X-RAY INDUCED VISIBLE LUMINESCENCE OF PORPHYRINS

A concept has been presented whereby X-ray irradiation can be used to induce visible luminescence of chromophores such as porphyrins. The essential aspects of the idea have been demonstrated in a supramolecular assembly consisting of a water-dispersed polystyrene latex with an embedded scintillating compound, 2,5-diphenyloxa-zole, and an externally attached hematoporphyrin. X-ray excitation of the assembly yields an emission spectra typical for hematoporphyrin with fluorescent yields. of up to 3% with respect to 2,5-diphenyloxazole emission. Significant quenching in the presence of dioxygen indicates that singlet oxygen is formed at atmospheric conditions.     

Tau-functions on Hurwitz Spaces

We construct a flat holomorphic line bundle over a connected component of the Hurwitz space of branched coverings of the Riemann sphere P ¹. A flat holomorphic connection defining the bundle is described in terms of the invariant Wirtinger projective connection on the branched covering corresponding to a given meromorphic function on a Riemann surface of genus g. In genera 0 and 1 we construct a nowhere vanishing holomorphic horizontal section of this bundle (the ‘Wirtinger tau-function’). In higher genus we compute the modulus square of the Wirtinger tau-function. In particular one gets formulas for the isomonodromic tau-functions of semisimple Frobenius manifolds connected with the Hurwitz spaces H _g,N (1,⋯,1). This revised version was published online in July 2006 with corrections to the Cover Date.     

On the spectrum of the C*-algebra of fourier multipliers in a cone

We describe the spectrum of the C^*-algebra generated by the Fourier multipliers (singular integral operators) on the space L₂ with a polynomial weight in an acute-angled convex cone of the space ⁿ. Bibliography: 12 titles.Translated fromProblemy Matematicheskogo Analiza, No. 12, 1992, pp. 61–82.     

Investigation of the degree of occupancy of 3d and 4s bands of 3d metals and their alloys on the basis of a four-band model

A four-band model is used as the basis for obtaining relationships suitable for the calculation of a number of the s electrons in 3d metals and their alloys. The results are given of calculations of this number in Fe, Co, Ni, and Cu, and their Fe-Co, Co-Ni, and Ni-Cu alloys. A quantitative agreement is found between the number of the s electrons and the available published data. The results indicate the presence of vacant states in the d band of Cu and in the d subband of Ni, which is usually assumed to be completely filled. The results demonstrate shortcomings of the four-band model in explaining the magnitude of the normal Hall coefficient of Co and of Fe-Co, Co-Ni, and Ni-Cu alloys.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 71–77, May, 1980.     

The neumann problem for the wave equation in a cone

The Neumann problem for the wave equation in a wedge is considered. The asymptotic behavior of solutions to the problem in a neighborhood of the edge of the wedge is studied. In order to deduce and justify asymptotic formulas, the solvability of the problem in the scale of weight function spaces is investigated. Bibliography: 30 titles. Translated fromProblemy Matematicheskogo Analiza, No. 20, 2000, pp. 71–110.     

Nonautonomous Integrable Systems Associated with Hurwitz Spaces in Genuses Zero and One

Briefly outlining our recent work, we construct a family of nonautonomous integrable systems (deformations of the principal chiral model) in connection with the Hurwitz spaces of meromorphic functions on the Riemann sphere, cylinder, and torus. We give differential equations describing the dependence of the critical points of the rational, elliptic, and trigonometric functions on the critical values. We outline a relation to the deformation framework of Burtzev–Mikhailov–Zakharov.     

Isomonodromic tau function on the space of admissible covers

The isomonodromic tau function of the Fuchsian differential equations associated to Frobenius structures on Hurwitz spaces can be viewed as a section of a line bundle on the space of admissible covers. We study the asymptotic behavior of the tau function near the boundary of this space and compute its divisor. This yields an explicit formula for the pullback of the Hodge class to the space of admissible covers in terms of the classes of compactification divisors.