There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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Convex Analysisの二,三の進展について

Finite-time stability is defined for equilibria of continuous but non-Lipschitzian autonomous systems. Continuity, Lipschitz continuity, and Holder continuity of the settling-time function are studied and illustrated with several examples. Lyapunov and converse Lyapunov results involving scalar differential inequalities are given for finite-time stability. It is shown that the regularity properties of the Lyapunov function and those of the settling-time function are related. Consequently, converse Lyapunov results can only assure the existence of continuous Lyapunov functions. Finally, the sensitivity of finite-time-stable systems to perturbations is investigated.

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Finite-Time Stability of Continuous Autonomous Systems

Fractional Differential Equations

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. 1. Preliminaries. 2. Oscillation and Nonoscillation of Linear Ordinary Differential Equations. 3. Oscillation and Nonoscillation of Half-Linear Differential Equations. 4. Oscillation Theory for Superlinear Differential Equations. 5. Oscillation Theory for Sublinear Differential Equations. 6. Further Results on the Oscillation of Differential Equations. 7. Oscillation Results for Differential Systems. 8. Asymptotic Behavior of Solutions of Certain Differential Equations. 9. Miscellaneous Topics. 10. Nonoscillation Theory for Multivalued Differential Equations. Subject Index.

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Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations

Boundary value problems for higher order differential equations

“Contemporary Mathematics and Its Applications” is a book series of monographs, textbooks, and edited volumes in all areas of pure and applied mathematics. Authors and/or editors should send their proposals to the Series Editors directly. For general information about the series, please contact cmia.ed@hindawi.com. For more information and online orders please visit http://www.hindawi.com/books/cmia/volume-1 For any inquires on how to order this title please contact books.orders@hindawi.com CMIA Book Series, Volume 1, ISBN: 977-5945-19-4

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Discrete Oscillation Theory

In this paper, the initial value problem is discussed for a class of fractional neutral functional differential equations and the criteria on existence are obtained.

Ravi P. Agarwal

Papers

Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations

Boundary value problems for higher order differential equations

Discrete Oscillation Theory

Existence of fractional neutral functional differential equations

A study of fractional Lotka-Volterra population model using Haar wavelet and Adams-Bashforth-Moulton methods