Generic extensions and generic polynomials for semidirect products

This paper presents a generalization of a theorem of Saltman on the existence of generic extensions with group AG over an infinite field K, where A is abelian, using less restrictive requirements on A and G. The method is constructive, thereby allowing the explicit construction of generic polynomials for those groups, and it gives new bounds on the generic dimension.Generic polynomials for several small groups are constructed.     

Conserved quantities and Hamiltonization of nonholonomic systems

This paper studies hamiltonization of nonholonomic systems using geometric tools, building on [1], [5]. The main novelty in this paper is the use of symmetries and suitable first integrals of the system to explicitly define a new bracket on the reduced space that codifies the nonholonomic dynamics and carries, additionally, an almost symplectic foliation (determined by the common level sets of the first integrals); in particular cases of interest, this new bracket is a Poisson structure that hamiltonizes the system. Our construction of the new bracket is based on a gauge transformation of the nonholonomic bracket by a global 2-form that we explicitly describe. We study various geometric features of the reduced brackets and apply our formulas to obtain a geometric proof of the hamiltonization of a homogeneous ball rolling without sliding in the interior side of a convex surface of revolution.     

Discrete Dirac systems on the semiaxis: rational reflection coefficients and Weyl functions

We consider the cases of the self-adjoint and skew-self-adjoint discrete Dirac systems, obtain explicit expressions for reflection coefficients and show that rational reflection coefficients and Weyl functions coincide.     

Solutions of the spatially-dependent mass Dirac equation with the spin and pseudospin symmetry for the Coulomb-like potential

We study the effect of spatially-dependent mass function over the solution of the Dirac equation with the Coulomb potential in the (3+1)-dimensions for any arbitrary spin-orbit κ state. In the framework of the spin and pseudospin symmetry concept, the analytic bound state energy eigenvalues and the corresponding upper and lower two-component spinors of the two Dirac particles are obtained by means of the Nikiforov-Uvarov method, in closed form. This physical choice of the mass function leads to an exact analytical solution for the pseudospin part of the Dirac equation. The special cases , the constant mass and the non-relativistic limits are briefly investigated.     

A reduction of the spectrum problem for odd sun systems and the prime case

A k‐cycle with a pendant edge attached to each vertex is called a k‐sun. The existence problem for k‐sun decompositions of K_v, with k odd, has been solved only when k = 3 or 5. By adapting a method used by Hoffmann, Lindner, and Rodger to reduce the spectrum problem for odd cycle systems of the complete graph, we show that if there is a $k$‐sun system of $K_v$ ( $k$ odd) whenever $v$ lies in the range $2k<v<6k$ and satisfies the obvious necessary conditions, then such a system exists for every admissible $v\ge 6k$. Furthermore, we give a complete solution whenever k is an odd prime.