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Series (mathematics)

About: Series (mathematics) is a(n) research topic. Over the lifetime, 31012 publication(s) have been published within this topic receiving 625614 citation(s). The topic is also known as: mathematical series. more

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Abstract: We present the first algorithms that allow the estimation of non-negative Lyapunov exponents from an experimental time series. Lyapunov exponents, which provide a qualitative and quantitative characterization of dynamical behavior, are related to the exponentially fast divergence or convergence of nearby orbits in phase space. A system with one or more positive Lyapunov exponents is defined to be chaotic. Our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems: we monitor the long-term growth rate of small volume elements in an attractor. The method is tested on model systems with known Lyapunov spectra, and applied to data for the Belousov-Zhabotinskii reaction and Couette-Taylor flow. more

7,366 citations

13 Dec 2005-
TL;DR: This volume explores the differential evolution (DE) algorithm in both principle and practice and is a valuable resource for professionals needing a proven optimizer and for students wanting an evolutionary perspective on global numerical optimization. more

Abstract: Problems demanding globally optimal solutions are ubiquitous, yet many are intractable when they involve constrained functions having many local optima and interacting, mixed-type variables.The differential evolution (DE) algorithm is a practical approach to global numerical optimization which is easy to understand, simple to implement, reliable, and fast. Packed with illustrations, computer code, new insights, and practical advice, this volume explores DE in both principle and practice. It is a valuable resource for professionals needing a proven optimizer and for students wanting an evolutionary perspective on global numerical optimization. more

5,443 citations

19 Aug 2009-
Abstract: 1 Stationary Time Series.- 2 Hilbert Spaces.- 3 Stationary ARMA Processes.- 4 The Spectral Representation of a Stationary Process.- 5 Prediction of Stationary Processes.- 6* Asymptotic Theory.- 7 Estimation of the Mean and the Autocovariance Function.- 8 Estimation for ARMA Models.- 9 Model Building and Forecasting with ARIMA Processes.- 10 Inference for the Spectrum of a Stationary Process.- 11 Multivariate Time Series.- 12 State-Space Models and the Kalman Recursions.- 13 Further Topics.- Appendix: Data Sets. more

5,258 citations

Journal ArticleDOI

4,700 citations

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No. of papers in the topic in previous years

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Topic's top 5 most impactful authors

Hari M. Srivastava

52 papers, 1.5K citations

Peter M. Robinson

32 papers, 1.5K citations

Peter C.B. Phillips

30 papers, 1.4K citations

Tibor K. Pogány

24 papers, 239 citations

G. H. Hardy

24 papers, 800 citations