On the shepherding of Uranian epsilon ring

To explain the long-term existence of Uranian narrow rings, we study the dynamical evolution of Uranian epsilon ring under the influence of its two shepherding satellites: Cordelia and Ophelia. The model of planar-elliptic restricted three-body problem is employed, in which the three bodies are Uranus, a satellite and a test particle. Dissipations due to interparticle collisions are also taken into consideration. A mapping system has been obtained based on the differential equation system. Numerical results show that only those particles originally lying in the libration region of the resonance can be shepherded. The size of the libration region depends mainly on the orbital eccentricity and mass of the shepherd satellite. For the outer shepherd Ophelia with larger orbital eccentricity, if its mass is a third of the nominal mass 2.5 × 10¹⁹ g, most of the orbits are regular and the outer edge of the ring can be shepherded, but more fuzzy than the inner edge. Thus we infer that Ophelia has a smaller mass.     

Lehmer's problem for compact Abelian groups

We formulate Lehmer's Problem concerning the Mahler measure of polynomials for general compact abelian groups, introducing a Lehmer constant for each such group. We show that all nontrivial connected compact groups have the same Lehmer constant and conjecture the value of the Lehmer constant for finite cyclic groups. We also show that if a group has infinitely many connected components, then its Lehmer constant vanishes.

     

On automorphisms of finite Abelian <Emphasis Type="Italic">p</Emphasis>-groups

Let A be a finitely generated abelian group. We describe the automorphism group Aut(A) using the rank of A and its torsion part p-part A _p . For a finite abelian p-group A of type (k ₁, ..., k _n ), simple necessary and sufficient conditions for an n × n-matrix over integers to be associated with an automorphism of A are presented. Then, the automorphism group Aut(A) for a finite p-group A of type (k ₁, k ₂) is analyzed. This work has begin during the visit of the second author to the Faculty of Mathematics and Computer Science, Nicolaus Copernicus University during the period July 31–August 13, 2005. This visit was supported by the Nicolaus Copernicus University and a grant from Cnpq.     

所有子群皆循环或正规的有限2-群

研究了所有子群皆循环或正规的有限2群,并给出了其完全分类.     

Universal abelian covers of superisolated singularities

We give explicit examples of Gorenstein surface singularities with integral homology sphere link, which are not complete intersections. Their existence was shown by Luengo–Velasco, Melle–Hernández and Némethi, thereby providing counterexamples to the universal abelian covering conjecture of Neumann and Wahl (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Elementary constructive theory of Henselian local rings

We give an elementary theory of Henselian local rings and construct the Henselisation of a local ring. All our theorems have an algorithmic content. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Schottky Mass Measurements of Cooled Exotic Nuclei

Projectile fragments of a ²⁰⁹Bi beam were separated in flight with the fragment separator FRS and injected into the experimental storage ring ESR. In the ESR a beam containing up to about 100 different isotopes was cooled to a relative velocity spread of δv/v=10⁻⁶ by means of the electron cooler. The image currents of the ions induced in a Schottky pick-up probe at each turn were recorded. A subsequent Fast Fourier Transformation of these signals yields the revolution frequencies of the different isotopes stored in the ESR. Unknown masses of more than 150 neutron-deficient nuclides in the element range of 52≤Z≤85 have been measured directly by Schottky Mass Spectrometry and in addition more than 60 new masses have been obtained from α-decay chains. These new mass data allow the location of the one-proton dripline and the prediction of the two-proton dripline for heavy nuclides. The experimental masses are compared with different theoretical predictions. This revised version was published online in July 2006 with corrections to the Cover Date.     

交换环上上三角矩阵代数在全矩阵代数中的扩代数及其若当导子

设R是任意含么交换环,2是R的可逆元.M(n,R)表示R上所有n×n级矩阵形成的代数,T(n,R)表示R上所有n×n级上三角矩阵形成的代数.决定了T(n,R)在M(n,R)中的扩代数,并具体刻画了这些扩代数的若当导子.     

On a theorem of Tate

We study applications of divisibility properties of recurrence sequences to Tate’s theory of abelian varieties over finite fields.      

所有子群皆交换或正规的有限群

本文研究所有子群皆交换或正规的有限群. 我们获得了非幂零的情形的一个特征刻画, 也给出了幂零情形的一些性质.