Operational Properties of Two Integral Transforms of Fourier Type and their Convolutions

In this paper we present the operational properties of two integral transforms of Fourier type, provide the formulation of convolutions, and obtain eight new convolutions for those transforms. Moreover, we consider applications such as the construction of normed ring structures on L₁(\mathbbR)L_{1}({\mathbb{R}}), further applications to linear partial differential equations and an integral equation with a mixed Toeplitz-Hankel kernel.     

Measurements of anomalous dispersion in rayleigh scattering of characteristic X-ray fluorescence

Summary When using characteristic fluorescence X-rays or γ-rays of energy under 100 keV to study the Rayleigh scattering of photons from atoms the effect of anomalous dispersion is not in general negligible. On the contrary, it may cause the atomic cross-section values to vary with respect to the tabulated values—usually calculated in nonresonant approximation—of an order of magnitude in the most critical cases. In this work we present experimental results of Rayleigh scattering where this effect is well evident. We used as sources of excitation a radioisotope (²⁴¹Am,E _γ 59.6 keV) and a X-ray tube with a series of different secondary anodes and solid-state detectors to detect the scattered radiation. We reviewed the atomic form factor formalism which describes the phenomenon in a nonrelativistic treatment and we show its strict analogy with QEDS-matrix theory. We obtained numerical values for the cross-sections by using the tabulated values of the photoelectric cross-sections and we made a comparison with the experimental values. The error of the measurements (∼3%) derives from the superposition of the Rayleigh scattering with the characteristic X-ray fluorescence lines. Within the error limits the agreement with the values from the form factor approximation is very satisfactory.

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Riassunto Quando si utilizza la radiazione X di fluorescenza caratteristica o la radiazione γ di energia minore di 100 keV per studiare la diffusione elastica da parte degli atomi (diffusione di Rayleigh), l'effetto della diffusione anomala non è in generale trascurabile. Al contrario, essa può causare variazioni anche di un ordine di grandezza dei valori delle sezioni d'urto atomiche rispetto ai valori tabulati che sono usualmente calcolati nell'approssimazione non risonante. In questo lavoro si presentano i risultati sperimentali di alcune misure di diffusione di Rayleigh nei quali questo effetto è ben evidente. Come sorgenti di radiazione sono stati utilizzati un isotopo radioattivo (²⁴¹Am,E _γ=59.6 keV) e una serie di anodi secondari associati a un tubo X. Per la rivelazione della radiazione X sono stati utilizzati rivelatori a stato solido. Si è eseguita una revisione del formalismo dei fattori di forma atomici per la descrizione del fenomeno in una trattazione non relativistica e si mostra la stretta analogia con la teoria della matriceS dell'elettrodinamica quantistica. Si sono ottenuti i risultati numerici per le sezioni d'urto di diffusione elastica utilizzando i valori tabulati per le sezioni d'urto fotoelettriche e si sono confrontati con i valori ottenuti sperimentalmente. L'errore delle misure (∼3%) deriva dalla sovrapposizione della diffusione di Rayleigh con le righe di fluorescenza caratteristica. Entro questi limiti di errore l'accordo con i valori ricavati nell'approssimazione dei fattori di forma è molto soddisfacente.

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Резюме При использовании характеристической рентгеновской или γ-лучевой флуоресценции с энергией до 100 кэВ для исследования рэлеевского рассеяния фотонов на атомах, влияние аномальной дисперсии не является в общем случае пренебрежимо малым. Наоборот, эффект аномальной дисперсии может изменить значения атомных поперечных сечений по сравнению с табулированными значениями, обычно вычисляемыми в нерезонансном приближении, в наиболее критических случаях на порядок величины. В этой работе приводятся резулятаты для рэлеевского рассеяния, где эффект аномальной дисперсии является существенным. Мы используем в качестве источников возбуждения радиоизотоп (²⁴¹Am,E _γ=59.6 кэВ) и рентгеновскую трубку с различными вторичными анодами и твердотельные детекторы для регистрации рассеянного излучения. Мы используем формализм атомного форм-фактора, который описывает явление в нерелятивистском приближении. Мы отмечаем точную аналогию с теориейS-матрицы в квантовой электродинамике. Получаются численные значения для поперечных сечений, используя табулированные величины для фотоэлектрических поперечных сечений. Проводится сравнение полученных значений с экспериментальными данными. Погрешность измерений (∼3%) определяется из суперпозиции рэлеевского рассеяния с линиями характеристической рентгеновской Флуоресценции. В пределах погрешностей получается удовлетворительное согласие с результатами, полученными из приближения атомного форм-фактора.

