Strominger--Yau--Zaslow geometry, Affine Spheres and Painlev\'e III

We give a gauge invariant characterisation of the elliptic affine sphere equation and the closely related Tzitz\'eica equation as reductions of real forms of SL(3, \C) anti--self--dual Yang--Mills equations by two translations, or equivalently as a special case of the Hitchin equation. We use the Loftin--Yau--Zaslow construction to give an explicit expression for a six--real dimensional semi--flat Calabi--Yau metric in terms of a solution to the affine-sphere equation and show how a subclass of such metrics arises from 3rd Painlev\'e transcendents.Comment: 38 pages. Final version. To appear in Communications in Mathematical Physic

Painleve I, Coverings of the Sphere and Belyi Functions

The theory of poles of solutions of Painleve-I is equivalent to the Nevanlinna problem of constructing a meromorphic function ramified over five points - counting multiplicities - and without critical points. We construct such meromorphic functions as limit of rational ones. In the case of the tritronquee solution these rational functions are Belyi functions.Comment: 33 pages, many figures. Version 2: minor corrections and minor changes in the bibliograph

Transients in the load node at power loss: group run-out of induction motors

The simulation of transient processes in the complex load node with powerful induction motors at the moment of power loss is carried out. For the modeling the method of synthetic schemes (Dommel’s algorithm) was used. Calculations are carried out within the dynamic model of motors in phase coordinates. The results of simulation and analysis modes of the load node with two induction motors connected to the electric buses of 10 kV and fed through a step-down transformer with 16 MVA capacity are presented. The applied model of power transformer consists of inductively coupled branches. The features of single and joint run-out of motors with different torque of mechanical loads are analyzed. Estimates of the parameters and time intervals at which the run-out of the motors is close to synchronous are obtained, the features of energy recuperation and the interaction of the motors in the load node are analyzed

Connection formulas for asymptotics of the fifth painleve transcendent on the real axis. Pt. 1

SIGLEAvailable from TIB Hannover: RR 1596(160) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Connection formulas for the asymptotics of the fifth Painleve transcendent on the real axis. Pt. 2

In this work, we complete the asymptotic description of general solutions of the fifth Painleve transcendent. In particular, our results contain asymptotics of the solutions with an infinite number of poles in the neighborhood of infinity. Our results are immediately applicable to constructing the connection formulas for small- and large-time asymptotics. (orig.)Available from TIB Hannover: RR 1596(196) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Exponentially small corrections to divergent asymptotic expansions of solutions of the fith Painleve equation

We calculate the leading term of asymptotics for the coefficients of certain divergent asymptotic expansions of solutions to the fifth Painleve equation (P_5) by using the isomonodromy deformation method and the Borel transform. Unexpectedly, these asymptotics appear to be periodic functions of the coefficients of P_5. We also show the relation of our results with some other facts already known in the theory of the Painleve equations established by other methods: (1) a connection formula for the third Painleve equation; (2) a conditions for the existence of rational solutions of P_5; and (3) a numerical study of the #tau#-function for P_5. (orig.)Available from TIB Hannover: RR 1596(271) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

On asymptotic cones of surfaces with constant curvature and the third Painleve equation

It is shown that for any surface in R"3 with constant negative Gaussian curvature and two straight asymptotic lines there exists a cone such that the distances from all its points to the surface are bounded. Analytic and geometric descriptions of the cone are obtained. This cone is asymptotic also for constant mean curvature planes in R"3 with inner rotational symmetry. (orig.)Available from TIB Hannover: RR 1596(315) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman