Global stabilization in nonlinear discrete systems with time-delay

A class of scalar nonlinear difference equations with delay is considered. Sufficient conditions for the global asymptotic stability of a unique equilibrium are given. Applications in economics and other fields lead to consideration of associated optimal control problems. An optimal control problem of maximizing a consumption functional is stated. The existence of optimal solutions is established and their stability (the turnpike property) is proved.     

1,3,2,4-Oxaazaphosphatitanetidine. Structure and Properties

The interaction of 1,3,2,4 -oxaazaphosphatitanetidines with chlorides of aluminium and zirconium, alcohols, piperidine and R₂NBr (R=SiMe₃) has been studied. The reaction routes have been determined with NMR spectra and X-ray structure analyses.     

On the regularization mechanism for the periodic Korteweg–de Vries equation

In this paper we develop and use successive averaging methods for explaining the regularization mechanism in the the periodic Korteweg–de Vries (KdV) equation in the homogeneous Sobolev spaces Ḣ^s for s ≥ 0. Specifically, we prove the global existence, uniqueness, and Lipschitz‐continuous dependence on the initial data of the solutions of the periodic KdV. For the case where the initial data is in L₂ we also show the Lipschitz‐continuous dependence of these solutions with respect to the initial data as maps from Ḣ^s to Ḣ^s for s ∈(−1,0]. © 2010 Wiley Periodicals, Inc.     

A study of Galerkin method for the heat convection equations

This article investigates the Galerkin method for an initial boundary value problem for heat convection equations. The new error estimates for the approximate solutions and their derivatives in strong norm are obtained.     

Plasmonic properties of silver nanocube monolayers on high refractive index substrates

Extinction spectra of nanocubes supported by a symmetry breaking dielectric substrate are very different from those in solution. In this work, we varied the refractive index of the substrate in order to optimize the refractive index sensitivity (RIS) of supported silver nanocube monolayers. We found that on thin (5?C7?nm) silicon films, the RIS is characterized by the figure of merit (FOM) for the quadrupolar plasmonic mode as high as 5.0, making silicon supported silver nanocube monolayers a promising sensing platform.     

Biochemical and Structural Studies of Conserved Maf Proteins Revealed Nucleotide Pyrophosphatases with a Preference for Modified Nucleotides

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