B\"acklund--Darboux transformations in Sato's Grassmannian

We define B\"acklund--Darboux transformations in Sato's Grassmannian. They can be regarded as Darboux transformations on maximal algebras of commuting ordinary differential operators. We describe the action of these transformations on related objects: wave functions, tau-functions and spectral algebras. This paper is the second of a series of papers (hep-th/9510211, q-alg/9602011, q-alg/9602012) on the bispectral problem.Comment: 13 pages, LaTeX2e, uses amsfonts.sty and latexsym.sty, no figure

Bispectral algebras of commuting ordinary differential operators

We develop a systematic way for constructing bispectral algebras of commuting ordinary differential operators of any rank $N$. It combines and unifies the ideas of Duistermaat-Gr\"unbaum and Wilson. Our construction is completely algorithmic and enables us to obtain all previously known classes or individual examples of bispectral operators. The method also provides new broad families of bispectral algebras which may help to penetrate deeper into the problem.Comment: 46 pages, LaTeX2e, uses amsfonts.sty and latexsym.sty, no figures, rearrangement of the introduction, skipping Conjecture 0.2 of the first version, to appear in Communications in Mathematical Physic

Highest Weight Modules of W1+∞, Darboux Transformations and the Bispectral Problem

This paper is a survey of our recent results on the bispectral problem. We describe a new method for constructing bispectral algebras of any rank and illustrate the method by a series of new examples as well as by all previously known ones. Next we exhibit a close connection of the bispectral problem to the representation theory of W1+∞–algerba. This connection allows us to explain and generalise to any rank the result of Magri and Zubelli on the symmetries of the manifold of the bispectral operators of rank and order two

Mathematical modeling of heat and mass transfer in a thermal protection coating with gas flow fluctuations

The thermochemical destruction of a carbon fiber-reinforced polymer when affected by a high enthalpy fluctuating gas flow is simulated numerically. The possibility of controlling the heat transfer process in the composite material is studied

Spine-sheath polarization structures in four active galactic nuclei jets

We present the results of multifrequency (15 + 8 + 5 GHz) polarization Very Long Baseline Array (VLBA) observations of the three BL Lacertae objects 0745 + 241, 1418 + 546 and 1652 + 398 together with 5-GHz VLBI Space Observatory Programme (VSOP) observations of 1418 + 546 and 1.6- and 5-GHz VSOP observations of the blazar 1055 + 018. The jets of all these sources have polarization structure transverse to the jet axis, with the polarization E vectors aligned with the jet along the jet spine and 'sheaths' of orthogonal E vectors at one or both edges of the jet. The presence of polarization aligned with the jet near the 'spine' may indicate that the jets are associated with helical B fields that propogate outward with the jet flow; the presence of orthogonal polarization near the edges of the jet may likewise be a consequence of a helical jet B field, or may be owing to an interaction with the ambient medium on parsec scales. We have tentatively detected interknot polarization in 1055 + 018 with E aligned with the local jet direction, consistent with the possibility that the jet of this source is associated with a helical B field