Optimization of a 2D photonic crystal add/drop multiplexer based on contra-directional coupling

We present a highly integrated add/drop multiplexer, where the contra-directional coupling is realized by phase matching two photonic crystal waveguides. The device band structure, the corresponding transmission and drop spectra, and the coupling length are carefully analysed. Different device configurations are discussed and by tailoring the coupling factor, we optimize the frequency response of the filter, obtaining a -sized channel selector, characterized by a very high drop efficiency.     

Propagation of Optical Beams in Active Media Inside Gaussian Cavities

The evolution of relevant beam parameters of a light beam propagating through an iterated sequence of spherical lenses and Gaussian apertures immersed in an active medium is investigated. This structure is a classical model for an optical resonator. The effective size of the field distribution, the beam quality factor and the radius of wave front curvature are calculated as functions of the number of transits. Steady-state values of these parameters are also determined and the dependence of the results on the gain of the medium, the aperture width and the focal length is illustrated. A comparison with the case without active medium is also discussed.     

Heterocyclic rearrangements. Phenylhydrazones and N-methyl-N-phenylhydrazones of 3-acylisoxazoles

The reaction of 3-benzoyl-5-phenylisoxazole ( 4 ) and 3-acetyl-5-methylisoxazole ( 5 ) with phenylhydrazine and N-methyl-N-phenylhydrazine has been investigated and the reactivity of (E)- and (Z)-phenylhydrazones and N-methyl-N-phenylhydrazones has been studied.     

On the relations between two types of convergence for convex functions

Theory and applications have shown that there are two important types of convergence for convex functions: pointwise convergence and convergence in a topology induced by the convergence of their epigraphs. We show that these two types of convergence are equivalent on the class of convex functions which are equi-lower semicontinuous. This turns out to be maximal classes of convex functions for which this equivalence can be obtained. We also indicate a number of implications of these results to the convergence of convex sets and the corresponding support functions and to the convergence of the infima of sequences of convex minimization problems.     

Differentiability of solutions of some evolution equations in nonreflexive Banach spaces

Summary The purpose of this paper is to present a regularity result that provides a unified treatment of the Cauchy problem for certain nonlinear partial differential equations that appear in kinetic theory. Part. 1 contain the main theorem, based on the theory of evolution equations. In part 2 it is indicated how these abstract results are applicable to the spatially homogeneous Boltzmann equazion and to the kinetic equation of vehicular traffic. Entrata in Redazione il 28 giugno 1978. Work performed under the auspices of the G.N.A.F.A. of the National Research Couucil.     

Catalytic enantioselective conjugate addition of dialkylzinc reagents to N-substituted-2,3-dehydro-4-piperidones

The first, highly enantioselective, copper/phosphoramidite-catalyzed conjugate addition of dialkylzinc reagents to N-substituted 2,3-dehydro-4-piperidones is described.     

Integral Theory for Hopf Algebroids

The theory of integrals is used to analyze the structure of Hopf algebroids. We prove that the total algebra of a Hopf algebroid is a separable extension of the base algebra if and only if it is a semi-simple extension and if and only if the Hopf algebroid possesses a normalized integral. It is a Frobenius extension if and only if the Hopf algebroid possesses a nondegenerate integral. We give also a sufficient and necessary condition in terms of integrals, under which it is a quasi-Frobenius extension, and illustrate by an example that this condition does not hold true in general. Our results are generalizations of classical results on Hopf algebras.