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.     

Infinite-order phase transition in a classical spin system

For an exactly soluble classical spin model with long-range inhomogeneous coupling it is proved that in the absence of external magnetic field the free energy is aC function of the temperature at the critical point.     

Diffusion coefficient measurement in a microfluidic analyzer using dual-beam microscale-refractive index gradient detection. Application to on-chip molecular size determination

We report a microchip-based detection scheme to determine the diffusion coefficient and molecular mass (to the extent correlated to molecular size) of analytes of interest. The device works by simultaneously measuring the refractive index gradient (RIG) between adjacent laminar flows at two different positions along a microchannel. The device, referred to as a microscale molecular mass sensor (micro-MMS), takes advantage of laminar flow conditions where the mixing of two streams occurs essentially by diffusion across the boundary between the two streams. Two flows merge on the microchip, one containing solvent only, referred to as the mobile phase stream and one which contains the analyte(s) of interest in the solvent, i.e. the sample stream. As these two streams merge and flow parallel to each other down the microchannel a RIG is created by the concentration gradient. The RIG is further influenced by analyte diffusion from the sample stream into the mobile phase stream. Measuring the RIG at a position close to the merging point (upstream signal) and simultaneously a selected distance further down the microchannel (downstream signal) provides real-time data related to the extent a given analyte has diffused, which can be readily correlated to analyte molecular mass by taking the ratio of the downstream-to-upstream signals. For the dual-beam RIG measurements, a diode laser output is coupled to a single mode fiber optic splitter with two output fibers. Light from each fiber passes through a graded refractive index (GRIN) lens forming a collimated beam that then passes through the microchannel and then on to a position sensitive detector (PSD). The RIG at both detection positions deflects the two collimated probe beams. The deflection angle of each beam is then measured on two separate PSDs. The micro-MMS was evaluated using polyethylene glycols (PEGs), sugars, and as a detector for size-exclusion chromatography (SEC). Peak purity can be readily identified using the micro-MMS with SEC. The limit of detection was 0.9 ppm (PEG at 11 840 g/mol) at the upstream detection position corresponding to a RI limit of detection (LOD) (3sigma) of 7-10(-8) RI. The pathlength for the RIG measurement was 200 microm and the angular LOD was 0.23 micro(rad) with a detection volume of 8 nl at both positions. The average molecular mass resolution was 9% (relative standard deviation) for a series of PEGs ranging in molecular mass from 106 to 22 800 g/mol. With this excellent mass resolution, small molecules such as monosaccharides, disaccharides, and so on, are readily distinguished. The sensor is demonstrated to readily determine unknown diffusion coefficients.     

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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Determination of selected neurotransmitter metabolites using monolithic column chromatography coupled with chemiluminescence detection

The oxidation of selected clinically important neurotransmitter metabolites with acidic potassium permanganate in the presence of polyphosphates evokes chemiluminescence of sufficient intensity to enable the sensitive determination of these species. Limits of detection for 5-hydroxyindole-3-acetic acid (5-HIAA), vanilmandelic acid (VMA; α,4-dihydroxy-3-methoxybenzeneacetic acid), 4-hydroxy-3-methoxyphenylglycol (MHPG), homovanillic acid (HVA, 4-hydroxy-3-methoxyphenylacetic acid) and 3,4-dihydroxyphenylacetic acid (DOPAC) were between 5 × 10⁻⁹ and 4 × 10⁻⁸ M, using flow-injection analysis methodology. In addition, we demonstrate the rapid determination of homovanillic acid and 5-hydroxyindole-3-acetic acid in human urine - without the need for extraction procedures - using monolithic column chromatography with chemiluminescence detection.     

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.