Special polynomials associated with rational solutions of the second Painlevé equation and other equations of its hierarchy are studied. A new method, which allows one to construct each family of polynomials is presented. The structure of the polynomials is established. Formulaes for their coefficients are found. The degree of every polynomial is obtained. The main achievement of the method lie...

For a two-parameter family of lower triangular matrices with entries involving Jacobi polynomials an explicit inverse is given, with entries involving a sum of two Jacobi polynomials. The formula simplifies in the Gegenbauer case and then one choice of the parameter solves an open problem in a recent paper by Koelink, van Pruijssen & Román. The twoparameter family is closely related to two two-...

A strategy to obtain sets of initial configuration to design freeform reflector surfaces is presented. This strategy brings the initial configuration of the reflector surface using a collection of elemental facets defined by Bezier surfaces and able to face the optimization process of the illumination system. The purpose of this communication is to provide initial configurations to obtain a set...

Naturally, with the mounting application of biometric systems, there arises a difficulty in storing and handling those acquired biometric data. Fingerprint recognition has been recognized as one of the most mature and established technique among all the biometrics systems. In recent times, with fingerprint recognition receiving increasingly more attention the amount of fingerprints collected ha...

Kida, Rikuna and Sato [6] developed a classification theory for Brumer’s quintic polynomials via Kummer arising from associated elliptic curves. We generalize their results to curves Lecacheux’s $F_{20}$-polynomials instead of $D_{5}$-polynomials.

We post-process lossy images compressed by JPEG algorithms (DCT and LOCO) using the Bezier function for enhancement. The Bezier function is done by table lookup for speed, and does blending (in contrast to interpolation) on low-activity regions. Active regions, detected by using a threshold of 3/2 of the quantization step size, are left alone. The threshold is theoretically justified, overcomes...

The smooth interpolation of keyframes of a rigid body, in particular their orientations, is an important problem in animation . Using the quaternion as a representation for orientation, several papers have solved this problem through the generation of smooth curves on the quaternion sphere. However, none of these methods have constructed rational curves. This paper develops a method for generat...

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...