A parallel wilf algorithm for complex zeros of a polynomial

A global recursive bisection algorithm is described for computing the complex zeros of a polynomial. It has complexityO(n 3 p) wheren is the degree of the polynomial andp the bit precision requirement. Ifn processors are available, it can be realized in parallel with complexityO(n 2 p); also it can be implemented using exact arithmetic. A combined Wilf-Hansen algorithm is suggested for reduction in complexity.

Application of ultraspherical polynomials to forced oscillations of a third-order non-linear system

In this paper the method of ultraspherical polynomial approximation is applied to study the steady-state response in forced oscillations of a third-order non-linear system. The non-linear function is expanded in ultraspherical polynomials and the expansion is restricted to the linear term. The equation for the response curve is obtained by using the linearized equation and the results are presented graphically. The agreement between the approximate solution and the analog computer solution is satisfactory. The problem of stability is not dealt with in this paper.

Application of ultraspherical polynomials to non-linear autonomous systems

This paper deals with the approximate solutions of non-linear autonomous systems by the application of ultraspherical polynomials. From the differential equations for amplitude and phase, set up by the method of variation of parameters, the approximate solutions are obtained by a generalized averaging technique based on the ultraspherical polynomial expansions. The method is illustrated with examples and the results are compared with the digital and analog computer solutions. There is a close agreement between the analytical and exact results.

Salmonella Typhimurium: Insight into the multi-faceted role of the LysR-type transcriptional regulators in Salmonella

The LysR-type transcriptional regulators (LTTRs) are widely distributed in various genera of prokaryotes LTTRs are DNA binding proteins that can positively or negatively regulate target gene expression and can also repress their own transcription Salmonella enterica comprises a group of Gram-negative bacteria capable of causing clinical syndromes that range from self-limiting diarrhoea to severe fibrinopurulent necrotizing enteritis and life threatening systemic disease. The survival and replication of Salmonella in macrophages and in infected host is brought about by the means of various two component regulatory systems, transporters and other virulence islands In Salmonella genome the existence of 44 LTTRs has been documented These LTTRs regulate bacterial stress response. systemic virulence in mice and also many virulence determinants in vitro. Here we focus on the findings that elucidate the structure and function of the LTTRs in Salmonella and discuss the importance of these LTTRs in making Salmonella a Successful pathogen...

Titration calorimetric studies to elucidate the specificity of the interactions of polymyxin B with lipopolysaccharides and lipid A

Lipopolysaccharide (LPS), the major cell wall constituent of Gram-negative bacteria, evokes a multitude of biological effects in mammals including pyrogenicity and toxic shock syndrome. Polymyxin B (PmB), a polycationic cyclic peptide, is known to neutralize most of its activities. The nature of the interaction of PmB with LPS and lipid A was investigated by isothermal titration calorimetry. PmB binds to LPS as well as lipid A stoichiometrically and non-co-operatively with micromolar affinity. These interactions are driven primarily by a favourable change in entropy (delta S) and are endothermic in nature. These positive changes in enthalpies decrease with increasing temperature, yielding a heat capacity change, delta Cp, of -2385 J.mol-1.degree-1 for PmB-LPS interactions while the binding of PmB to lipid A displays a delta Cp of -2259 J.mol-1.degree-1. The negative heat capacity changes provide strong evidence for the role of hydrophobic interactions as the driving force for the association of PmB with LPS and lipid A. A correlation of the energetics of these interactions with analyses of the molecular models of PmB suggests that a cluster of solvent-exposed non-polar amino acid side-chains that line one surface of the molecule, together with a ring of positively charged residues on its other surface, are responsible for its strong and stoichiometric binding to LPS.

An approximate analysis of non-linear non-conservative systems subjected to step function excitation

This paper deals with the approximate analysis of the step response of non-linear nonconservative systems by the application of ultraspherical polynomials. From the differential equations for amplitude and phase, set up by the method of variation of parameters, the approximate solutions are obtained by a generalized averaging technique based on ultraspherical polynomial expansions. The Krylov-Bogoliubov results are given by a particular set of these polynomials. The method has been applied to study the step response of a cubic spring mass system in presence of viscous, material, quadratic, and mixed types of damping. The approximate results are compared with the digital and analogue computer solutions and a close agreement has been found between the analytical and the exact results.

Synthesis, structure and DNA cleavage studies of coumarin analogues of tetrahydroisoquinoline and protoberberine alkaloids

Novel molecular matrices have been derived from coumarin-4-acetic acids and beta-phenylethylamines using the Bischler-Napieralski protocol which has led to the synthesis of analogues of tetrahydropapaverine in which the dimethoxybenzene moiety has been replaced by substituted coumarins. One carbon homologation has led to cyclization at the C3 position of coumarin generating the protoberberine skeleton. Structures have been confirmed by diffraction studies. The results showed that compounds 6e, 6f, 7e and 7f were found to be very effective against DNA samples of Gram positive bacterium Staphylococcus aureus and fungus Aspergillus niger. (C) 2010 Elsevier Masson SAS. All rights reserved.

