Abstract Self-excited vibrations can occur in the spline-shafting system due to internal friction of tooth surface. However, manufacturing errors, design tolerances, and time-varying factors, parameters that induce self-excited are always uncertain. This study provides new insights into uncertainty quantification sensitivity analysis a spline-shaft suffering from vibrations. The non-intrusive g...

This paper describes an algebraic construction of bivariate interpolatory subdivision masks induced by three-directional box spline subdivision schemes. Specifically, given a three-directional box spline, we address the problem of defining a corresponding interpolatory subdivision scheme by constructing an appropriate correction mask to convolve with the three-directional box spline mask. The p...

Given a grid in R, consisting of d bi-infinite sequences of hyperplanes (possibly with multiplicities) orthogonal to the d axes of the coordinate system, we consider the spaces of tensor-product spline functions of a given degree on a multi-cell domain. Such a domain consists of finite set of cells which are defined by the grid. A piecewise polynomial function belongs to the spline space if its...

Support vector machine (SVM) is a very popular method for binary data classification in data mining (machine learning). Since the objective function of the unconstrained SVM model is a non-smooth function, a lot of good optimal algorithms can’t be used to find the solution. In order to overcome this model’s non-smooth property, Lee and Mangasarian proposed smooth support vector machine (SSVM) i...

BACKGROUND There is increasing emphasis in medical research on modelling growth across the life course and identifying factors associated with growth. Here, we demonstrate multilevel models for childhood growth either as a smooth function (using fractional polynomials) or a set of connected linear phases (using linear splines). METHODS We related parental social class to height from birth to ...

Abstract Polynomial splines are ubiquitous in the fields of computer-aided geometric design and computational analysis. Splines on T-meshes, especially, have potential to be incredibly versatile since local mesh adaptivity enables efficient modeling approximation features. Meaningful use such for requires construction a suitable spanning set linearly independent splines, theoretical understandi...

Pseudo-splines are a rich family of functions that allows the user to meet various demands for balancing polynomial reproduction (i.e., approximation power), regularity and support size. Such a family includes, as special members, B-spline functions, universally known for their usefulness in different fields of application. When replacing polynomial reproduction by exponential polynomial reprod...

This paper introduces a methodology for constructing pen and ink style landscape illustrations using B-spline surface models. After a brief discussion of the history of 19 and 20 century manual techniques and recent developments in automated non-photorealistic rendering (NPR) techniques, the paper discusses polynomial models for surface rendering and their implementation in the OpenGL graphics ...