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COŞKUN DENIZ 《Pramana》2017,88(1):20
Common recipe for the lengthening pendulum (LP) involves some change of variables to give a relationship with the Bessel’s equation. In this work, conventional semiclassical JWKB solution (named after Jeffreys, Wentzel, Kramers and Brillouin) of the LP is being obtained by first transforming the related Bessel’s equation into the normal form ‘via the suggested change of independent variable’. JWKB approximation of the first-order Bessel functions (ν=1) of both types along with their zeros are being obtained analytically with a very good accuracy as a result of the appropriately chosen associated initial values and they are extended to the neighbouring orders (ν=0 and 2) by the recursion relations. The required initial values are also being studied and a quantization rule regarding the experimental LP parameters is being determined. Although common numerical methods given in the literature require adiabatic LP systems where the lengthening rate is slow, JWKB solution presented here can safely be used for higher lengthening rates and a criterion for its validity is determined by the JWKB applicability criterion given in the literature. As a result, the semiclassical JWKB method which is normally used for the quantum mechanical and optical waveguide systems is applied to the classical LP system successfully. 相似文献
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[reaction: see text] Ni-catalyzed reductive coupling of aryl alkynes (1) and enantiomerically enriched alpha-oxyaldehydes (2) afford differentiated anti-1,2-diols (3) with high diastereoselectivity and regioselectivity, despite the fact that the methoxymethyl (MOM) and para-methoxybenzyl (PMB) protective groups typically favor syn-1,2-diol formation in carbonyl addition reactions of this family of aldehydes. 相似文献
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Bicyclization of peptide acetals via nucleophilic attack of a phenyl group on an endocyclic acyliminium ion 4 was explored as a route to novel amino acid derived heterocycles and peptidomimetic scaffolds. In the presence of protic acid, bridged structures such as 6 are formed readily from phenylalanine derivatives, but the fused-ring analogues 5 could not be obtained in good yield. In contrast, radical cyclization of the bromophenyl dihydropyrazinone 7 provides an effective alternative for the synthesis of 5 (n = 0, 1, 2). Additional versatility in this process was demonstrated by efficient synthesis of a different fused ring system, represented by the antihelmintic praziquantel, 8. 相似文献
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