Farthest-point queries with geometric and combinatorial constraints

In this paper we discuss farthest-point problems in which a set or sequence S of n points in the plane is given in advance and can be preprocessed to answer various queries efficiently. First, we give a data structure that can be used to compute the point farthest from a query line segment in O(log²n) time. Our data structure needs O(nlogn) space and preprocessing time. To the best of our knowledge no solution to this problem has been suggested yet. Second, we show how to use this data structure to obtain an output-sensitive query-based algorithm for polygonal path simplification. Both results are based on a series of data structures for fundamental farthest-point queries that can be reduced to each other.     

A new kinetic approach to flowing chemical systems with linearly dependent reactions

A new kinetic approach to flowing chemical system is introduced, based on the elimination of reaction extents attached to linearly dependent reactions. The method is applied to analyze the propagation of acoustic waves in a reacting chemical mixture.

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Certification of nitrate in spinach powder reference material SPIN-1 by high-precision isotope dilution GC–MS

A high-precision exact-matching quadruple isotope dilution method (ID⁴MS) was employed for the quantitation of nitrate in an air-dried spinach powder Certified Reference Material (CRM). The analyte was extracted in hot water following addition of ¹⁵NO\({}_{3}^{-}\) internal standard. The blend was then treated with sulfamic acid to remove nitrite and with triethyloxonium tetrafluoroborate to promote aqueous conversion of nitrate into volatile EtONO₂. The derivative was analyzed by headspace GC–MS with 3-min elution time. The method performance was validated with a series of tests which demonstrated adequate selectivity and ruggedness. This method supported the development of novel SPIN-1 CRM giving a modest contribution to its uncertainty (u_char = 0.85%). With respect to previous attempts, the SPIN-1 was proven stable, homogeneous (u_hom = 0.44%), and suitable for spinach monitoring under EU regulations. On dried basis, the nitrate content of SPIN-1 was found to be 22.53 ± 0.43 mg/g (U_c = 1.9%, k = 2). The material was also used in an inter-laboratory study where four laboratories employed a total of ten measurement methods.

SPIN-1 Certified Reference Material for nitrate in spinach powder

     

Liquid Injection Field Desorption Ionization Mass Spectrometry of Cyclic Metal Carbonyl Complexes with Tetra-Antimony Ligands

Reactions of (norbornadiene)Cr(CO)₄ or cis-(piperidine)₂Mo(CO)₄ with R₂Sb-SbR₂, and cyclo-(R′Sb)_n (R′ = Et, n-Pr; n = 4, 5) give the complexes cyclo-[M(CO)₄(R₂Sb-SbR′- SbR′-SbR₂)] (1: M = Cr, R = Me, R′= Et; 2: M = Mo, R = Et, R′ = Et; 3: M = Mo, R = Et, R′ = n-Pr). Not accessible to established characterization methods, the oily, extremely reactive unpurified mixture of 3 with scrambled ligands was characterized by mass spectrometry using liquid injection field desorption ionization (LIFDI).      

Photonic band gap architectures for holographic lithography

Using symmetry considerations, we identify three families of large photonic band-gap (PBG) architectures defined by the isointensity surfaces of four beam laser interference. For particular choices of beam intensities, directions, and polarizations, we obtain a diamondlike crystal, a novel body-centered cubic architecture, and a simple cubic structure with PBG to center frequency ratios of 25%, 21%, and 11%, respectively, when the isointensity surface defines a silicon (dielectric constant of 11.9) to air boundary.     

Photonic band gaps based on tetragonal lattices of slanted pores

We describe broad new classes of three-dimensional (3D) structures which, when made of silicon, exhibit robust 3D photonic band gaps of up to 25% of the gap center frequency. The proposed photonic crystals are readily amenable to very high precision microfabrication using established techniques such as x-ray lithography and template inversion. Each architecture consists of a set of oriented cylindrical pores emanating from a two-dimensional (2D) square lattice mask with a two-point basis. Large bandwidth, microcircuits for light may be incorporated within the resulting photonic band gaps using an intercalated 2D photonic crystal layer.     

Shear banding in reaction-diffusion models

Shear banding occurs in the flow of complex fluids: various types of shear thinning and shear thickening micelle solutions and liquid crystals. In order to cope with the strongly inhomogeneous interface between the bands, constitutive models used in standard rheology must be supplemented by non-local terms. This leads rather generally to non-linear partial differential equations of the reaction-diffusion type. We use this formalism in order to explain some observed experimental features and as a guide for future research in this field. Received: 17 May 1999/Accepted: 3 August 1999     

Reactions of Distibanes with [Fe2(CO)9]: Synthesis,Structure and DFT Calculations of [(Et2Sb)4Fe4(CO)14], [(nPr2Sb)4Fe3(CO)10], [{(Me3SiCH2)2Sb}4Fe2(CO)6], and [2‐(Me2NCH2)C6H4SbFe2(CO)8]

The iron complexes [(Et₂Sb)₄Fe₄(CO)₁₄] ( 1 ), [(nPr₂Sb)₄Fe₃(CO)₁₀] ( 2 ), [{(Me₃SiCH₂)₂Sb}₄Fe₂(CO)₆] ( 3 ), and [2‐(Me₂NCH₂)C₆H₄SbFe₂(CO)₈] ( 4 ) were prepared by reactions of distibanes with Fe₂(CO)₉. Compounds 1 – 4 were characterized by X‐ray diffraction, ¹H NMR and IR spectroscopy as well as mass spectrometry; complex 1 was additionally characterized by density functional calculations.