Reconstructing small perturbations of an obstacle for acoustic waves from boundary measurements on the perturbed shape itself

We derive relationships between the shape deformation of an impenetrable obstacle and boundary measurements of scattering fields on the perturbed shape itself. Our derivation is rigorous by using a systematic way, based on layer potential techniques and the field expansion (FE) method (formal derivation). We extend these techniques to derive asymptotic expansions of the Dirichlet-to-Neumann (DNO) and Neumann-to-Dirichlet (NDO) operators in terms of the small perturbations of the obstacle as well as relationships between the shape deformation of an obstacle and boundary measurements of DNO or NDO on the perturbed shape itself. All relationships lead us to very effective algorithms for determining lower order Fourier coefficients of the shape perturbation of the obstacle.     

Synthesis of 6-amino-5-cyano-1,4-disubstituted-2(1H)-pyrimidinones via copper-(I)-catalyzed alkyne-azide 'click chemistry' and their reactivity

In this paper we present the room temperature synthesis of a novel serie of 1,4-disubstituted-1,2,3-triazoles 4a-l by employing the (3+2) cycloaddition reaction of pyrimidinones containing alkyne functions with different model azides in the presence of copper sulphate and sodium ascorbate. To obtain the final triazoles, we also synthesized the major precursors 6-amino-5-cyano-1,4-disubstituted-2(1H)-pyrimidinones 3a-r from ethyl 2,2-dicyanovinylcarbamate derivatives 2a-c and various primary aromatic amines containing an alkyne group. The triazoles were prepared in good to very good yields.     

Microwave irradiation： Novel and facile methods for the synthesis of new pyrimidinones

We describe here a rapid process for the preparation of new 9-chloromethyl-12-aryl-10,12-dihydrobenzo[5,6]chromeno[2,3-d]pyrimidin-11-ones 5a-d and 10-chloromethyl-7-aryl-7,9-dihydrobenzo[7,8]chromeno[2,3-d]pyrimidin-8-ones 6a-d by two different methods utilizing microwave irradiation. This methodology provides better yields(72%–80%) and high purity of the title compounds.     

A monopole mass filter with a hyperbolic V-shaped electrode

In this article we compare the classical monopole mass filter of von Zahn and the monopole mass filter with a hyperbolic V-shaped electrode. The experimental results and those of computer simulation for both mass spectrometers are presented. We show that the replacement of a conventional 90 degrees V-shaped electrode by an electrode with a hyperbolic profile substantially improves the peak shape of any given mass, and increases the mass resolution by a factor of 3-4 and the abundance sensitivity by a factor of 100. The potential of high analytical performance combined with electroforming techniques for electrode manufacture indicate future practical uses of such instruments. Copyright 1999 John Wiley & Sons, Ltd.     

Modelling and control of two robotic manipulators handling a constrained object

In this paper, the problem of modelling and controlling two manipulators handling a constrained object is addressed. At first, a reduced order dynamic model of the system is derived, and several of its properties are outlined. Using the reduced order model, an adaptive control scheme that guarantees the asymptotic convergence of the position of the object, and the forces acting on the object to their desired values is developed. Simulation results of two planar robots moving an object along a plane illustrate the effectiveness of the proposed control scheme.     

Existence results for some polyharmonic problems in the half-space

We study the existence of positive solutions of the m-polyharmonic nonlinear elliptic equation m(−Δ)u+f(⋅,u)=0 in the half-space , n?2 and m?1. Our purpose is to give two existence results for the above equation subject to some boundary conditions, where the nonlinear term f(x,t) satisfies some appropriate conditions related to a certain Kato class of functions .     

Structure and dynamics of liquid crystalline pattern formation in drying droplets of DNA

We investigate the formation of ringlike deposits in drying drops of DNA. In analogy with the colloidal "coffee rings," DNA is transported to the perimeter by the capillary flow. At the droplet edge, however, DNA forms a lyotropic liquid crystal (LC) with concentric chain orientations to minimize the LC elastic energy. During the final stages of drying, the contact line retracts, and the radial stress causes undulations at the rim that propagate inward through the LC and form a periodic zigzag structure. We examine the phenomenon in terms of a simple model based on LC elasticity.     

Reconstructing small perturbations of scatterers from electric or acoustic far‐field measurements

In this paper, we consider the problem of determining the boundary perturbations of an object from far‐field electric or acoustic measurements. Assuming that the unknown scatterer boundary is a small perturbation of a circle, we develop a linearized relationship between the far‐field data and the shape of the object. This relationship is used to find the Fourier coefficients of the perturbation of the shape. Copyright © 2008 John Wiley & Sons, Ltd.     

On a New Kato Class and Singular Solutions of a Nonlinear Elliptic Equation in Bounded Domains of $$\mathbb{R}^n$$

Using a new form of the 3G-Theorem for the Green function of a bounded domain Ω in , we introduce a new Kato class K(Ω) which contains properly the classical Kato class K_n(Ω). Next, we exploit the properties of this new class, to extend some results about the existence of positive singular solutions of nonlinear differential equations. Mathematics Subject classification (1991): 34B15, 34B27.     

Nonlinear and Robust Control Schemes for Offshore Steel Jacket Platforms

This paper presents two control schemes to control the dynamicresponse of an offshore steel jacket platform due to wave-inducedforces. The objective of the controllers is to greatly reduce theinternal system oscillations and to obtain a smooth response ofthe steel jacket platform when subjected to nonlinear self-excitedhydrodynamic forces. The first controller is a nonlinearcontroller whose design is based on Lyapunov theory. The secondcontroller is a robust state feedback linear controller whosedesign is based on an optimal control approach. Both controlschemes guarantee the asymptotic stability of the system. Thetheoretical developments are illustrated through simulationresults of the proposed control schemes. Furthermore, theperformance of the offshore steel jacket platform is presentedwhen a direct velocity feedback controller is applied to thesystem. It is found that the performance of the system with theproposed controllers is better than the performance of the systemwith the direct velocity feedback controller.