Extended Camassa-Holm Hierarchy and Conserved Quantities

An extension of the Camassa-Holm hierarchy is constructed in this paper. The conserved quantities of the hierarchy are studied and a recurrent formula for the integrals of motion is derived. - PACS numbers: 02.30.Ik; 05.45.Yv; 45.20.Jj; 02.30.Jr.

On One Estimate for Periodic Functions

For , the estimate is derived, where and 𝑑𝑛 are defined by a certain recurrent formula.

q-TENSOR METHOD OF DETERMINING IRREDUCIBLE REPRESENTATION OF QUANTUM ALGEBRA SUq(3)

In this paper, we construct irreducible q-tensor operators of rank [Formula: see text] of quantum algebra SU q(2) using the generators of quantum algebra SU q(3). By means of property of q-tensor operator, we can easily obtain irreducible representation (IR) of SU q(3). A recurrent formula to calculate reduced coefficients of SU q(3) is obtained and the multiplicity of reduced coefficients is discussed.

Determination of rate constants of redox reactions of second order from current-less potential-time curves by a simplified graphical-numerical method

A method for constructing curves is proposed that are linear in a wide region and from whose slopes it is possible to determine the rate constant, if a parameter, θ, is calculated numerically from a rapidly converging recurrent formula or from its explicit form. The values of rate constants and parameter θ thus simply found are compared with those found by an optimization algorithm on a computer; the deviations do not exceed ±10%.