Bücher der Reihe Interdisciplinary Mathematical Sciences

This book is written for scientists and engineers who use HHT (Hilbert-Huang Transform) to analyze data from nonlinear and non-stationary processes. It can be treated as a HHT user manual and a source of reference for HHT applications. The book contains the basic principle and method of HHT and various application examples, ranging from the correction of satellite orbit drifting to detection of failure of highway bridges.The thirteen chapters of the first edition are based on the presentations made at a mini-symposium at the Society for Industrial and Applied Mathematics in 2003. Some outstanding mathematical research problems regarding HHT development are discussed in the first three chapters. The three new chapters of the second edition reflect the latest HHT development, including ensemble empirical mode decomposition (EEMD) and modified EMD.The book also provides a platform for researchers to develop the HHT method further and to identify more applications.

The study of attractors of dynamical systems occupies an important position in the modern qualitative theory of differential equations.

Stochastic dynamical systems tools for modeling and simulation are highly demanded in investigating complex phenomena in, for example, environmental and geophysical sciences, materials science, physical and chemical sciences, finance and economics. This book offers reviews on the developments in stochastic dynamics and stochastic analysis.

In an attempt to introduce application scientists and graduate students to the exciting topic of positive definite kernels and radial basis functions, this book presents modern theoretical results on kernel-based approximation methods and demonstrates their implementation in a variety of fields of application. With the aim of providing researchers involved in function approximation, boundary value problems, spatial statistics and machine learning with the flexible and high-order tools developed using kernels, the authors explore their historical context and explain recent advances as strategies to address long-standing problems. The examples are drawn from fields as diverse as surrogate modeling, machine learning and finance, and researchers from those and other fields will be able to follow the examples on their own machines using the included MATLAB code accessible through the library online. In combining the theoretical foundation of positive definite kernels with accessible experimentation from which to build on, the authors are empowering readers to use these powerful tools on their problems of interest.

The Hilbert?Huang Transform (HHT) represents a desperate attempt to break the suffocating hold on the field of data analysis by the twin assumptions of linearity and stationarity. Unlike spectrograms, wavelet analysis, or the Wigner?Ville Distribution, HHT is truly a time-frequency analysis, but it does not require an a priori functional basis and, therefore, the convolution computation of frequency. The method provides a magnifying glass to examine the data, and also offers a different view of data from nonlinear processes, with the results no longer shackled by spurious harmonics ? the artifacts of imposing a linearity property on a nonlinear system or of limiting by the uncertainty principle, and a consequence of Fourier transform pairs in data analysis. This is the first HHT book containing papers covering a wide variety of interests. The chapters are divided into mathematical aspects and applications, with the applications further grouped into geophysics, structural safety and vis

This book contains original research papers by leading experts in the fields of probability theory, stochastic analysis, potential theory and mathematical physics. There is also a historical account on Masatoshi Fukushima's contribution to mathematics, as well as authoritative surveys on the state of the art in the field.

Focuses on fields such as consensus and voting theory, clustering, location theory, mathematical biology, and optimization that have seen an upsurge of exciting works over the years using discrete models in modern applications. This book discusses advances in the fields, highlighting the approach of cross-fertilization of ideas across disciplines.

This volume is devoted to original research results and survey articles reviewing recent developments in reduction for stochastic PDEs with multiscale as well as application to science and technology, and to present some future research direction. This volume includes a dozen chapters by leading experts in the area, with a broad audience in mind. It should be accessible to graduate students, junior researchers and other professionals who are interested in the subject. We also take this opportunity to celebrate the contributions of Professor Anthony J Roberts, an internationally leading figure on the occasion of his 60th years birthday in 2017.

The nature of time in a nonautonomous dynamical system is very different from that in autonomous systems, which depend only on the time that has elapsed since starting rather than on the actual time itself.