Equivalence of regularity for the Bergman projection and the\bar \partial-neumann operator

A necessary and sufficient condition for regularity of the -Neumann operator on (0,q)-forms in a smooth bounded pseudoconvex domain in Cⁿ is that the orthogonal projections onto -closed forms of degrees (0,q−1), (0,q), and (0,q+1) all be regular. The first author partially supported by NSF Grant DMS-8701038     

Potentiometric, luminescence and NMR study of the interaction of Eu with glyceryl phosphates

Complexation of europium(III) with glyceryl-1- and -2-phosphates has been studied by metal ion luminescence, ¹H and ¹³C NMR spectroscopy and potentiometry. From the luminescence and NMR studies, the formation of a 1:1 inner-sphere complex, in which the glyceryl phosphate is directly bound to the metal, is confirmed. Similar apparent binding constants at pH 2 were obtained by the three methods. Values obtained by NMR at pH 2 are 53 M⁻¹ and 12 M⁻¹ for glyceryl-1- and -2-phosphate, respectively. By comparison with literature data on related systems it is suggested that the ligands bind through the phosphate group. To obtain structural information from the NMR data, complexation has also been studied with the lanthanide ions Dy(III), Er(III) and Gd(III) using both chemical shift and relaxation data. From this, metal-proton distance ratios have been calculated. Comparison of ¹H and ¹³C NMR spectral data in the presence of paramagnetic lanthanides suggests conformational equilibria in the solutions. From the potentiometric studies, global formation constants have been determined, and speciation diagrams obtained over the pH range 1.5pH7.0 for ligand/metal ratios of 1 and 30. Implications of these results on lanthanide induced fusion of phospholipid membranes are discussed.     

Optimal Control for Switched Systems with Pre-defined Order and Switch-Dependent Dynamics

The optimal control problem for switched systems, with a predefined order of switches, is considered. The differential equations may depend explicitly on previous switching instants, and the latter may be state dependent. The solution is based on the Calculus-of-Variations, which leads to a single two-point boundary-value problem. A new condition for the Hamiltonian jump at the switching instants is obtained. Simple numerical examples demonstrate the results.     

Real-time analysis of partially polarized light with a space-variant subwavelength dielectric grating

A novel method for real-time polarization measurement is presented. The method is based on a space-variant wave plate that we realized as a computer-generated space-variant subwavelength dielectric grating. The Stokes parameters of the incident beam are determined by Fourier analysis of the space-variant intensity transmitted through the grating and an analyzer. We discuss the design and realization of such wave plates and demonstrate our technique with polarization measurements of both polarized and partially polarized CO(2)-laser radiation at a wavelength of 10.6 mum.     

Space-variant Pancharatnam-Berry phase optical elements with computer-generated subwavelength gratings

Space-variant Pancharatnam-Berry phase optical elements based on computer-generated subwavelength gratings are presented. By continuously controlling the local orientation and period of the grating we can achieve any desired phase element. We present a theoretical analysis and experimentally demonstrate a Pancharatnam-Berry phase-based diffraction grating for laser radiation at a wavelength of 10.6microm.     

Formation of helical beams by use of Pancharatnam-Berry phase optical elements

Spiral phase elements with topological charges based on space-variant Pancharatnam-Berry phase optical elements are presented. Such elements can be achieved by use of continuous computer-generated space-variant subwavelength dielectric gratings. We present a theoretical analysis and experimentally demonstrate spiral geometrical phases for infrared radiation at a wavelength of 10.6microm .     

The Bergman kernel function: Explicit formulas and zeroes

We show how to compute the Bergman kernel functions of some special domains in a simple way. As an application of the explicit formulas, we show that the Bergman kernel functions of some convex domains, for instance the domain in defined by the inequality , have zeroes.