Reflectivity and transmitivity of a spatially dispersive crystal

The reflectivity and transmitivity of a spatially dispersive crystal for S-polarized incident light are calculated for a microscopical model in which the interaction among the crystal planes is assumed to fall exponentially with distance. The angle of incidence is arbitrary and the deduced formulae are valid from X-ray to the visible light region. The generalization to the more complicated models is briefly discussed. For solving the problem an algebraic formulation of the Ewald dynamical theory of diffraction is used.     

The Menšov-Paley theorem and related results for double orthogonal series

клАссИЧЕскИЕ тЕОРЕМ ы Ф. РИссА, шлИ И МЕНьшО ВА (сМ., НАпРИМЕР, [3. стР. 102, 121 И 189]) РАспРОстРАНьУтсь, И пРИ ЁтОМ В ОБОБЩЕННОИ пОстАНОВкЕ МАРпИНкЕ ВИЧА И жИгМУНДА [1], с ОДНОМЕРНОгО НА ДВУМ ЕРНыИ слУЧАИ. пУсть {?_i(x)} (i=1, 2,...) И (ψ_k(y) (k=1, 2,...) — ДВЕ сИстЕМы ФУНкцИИ, ОРтО НОРМИРОВАННыЕ НА (НЕ О БьжАтЕльНО кОНЕЧНых) ИНтЕРВАлАх (А, ь) И (с, d), сООтВЕтстВЕННО. пР ЕДпОлАгАЕтсь, ЧтО ∥?_i¦|_v≦M_i И ψ_{k v}≦N_k Дль НЕкОтОРОгОv>2, гДЕМ _iИN _k кОНЕЧНы. ИжУ Ч АУтсь сВОИстВА схОДИ МОстИ ДВОИНых РьДОВ \(\mathop \Sigma \limits_{\iota = 1}^\infty \mathop \Sigma \limits_{\kappa = 1}^\infty c_{ik} \varphi _i (x)\psi _k (y).\) ОсНОВНОИ РЕжУльтАт с ОстОИт В слЕДУУЩЕМ Ут ВЕРжДЕНИИ. тЕОРЕМА 5. пУсть 2u ВыпО лНЕНО УслОВИЕ (3.2).ЕслИ Р ьД (3.3)схОДИтсь, тО РьД (1.16)схОДИтсь пОЧтИ ВсУД У пРИ пРОИжВОльНОИ пЕРЕстАНОВкЕ ЕгО ЧлЕ НОВ. ЕслИ (1.17) —пРОИжВОл ьНАь пЕРЕстАНОВкА РьДА (1.16),mО ВыпОлНЕНА ОцЕНкА (3.4),пР ИЧЕМ ВЕлИЧИНА Ag _q,v ^* жАВИсИт тОлькО От q И v. тЕОРЕМА 5 Дльv=∞ ьВльЕт сь ДВУМЕРНыМ АНАлОгО М тЕОРЕМы МЕНьшОВА—пЁлИ.     

Rapid spectrophotometric determination of chlorate with dimedone bisthiosemicarbazone monohydrochloride

Summary Dimedone bisthiosemicarbazone monohydrochloride has been examined to evaluate its usefulness as a reagent for rapid and sensitive Spectrophotometric determination of chlorate (0.5–5.0 ppm) by oxidation of the reagent in 70% perchloric acid medium and measurement of the yellow product. The molar absorptivity at 417 nm is 1.86×10⁴ l·mole^–1·cm^–1. The relative standard deviation is 1.6% for 2.5 ppm of chlorate.

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Spektropbotometrische Bestimmung von Chlorat mit Dimedonbisthiosemicarbazon-monocblorhydrat (I)

Zusammenfassung Die Verwendbarkeit von I als Reagens für die rasche und empfindliche spektrophotometrische Bestimmung von 0,5–5,0 ppm Chlorat durch Oxydation von I in 70%iger Perchlorsäure und Messung des gelben Reaktionsproduktes wurde untersucht. Die molare Absorptivität bei 417 nm beträgt 1,86×10⁴ l·mol^–1·cm^–1. Die relative Standardabweichung beträgt 1,6% für 2,5 ppm Chlorat.

