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. 相似文献
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. 相似文献
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. 相似文献
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. 相似文献
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 . 相似文献
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. 相似文献
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 Kn(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. 相似文献
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. 相似文献
This paper deals with the design of nonlinear controllers for the wing-rock phenomenon of a delta wing aircraft. A fifth order dynamic model is used to describe this phenomenon. A state transformation is introduced such that the transformed dynamic model is in a form which is suitable for a variety of control designs. A feedback linearization control scheme and a sliding-mode control (SMC) scheme are then proposed to suppress wing rock oscillations. It is shown that the two controllers successfully suppress the undesired oscillations and guarantee the asymptotic convergence of all system trajectories to their desired values. The effectiveness of the proposed controllers is verified through simulation studies.