This paper proves approximation order properties of various nonlinear subdivision schemes. Building on some recent results on the stability of nonlinear multiscale transformations, we are able to give very short and concise proofs. In particular we point out an interesting connection between stability properties and approximation order of nonlinear subdivision schemes.

newspapers and past students' theses. These imaged documents will not be OCR'ed as originally planned due to the overwhelming cost involved. The images are available for public viewing and downloading. The present method will provide an automated means of retrieving similar document images from the library website without having to download every image for inspection of its content to decide it...

The superharmonic instability is pervasive in large-amplitude water-wave problems and numerical simulations have predicted a close connection between it and crest instabilities and wave breaking. In this paper we present a nonlinear theory, which is a generic nonlinear consequence of superharmonic instability. The theory predicts the nonlinear behaviour witnessed in numerics, and gives new info...

Spectra of nonlinear waves in infinite-dimensional Hamiltonian systems are investigated. We establish a connection via the Krein signature between the number of negative directions of the second variation of the energy and the number of potentially unstable eigenvalues of the linearization about a nonlinear wave. We apply our results to determine the effect of symmetry-breaking on the spectral ...

The geometry of the second order osculating bundle OscM , is in many cases determined by its spray and the associated nonlinear connection. For a Banach manifold M , we firstly endow OscM with a fiber bundle structure over M . Three different concepts which are used in many finite dimensional literatures, that is the horizontal distributions, nonlinear connections and sprays are studied in deta...

In this article, the cascade connection of two “buck” converters is examined from the perspective of differential flatness and Generalized Proportional Integral (GPI) observer–based control. The multi-variable nonlinear “buckbuck” converter is subject to unknown, time-varying, load current demands, at each one of the outputs of the two constitutive stages. The linear output feedback controllers...

In this paper, it is elaborated the theory the Ricci flows for manifolds enabled with nonintegrable (nonholonomic) distributions defining nonlinear connection structures. Such manifolds provide a unified geometric arena for nonholonomic Riemannian spaces, Lagrange mechanics, Finsler geometry, and various models of gravity (the Einstein theory and string, or gauge, generalizations). We follow th...

In this work we are interested in nonlinear symmetric cone problems (NSCPs), which contain as special cases nonlinear semidefinite programming, nonlinear second order cone programming and the classical nonlinear programming problems. We explore the possibility of reformulating NSCPs as common nonlinear programs (NLPs), with the aid of squared slack variables. Through this connection, we show ho...