Numerical reconstruction stability of fiber Bragg gratings

Traditional algorithms for solving the inverse scattering problem for a fiber Bragg grating are described, and a new numerical method for this problem is developed. The method is based on the fast inversion of a matrix using its Toeplitz symmetry and on a special “inner-bordering” procedure. It is shown that the method is equally efficient as the well-known discrete layer peeling method but exceeds the latter in accuracy, especially for high-reflectance gratings. The stability of the proposed method with respect to initial data errors is demonstrated.     

Inverse scattering for the one-dimensional Helmholtz equation: fast numerical method

The inverse scattering problem for the one-dimensional Helmholtz wave equation is studied. The equation is reduced to a Fresnel set that describes multiple bulk reflection and is similar to the coupled-wave equations. The inverse scattering problem is equivalent to coupled Gel'fand-Levitan-Marchenko integral equations. In the discrete representation its matrix has T?plitz symmetry, and the fast inner bordering method can be applied for its inversion. Previously the method was developed for the design of fiber Bragg gratings. The testing example of a short Bragg reflector with deep modulation demonstrates the high efficiency of refractive-index reconstruction.     

Interpretation of scoring functions using 3D molecular fields. Mapping the diacyl-hydrazine-binding pocket of an insect ecdysone receptor

A method is presented for the interpretation of receptor docking score values (rough measures of binding affinities) of ligands in terms of 3D molecular field interaction contributions. The FlexX and FlexX-Pharm methods were used to dock the structures of designed sets of ligands into the ligand-binding pocket of a selected receptor. In the next step the relationship was investigated between the FlexX and CScore scores and 3D molecular fields obtained for the docked conformations of the ligands, using the CoMFA (Comparative Molecular Field Analysis) and CoMSIA (Comparative Molecular Similarity Indices Analysis) methods. The approach yielded highly significant CoMFA and CoMSIA models demonstrating that a high portion of the variance in the docking score values of the ligands can be explained by steric, electrostatic, hydrophobic, and hydrogen bond donor and acceptor molecular field interaction contributions. The approach was exemplified by using the crystal structure of the ligand-binding domain of the ecdysone receptor (EcR) of the moth Heliotis virescens as well as virtual molecule libraries of analogues of known diacyl-hydrazine (DAH) type ecdysteroid agonists. By docking appropriately designed virtual compound libraries into the DAH binding pocket of EcR followed by CoMFA and CoMSIA of the docked conformations, hitherto unexplored regions of the receptor cavity could be mapped. By mapping the significant molecular field interaction contributions onto the model of the receptor-ligand complex, important receptor-ligand interactions could be highlighted that may help the design of novel highly scored receptor ligands. An advantage of the method is that no experimental biological activity data are required to exhaustively map the receptor-binding site.     

A monopole mass filter with a hyperbolic V-shaped electrode

In this article we compare the classical monopole mass filter of von Zahn and the monopole mass filter with a hyperbolic V-shaped electrode. The experimental results and those of computer simulation for both mass spectrometers are presented. We show that the replacement of a conventional 90 degrees V-shaped electrode by an electrode with a hyperbolic profile substantially improves the peak shape of any given mass, and increases the mass resolution by a factor of 3-4 and the abundance sensitivity by a factor of 100. The potential of high analytical performance combined with electroforming techniques for electrode manufacture indicate future practical uses of such instruments. Copyright 1999 John Wiley & Sons, Ltd.     

