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.     

Cyclisations par l'intermédiaire de fonctions phénylthioet phénoxy-carbamyle. I. Diphényl-1,2-alcoyl-5-dioxo-3,6-hexahydro-triazines-1,2,4

The N-(p-nitrophenoxy-carbonyl) and N-(phenylthio-carbonyl) derivatives of α-amino-acyl-hydrazides cyclize in presence of diazomethane, yielding hexahydro-1, 2, 4-triazines with simultaneous formation of p-nitro-anisole or thio-anisole respectively. The molecules with a phenoxycarbonyl function such as N-(phenoxycarbonyl)-glycyl-(N, N′-diphenylhydrazide) give the corresponding ring products and anisole only in solvents with high dielectric constant (e.g. nitromethane). The phenylthio-carbonyl derivatives give the same ring products in presence of lead acetate by the intervention of HO^?. The p-nitrophenoxycarbonyl derivatives give rise to the same cyclisations in the presence of pyridine by the intermediate of carbamyle-pyridinium ion acting as electrophile. These different types of intramolecular reactions are illustrated by the formation of 1, 2-diphenyl-5-alcoyl-3, 6-dioxo-1, 2, 4-hexahydro-triazines.     

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.

---

, , . .

     

Colour formation in poly(ethylene terephthalate) during melt processing

The discolouration, that occurs in virgin poly(ethylene terephthalate) - PET during melt processing, was studied using various bulk and surface analytical techniques. Proton nuclear magnetic resonance (¹H NMR) was used to study the bulk chemical changes occurring in the polymer during thermo-oxidative degradation. Chemical derivatisation with trifluoroacetic anhydride (TFAA) was used to label the hydroxyl groups introduced on the polymer surface by thermal oxidation.From the surface analysis studies using photoacoustic Fourier transform infrared spectroscopy (PA/FT-IR), diffuse reflectance infrared Fourier transform spectroscopy (DRIFT) and X-ray photoelectron spectroscopy (XPS) it was evident that colour formation starts initially with the hydroxylation of the terephthalic ring. Further, the formation of additional carbonyl functionalities and conjugated chromophoric systems complete the colour formation process.     

Surface influence on the rotational and translational dynamics of molecules confined inside a mesoporous carbon xerogel

Low-field nuclear magnetic resonance techniques are employed to extract information about the effects introduced by the interaction with the surface on the rotational and translational dynamics of molecules confined inside a mesoporous carbon xerogel. The molecules under study were water, cyclohexane, and hexane. They were chosen due to their different interaction strength with the carbonaceous matrix. Frequency dependent longitudinal relaxation measurements, using the fast field cycling technique, allowed extraction of the fractal dimension of the carbon xerogel surface. It was observed that the measured value is influenced by the molecule affinity to the surface. Diffusion measurements, using the pulse field gradient technique, have revealed that the stronger interaction with the surface of cyclohexane and hexane molecules leads to an increased diffusive tortuosity, as compared with water.     

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).