Elliptic Schlesinger system and Painlev{\'e} VI

We construct an elliptic generalization of the Schlesinger system (ESS) with positions of marked points on an elliptic curve and its modular parameter as independent variables (the parameters in the moduli space of the complex structure). ESS is a non-autonomous Hamiltonian system with pair-wise commuting Hamiltonians. The system is bihamiltonian with respect to the linear and the quadratic Poisson brackets. The latter are the multi-color generalization of the Sklyanin-Feigin-Odeskii classical algebras. We give the Lax form of the ESS. The Lax matrix defines a connection of a flat bundle of degree one over the elliptic curve with first order poles at the marked points. The ESS is the monodromy independence condition on the complex structure for the linear systems related to the flat bundle. The case of four points for a special initial data is reduced to the Painlev{\'e} VI equation in the form of the Zhukovsky-Volterra gyrostat, proposed in our previous paper.Comment: 16 pages; Dedicated to the centenary of the publication of the Painleve VI equation in the Comptes Rendus de l'Academie des Sciences de Paris by Richard Fuchs in 190

Fuchs versus Painlev\'e

We briefly recall the Fuchs-Painlev\'e elliptic representation of Painlev\'e VI. We then show that the polynomiality of the expressions of the correlation functions (and form factors) in terms of the complete elliptic integral of the first and second kind, $K$ and $E$, is a straight consequence of the fact that the differential operators corresponding to the entries of Toeplitz-like determinants, are equivalent to the second order operator $L_E$ which has $E$ as solution (or, for off-diagonal correlations to the direct sum of $L_E$ and $d/dt$). We show that this can be generalized, mutatis mutandis, to the anisotropic Ising model. The singled-out second order linear differential operator $L_E$ being replaced by an isomonodromic system of two third-order linear partial differential operators associated with $\Pi_1$, the Jacobi's form of the complete elliptic integral of the third kind (or equivalently two second order linear partial differential operators associated with Appell functions, where one of these operators can be seen as a deformation of $L_E$). We finally explore the generalizations, to the anisotropic Ising models, of the links we made, in two previous papers, between Painlev\'e non-linear ODE's, Fuchsian linear ODE's and elliptic curves. In particular the elliptic representation of Painlev\'e VI has to be generalized to an ``Appellian'' representation of Garnier systems.Comment: Dedicated to the : Special issue on Symmetries and Integrability of Difference Equations, SIDE VII meeting held in Melbourne during July 200

The RNA acetyltransferase driven by ATP hydrolysis synthesizes N4-acetylcytidine of tRNA anticodon

The wobble base of Escherichia coli elongator tRNAMet is modified to N4-acetylcytidine (ac4C), which is thought to ensure the precise recognition of the AUG codon by preventing misreading of near-cognate AUA codon. By employing genome-wide screen of uncharacterized genes in Escherichia coli (‘ribonucleome analysis'), we found the ypfI gene, which we named tmcA (tRNAMet cytidine acetyltransferase), to be responsible for ac4C formation. TmcA is an enzyme that contains a Walker-type ATPase domain in its N-terminal region and an N-acetyltransferase domain in its C-terminal region. Recombinant TmcA specifically acetylated the wobble base of E. coli elongator tRNAMet by utilizing acetyl-coenzyme A (CoA) and ATP (or GTP). ATP/GTP hydrolysis by TmcA is stimulated in the presence of acetyl-CoA and tRNAMet. A mutation study revealed that E. coli TmcA strictly discriminates elongator tRNAMet from the structurally similar tRNAIle by mainly recognizing the C27–G43 pair in the anticodon stem. Our findings reveal an elaborate mechanism embedded in tRNAMet and tRNAIle for the accurate decoding of AUA/AUG codons on the basis of the recognition of wobble bases by the respective RNA-modifying enzymes

A STRING MAGNETOMETER USING THE METHOD OF SMALL PERTURBATIONS

Subject and Purpose. The existing interest in nanosized magnetic materials requires equipment for express post-synthesis measurements of magnetic properties of these nanostructures in such a way as to exclude any mechanical displacement of the sample. Although there exist plenty of methods and devices for studying magnetic properties of materials, the development of novel schemes based on the known techniques for examining properties of magnetic nanomaterials, for example magnetic nanopowders, is a hot problem. The measurement equipment of the sort will detect changes in the magnetic properties of materials over time and under the influence of various factors, such as temperature, external magnetic fields, stabilizing substances. Method and Methodology. The developed setup for registering magnetic hysteresis loops is based on the method of small perturbations performed by an alternating magnetic field. The devised scheme combines conventional physical principles of both hysterometers and vibrating-sample magnetometers. Results. With the aid of the developed setup, magnetic hysteresis loops of La 0.775 Sr 0.225 MnO3 nanopowder have been obtained and compared with the data provided by the well-known technique. A good agreement was observed. The measurement error was 10%. Conclusion. The suggested scheme can be used for the express registration of magnetic hysteresis loops of miscellaneous magnetic materials of various compositions, including nanoscale magnets

STUDY OF MECHANISMS RESPONSIBLE FOR THE EFFICIENCY DEGRADATION OF THE III-NITRIDES LIGHT EMITTING DIODES

The results for external quantum efficiency degradation of two types of light emitting diodes based on III-nitrides: blue and ultraviolet ones are presented. Existing mechanisms proposed for the degradation are considered briefly. Applying several techniques for studying the light emitting diodes at various stages of the aging test gives the possibility to reveal a new mechanism of defects formations with a help of multi-phonon recombination of carriers in an extended defects system and in local regions of random alloy fluctuations. These techniques include analysis of current voltage characteristics evolution at V<2V, the low frequency noise methods, and infrared microscopy. The multi-phonon recombination of carriers is accomplished by generation of native defects, in particular, In- or Ga-atoms and their migration. These processes lead to modification of the extended defects system properties and local composition of InGaN alloys in several regions that result in decreasing of the carriers participating in a radiative recombination and degradation of the external quantum efficiency. It was demonstrated that this mechanism of the defects formation can be responsible for the degradation of the blue and ultraviolet light emitting diodes. The mechanism can explain non monotonic dependence of the degradation process during the aging test, catastrophic failures of the light emitting diodes and low lifetime of the ultraviolet light emitting diodes