化而变化的规律.

T-Splines在工业设计中的应用

本文主要讲述网格建模插件T-Splines在工业设计中的应用,为工业设计的曲面创建提供了新的曲面建模方法。并详细展示T-Splines从实体创建曲面、从线创建曲面和从输入曲面创建曲面的曲面案例效果。作为网格曲面、NURBS曲面的下一代的曲面建模技术,必将有广阔的发展前景。

以NURBS为输入曲面的T-Splines建模思路研究

建模是现代工业设计中一个重要步骤,随着建模软件的不断增加,不同的建模思路也相互影响,采取合理的建模方法是提高产品设计效率的有效方法。以犀牛NURBS曲面为载体,探究NURBS-TS-NURBS的建模思路,弥补RHINO中NURBS曲面建模的不足,并且列举汽车前盖的建模案例,形象展现该方法灵活可反复修改曲面的优势。该方法适用于建模中期反复修改曲面形态。

On the Implementation of Exponential B-Splines by Poisson Summation Formula

Polynomial splines have played an important role in image processing, medical imaging and wavelet theory. Exponential splines which are of more general concept have been recently investigated.We focus on cardinal exponential splines and develop a method to implement the exponential B-splines which form a Riesz basis of the space of cardinal exponential splines with finite energy.

Multivariate adaptive regression splines and neural network models for prediction of pile drivability

Piles are long, slender structural elements used to transfer the loads from the superstructure through weak strata onto stiffer soils or rocks. For driven piles, the impact of the piling hammer induces compression and tension stresses in the piles. Hence, an important design consideration is to check that the strength of the pile is sufficient to resist the stresses caused by the impact of the pile hammer. Due to its complexity, pile drivability lacks a precise analytical solution with regard to the phenomena involved.In situations where measured data or numerical hypothetical results are available, neural networks stand out in mapping the nonlinear interactions and relationships between the system’s predictors and dependent responses. In addition, unlike most computational tools, no mathematical relationship assumption between the dependent and independent variables has to be made. Nevertheless, neural networks have been criticized for their long trial-and-error training process since the optimal configuration is not known a priori. This paper investigates the use of a fairly simple nonparametric regression algorithm known as multivariate adaptive regression splines（MARS）, as an alternative to neural networks, to approximate the relationship between the inputs and dependent response, and to mathematically interpret the relationship between the various parameters. In this paper, the Back propagation neural network（BPNN） and MARS models are developed for assessing pile drivability in relation to the prediction of the Maximum compressive stresses（MCS）, Maximum tensile stresses（MTS）, and Blow per foot（BPF）. A database of more than four thousand piles is utilized for model development and comparative performance between BPNN and MARS predictions.

Advanced reliability analysis of slopes in spatially variable soils using multivariate adaptive regression splines

This study aims to extend the multivariate adaptive regression splines(MARS)-Monte Carlo simulation(MCS) method for reliability analysis of slopes in spatially variable soils. This approach is used to explore the influences of the multiscale spatial variability of soil properties on the probability of failure(P_f) of the slopes. In the proposed approach, the relationship between the factor of safety and the soil strength parameters characterized with spatial variability is approximated by the MARS, with the aid of Karhunen-Loeve expansion. MCS is subsequently performed on the established MARS model to evaluate Pf.Finally, a nominally homogeneous cohesive-frictional slope and a heterogeneous cohesive slope, which are both characterized with different spatial variabilities, are utilized to illustrate the proposed approach.Results showed that the proposed approach can estimate the P_f of the slopes efficiently in spatially variable soils with sufficient accuracy. Moreover, the approach is relatively robust to the influence of different statistics of soil properties, thereby making it an effective and practical tool for addressing slope reliability problems concerning time-consuming deterministic stability models with low levels of P_f.Furthermore, disregarding the multiscale spatial variability of soil properties can overestimate or underestimate the P_f. Although the difference is small in general, the multiscale spatial variability of the soil properties must still be considered in the reliability analysis of heterogeneous slopes, especially for those highly related to cost effective and accurate designs.

