In this paper we construct a flatlet biorthogonal multiwavelets System. Then, we use this system for numerical solution of Integro-differential equations. The good properties of this system, i.e., biorthogonality and more vanishing moments lead to efficient and accurate solutions. Some test problems with known solutions are presented and the numerical results are given to show the efficiency of...

Given a pair of biorthogonal, compactly supported multiwavelets, we present an algorithm for raising their approximation orders to any desired level, using one lifting step and one dual lifting step. Free parameters in the algorithm are explicitly identified, and can be used to optimize the result with respect to other criteria.

Let us assume 1 ≥ −−∞. The goal of the present article is to classify finite, canonically sub-Shannon, ultra-integral measure spaces. We show that D > i. Recently, there has been much interest in the characterization of multiply Hermite curves. We wish to extend the results of [39, 39] to sub-countably associative numbers.

introduction 3d reconstruction of an object from its 2d cross-sections (slices) has many applications in different fields of sciences such as medical physics and biomedical engineering. in order to perform 3d reconstruction, at first, desired boundaries at each slice are detected and then using a correspondence between points of successive slices surface of desired object is reconstructed. mate...

Motivated by the Novikov equation and its peakon problem, we propose a new mixed type Hermite–Padé approximation whose unique solution is sequence of polynomials constructed with help Pfaffians. These belong to family recently proposed partial-skew-orthogonal polynomials. The relevance especially visible in problem germane so that obtain explicit inverse formulae terms Pfaffians reformulating s...

Quadratic Bézier curves are important geometric entities in many applications. However, it was often ignored by the literature the fact that a single segment of a quadratic Bézier curve may fail to fit arbitrary endpoint unit tangent vectors. The purpose of this paper is to provide a solution to this problem, i.e., constructing G quadratic Bézier curves satisfying given endpoint (positions and ...

The authors study the Hilbert Transform on the real line. They introduce some polynomial approximations and some algorithms for its numerical evaluation. Error estimates in uniform norm are given.

Based on the smoothness criterion of minimum curvature variation of the curve, tangent angle constraints guaranteeing an optimized geometric Hermite (OGH) curve both mathematically and geometrically smooth is given, and new methods for constructing composite optimized geometric Hermite (COH) curves are presented in this paper. The comparison of the new methods with Yong and Cheng’s methods base...

We propose a novel semi-supervised learning scheme using adaptive interpolation on multiple one-dimensional (1-D) embedded data. For a give high dimensional data set, we smoothly map it onto several different one-dimensional (1-D) sequences, so that the labeled subset is converted to a 1-D subset for each of these sequences. Applying the cubic interpolation of the labeled subset, we obtain a su...

abstract We give a formula for the duals of the mask associated with trivariate box spline functions. We show how to construct trivariate nonseparable compactly supported biorthogonal wavelets associated with box spline functions. The biorthogonal wavelets may have arbitrarily high regularities.