Genetic Algorithms for Design of Discrete Phase-only Reconfigurable Array Antennas with Fixed Dynamic Range Ratio

In this paper, we present a new method based on real-coded Genetic Algorithm (GA) with elitist model for optimal design of a reconfigurable symmetrical dual-beam uniformly spaced linear isotropic antenna array with phase-only control of quantized phase shifters. The problem is to find a common amplitude distribution that will generate a pencil beam with zero phases and a flat-top beam with discrete phases of a six-bit discrete phase shifter, without or with pre-fixing the value of dynamic range ratio (|I _max/I _min|) of excitation current amplitude distribution equal to or less than five.     

Inelastic cross sections for pentane isomers by positron impact

ABSTRACT

This work aims at the calculation of various inelastic cross sections for three pentane isomers, namely normal pentane, isopentane and neopentane. The direct ionisation, positronium formation, total ionisation and total inelastic cross section are reported for these targets using modified spherical complex optical potential (mSCOP) and complex scattering potential-ionisation contribution (CSP-ic) method. The cross sections are computed for a wide energy range from their respective thresholds to 5?keV. We have also attempted to probe the isomeric effect in the inelastic scattering of positrons from the pentane isomers. The cross sections for the three isomers were found to overlap for the entire comparative energy range except at the peak region. Hence, in general no appreciable isomeric effect was beheld for the pentane isomers.     

A gauge-variational calculation of molecular diamagnetic susceptibility

In order to avoid the determination of the perturbed wave function in the susceptibility calculation of closed shell molecules, several authors have developed gauge-variation methods based on Rebane's work. The present work illustrates that introduction of a certain restriction in the gauge-variation method makes the susceptibility calculations exceptionally simple. The restriction involves the use of the Coulomb gauge so that the gauge-function satisfies Laplace's equation. The restriction was dictated by the demonstration of gauge-invariance of the Rayleigh–Schrouml;dinger perturbation theory of diamagnetism. The method with the prescribed restriction has been applied to the H₂O molecule, as an example, to demonstrate the advantages.     

Numerical simulation of storm surges in Bangladesh using a multi-level model

A comparative study with a vertically integrated model and the multi-level model has shown that the former can remain a good substitute for the latter in the prediction of sea-surface elevation as long as the bottom friction coefficients in the vertically integrated models are properly specified.     

Higher Mahler measure for cyclotomic polynomials and Lehmer’s question

The k-higher Mahler measure of a non-zero polynomial P is the integral of log  ^k |P| on the unit circle. In this note, we consider Lehmer’s question (which is a long-standing open problem for k=1) for k>1 and find some interesting formulas for 2- and 3-higher Mahler measure of cyclotomic polynomials.     

Compact operators which factor through subspaces of lp

Let 1 ≤ p ≤ ∞. A subset K of a Banach space X is said to be relatively p ‐compact if there is an 〈x_n 〉 ∈ l^s _p (X) such that for every k ∈ K there is an 〈α_n 〉 ∈ l_{p ′} such that k = σ^∞_n=1 α_n x_n . A linear operator T: X → Y is said to be p ‐compact if T (Ball (X)) is relatively p ‐compact in Y. The set of all p ‐compact operators K_p (X, Y) from X to Y is a Banach space with a suitable factorization norm κ_p and (K_p , κ_p ) is a Banach operator ideal. In this paper we investigate the dual operator ideal (K^d _p , κ^d _p ). It is shown that κ^d _p (T) = π_p (T) for all T ∈ B (X, Y) if either X or Y is finite‐dimensional. As a consequence it is proved that the adjoint ideal of K^d _p is I_{p ′}, the ideal of p ′‐integral operators. Further, a composition/decomposition theorem K^d _p = Π_p K is proved which also yields that (Π^min _p )^inj = K^d _p . Finally, we discuss the density of finite rank operators in K^d _p and give some examples for different values of p in this respect. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A new type of symmetrical banana-shaped material based on N-methyldiphenylamine as a core moiety exhibiting an Ad→A2 transition

The synthesis and characterization of a homologous series of Schiff bases consisting of an N-methyldiphenylamine moiety as the central core is reported, which exhibits smectic A phase and transitions from the partial bilayer SmA_d phase to the bilayer SmA₂ phase as the temperature is lowered.     

Optical image encryption using fractional Fourier transform and chaos

We propose a new method for image encryption using fractional Fourier transform and chaos theory. Random phase masks are generated using iterative chaos functions. The input image is combined with the first random phase mask at the object plane and is then transformed using the fractional Fourier transform. After the first fractional Fourier transform, the second random phase mask, again generated by using the chaos functions, is used at the fractional plane. The second fractional Fourier transform operation is then carried out to obtain the encrypted image. Three types of chaos functions have been used: the logistic map, the tent map and the Kaplan–Yorke map. The mean square error and the signal-to-noise ratio between the decrypted image and the input image for the correct order and the incorrect order of the fractional Fourier transform have been calculated. The computer simulations are presented to verify the validity of the proposed technique.