A comparison of piecewise cubic Hermite interpolating polynomials,cubic splines and piecewise linear functions for the approximation of projectile aerodynamics

Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics.The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions:they are continuous,differentiable at least once,and have a relatively low degree.The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools,and then compares Piecewise Cubic Hermite Interpolating Polynomial(PCHIP),cubic splines,and piecewise linear functions,and their variant,as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile.A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics,and its evaluation against a set of criteria.Finally,the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.

Using multivariate adaptive regression splines to develop relationship between rock quality designation and permeability

The assessment of in situ permeability of rock mass is challenging for large-scale projects such as reservoirs created by dams,where water tightness issues are of prime importance.The in situ permeability is strongly related to the frequency and distribution of discontinuities in the rock mass and quantified by rock quality designation(RQD).This paper analyzes the data of hydraulic conductivity and discontinuities sampled at different depths during the borehole investigations in the limestone and sandstone formations for the construction of hydraulic structures in Oman.Cores recovered from boreholes provide RQD data,and in situ Lugeon tests elucidate the permeability.A modern technique of multivariate adaptive regression splines(MARS)assisted in correlating permeability and RQD along with the depth.In situ permeability shows a declining trend with increasing RQD,and the depth of investigation is within 50 m.This type of relationship can be developed based on detailed initial investigations at the site where the hydraulic conductivity of discontinuous rocks is required to be delineated.The relationship can approximate the permeability by only measuring the RQD in later investigations on the same site,thus saving the time and cost of the site investigations.The applicability of the relationship developed in this study to another location requires a lithological similarity of the rock mass that can be verified through preliminary investigation at the site.

Medical images application of contour extraction based on Hermite splines contour model

Active Contour Model or Snake model is an efficient method by which the users can extract the object contour of Region Of Interest （ROI）. In this paper, we present an improved method combining Hermite splines curve and Snake model that can be used as a tool for fast and intuitive contour extraction. We choose Hermite splines curve as a basic function of Snake contour curve and present its energy function. The optimization of energy minimization is performed hy Dynamic Programming technique. The validation results are presented, comparing the traditional Snake model and the HSCM, showing the similar performance of the latter. We can find that HSCM can overcome the non-convex constraints efficiently. Several medical images applications illustrate that Hermite Splines Contour Model （HSCM） is more efficient than traditional Snake model.

Average of Distribution and Remarks on Box-Splines

A class of generalized moving average operators is introduced, and the integral representations of an average function are provided. It has been shown that the average of Dirac δ distribution is just the well known box spline. Some remarks on box splines, such as their smoothness and the corresponding partition of unity, are made. The factorization of average operators is derived. Then, the subdivision algorithm for efficient computing of box splines and their linear combinations follows.

Blending Basic Shapes By C-Type Splines and Subdivision Scheme

In this article,we adopt the C-type spline of degree 2 to model and blend basic shapes including conics and circle arcs.The C-type spline belongs to theωB-spline category of splines that are capable of blending polynomial,trigonometric and hyperbolic functions.Commonly used basic shapes can be exactly represented by these types of splines.We derive explicit formulas for the convenience of modeling the basic curves.The entire blending curve is C^1-continuous.In comparison with the existing best blending method by rational G^2 splines,which are rational splines of degree 3,the proposed method allows simpler representation and blending of the basic curves,and it can represent numerous basic shapes including the hyperbolic types.We also design a subdivision method to generate blending curves;this method is precise for the basic curves and approximate for the blending sections.The subdivision process is efficient for modeling and rendering.It has also proven to be C^1-continuous by the asymptotically equivalent theory and the continuity of stationary subdivision method.In addition,we extend the proposed methods to cases involving the modeling and blending of basic surfaces.We provide many examples that illustrate the merits of our methods.

A NOTE ON THE RECURRENCE RELATIONS OF MULTIVARIATE TRUNCATED POWERS AND BOX SPLINES

This paper gives an additional definition to multivariate truncated power T(x|x1 ,…,xn) when the knots x1 ,…,xn do not span the whole space to which x1 ,…,xn belong. By which, together with the recurrence relation, the practical evaluation of T(x|x1,…,xn ) will be very convenient and efficient. The same discussion is also done to box splines.

