Factorization in generalized power series

The field of generalized power series with real coefficients and exponents in an ordered abelian divisible group is a classical tool in the study of real closed fields. We prove the existence of irreducible elements in the ring consisting of the generalized power series with non-positive exponents. The following candidate for such an irreducible series was given by Conway (1976): . Gonshor (1986) studied the question of the existence of irreducible elements and obtained necessary conditions for a series to be irreducible. We show that Conway's series is indeed irreducible. Our results are based on a new kind of valuation taking ordinal numbers as values. If we can give the following test for irreducibility based only on the order type of the support of the series: if the order type is either or of the form and the series is not divisible by any monomial, then it is irreducible. To handle the general case we use a suggestion of
M.-H. Mourgues, based on an idea of Gonshor, which allows us to reduce to the special case . In the final part of the paper we study the irreducibility of series with finite support.

     

Design of Stacked Self-Healing Rings Using a Genetic Algorithm

Ring structures in telecommunications are taking on increasing importance because of their self-healing properties. We consider a ring design problem in which several stacked self-healing rings (SHRs) follow the same route, and, thus, pass through the same set of nodes. Traffic can be exchanged among these stacked rings at a designated hub node. Each non-hub node may be connected to multiple rings. It is necessary to determine to which rings each node should be connected, and how traffic should be routed on the rings. The objective is to optimize the tradeoff between the costs for connecting nodes to rings and the costs for routing demand on multiple rings. We describe a genetic algorithm that finds heuristic solutions for this problem. The initial generation of solutions includes randomly-generated solutions, complemented by seed solutions obtained by applying a greedy randomized adaptive search procedure (GRASP) to two related problems. Subsequent generations are created by recombining pairs of parent solutions. Computational experiments compare the genetic algorithm with a commercial integer programming package.     

Nuclear electric dipole moments at ion storage rings

Upper limits on the electric dipole moments (EDM) of elementary particles and atoms are presented, and their physical implications are discussed. The implications following from the neutron and atomic experiments are of comparable interest. The nuclear EDMs can be studied at ion storage rings, with the expected sensitivity much better than . This would represent a serious progress in studies of the CP-violation problem. This revised version was published online in August 2006 with corrections to the Cover Date.     

牛顿环实验测量结果不确定度的评定

详细分析了牛顿环实验中测量结果不确定度评定,由于干涉图样中各级暗环弦长左右读数的测量为不等精度测量,因此本文提出一种既简单又易操作的不确定度评定方法。     

两共轴带电圆环的相互作用能和作用力

计算了两共轴均匀带电圆环的相互作用能,并求出它们之间的相互作用力,绘制出电场力的空间分布图,进而讨论了作用力和两圆环半径和中心距离等参量的关系.     

Piecewise linear integrated optical device as an optical isolator using two-port nonlinear ring resonators

A nonlinear (piecewise linear) optical transfer function for optical applications generally and isolator especially is introduced and a realization method for the introduced block based on array of two-port nonlinear ring resonators is proposed. The effect of system parameters on the transfer function is studied. The characteristics of the introduced nonlinear device such as the threshold value and the slope of linear part can be controlled using the coupling coefficients and ring lengths. We show that using our proposed idea, easily more than 30-dB isolation well over 3 THz can be obtained only with similar two rings. Also, insertion loss less than 1 dB can be obtained using optical amplifier between rings. The proposed circuit is compact (0.2 mm²) and easily can be integrated with semiconductor lasers as well as other integrated devices and systems. Finally, the analytical result for approximation of the threshold and slope of linear part is presented.     

Free Subgroups in the Units of ℤ[K 8 × C p ]

Abstract

Marciniak and Sehgal (Marciniak, Z., Sehgal, S. K. (1997). Constructing free subgroups of integral group rings units. Proc. Amer. Math. Soc.125(4):1005–1009) constructed free subgroups in U(?[G]) whenever Ghas a non normal finite subgroup. In this paper we construct free subgroups in U(?[G]), where Gis a group whose subgroups are all normal.     

Numerical investigation of the effects of sluice spillway roof profiles on the hydraulic characteristics

There is a need for evolving hydraulically efficient roof profile of bellmouth for high head sluice spillways, as sluice roof is susceptible to cavitation damage. In this paper, formulation and development of a numerical model for simulating the spillway flow and its application to a sluice spillway are presented. The main focus of the simulation study is to apply the developed model to investigate the effects of sluice roof profile geometry on the pressure distribution, the discharge coefficient and the nature of flow regime within the sluice bellmouth. From the analysis of results for eight different roof profiles by varying the entry and exit angles of elliptic bellmouth transition, some important observations have been suggested, which are of practical relevance to hydraulic design engineers. The numerical model results are compared for one profile with physical model study. The simulated results are in close agreement with the measured values. Copyright © 2007 John Wiley & Sons, Ltd.     

Gorenstein flatness and injectivity over Gorenstein rings

Let R be a Gorenstein ring.We prove that if I is an ideal of R such that R/I is a semi-simple ring,then the Gorenstein flat dimension of R/I as a right R-module and the Gorenstein injective dimension of R/I as a left R-module are identical.In addition,we prove that if R→S is a homomorphism of rings and SE is an injective cogenerator for the category of left S-modules,then the Gorenstein flat dimension of S as a right R-module and the Gorenstein injective dimension of E as a left R-module are identical.We also give some applications of these results.     

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.