Nonlinear analysis has played a prominent role in the recent developments in geometry and topology. The study of the Yang-Mills equation and its cousins gave rise to the Donaldson invariants and more recently, the Seiberg-Witten invariants. Those invariants have enabled us to prove a number of striking results for low dimensional manifolds, particularly, 4-manifolds. The theory of Gromov-Witten...

In this paper, a novel nonlinear discriminant analysis is proposed. Experimental results show that the new method provides state of the art performance when combined with LSVM in terms of training time and accuracy.

ACKNOWLEDGMENTS The present monograph, except for minor revisions, was presented as a doctoral dissertation at the University of New England in 1963. I wish to thank my supervisor, Dr. J. A. Keats of the University of Queensland, for his encouragement, advice, and criticism in the course of this work. I am particularly indebted to Dr. E. J. Burr, of the Department of Mathematics, University of ...

This paper presents an approach to the robust state reconstruction for a class of nonlinear switched systems affected by model uncertainties. Under the assumption that the continuous state is available for measurement, an approach is presented based on concepts and methodologies derived from the sliding mode control theory. With noisefree state measurements, the time needed for reconstructing t...

A. Two quite different forms of nonlinear principal component analysis have been proposed in the literature. The first one is associated with the names of Guttman, Burt, Hayashi, Benzécri, McDonald, De Leeuw, Hill, Nishisato. We call itmultiple correspondence analysis. The second form has been discussed by Kruskal, Shepard, Roskam, Takane, Young, De Leeuw, Winsberg, Ramsay. We call it no...

This book represents a modern approach to time series analysis which is based on the theory of dynamical systems. It starts from a sound outline of the underlying theory to arrive at very practical issues, which are illustrated using a large number of empirical data sets taken from various fields. This book will hence be highly useful for scientists and engineers from all disciplines who study ...

SUMMARY The nonlinear multigrid is an eecient algorithm for solving the system of nonlinear equations arising from the numerical discretization of nonlinear elliptic boundary problems 7],,9]. In this paper, we present a new nonlinear multigrid analysis as an extension of the linear multigrid theory presented by Bramble, et al. in 5], 6], and 17]. In particular, we prove the convergence of the n...

A general method for state space analysis is presented where not only underlying factors generating the data are estimated, but also the dynamics behind time series in factor space are modelled. The mappings and the states are all unknown. The nonlinearity of the mappings makes the problem highly under-determined and thus challenging. The Bayesian approach is able to nd a set of mappings which ...

Classical methods such as Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are ubiquitous in statistics. However, these techniques are only able to reveal linear relationships in data. Although nonlinear variants of PCA and CCA have been proposed, these are computationally prohibitive in the large scale. In a separate strand of recent research, randomized methods have...

The nonlinear bending behavior of sector graphene sheets is studied subjected to uniform transverse loads resting on a Winkler-Pasternak elastic foundation using the nonlocal elasticity theory. Considering the nonlocal differential constitutive relations of Eringen theory based on first order shear deformation theory and using the von-Karman strain field, the equilibrium partial differential eq...