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Table Of Integrals Series And Products

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Preface * The Time Scales Calculus * First Order Linear Equations * Second Order Linear Equations * Self-Adjoint Equations * Linear Systems and Higher Order Equations * Dynamic Inequalities * Linear Symplectic Dynamic Systems * Extensions * Solutions to Selected Problems * Bibliography * Index

Dynamic Equations on Time Scales: An Introduction with Applications

This paper features a survey of some recent developments in asymptotic techniques, which are valid not only for weakly nonlinear equations, but also for strongly ones. Further, the obtained approximate analytical solutions are valid for the whole solution domain. The limitations of traditional perturbation methods are illustrated, various modied perturbation techniques are proposed, and some mathematical tools such as variational theory, homotopy technology, and iteration technique are introduced to overcome the shortcomings. In this paper the following categories of asymptotic methods are emphasized: (1) variational approaches, (2) parameter-expanding methods, (3) parameterized perturbation method, (4) homotopy perturbation method (5) iteration perturbation method, and ancient Chinese methods. The emphasis of this article is put mainly on the developments in this eld in China so the references, therefore, are not exhaustive.

Some asymptotic methods for strongly nonlinear equations

Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

Numerical instabilities non-standard finite difference schemes first order ordinary differential equations second order, nonlinear oscillator equations Schrodinger type ordinary differential equations two first order, coupled ordinary differential equations partial differential equations summary and discussion linear difference equations linear stability analysis.

Nonstandard Finite Difference Models of Differential Equations

Nonstandard finite difference schemes, R.E. Mickens nonstandard methods for advection-diffusion-reaction equations, H.V. Kojouharov and B.M. Chen application of nonstandard finite differences to solve the wave equation and Maxwell's equations, J.B. Cole nonstandard discretization methods for some biological models, H. Al-Kahby et al an introduction to numerical integrators preserving physical properties, M.J. Gander and R. Meyer-Spasche.

Applications of nonstandard finite difference schemes

Oscillatory systems harmonic balance Lindstedt-Poincare perturbation methods method of Krylov-Bogoliubov-Mitropolsky general second-order systems numerical techniques. Appendices: mathematical relations summary of results on second-order differential equations asymptotic expansions bibliography.

Oscillations in planar dynamic systems

Arguably one of the most important effects of climate change is the potential impact on human health. While this is likely to take many forms, the implications for future transmission of vector-borne diseases (VBDs), given their ongoing contribution to global disease burden, are both extremely important and highly uncertain. In part, this is owing not only to data limitations and methodological challenges when integrating climate-driven VBD models and climate change projections, but also, perhaps most crucially, to the multitude of epidemiological, ecological and socio-economic factors that drive VBD transmission, and this complexity has generated considerable debate over the past 10–15 years. In this review, we seek to elucidate current knowledge around this topic, identify key themes and uncertainties, evaluate ongoing challenges and open research questions and, crucially, offer some solutions for the field. Although many of these challenges are ubiquitous across multiple VBDs, more specific issues also arise in different vector–pathogen systems.

https://digitalcommons.odu.edu/cgi/viewcontent.cgi?article=1326&context=biology_fac_pubs

Climate, environmental and socio-economic change: weighing up the balance in vector-borne disease transmission

This paper gives an introduction to nonstandard finite difference methods useful for the construction of discrete models of differential equations when numerical solutions are required. While the general rules for such schemes are not precisely known at the present time, several important criterion have been found. We provide an explanation of their significance and apply them to several model ordinary and partial differential equations. The paper ends with a discussion of several outstanding problems in this area and other related issues.

Ronald E. Mickens

Papers

Nonstandard Finite Difference Models of Differential Equations

Applications of nonstandard finite difference schemes

Oscillations in planar dynamic systems

Climate, environmental and socio-economic change: weighing up the balance in vector-borne disease transmission

Nonstandard Finite Difference Schemes for Differential Equations