We wish to describe how the hyperbolic geometry of a Riemann surface of genus g y g > 2, leads to a symplectic geometry on Tg, the genus g Teichmüller space, and ~Mg, the moduli space of genus g stable curves. The symplectic structure has three elements: the Weil-Petersson Kahler form, the FenchelNielsen vector fields t+, and the geodesic length functions I*. Weil introduced a Kahler metric for...

The problem of finding Lie point symmetries for a certain class multi-dimensional nonlinear partial fractional differential equations and their systems is studied. It assumed that considered involve derivatives with respect to only one independent variable, each equation contains single derivative. most significant examples such are time-fractional models processes memory power-law type. Two di...

There are many routines developed for solving ordinary differential Equations (ODEs) of different types. In the case an nth-order ODE that admits r-parameter Lie group (3≤r≤n), there is a powerful method symmetry analysis by which reduced to (n−r)th-order plus r quadratures provided algebra formed infinitesimal generators solvable. It would seem this not widely appreciated and/or used as it men...

Infinitesimal bialgebras were introduced by Joni and Rota [J-R]. An infinitesimal bialgebra is at the same time an algebra and a coalgebra, in such a way that the comultiplication is a derivation. In this paper we define infinitesimal Hopf algebras, develop their basic theory and present several examples. It turns out that many properties of ordinary Hopf algebras possess an infinitesimal versi...

We introduce the categories of infinitesimal Hopf modules and bimodules over an infinitesimal bialgebra. We show that they correspond to modules and bimodules over the infinitesimal version of the double. We show that there is a natural, but non-obvious way to construct a pre-Lie algebra from an arbitrary infinitesimal bialgebra and a dendriform algebra from a quasitriangular infinitesimal bial...

background: 99mtc is a widely used radioisotope in nuclear medicine centers which is obtained by elution from mo-99/tc-99m generators. usually the generators are either supplied by the iran atomic energy agency or by private companies from foreign countries. in this study we have measured 99mo contamination in 99mtc elute from different generators in a period of one year. materials and methods:...

We prove that the extended Toda hierarchy of [1] admits nonabelian Lie algebra of infinitesimal symmetries isomorphic to the half of the Virasoro algebra. The generators Lm, m ≥ −1 of the Lie algebra act by linear differential operators onto the tau function of the hierarchy. We also prove that the tau function of a generic solution to the extended Toda hierarchy is annihilated by a combination...