Finite Element Solution of Conical Diffraction Problems

This paper is devoted to the numerical study of diffraction by periodic structures of plane waves under oblique incidence. For this situation Maxwell's equations can be reduced to a system of two Helmholtz equations in R ² coupled via quasiperiodic transmission conditions on the piecewise smooth interfaces between different materials. The numerical analysis is based on a strongly elliptic variational formulation of the differential problem in a bounded periodic cell involving nonlocal boundary operators. We obtain existence and uniqueness results for discrete solutions and provide the corresponding error analysis.     

Compactness in fuzzy convergence spaces

Lowen and Lowen [Applications of category theory to fuzzy subsets (Kluwer, 1992) p. 153] and Lowen et al. [Fuzzy Sets and Systems 40 (1991) 347] recently introduced the category FCS of fuzzy convergence spaces, a topological quasitopos which is a supercategory of FTS, the category of fuzzy topological spaces. In this paper, compactness in FCS is examined. Doing so we found that to define compactness as an absolute property we had to generalize the definition of fuzzy convergence space to fuzzy subsets. All basic theorems are proved including the Tychonoff product theorem. Based on the theory developed here, in a following publication, a Richardson compactification for fuzzy convergence spaces will be given.     

Probing for electrical inclusions with complex spherical waves

Let a physical body Ω in ?² or ?³ be given. Assume that the electric conductivity distribution inside Ω consists of conductive inclusions in a known smooth background. Further, assume that a subset Γ ? ?Ω is available for boundary measurements. It is proved using hyperbolic geometry that certain information about the location of the inclusions can be exactly recovered from static electric measurements on Γ. More precisely: given a ball B with center outside the convex hull of Ω and satisfying (B? ∩ ?Ω) ? Γ, boundary measurements on Γ with explicitly given Dirichlet data are enough to determine whether B intersects the inclusion. An approximate detection algorithm is introduced based on the theory. Numerical experiments in dimension two with simulated noisy data suggest that the algorithm finds the inclusion‐free domain near Γ and is robust against measurement noise. © 2007 Wiley Periodicals, Inc.     

Effect of post-metallization annealing on the ferroelectric properties of sol-gel derived PZT thin films

A series of monolithic Pt-PZT-Pt capacitors was prepared based on sol-gel derived PZT 53/47 films fired to 700 C. After deposition of top Pt electrodes, the capacitors were subjected to post-metallization annealing (PMA) temperatures of 100 C to 700 C. Dielectric and ferroelectric (FE) characterizations were performed. Increasing the PMA temperature produced lower values of spontaneous and remanent polarizations, dielectric constant and leakage currents. The observations are correlated with a proposed FE capacitor model.     

AUTOMATED MECHANICAL STIMULATION AND MEASUREMENT OF BIOLUMINESCENCE IN MARINE DINOFLAGELLATES

A new integrated system for reproducible, automated mechanical stimulation and measurement of bioluminescence (BL) in multiple samples of marine dinoflagellate cell suspensions is described. The system was designed to allow the application of standardized experimental routines to parallel test vials for the purpose of toxicity testing. A sample tray delivered test vials to the position of mechanical stimulation and BL measurement. Mechanical stimulation of BL was applied as sharp rotation-onset of the test vial about its vertical axis. Thus, any direct chemical or physical perturbation of the cell suspension was avoided. A silicon photovoltaic cell measured the emitted light. Stimulation, measurement and recording of BL were integrated and controlled by specially developed software, which runs on a personal computer in the graphic environment of MS-Windows. Precise scheduling, flexible programming and identical repetition of experimental routines are possible in practice. For Gonyaulax polyedra, details of BL, as stimulated and measured with the new system, are presented and discussed. We conclude that the system exhibits specific features that offer wide potential of application in several fields of research on dinoflagellate BL, particularly for toxicity testing.     

An improved algorithm for satellite-derived UV radiations

The improved algorithm surface irradiance derived from a range of satellite-based sensors (SIDES) is presented in this article. It calculates various types of surface UV intensities, such as biologically weighted or unweighted UV spectra, integrated doses or irradiance at specific wavelengths, using data from satellite instruments. These surface UV data are mainly useful for environmental impact or process studies where high accuracy or a high temporal resolution is required. In contrast to several previous studies, SIDES has been validated with spectral measurements. By this method an averaging of positive or negative deviations over the complete wavelength range is avoided. This is especially important for UV wavelengths around 300 nm where biological effectiveness is highest. The results of SIDES deviate less than 7% from ground-based observations for wavelengths between 295 and 400 nm. In contrast, the corresponding deviations of the joint research center algorithm escalate for shorter wavelengths, reaching 35% at 295 nm. This large deviation is due to an inaccurate interpolation procedure that has been detected by spectral analysis. Thus, spectral validation is demonstrated to be an appropriate tool to detect weaknesses in such an algorithm and provides information essential for improvement.     

The Fermi doublet V2−V3 + V4 of CH3CN as a probe of molecular interactions

The Fermi doublet V₂?V₃ + V₄ of CH₃CN in basic, inert and acidic solvents has been studied by IR and Raman spectroscopy. The values of W, the Fermi coupling coefficient, obtained from IR spectra varies with the nature of the solvent while W evaluated from Raman data remains constant at 12.5 ± 0.5 cm^?1. The similar effects of Bronsted and Lewis acids on the band frequencies and intensities is evidence that the CN group complexes with acids via the N atom “n” electron pair and not the π bond.     

Glycosylidene Carbenes. Part 9. Regioselective glycosidation of diols and triols: Intra- and intermolecular hydrogen bonds

Glycosidation of the myo-inositol derivatives 2 and 3 by the diazirine 1 yields 90% of a diastereoisomer pair of β-D -glycosides in a 1:1 ratio, i.e. 5/6 and 7/8 , respectively (Scheme 1). The crystal structure of 3 shows a strong intramolecular H-bond, which persists in solution, as indicated by FT-IR and ¹H-NMR spectra. Yields and diastereoselectivity are lower for the glycosidation of 24 by 1 (Scheme 3). The resulting 1,2- and 1,4-linked disaccharides 25–28 were isolated as their acetates 29–32 . The previously determined crystal structure of 24 shows no intramolecular H-bonds. The yield of the glycosidation of 24 , but not of 3 , depends upon the concentration, indicating that activation of 24 by intermolecular H-bonds is required. Glycosidation of 2 and 3 with the trichloroacetimidate 14 gave mixtures of four ( 5,6,15 , and 16 ), and six ( 7,8 , and 17–20 ) disaccharides, respectively (Scheme 2).     

Metallkomplexe des Hexamethyl-trisila-tetraphospha-nortricyclen P4 (Sime2)3

Transition Metal Complexes of the Hexamethyl-trisila-tetraphospha-nortricyclene P₄ (Sime ₂) ₃ P₄(Sime₂)₃ 1 reacts with Mo(CO)₆, Cr(CO)₅THF, and Mn(η-C₅H₅)(CO)₂THF to give crystalline complexes in which 1 functions as a monodentate ligand. In each compound one phophorus atom of the cyclotriphosphane ring coordinates to the metal atom. Using Mn(η-C₅H₅)(CO)₂THF, two different P atoms of the P₃ Cr(CO)₄ norbornadiene and 1 react, yielding the dimeric, red, crystalline compound (CO) ₄Cr[μ-P₄(Sime₂)₃]₂Cr(CO)₄. In this complex the two molecules of 1 are both bonded by two P atoms of the P ₃ ring to the two Cr(CO)₄ Units, forming a six-memered (CrP₂)₂ring.