Comment on "Two Fermi points in the exact solution of the Kondo problem"

Comment on paper by A. Zvyagin, Phys. Rev. B 64, R060405 (2001).Comment: 3 pages, no figure

A bicontinuous structure in some systems with cubic mesophases

A cubic structure of polymer colloid complexes is studied. The technique of the research includes i) an analysis of well-known literature SAXS data; on this base, at some assumptions, ii) constructing a simple model to estimate geometric structure parameters and to receive a simulated scattering curve, iii) calculations of energetic parameters by help of the analytical fluctuation theory of the phase transitions; iv) comparing the model with the real structure obtained from the SAXS data by the electron density distribution reconstruction method. In the presence of an effective field the 2-nd order phase transition transforms to the 1-st order one in the vicinity of the Lifshitz point. As a result, a bicontinuous structure in cubic mesophases is formed.Comment: 23 pages, 3 figure

Why Quantitative Structuring?

Quality-designed consumer products are easy to recognize. Wouldn't it be great if the quality of financial products became just as apparent? This paper is addressed to financial practitioners. It provides an informal introduction to Quantitative Structuring -- a technology of manufacturing quality financial products (information derivatives). The presentation is arranged in three parts: the main text assumes no prior knowledge of the topic; important detailed discussions are arranged as a set of appendices; finally, a list of references provides further details including applications beyond product design: from model risk to economics and statistics.Comment: 12 page

Polymer Melt Viscosity

The research is important for a molecular theory of liquid and has a wide interest as an example solving the problem when dynamic parameters of systems can be indirectly connected with their equilibrium properties. In frameworks of the reptation model the power law with the 3.5-exponent for the melt viscosity relation to the molecular weight of flexible-chain polymer is obtained. In order to find the exponent close to experimental values it should be taken into account the rotation vibration precession motion of chain ends with respect to the polymer melt flow direction.Comment: 10 pages, 1 figure, 4 Internetional Symposium "Molecular Order and Mobility in Polymer Systems", St.Petersburg, June 3-7, 2002, P-05

On the Mumford - Narasimhan problem

Here we discuss an old problem of algebraic geometry using some new techniques. Namely we prove that over a generic curve stable vector bundle admits the Schottki representation.Comment: To Prof. M. Narasimhan on his 70th birthda

Rotation Diffusion as an Additional Mechanism of Energy Dissipation in Polymer Melts

The research is important for a molecular theory of liquid and has a wide interest as an example solving the problem when dynamic parameters of systems can be indirectly connected with their equilibrium properties. In frameworks of the reptation model the power law with the 3.4-exponent for the melt viscosity relation to the molecular weight of linear flexible-chain polymer is predicted as distinct from the value 3 expected for a melt of ring macromolecules. To find the exponent close to experimental values it should be taken into account the rotation vibration precession motion of chain ends about the polymer melt flow direction.Comment: 14 pages, 1 figur

Complexity analysis for algorithmically simple strings

Given a reference computer, Kolmogorov complexity is a well defined function on all binary strings. In the standard approach, however, only the asymptotic properties of such functions are considered because they do not depend on the reference computer. We argue that this approach can be more useful if it is refined to include an important practical case of simple binary strings. Kolmogorov complexity calculus may be developed for this case if we restrict the class of available reference computers. The interesting problem is to define a class of computers which is restricted in a {\it natural} way modeling the real-life situation where only a limited class of computers is physically available to us. We give an example of what such a natural restriction might look like mathematically, and show that under such restrictions some error terms, even logarithmic in complexity, can disappear from the standard complexity calculus. Keywords: Kolmogorov complexity; Algorithmic information theory.Comment: 10 page

Elasticity theory of structuring

Financial derivatives have often been criticized as casino-style betting instruments. It turns out that many naive ways of making them are indeed equivalent to gambling. Fortunately, this inadvertent effect can be understood and prevented. We present a theory of product design which achieves that.Comment: 16 pages, 3 figure

Esseen type bounds of the remainder in a combinatorial CLT

We derive Esseen type bounds of the remainder in a combinatorial central limit theorem for independent random variables without third moments

Hitchin systems on ll- curves

One investigates the Hitchin systems over "large limit" curves.Comment: This text was almost ready prepared by Professor Andrei N. Tyurin at the 27th of October. Now it is just slightly edited by Alexei Gorodentsev and Nikolai Tyurin and will be published as a preprint of MPI (Bonn