Pentavalent uranium oxide via reduction of [UO2]2+ under hydrothermal reaction conditions

The synthesis, crystal structure, and spectroscopic characterization of [U(V)(H2O)2(U(VI)O2)2O4(OH)](H2O)4 (1), a mixed-valent U(V)/U(VI) oxide material, are reported. The hydrothermal reaction of UO2(2+) with Zn and hydrazine at 120 degrees C for three days yields 1 in the form of a dark red crystalline solid. Compound 1 has been characterized by a combination of single-crystal and powder X-ray diffraction (XRD), elemental analysis, thermogravimetric analysis, X-ray photoelectron spectroscopy (XPS) and X-ray absorption spectroscopy (XAS). The structure consists of an extended sheet of edge and corner shared U(VI) pentagonal bipyramids that are further connected by edge sharing to square bipyramidal U(V) units. The overall topology is similar to the mineral ianthinite. The uranium L(III)-edge XAS revealed features consistent with those observed by single-crystal X-ray diffraction. High resolution XPS data analysis of the U4f region confirmed the oxidation states of U as originally assigned from XRD analysis and bond valence summations.     

Scattering of evanescent electromagnetic waves by a cylinder near the flat boundary: the Green function and fast numerical method

The scattering of plane evanescent waves by a cylinder is studied. The Green function for the Helmholtz equation for two dielectrics with flat interface is found and applied for the numerical calculation of the scattered field by the boundary elements method. The Green function keeps close track of scattering, including multiple reflections. The result may be applicable for the data analysis in near-field optical microscopy.     

FBG filter with minimal dispersion

An optimal filter for super-fast fiber-optic communication lines should cause minimal phase distortions. The simplest case of Bragg grating with a symmetric profile is considered. A distortion functional is presented, which is the mean square group delay over the Bragg reflection band at a fixed integral reflectivity. The functional is minimized analytically in the simplest limiting case. Numerical calculations confirm that the optimal reflection spectrum is realizable.     

Ultra-performance liquid chromatographic determination of manufacturing intermediates and subsidiary colors in D&C Red No. 34 and its lakes

An ultra-performance liquid chromatography (UPLC) method was developed to determine the manufacturing intermediates and subsidiary colors in the monosulfo monoazo color additive D&C Red No. 34 and its lakes. This method is currently used for batch certification of the color additives by the U.S. Food and Drug Administration to ensure that each lot meets published specifications for coloring drugs and cosmetics. The new UPLC method has replaced an HPLC method for determining the intermediates and a TLC method for determining the subsidiary colors. The intermediates are 2-amino-1-naphthalenesulfonic acid (Tobias acid) and 3-hydroxy-2-naphthalenecarboxylic acid (3-hydroxy-2-naphthoic acid). Subsidiary colors are positional isomers of the major dye component or related compounds containing lower numbers of substituent groups. The analytes are identified by comparison of their UPLC retention times and UV or visible absorption spectra with those of standards. Validation studies showed that peak area calibrations for the analytes were generally linear (R > 0.999), and recoveries were 98-103%. The LODs were 0.002-0.02%, and the RSDs at the specification levels were 0.7-2.2%. Survey analyses of 12 samples of certified D&C Red No. 34 straight colors and lakes from six domestic and foreign manufacturers yielded results for the intermediates by UPLC and HPLC that were consistent within experimental error. The UPLC analyses yielded results for the subsidiary colors that were consistently lower than results previously obtained by TLC, which we attribute to limitations of the TLC method. The new UPLC method provides sharper peaks, better peak separation, and faster analysis times than the formerly used HPLC method and is more accurate, much faster, and much less labor-intensive than the formerly used TLC method.     

Justification of the Kirchhoff hypotheses and error estimation for two-dimensional models of anisotropic and inhomogeneous plates, including laminated plates

Asymptotic analysis of the problem describing deformation ofa thin cylindrical plate with clamped lateral side is performed.The problem is considered under the most general statement withthe plate being laminated and consisting of an arbitrary numberof nonhomogeneous and anisotropic (21 elastic moduli) layers.Explicit integral representations of the differential operatorswhich form the two-dimensional model of the plate are derived.In the case when the elastic moduli of each of the layers areconstant, these integral representations turn into algebraicones. The asymptotic procedure is justified with the help ofa weighted inequality of Korn's type. The error estimates obtainedgive a rigorous mathematical proof of both of Kirchhoff's hypotheses(kinematic and static) and shed light on the well-known intrinsicinconsistency of two of the hypotheses.