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Journal ArticleDOI

Complexity perspectives: an anomalous diffusion approach

TL;DR: In this paper, the authors discuss how simple ideas of diffusion can be used to deal with the description of most complex structure, and how to apply them to the problem of complexity analysis.
Abstract: The science of complexity is far from being fully understood and even its foundations are not well established. On the other hand, during the last decade, the random motion of particles or waves – the so-called diffusion – has been known better. In this paper, we discuss how simple ideas of diffusion can be used to deal with the description of most complex structure.

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Journal ArticleDOI
TL;DR: The present work considers two published generalisations of the Laplace-transform final value theorem and some recently appeared applications of one of these generalisations to the fields of physical stochastic processes and Internet queueing.
Abstract: The present work considers two published generalisations of the Laplace-transform final value theorem (FVT) and some recently appeared applications of one of these generalisations to the fields of physical stochastic processes and Internet queueing. Physical sense of the irrational time functions, involved in the other generalisation, is one of the points of concern. The work strongly extends the conceptual frame of the references and outlines some new research directions for applications of the generalised theorem.

14 citations

Journal ArticleDOI
TL;DR: The generalized final-value theorems of the Laplace and z-transforms are extended to more general time functions and sequences relevant to functions not having a limit at infinity, but having a well-defined average.
Abstract: The determination of the time averages of continuous functions or discrete time sequences is important for various problems in physics and engineering, and the generalized final-value theorems of the Laplace and z-transforms, relevant to functions and sequences not having a limit at infinity, but having a well-defined average, can be very helpful in this determination. In the present contribution, we complete the proofs of these theorems and extend them to more general time functions and sequences. Besides formal proofs, some simple examples and heuristic and pedagogical comments on the physical nature of the limiting processes defining the averaging are given. Copyright © 2012 John Wiley & Sons, Ltd.

3 citations

References
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BookDOI
01 Jan 1985

1,748 citations

Book ChapterDOI
01 Jan 1974
TL;DR: In earlier centuries, science advanced steadily but slowly through the work of the most select minds, just as an old town constantly grows through new buildings put up by industrious and enterprising citizens as mentioned in this paper.
Abstract: In earlier centuries, science advanced steadily but slowly through the work of the most select minds, just as an old town constantly grows through new buildings put up by industrious and enterprising citizens. In contrast, our present century of steam and telegraphy has set its seal of nervous and precipitate activity on scientific progress too. Especially the development of natural science in recent times resembles rather that of a modern American town which in a few decades grows from a village into a city of millions.

36 citations