Efficiency of the Incomplete Enumeration Algorithm for Monte-Carlo Simulation of Linear and Branched Polymers

We study the efficiency of the incomplete enumeration algorithm for linear and branched polymers. There is a qualitative difference in the efficiency in these two cases. The average time to generate an independent sample of configuration of polymer with n monomers varies as n ² for linear polymers for large n, but as exp(cn ^α) for branched (undirected and directed) polymers, where 0<α<1. On the binary tree, our numerical studies for n of order 10⁴ gives α = 0.333±0.005. We argue that α =1/3 exactly in this case. An erratum to this article can be found at .     

Synthesis and structural characterisation of new Re(III) complexes using aldimines of α-amino acids as coligands

Complexes of the general formula [Re^III(L)Cl(PPh₃)₂] have been synthesised by reacting H₂L and [ReOCl₃(PPh₃)₂] in ethanol. Here H₂L represents imines of α-amino acids (glycine, l-alanine, l-valine, l-phenylalanine) derived from salicylaldehyde and naphthaldehyde. The crystal structure of one complex has been determined. The complexes are mononuclear, paramagnetic and display paramagnetic ¹H NMR in CDCl₃ solution. Their spectral and redox properties are scrutinised.     

Uhf to Ka band upconverter

A balanced upconverter circuit has been developed in planar transmission line configuration using NEC GaAs beam lead Schottky barrier diodes. RF power output of +1.6 dBm SSB is obtained at Ka-band when up converter is driven by +17 dBm IF and +20 dBm LO signal.     

On the topological characterization of two-dimensional phase transitions

It is shown that for the two-dimensional planar-rotator model the variance of the number of vortices inside a large loop is proportional to the perimeter of the loop at all temperatures. A similar result holds for the variance of the charge inside a loop in the lattice Coulomb gas model. Hence a topological distinction between the high and low temperature phases of these models (area law versus perimeter law) is not possible.     

Symmetry adapted functions belonging to the dirac groups

An earlier analysis of the canonical form of a pair of invertible operators obeying the exchange rule is extended to cover a set of operators, between each pair of which a relation of this type exists; and for which a power of each operator is the unit matrix. Such relations define a system which may be regarded as a generalization of the Dirac matrices of relativistic quantum mechanics. We concentrate upon the group theoretic aspects of such a system and its matrix representations. Applications arise from the fact that all projective representations of finite abelian groups take the form of a Dirac Group. In particular, the representations of the magnetic space groups, which are projective representations of the lattice groups, arise in this manner.     

Scaling relation for determining the critical threshold for continuum percolation of overlapping discs of two sizes

We study continuum percolation of overlapping circular discs of two sizes. We propose a phenomenological scaling equation for the increase in the effective size of the larger discs due to the presence of the smaller discs. The critical percolation threshold as a function of the ratio of sizes of discs, for different values of the relative areal densities of two discs, can be described in terms of a scaling function of only one variable. The recent accurate Monte Carlo estimates of critical threshold by Quintanilla and Ziff [Phys. Rev. E76, 051115 (2007)] are in very good agreement with the proposed scaling relation.     

Multiobjective analog/RF circuit sizing using an improved brain storm optimization algorithm

This paper presents a multiobjective analog/RF circuit sizing tool using an improved brain storm optimization (IMBSO) algorithm with the purpose of analyzing the tradeoffs between competing performance specifications of analog/RF circuit block. A number of improvements are incorporated into IMBSO algorithm at different steps. At first, the clustering step of IMBSO algorithm is augmented with k-means\(++\) seeding technique to select the initial cluster centroids while clustering using k-means clustering technique. As a second improvement, the proposed IMBSO algorithm makes use of random probabilistic decision-making of river formation dynamics scheme to select optimal cluster centroids during population generation step. As a third improvement, an adaptive mutation operator is incorporated inside the IMBSO algorithm to generate new population. Finally, two separate constraint handling techniques are employed to handle both boundary and functional constraints during analog/RF circuit optimization. The performance of the proposed IMBSO algorithm is demonstrated in finding optimal Pareto fronts among different performance specifications of a two-stage operational amplifier circuit, a folded cascode amplifier circuit and a low noise amplifier circuit.     

The Conjugacy Class Number k(G): A Different Perspective

For a finite group G, let m(G) denote the least positive integer such that the union of any m(G) distinct nontrivial conjugacy classes of G together with the identity of G is a subgroup of G. We prove that m(G) = k(G) ?1 for all m(G) ≥2.     

On an M (X)/G/1 Retrial System with Two Types of Search of Customers from the Orbit

Single server retrial queueing models in which customers arrive according to a batch Poisson process are considered here. An arriving batch, finding the server busy, enters an orbit. Otherwise, one customer from the arriving batch enters for service immediately while the rest join the orbit. The customers from the orbit (the orbital customers) try to reach the server subsequently with the inter-retrial times exponentially distributed. Additionally, at each service completion epoch, two different search mechanisms, that is, type I and type II search, to bring the orbital customers by the system to service, are switched on. Thus, when the server is idle, a competition takes place among primary customers, customers who come by retrial and by two types of searches. The type I search selects a single customer whereas the type II search considers a batch of customers from the orbit. Depending on the maximum size of the batch being considered for service by a type II search, two cases are addressed here. In the first case, no restriction on batch size is assumed, whereas in the second case, maximum size of the batch is restricted to a pre-assigned value. We call the resulting models as model 1 and model 2 respectively. In all service modes other than type II search, only a single customer is qualified for service. Service times of the four types of customers, namely, primary, repeated, and those who come by two types of searches are arbitrarily distributed (with different distributions which are independent of each other). Steady state analysis is performed and stability conditions are established. A control problem for model 2 is considered and numerical illustrations are provided.