Generalization of a Conjecture in the Geometry of Polynomials

In this paper we survey work on and around the following conjecture, which was first stated about 45 years ago: If all the zeros of an algebraic polynomial p (of degree n ≥ 2) lie in a disk with radius r, then, for each zero z1 of p, the disk with center z1 and radius r contains at least one zero of the derivative p′ . Until now, this conjecture has been proved for n ≤ 8 only. We also put the conjecture in a more general framework involving higher order derivatives and sets defined by the zeros of the polynomials.

Fuzzy sets: Abstraction Axiom, Statistical Interpretation, Observations of Fuzzy Sets

The issues relating fuzzy sets definition are under consideration including the analogue for separation axiom, statistical interpretation and membership function representation by the conditional Probabilities.

Geometry of Warped Product Semi-Invariant Submanifolds of a Locally Riemannian Product Manifold

2000 Mathematics Subject Classification: 53C42, 53C15.

Basic Structure of the General Information Theory

The basic structure of the General Information Theory (GIT) is presented in the paper. The main divisions of the GIT are outlined. Some new results are pointed.

Interior Boundaries for Degenerate Elliptic Equations of Second Order Some Theory and Numerical Observations

2010 Mathematics Subject Classification: Primary 35J70; Secondary 35J15, 35D05.

A Simple Example of Localized Parametric Resonance for the Wave Equation

2000 Mathematics Subject Classification: 35L05, 35P25, 47A40.

Data Mining for Browsing Patterns in Weblog Data by Art Neural Networks

Categorising visitors based on their interaction with a website is a key problem in Web content usage. The clickstreams generated by various users often follow distinct patterns, the knowledge of which may help in providing customised content. This paper proposes an approach to clustering weblog data, based on ART2 neural networks. Due to the characteristics of the ART2 neural network model, the proposed approach can be used for unsupervised and self-learning data mining, which makes it adaptable to dynamically changing websites.

Solving a Direct Marketing Problem by Three Types of ARTMAP Neural Networks

An important task for a direct mailing company is to detect potential customers in order to avoid unnecessary and unwanted mailing. This paper describes a non-linear method to predict profiles of potential customers using dARTMAP, ARTMAP-IC, and Fuzzy ARTMAP neural networks. The paper discusses advantages of the proposed approaches over similar techniques based on MLP neural networks.

Lack of Answer Estimation by Fuzzy Control

The problem of the lack of answer in questions of survey is usually dealt with different estimation and classification procedures from the answers to other questions. In this document, the results of applying fuzzy control methods for the vote -one of the variables with bigger lack of answer in opinion polls- are presented.