Multiple Roots of Systems of Equations by Repulsion Merit Functions

In this paper we address the problem of computing multiple roots of a system of nonlinear equations through the global optimization of an appropriate merit function. The search procedure for a global minimizer of the merit function is carried out by a metaheuristic, known as harmony search, which does not require any derivative information. The multiple roots of the system are sequentially determined along several iterations of a single run, where the merit function is accordingly modified by penalty terms that aim to create repulsion areas around previously computed minimizers. A repulsion algorithm based on a multiplicative kind penalty function is proposed. Preliminary numerical experiments with a benchmark set of problems show the effectiveness of the proposed method.

On the dominance of roots of characteristic equations for neutral functional differential equations

We present a sufficient condition for a zero of a function that arises typically as the characteristic equation of a linear functional differential equations of neutral type, to be simple and dominant. This knowledge is useful in order to derive the asymptotic behaviour of solutions of such equations. A simple characteristic equation, arisen from the study of delay equations with small delay, is analyzed in greater detail. (C) 2009 Elsevier Inc. All rights reserved.

The root extractor, exhibiting new rules and processes, for the formation and the resolution of equations of all orders in algebra; and for the evolution of the roots of any power in numbers: serving likewise as a key to all the examples of the cubic and higher equations in Bonnycastle's introduction to algebra.

Mode of access: Internet.

Generalization of Ehrlich-Kjurkchiev Method for Multiple Roots of Algebraic Equations

In this paper a new method which is a generalization of the Ehrlich-Kjurkchiev method is developed. The method allows to find simultaneously all roots of the algebraic equation in the case when the roots are supposed to be multiple with known multiplicities. The offered generalization does not demand calculation of derivatives of order higher than first simultaneously keeping quaternary rate of convergence which makes this method suitable for application from practical point of view.

Polymer melt dynamics: Microscopic roots of fractional viscoelasticity

The rheological properties of polymer melts and other complex macromolecular fluids are often successfully modeled by phenomenological constitutive equations containing fractional differential operators. We suggest a molecular basis for such fractional equations in terms of the generalized Langevin equation (GLE) that underlies the renormalized Rouse model developed by Schweizer [J. Chem. Phys. 91, 5802 (1989)]. The GLE describes the dynamics of the segments of a tagged chain under the action of random forces originating in the fast fluctuations of the surrounding polymer matrix. By representing these random forces as fractional Gaussian noise, and transforming the GLE into an equivalent diffusion equation for the density of the tagged chain segments, we obtain an analytical expression for the dynamic shear relaxation modulus G(t), which we then show decays as a power law in time. This power-law relaxation is the root of fractional viscoelastic behavior.

A simultaneous equations model of crash frequency by collision type for rural intersections

Safety at roadway intersections is of significant interest to transportation professionals due to the large number of intersections in transportation networks, the complexity of traffic movements at these locations that leads to large numbers of conflicts, and the wide variety of geometric and operational features that define them. A variety of collision types including head-on, sideswipe, rear-end, and angle crashes occur at intersections. While intersection crash totals may not reveal a site deficiency, over exposure of a specific crash type may reveal otherwise undetected deficiencies. Thus, there is a need to be able to model the expected frequency of crashes by collision type at intersections to enable the detection of problems and the implementation of effective design strategies and countermeasures. Statistically, it is important to consider modeling collision type frequencies simultaneously to account for the possibility of common unobserved factors affecting crash frequencies across crash types. In this paper, a simultaneous equations model of crash frequencies by collision type is developed and presented using crash data for rural intersections in Georgia. The model estimation results support the notion of the presence of significant common unobserved factors across crash types, although the impact of these factors on parameter estimates is found to be rather modest.

The Roots of Danger: Violent Crime in Global Perspective

Prentice Hall’s Masters Series in Criminology brings the work of true masters to life for a new audience of readers, presenting brief and accessible introductions to crime and criminology topics from some of the leading scholars in criminology today. All authors in the series are true academic pioneers, and each book in the series pulls from the authors’ decades of research and writing in their fields. The first and only series of its kind, Prentice Hall’s Masters Series in Criminology introduces readers to the scholars and issues that are at the core of modern criminology.

Returning to the roots of culture : a review and re-conceptualisation of safety culture

Despite significant research, there is still little agreement over how to define safety culture or of what it is comprised. Due to this lack of agreement, much of the safety culture research has little more than safety management strategies in common. There is, however, a degree of acceptance of the close relationship between safety culture and organisational culture. Organisational culture can be described using traditional views of culture drawn from the anthropology and cultural psychology literature. However, the safety culture literature rarely ventures beyond organisational culture into discussions of these more traditional concepts of culture. There is a need to discuss how these concepts of culture can be applied to safety culture to provide greater understanding of safety culture and additional means by which to approach safety in the workplace. This review explores how three traditional conceptualisations of culture; the normative, anthropological and pragmatist conceptualisations, can and have been be applied to safety culture. Finally the review proposes a synthesised conceptualisation of safety culture which can be used to provide greater depth and practical applicability of safety culture, by increasing our understanding of the interactions between cultural and contextual variables in a given workplace and the effect they have on safety.

De novo synthesis of acetylcholinesterase in roots of Pisum sativum

Pisum sativum seeds contain a conserved acetylcholinesterase (AChE) which is active during the early stages of germination. The enzyme activity soon disappears and reappears after 72 hr of germination. A protein devoid of catalytic ability, but exhibiting similar chromatographic and electrophoretic properties as the active AChE, could be detected after 24 hr of germination. The pattern of incorporation of labelled amino acids into AChE and the influence of cycloheximide revealed that the AChE found in the roots from 72 hr onwards was entirely new. During this period of growth, the AChE protein accounts for 4–10% of the total proteins in the root tissue.

Roots of prosperity: the Pacific Coast Watershed Partnership

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