     

Iron(III)-catalyzed Prins-type cyclization using homopropargylic alcohol: a method for the synthesis of 2-alkyl-4-halo-5,6-dihydro-2H-pyrans

[reaction: see text] A new Prins-type cyclization between homopropargylic alcohol and aldehydes in the presence of FeX(3) to obtain 2-alkyl-4-halo-5,6-dihydro-2H-pyrans in good yield is described. Osmium-catalyzed cis dihydroxylation provided direct access to trans-2-alkyl-3-hydroxy-tetrahydro-pyran-4-ones. Anhydrous ferric halides are also shown to be excellent catalysts for the standard Prins cyclization using homoallylic alcohol. Isolation of an intermediate acetal provides substantiation of a proposed mechanism.     

A density functional theory study on the electrocyclization of 1,2,4,6-heptatetraene analogues: converting a pericyclic to a pseudopericyclic reaction

A comprehensive B3LYP/6-31+G* study on the electrocyclization of 1,2,4,6-heptatetraene analogues was conducted. Starting from the cyclization of (2Z)-2,4,5-hexatrienal, a pericyclic disrotatory process favored by the assistance of a electron lone pair, we incorporated small modifications in its molecular structure to obtain a truly pseudopericyclic process. To this purpose electronegative atoms (fluorine and nitrogen) were added to give a more electrophilic character on the carbon atom which is attacked by the electron lone pair of the oxygen atom. The complete pathway for each reaction was determined, and changes in magnetic properties were monitored with a view to estimating the aromatization associated with each process. This information, together with the energetic and structural results, allowed us to classify the reactions as pseudopericyclic or pericyclic. Among all studied reactions only one was a truly pseudopericyclic process and another was a borderline case. The features of this unequivocally pseudopericyclic case were analyzed in depth.     

The group identification of organic compounds by means of thin-layer chromatography

The group identification method was presented based on the constant differences ΔR_f and ΔR_M, calculated from the chromatographic parameters obtained in two different mobile phases. The applicability of this method was proved with higher aliphatic alcohols, acids, and esters.     

Combining thermal analysis with other techniques to monitor the decomposition of poly(m-phenylene isophthalamide)

The pyrolysis behaviour of Nomex, poly(m-phenylene isophthalamide) fibres under argon has been investigated up to a temperature of 1173 K with different methods to get direct information on the progressive changes taking place in the solid material and its carbon fibre residues. The main stages of the pyrolytic degradation of the fibres were determined by thermal analysis (TG and DTA) and their chemical and morphological evolution through the different steps was subsequently followed by Fourier transform infrared spectroscopy (FTIR) and atomic force microscopy (AFM) measurements, respectively, on samples treated to various temperatures. This revised version was published online in July 2006 with corrections to the Cover Date.     

A universal temperature controlled membrane interface for the analysis of volatile and semi-volatile organic compounds

A universal temperature controlled membrane interface (TCMI) has been constructed for hollow-fibre membranes. The membrane temperature is controllable in the range -70 to 250 degrees C using an electric heater and a flow of cooled nitrogen or helium gas. Volatile and semi-volatile organic compounds may be detected either by continuous diffusion across the membrane or by in-membrane pre-concentration followed by thermal desorption into the detector. The TCMI interface is demonstrated in combination with mass spectrometry and GC-MS, for the determination of VOCs and SVOCs in aqueous and air samples and for the on-line monitoring of a bioreactor.     

Color Displays with Gel-Glass Dispersed Liquid Crystals

Liquid crystal microdroplets trapped into silica gel-glasses by sol-gel processes may be used for display applications. Gel-glass dispersed liquid crystals (GDLC) are switched between opaque and transparent states by applying external AC-voltage signals; no polarizers are required. The feasibility of applying these materials to colored displays has been explored. A comparative study of different dyes for GDLC color displays, which were either embedded in the sol-gel matrix or dissolved in the liquid crystal microdroplets is presented.