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In solving a nonlinear equation by the use of a continuation method one of the crucial problems is the choice of the step sizes. We present a model for the total computational cost of a standard numerical continuation process and solve the problem of optimal step size control for this model. Using the theoretical results as a basis, we develop an adaptive step size algorithm for Newton's method. This procedure is computationally inexpensive and it gives quite satisfactory results compared to some other numerical experiments found in the literature. 相似文献
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On the basis of a pyrrolidine tweezer 1, a library of peptidosulfonamide tweezers (15a-e, 16a-e) was synthesized on the solid phase. This library was screened in a simultaneous substrate screening procedure for the ability to enantioselectively catalyze the Ti(O-i-Pr)(4)-mediated addition of diethylzinc to aldehydes. One of the best solid-phase tweezer catalyst (i.e., 16d, giving an ee of 32% in solid-phase catalysis) was resynthesized in solution (compounds 20 and 21). The now homogeneous solution-phase catalysis showed even better enantioselectivity (i.e., up to 66%). 相似文献
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In this Letter, we explore transmission properties of a single subwavelength slit flanked by a finite array of grooves made on a thick metallic film. We identify three main mechanisms that can enhance optical transmission: groove cavity mode excitation (controlled by the depth of the grooves), in-phase groove reemission (controlled by the period of the groove array), and slit waveguide mode (controlled by the thickness of the metal film). By tuning these geometrical parameters, enhancements of transmission of light by up to 2 orders of magnitude can be achieved when all three mechanisms coincide. Experimental verification of these findings is also shown for structured silver films fabricated by focused-ion-beam milling. 相似文献