A new method to build boundary conditions for nonuniform B-splines interpolation

Discusses a new method to build boundary conditions for nonuniform B splines interpolation based on the curvature parameters with two advantages: no derivative of curve end is required and zero curvature at curve end is avoided, so that the shapes of the two end segments of curve can be controlled easily by adjusting the curvature parameters to meet the designer’s requirements.

Generalized fairing algorithm of parametric cubic splines

Kjellander has reported an algorithm for fairing uniform parametric cubic splines. Poliakoff extended Kjellander’s algorithm to non-uniform case. However, they merely changed the bad point’s position, and neglected the smoothing of tangent at bad point. In this paper, we present a fairing algorithm that both changed point’s position and its corresponding tangent vector. The new algorithm possesses the minimum property of energy. We also proved Poliakoff’s fairing algorithm is a deduction of our fairing algorithm. Several fairing examples are given in this paper.

DEFICIENT CUBIC SPLINES WITH AVERAGE SLOPE MATCHING

We obtain a deficient cubic spline function which matches the functions with certain area matching oner a greater mesh intervals, and also provides a greater flexibility in replacing area matching as interpolation. We also study their convergence properties to the interpolating functions.

B-splines smoothed rejection sampling method and its applications in quasi-Monte Carlo integration

The rejection sampling method is one of the most popular methods used in Monte Carlo methods. It turns out that the standard rejection method is closely related to the problem of quasi-Monte Carlo integration of characteristic functions, whose accuracy may be lost due to the discontinuity of the characteristic functions. We proposed a B-splines smoothed rejection sampling method, which smoothed the characteristic function by B-splines smoothing technique without changing the integral quantity. Numerical experiments showed that the convergence rate of nearly O( N^-1 ) is regained by using the B-splines smoothed rejection method in importance sampling.

A BEST APPROX！MATION PROPERTY OF DISCRETE QUADRATIC INTERPOLATORY SPLINES

We investigate the following problem in this paper: where there is an unique 1-periodic discrete quadratic spline s∈S(3, p, h) satisfying certain interpolatory condition for a 1-periodic discrete function de- fined on [0, 1]_k. The anwser is affirmative.

INTEGRAL REPRESENTATION OF SLOWLY GROWING EQUIDISTANT SPLINES

In this paper we consider polynomial splines S(x) with equidistant nodes which may grow a5 O (|x|~5). We present an integral representation of such splines with a distribution kernel. This repre- sentation is related to the Fourier integral of slowly growing functions. The part of the Fourier ex- ponentials herewith play the so called exponential splines by Schoenberg. The integral representation provides a flexible tool for dealing with the growing equidistant splines. First. it allows us to con- struct a rich library of splines possessing the property that translations of any such spline form a ba- sis of corresponding spline space. It is shown that any such spline is associated with a dual spline whose translations form a biorthogonal basis. As examples we present solutions of the problems of projection of a growing function onto spline spaces and of spline interpolation of growing func- tion. We derive formulas for approximate evaluation of splines projecting a function onto the spline space and establish therewith exact estimations of the approximation errors.

Multivariate adaptive regression splines based simulation optimization using move-limit strategy

This paper makes an approach to the approximate optimum in structural design,which combines the global response surface（GRS） based multivariate adaptive regression splines（MARS） with Move-Limit strategy（MLS）.MARS is an adaptive regression process,which fits in with the multidimensional problems.It adopts a modified recursive partitioning strategy to simplify high-dimensional problems into smaller highly accurate models.MLS for moving and resizing the search sub-regions is employed in the space of design variables.The quality of the approximation functions and the convergence history of the optimization process are reflected in MLS.The disadvantages of the conventional response surface method（RSM） have been avoided,specifically,highly nonlinear high-dimensional problems.The GRS/MARS with MLS is applied to a high-dimensional test function and an engineering problem to demonstrate its feasibility and convergence,and compared with quadratic response surface（QRS） models in terms of computational efficiency and accuracy.