The General Differential Operators Generated by a Quasi-Differential Expressions with their Interior Singular Points

The general ordinary quasi-differential expression M of n-th order with complex coefficients and its formal adjoint M + are considered over a regoin (a, b) on the real line, −∞ ≤ a < b ≤ ∞, on which the operator may have a finite number of singular points. By considering M over various subintervals on which singularities occur only at the ends, restrictions of the maximal operator generated by M in L2|w (a, b) which are regularly solvable with respect to the minimal operators T0 (M ) and T0 (M + ). In addition to direct sums of regularly solvable operators defined on the separate subintervals, there are other regularly solvable restrications of the maximal operator which involve linking the various intervals together in interface like style.

Compositions, Generated by Special Nets in Affinely Connected Spaces

Special nets which characterize Cartesian, geodesic, Chebyshevian, geodesic- Chebyshevian and Chebyshevian-geodesic compositions are introduced. Con- ditions for the coefficients of the connectedness in the parameters of these special nets are found.

Relationship between Extremal and Sum Processes Generated by the same Point Process

2000 Mathematics Subject Classification: Primary 60G51, secondary 60G70, 60F17.

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.

The Variety of Leibniz Algebras Defined by the Identity x(y(zt)) ≡ 0

2000 Mathematics Subject Classification: Primary: 17A32; Secondary: 16R10, 16P99, 17B01, 17B30, 20C30

Polynomial automorphisms over finite fields: Mimicking tame maps by the Derksen group

2010 Mathematics Subject Classification: 14L99, 14R10, 20B27.