On the basis property of a two-part trigonometric series

Conditions are presented under which two-part trigonometric systems arising in mixed type equations form a Riesz basis in the space of Lebesgue square integrable functions. For such systems, biorthogonal systems can be obtained in explicit form. As a result, an integral representation of the solution to the Frankl problem in a special domain can be found. The results are extended to two-part systems of broader functions.     

The completeness of the sines and cosines in the space of integrable functions

The paper addresses the completeness of sines and cosines with non-integer indices in the space of Lebesgue-integrable functions. The criteria for the variation from the integer value have been found such that sine and cosine systems are complete.     

TETRAPHOSPHORUS TRISULFIDE IN REACTIONS WITH THIOACETALS,AMINALS, SULFENAMIDES AND DISULFIDES. INFLUENCE OF AMINES AND BENZOYL PEROXIDE

Abstract

The reactions of tetraphosphorus trisulfide with thioacetals, aminals, sulfenamides and disulfides were studied. The reactions were found to give organothiophosphorus compounds and to be facilitated by organic amines and benzoyl peroxide.     

Interaction of PH3 with acetaldehyde in aqueous media and chemistry of [HO(Me)CH]4PCl

The known phosphonium chloride [HO(Me)CH]₄PCl was prepared at ambient conditions from PH₃ and acetaldehyde in aqueous HCl, and characterized by elemental analysis and ¹H and ³¹{¹H} NMR spectroscopy. Attempts to obtain the tertiary phosphine [HO(Me)CH]₃P via reaction of [HO(Me)CH]₄PCl with Na₂SO₃ or Et₃N in aqueous media under Ar revealed that [HO(Me)CH]₃P is unstable and equilibrates with the secondary phosphine [HO(Me)CH]₂PH and acetaldehyde. A 1:4 reaction of [HO(Me)CH]₄PCl with NaHSO₃ at room temperature under Ar affords first the oxide [HO(Me)CH]₂P(O)H and then the phosphinic acid [HO(Me)CH]₂P(O)OH. A 1:1 reaction of [HO(Me)CH]₄PCl with Na₂S₂O₃ affords the sulfide [HO(Me)CH]₃PS. ³¹{¹H} and ¹H NMR data for all the (α-hydroxyethyl)phosphorus species are reported for the first time.     

Synthesis,X‐ray Studies,and Catalytic Efficacy of a Novel Iron Complex Containing an N,O‐Type Bidentate Thiazoline Ligand

The reactions of FeCl₃ · 6H₂O and 2‐(2′‐hydroxyphenyl)‐2‐thiazoline as a bidentate O‐N donor thiazoline ligand (thoz) afford a five‐coordinate Fe^III complex [Fe(thoz)₂Cl] with a distorted square pyramidal configuration. Complex [Fe(thoz)₂Cl] was isolated as air‐stable crystalline solids and fully characterized, including by single‐crystal X‐ray structure analysis. Complex [Fe(thoz)₂Cl] shows very efficient reactivity in the oxidation of sulfides to their corresponding sulfoxides using urea hydrogen peroxide (UHP) as the oxidant at room temperature in air.     

A Regioselective Synthesis of Novel Functionalized Organochalcogen Compounds by Chalcogenocyclofunctionalization Reactions Based on Chalcogen Halides and Natural Products

The regioselective synthesis of novel functionalized condensed organochalcogen compounds by chalcogenocyclofunctionalization reactions based on chalcogen halides and the natural products thymol and carvacrol has been developed. The reactions of selenium dibromide with allyl thymol and allyl carvacrol proceeded in methylene chloride at room temperature in the presence of NaHCO₃ affording bis[(7-isopropyl-4-methyl-2,3-dihydro-1-benzofuran-2-yl)methyl] and bis[(4-isopropyl-7-methyl-2,3-dihydro-1-benzofuran-2-yl)methyl] selenides in 90–92% yield. Similar sulfides were obtained in 70–72% yields by the reaction of sulfur dichloride in chloroform under reflux. Trihalotellanes containing the same organic moieties were synthesized from allyl thymol, allyl carvacrol and tellurium tetrachloride or tetrabromide in quantitative yields. Corresponding functionalized ditellurides were prepared in 91–92% yields by the reduction of the trichlorotellanes with sodium metabisulfite in two-phase solvent system. The comparison of reactivity of sulfur, selenium and tellurium halides in chalcogenocyclofunctionalization and distinguishing features of each reaction were discussed.     

