Covering the sphere by equal zones

A zone of half-width w on the unit sphere S² in Euclidean 3-space is the parallel domain of radius w of a great circle. L. Fejes Tóth raised the following question in [6]: what is the minimal w_n such that one can cover S² with n zones of half-width w_n? This question can be considered as a spherical relative of the famous plank problem of Tarski. We prove lower bounds for the minimum half-width w_n for all n ≧ 5.     

On the angle sum of lines

What is the maximum of the sum of the pairwise (non-obtuse) angles formed by n lines in the Euclidean 3-space? This question was posed by Fejes Tóth in (Acta Math Acad Sci Hung 10:13–19, 1959). Fejes Tóth solved the problem for \({n \leq 6}\), and proved the asymptotic upper bound \({n^{2} \pi /5}\) as \({n \to \infty}\). He conjectured that the maximum is asymptotically equal to \({n^{2} \pi /6}\) as \({n \to \infty}\). The main result of this paper is an upper bound on the sum of the angles of n lines in the Euclidean 3-space that is asymptotically equal to \({3n^{2} \pi /16}\) as \({n \to \infty}\).     

An expeditious synthesis for γ-carboline analogue 4-aryl-1,3-thiazino[6,5-b]indole derivatives via the trifluoromethanesulfonic acid-promoted isomerization of 3-amidomethylthioindole intermediates to 2-indolyl sulfides

A highly efficient trifluoromethanesulfonic acid-mediated rearrangement of the benzoylaminomethylthio group of 3-benzoylaminomethylthioindoles (7a-e) to position 2 of the indole ring was developed. Thus, 2-benzoylaminomethylthioindoles (9a-e) were obtained in good yields and were involved as key intermediates in the synthesis of the new γ-carboline analogue ring system: 2,9-dihydro-4-aryl-1,3-thiazino[6,5-b]indole derivatives (11a-e). The target thiazinoindoles (11a-e) were prepared via 2-thiobenzoylaminomethylindoles (10a-e) in modified Bischler-Napieralski reactions.     

Development of a liquid chromatography/electrospray selected reaction monitoring method for the determination of organoarsenic species in marine and freshwater samples

Cation- and anion-exchange high-performance liquid chromatography/electrospray selected reaction monitoring (HPLC/ES-SRM) methods were developed for the determination of 15 organoarsenic compounds in marine and freshwater samples. The results demonstrate that the developed HPLC/ES-SRM methods are powerful approaches for the identification of organoarsenic species in crude sample extracts. The detection limits, linearity as well as reproducibility for most of the species are comparable or even better than those measured by the HPLC/inductively coupled plasma mass spectrometry (ICPMS) technique. The qualitative analysis of the extracts shows that the developed methods allow for the identification of arsenicals which were not detectable by ICPMS.It was also demonstrated that the signal suppression caused by matrix effects means a significant limitation in the quantification of arsenicals by ES-SRM detection. This drawback is manifested especially in the case of the slightly retained species. The three sample-cleanup chromatographic methods including off-line size-exclusion, on-line reversed-phase and on-line oppositely charged ion-exchange approaches proved to be ineffective for separation of the signal-suppressive matrix from the analytes. The standard addition calibration seems to be a suitable solution for such problems.     

New isomers of 4,1-benzothiazepines. The first evidence for the desmotropy of seven-membered heterocycles

A novel procedure was developed for the preparation of 2,3-disubstituted 4,1-benzothiazepines, via the ring transformation of (2R^∗,2aS^∗)-2-chloro-2a-phenyl-2,2a-dihydro-2H,4H-azeto[1,2-a][3,1]benzothiazin-1-one (1) with sodium ethoxide in ethanol. The tautomeric products (R^∗)-3-ethoxycarbonyl-2-phenyl-3,5-dihydro-4,1-benzothiazepine (4) and 3-ethoxycarbonyl-2-phenyl-1,5-dihydro-4,1-benzothiazepine (5) exhibit the rare phenomenon of desmotropy of the condensed seven-membered heterocycles. Surprisingly, these desmotropes could be separated by column chromatography. The products are unexpectedly stable in solution and their structures were proved by means of NMR and mass spectrometry.     

In vivo XANES measuring technique for studying the arsenic uptake in cucumber plants

New in vivo X‐ray absorption near edge structure measuring technique was developed by using liquid nitrogen steam flow for cooling cucumber samples keeping them under cryogenic conditions during the measurement in order to preserve the original chemical states of arsenic species in the hypocotyl. The aim of this study was to determine the As oxidation state in order to identify the possible metabolic processes during the nutrient uptake in cucumber (Cucumis sativus L. cv Joker) as model plant. The plants were grown in Hoagland's modified nutrient solution. The ratio of the quantity of two As species was determined in the hypocotyls of the cucumber samples: arsenite, As(III) and arsenate, As(V). The ultimate biological goal of the in vivo experiments was to investigate the applicability of the X‐ray absorption near edge structure technique under cryogenic conditions and to specify the resistance level of the plants to arsenic toxicity when different chemical forms of iron, FeCl₃ and Fe‐ascorbate were supplied in the nutrient solution. We have examined the influence of the intense synchrotron radiation beam on the transformation of the oxidation number of both As species when the effect of the reactive oxygen forms was eliminated by the presence of ascorbate. Copyright © 2016 John Wiley & Sons, Ltd.     

Novel indole syntheses by ring transformation of β-lactam-condensed 1,3-benzothiazines into indolo[2,3-b][1,4]benzothiazepines and indolo[3,2-c]isoquinolines

ortho-Nitrophenyl-substituted condensed 1,3-benzothiazines proved to be a useful core unit in indole syntheses under non-reductive conditions. Thus, the treatment of ortho-nitro-2-aryl-2a-chloro-4H-azeto[2,1-b][1,3]benzothiazin-1-ones with sodium methoxide in methanol provided indolo-1,4-benzothiazepines via a novel rearrangement. Through the sulfur extrusion reaction of indolo[2,3-b][1,4]benzothiazepines, further alkaloid-type indole derivatives, indolo[3,2-c]isoquinolines, were obtained. The structures of the new ring systems were determined by means of NMR spectroscopy.