Molecular mass distribution of sodium alginate by high-performance size-exclusion chromatography

A sensitive high-performance size-exclusion chromatography (HPSEC) method with simple UV detection was developed for the molecular mass analysis of sodium alginate. It was used to evaluate alginates of varying molecular mass and the results were compared with the viscosity measurements. This HPSEC method was sensitive to serve as the stability indicating method for alginate after storage under different conditions. The information of relative molecular mass distribution of alginate was provided with reference to pullulan molecular mass standards. The comparison of the HPSEC chromatograms of alginate, pullulan and dextran revealed the effect of chemical composition of a polysaccharide and its effect on apparent molecular mass distribution.     

The Inverse Scattering Method and Systems of Equations qxy = F(q,qy)

Consider equations of the form where q is in general a complex vector and the function F depends nontrivially both on q and on q_y. We show that a family S of such equations can be investigated by the inverse scattering method. If an equation (*) belongs to S, the function F depends linearly on q and algebraically on q_y. We show that the family S contains a subfamily in which each equation can be obtained from the two dimensional Toda lattice equations by a Bäcklund transformation.     

Inverse Scattering and the Bäcklund Transformation for the Generalized Wave and Generalized Sine-Gordon Equations

The generalized wave equations and generalized sine-Gordon equations are known to be associated to linear spectral problems. In this paper we show that the geometric Backlund transformation for the nonlinear equations corresponds to changing the discrete part of the scattering data for the linear problems.     

Some Isoperimetric Inequalities in Electrochemistry and Hele Shaw Flows

Isoperimetric inequalities are applied to a moving-boundaryproblem for doubly-connected domains. This problem occurs forexample in electrochemistry, in which case the domains in questionare the electrolyte of an electrolytic cell. The two electrodessurrounding the electrolyte are assumed to grow or dissolve,at different rates in general, by electrochemical reaction.We obtain optimal estimates showing, for example, that the leastchange in volume of each electrode always occurs in sphericalsymmetry.     

Exact propagators for some degenerate hyperbolic operators

Exact propagators are obtained for the degenerate second order hyperbolic operators ∂² _t -t ^2l Δ _x , l=1,2,..., by analytic continuation from the degenerate elliptic operators ∂² _t +t ^2l Δ _x . The partial Fourier transforms are also obtained in closed form, leading to integral transform formulas for certain combinations of Bessel functions and modified Bessel functions.