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.     

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.     

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.     

Size of random Galois lattices and number of closed frequent itemsets

Given a sample of binary random vectors with i.i.d. Bernoulli(p) components, that is equal to 1 (resp. 0) with probability p (resp. 1−p), we first establish a formula for the mean of the size of the random Galois lattice built from this sample, and a more complex one for its variance. Then, noticing that closed α-frequent itemsets are in bijection with closed α-winning coalitions, we establish similar formulas for the mean and the variance of the number of closed α-frequent itemsets. This can be interesting for the study of the complexity of some data mining problems such as association rule mining, sequential pattern mining and classification.     

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.