Probability Distribution of the Eigenvalues of the Random String Equation

The probability distribution of the eigenvalues of a second-order stochastic boundary value problem is considered. The solution is characterized in terms of the zeros of an associated initial value problem. It is further shown that the probability distribution is related to the solution of a first-order nonlinear stochastic differential equation. Solutions of this equation based on the theory of Markov processes and also on the closure approximation are presented. A string with stochastic mass distribution is considered as an example for numerical work. The theoretical probability distribution functions are compared with digital simulation results. The comparison is found to be reasonably good.

Invariant norm quantifying nonlinear content of Hamiltonian systems

Given a Hamiltonian system, one can represent it using a symplectic map. This symplectic map is specified by a set of homogeneous polynomials which are uniquely determined by the Hamiltonian. In this paper, we construct an invariant norm in the space of homogeneous polynomials of a given degree. This norm is a function of parameters characterizing the original Hamiltonian system. Such a norm has several potential applications. (C) 2010 Elsevier Inc. All rights reserved.

Improving the phenomenology of Kl3 form factors with analyticity and unitarity

The shape of the vector and scalar K-l3 form factors is investigated by exploiting analyticity and unitarity in a model-independent formalism. The method uses as input dispersion relations for certain correlators computed in perturbative QCD in the deep Euclidean region, soft-meson theorems, and experimental information on the phase and modulus of the form factors along the elastic part of the unitarity cut. We derive constraints on the coefficients of the parameterizations valid in the semileptonic range and on the truncation error. The method also predicts low-energy domains in the complex t plane where zeros of the form factors are excluded. The results are useful for K-l3 data analyses and provide theoretical underpinning for recent phenomenological dispersive representations for the form factors.

A field-consistent and variationally correct representation of transverse shear strains in the nine-noded plate element

We present a biquadratic Lagrangian plate bending element with consistent fields for the constrained transverse shear strain functions. A technique involving expansion of the strain interpolations in terms of Legendre polynomials is used to redistribute the kinematically derived shear strain fields so that the field-consistent forms (i.e. avoiding locking) are also variationally correct (i.e. do not violate the variational norms). Also, a rational method of isoparametric Jacobian transformation is incorporated so that the constrained covariant shear strain fields are always consistent in whatever general quadrilateral form the element may take. Finally the element is compared with another formulation which was recently published. The element is subjected to several robust bench mark tests and is found to pass all the tests efficiently.

Path integral description of polymers using fractional Brownian walks

The statistical properties of fractional Brownian walks are used to construct a path integral representation of the conformations of polymers with different degrees of bond correlation. We specifically derive an expression for the distribution function of the chains’ end‐to‐end distance, and evaluate it by several independent methods, including direct evaluation of the discrete limit of the path integral, decomposition into normal modes, and solution of a partial differential equation. The distribution function is found to be Gaussian in the spatial coordinates of the monomer positions, as in the random walk description of the chain, but the contour variables, which specify the location of the monomer along the chain backbone, now depend on an index h, the degree of correlation of the fractional Brownian walk. The special case of h=1/2 corresponds to the random walk. In constructing the normal mode picture of the chain, we conjecture the existence of a theorem regarding the zeros of the Bessel function.

A waveguide problem involving a thick iris in the theory of electromagnetism

The problem of electromagnetic wave propagation in a rectangular waveguide containing a thick iris is considered for its complete solution by reducing it to two suitable integral equations, one of which is of the first kind and the other is of the second kind. These integral equations are solved approximately, by using truncated Fourier series for the unknown functions. The reflection coefficient is computed numerically from the two integral equation approaches, and almost the same numerical results are obtained. This is also depicted graphically against the wave number and compared with thin iris results, which are computed by using complementary formulations coupled with Galerkin approximations. While the reflection coefficient for a thin iris steadily increases with the wave number, for a thick iris it fluctuates and zero reflection occurs. The number of zeros of the reflection coefficient for a thick iris increases with the thickness. Thus a thick iris becomes completely transparent for some discrete wave numbers. This phenomenon may be significant in the modelling of rectangular waveguides.

The canonic linear-phase FIR lattice structures

The Linear phase(LP) Finite Impulse Response(FIR) filters are widely used in many signal processing systems which are sensitive to phase distortion. In this article, we obtain a canonic lattice structure of an LP-FIR filter with a complex impulse response. This lattice structure is based on some novel lattice stages obtained from some properties of symmetric polynomials.This canonic lattice structure exploits the redundancy in the zeros of an LP-FIR filter.

On existence of periodic solutions for stable interval plants with odd, sector type nonlinearities

In several systems, the physical parameters of the system vary over time or operating points. A popular way of representing such plants with structured or parametric uncertainties is by means of interval polynomials. However, ensuring the stability of such systems is a robust control problem. Fortunately, Kharitonov's theorem enables the analysis of such interval plants and also provides tools for design of robust controllers in such cases. The present paper considers one such case, where the interval plant is connected with a timeinvariant, static, odd, sector type nonlinearity in its feedback path. This paper provides necessary conditions for the existence of self sustaining periodic oscillations in such interval plants, and indicates a possible design algorithm to avoid such periodic solutions or limit cycles. The describing function technique is used to approximate the nonlinearity and subsequently arrive at the results. Furthermore, the value set approach, along with Mikhailov conditions, are resorted to in providing graphical techniques for the derivation of the conditions and subsequent design algorithm of the controller.