Electrophysiological Activity and Survival Rate of Rats Nervous Tissue Cells Depends on D/H Isotopic Composition of Medium

The deuterium content modification in an organism has a neuroprotective effect during the hypoxia model, affecting anxiety, memory and stress resistance. The aim of this work was to elucidate the possible mechanisms of the medium D/H composition modification on nerve cells. We studied the effect of an incubation medium with a 50 ppm deuterium content compared to a medium with 150 ppm on: (1) the activity of Wistar rats’ hippocampus CA1 field neurons, (2) the level of cultured cerebellar neuron death during glucose deprivation and temperature stress, (3) mitochondrial membrane potential (MMP) and the generation of reactive oxygen species in cultures of cerebellar neurons. The results of the analysis showed that the incubation of hippocampal sections in a medium with a 50 ppm deuterium reduced the amplitude of the pop-spike. The restoration of neuron activity was observed when sections were returned to the incubation medium with a 150 ppm deuterium content. An environment with a 50 ppm deuterium did not significantly affect the level of reactive oxygen species in neuron cultures, while MMP decreased by 16–20%. In experiments with glucose deprivation and temperature stress, the medium with 50 ppm increased the death of neurons. Thus, a short exposure of nerve cells in the medium with 50 ppm deuterium acts as an additional stressful factor, which is possibly associated with the violation of the cell energy balance. The decrease in the mitochondrial membrane potential, which is known to be associated with ATP synthesis, indicates that this effect may be associated with the cell energy imbalance. The decrease in the activity of the CA1 field hippocampal neurons may reflect reversible adaptive changes in the operation of fast-reacting ion channels.     

Features of an InAsSbP epilayer formation on an InAs support by metalorganic vapor phase epitaxy

Epitaxial layers in a system of InAs_1–x–ySb_yP_x solid solutions in the composition range of 0 < x < 0.72 were obtained on an InAs(001) substrate by metalorganic vapor phase epitaxy (MOVPE). The layer-by-layer analysis of obtained structures by secondary ion mass spectrometry showed a gradient change in the composition along the growth direction. A dramatic change in the composition at the layer/substrate heteroboundary was observed for the quaternary InAsSbP solid solutions due to the presence of radicals of arsenic compounds in the gas phase. Upon MOVPE deposition on the InAs substrate in a system of InAsSbP solid solutions, the decrease in the solid-phase content of arsenium by less than (1–x–y) < 0.3 resulted in a suppression of the deposited layer gradientness, as well as suppressed fluctuations in the composition in the initial transition layer.     

Conversion of ethanol into hydrocarbon components of fuels in the presence of Pd-Zn-containing catalysts

The features of ethanol conversion into hydrocarbons C₄-C₁₂ in the presence of the novel catalyst Pd-Zn/γ-alumina and pilot zeolite system Pd-Zn/MFI/γ-alumina were studied (MFI is high-siliceous zeolite with ZSM-5 type structure). The structure of active sites changes noticeably in the course of preliminary activation and catalytic reaction. High selectivity and stability of the zeolite-containing Pd-Zn catalyst in alcohol conversion into hydrocarbon components of fuels is related to the stable composition of the alloy that forms clusters PdZn. At the same time, the alumina-based catalyst loses stability due to zinc diffusion from the alloy into γ-Al₂O₃ to form the spinel structure.