Highest Weight Modules of W1+∞, Darboux Transformations and the Bispectral Problem

This paper is a survey of our recent results on the bispectral problem. We describe a new method for constructing bispectral algebras of any rank and illustrate the method by a series of new examples as well as by all previously known ones. Next we exhibit a close connection of the bispectral problem to the representation theory of W1+∞–algerba. This connection allows us to explain and generalise to any rank the result of Magri and Zubelli on the symmetries of the manifold of the bispectral operators of rank and order two.

Peculiarities of the Electronic Educational and Methodological Complex under the Point-rating Technology

At present in the sphere of electronic learning in the light of solving tasks put by the Bologna Declaration an important place is being taken by electronic educational and methodological complexes (EMC).The authors have put forward new components of EMC necessary for the organization of educational process and for the determination of labour intensity according to modules and students’ activity type. They also suggested a technology of defining the rating of the grade in the credit-module system.

Development and Implementation of NURBS Models of Quadratic Curves and Surfaces

This article goes into the development of NURBS models of quadratic curves and surfaces. Curves and surfaces which could be represented by one general equation (one for the curves and one for the surfaces) are addressed. The research examines the curves: ellipse, parabola and hyperbola, the surfaces: ellipsoid, paraboloid, hyperboloid, double hyperboloid, hyperbolic paraboloid and cone, and the cylinders: elliptic, parabolic and hyperbolic. Many real objects which have to be modeled in 3D applications possess specific features. Because of this these geometric objects have been chosen. Using the NURBS models presented here, specialized software modules (plug-ins) have been developed for a 3D graphic system. An analysis of their implementation and the primitives they create has been performed.

Modular Digital Watermarking for Image Verification and Secure Data Storage in Web Applications

Our modular approach to data hiding is an innovative concept in the data hiding research field. It enables the creation of modular digital watermarking methods that have extendable features and are designed for use in web applications. The methods consist of two types of modules – a basic module and an application-specific module. The basic module mainly provides features which are connected with the specific image format. As JPEG is a preferred image format on the Internet, we have put a focus on the achievement of a robust and error-free embedding and retrieval of the embedded data in JPEG images. The application-specific modules are adaptable to user requirements in the concrete web application. The experimental results of the modular data watermarking are very promising. They indicate excellent image quality, satisfactory size of the embedded data and perfect robustness against JPEG transformations with prespecified compression ratios. ACM Computing Classification System (1998): C.2.0.

Double complexes and vanishing of Novikov cohomology

2010 Mathematics Subject Classification: Primary 18G35; Secondary 55U15.