Dubrovin Type Equations for Completely Integrable Systems Associated with a Polynomial Pencil

Dubrovin type equations for the N -gap solution of a completely integrable system associated with a polynomial pencil is constructed and then integrated to a system of functional equations. The approach used to derive those results is a generalization of the familiar process of finding the 1-soliton (1-gap) solution by integrating the ODE obtained from the soliton equation via the substitution u = u(x + λt).

A Note on Multipliers for Integrable Boehmians

2000 Mathematics Subject Classification: 44A40, 42A38, 46F05

Closed Form Solutions of Integrable Nonlinear Evolution Equations

2010 Mathematics Subject Classification: 35Q55.

Logic Based Pattern Recognition - Ontology Content (2)

Logic based Pattern Recognition extends the well known similarity models, where the distance measure is the base instrument for recognition. Initial part (1) of current publication in iTECH-06 reduces the logic based recognition models to the reduced disjunctive normal forms of partially defined Boolean functions. This step appears as a way to alternative pattern recognition instruments through combining metric and logic hypotheses and features, leading to studies of logic forms, hypotheses, hierarchies of hypotheses and effective algorithmic solutions. Current part (2) provides probabilistic conclusions on effective recognition by logic means in a model environment of binary attributes.

Riemann-Hilbert Problems with Canonical Normalization and Families of Commuting Operators

2010 Mathematics Subject Classification: 35Q15, 31A25, 37K10, 35Q58.

Canonically Conjugate Variables for the μCH Equation

2010 Mathematics Subject Classification: 35Q35, 37K10.

On the Mixed Modulus of Smoothness and a Class of Double Fourier Series

MSC 2010: 42A32; 42A20

Density of Polynomials in the L^2 Space on the Real and the Imaginary Axes and in a Sobolev Space

2000 Mathematics Subject Classification: 41A10, 30E10, 41A65.

Contact CR-Submanifolds of Kenmotsu Manifolds

2000 Mathematics Subject Classification: 53C15, 53C42.

Special compositions in affinely connected spaces without a torsion

2000 Mathematics Subject Classification: 53B05, 53B99.