     

The subgroups of the special linear group over a skew field that contain the group of diagonal matrices

For any (noncommutative) skew field T, the lattice of subgroups of the special linear group Λ=SL(n,T) that contain the subgroup Δ=SD(n,T) of diagonal matrices (with Dieudonné determinants equal to 1) is studied. It is established that for any subgroup H, Δ≤H≤Λ, there exists a uniquely determined unital net σ such that Λ(σ)≤H≤N(σ), where Λ(σ) is the net subgroup associated with the net σ and N(σ) is its normalizer in Λ. Bibliography: 11 titles. Published inZapiski Nauchnykh Seminarov POMI, Vol. 211, 1994, pp. 91–103. Translated by Bui Xuan Hai.     

Crossed products of Hilbert -modules

We define the notion of crossed products of Hilbert -modules by regular multiplicative unitaries, which is a generalization of the notion of crossed products of -algebras. Crossed products of Hilbert -modules arise naturally as imprimitivity bimodules for the crossed products of Morita equivalent -algebras.

     

Mercurophilic interaction in novel polynuclear Hg(II)-2-aminoethanethiolates

The reaction of 2-aminoethanethiol hydrochloride with Hg(2)Cl(2) in water yielded elemental mercury and one-dimensional polynuclear compounds [{Hg(3)Cl(5)(SCH(2)CH(2)NH(3))(3)}Cl](n) and [HgCl(SCH(2)CH(2)NH(2))(H(2)O)(2)](n) (2). The coordination environment around Hg in 1 and 2 is quite variable despite similar reaction conditions. The formation of a five-membered S/N chelate in 2 can be attributed to the use of base to produce a neutral ligand. Three independent types of Hg atoms, both three- and four-coordinate are observed in 1, whereas in 2, the Hg atom is tetracoordinate with S, N and Cl atoms in the primary coordination sphere. Despite distinct structural chemistry, the coordination environments in 1 and 2 are fairly similar with repeating units connected with bridged thiolate S atoms in addition to a terminal Cl attached to Hg. Intermolecular hydrogen-bonding involving amine protons, Cl and water molecules are responsible for a three-dimensional network in both 1 and 2. A short Hg...Hg distance of 3.564 A, indicates the presence of a mercurophilic interaction in 1. The compounds have been characterized by (1)H and (13)C NMR, UV-Vis, FT-IR, Raman, mass spectrometry, TGA and single X-ray crystallography.     

Influence of low energy ions in the degradation of polyethylene by partial discharges

An ion gun has been built to study the degradation of polyethylene by O⁺, A⁺, Ne⁺ and He⁺. Films, degraded under conditions of 200–2000 eV impinging energy, are examined with regard to surface changes and infra-red spectrum. Proportionality between the ion mass and the rate of degradation is found. Comparison with partial discharges shows similar deterioration but only as regards qualitative effects. Hypotheses are advanced to explain the mechanical degradation of the insulating material by partial discharges.     

Natural radionuclides and assessment of radiological hazards in different geological formations in Khammouan province,Laos

Journal of Radioanalytical and Nuclear Chemistry - The 226Ra, 232Th (228Ra), 40K activity concentrations in soil distributed in 67 points belonging to different geological formations in Khammouan,...     

Polysaccharide- and β-Cyclodextrin-Based Chiral Selectors for Enantiomer Resolution: Recent Developments and Applications

Polysaccharides, oligosaccharides, and their derivatives, particularly of amylose, cellulose, chitosan, and β-cyclodextrin, are well-known chiral selectors (CSs) of chiral stationary phases (CSPs) in chromatography, because they can separate a wide range of enantiomers. Typically, such CSPs are prepared by physically coating, or chemically immobilizing the polysaccharide and β-cyclodextrin derivatives onto inert silica gel carriers as chromatographic support. Over the past few years, new chiral selectors have been introduced, and progressive methods to prepare CSPs have been exploited. Also, chiral recognition mechanisms, which play a crucial role in the investigation of chiral separations, have been better elucidated. Further insights into the broad functional performance of commercially available chiral column materials and/or the respective newly developed chiral phase materials on enantiomeric separation (ES) have been gained. This review summarizes the recent developments in CSs, CSP preparation, chiral recognition mechanisms, and enantiomeric separation methods, based on polysaccharides and β-cyclodextrins as CSs, with a focus on the years 2019–2020 of this rapidly developing field.     

Microalgae and bioremediation of domestic wastewater

Domestic wastewaters are produced in huge volumes and abundant with carbon, nitrogen and phosphorous, which are a promising source of nutrients for production of microalgae. Microalgae-based bioremediation of domestic wastewater offers various advantages over traditional treatment approaches because the process consumes CO₂, completely removes nitrogen and phosphorous for production of green biomass and oxygen. Moreover, the abundance of biochemical compositions (e.g., lipids, proteins, carbohydrates, bioactive compounds) of microalgae biomass is superior to terrestrial plant biomass in refining to multi-products having variety of commercial values. In this review, the most dominant microalgae used for simultaneous removal of pollutants and production of biomass and metabolites from domestic wastewater are presented. Biorefinery of microalgae biomass produced from domestic wastewater for production of multiple products is also explored. Finally, challenges and perspectives of successful microalgae-based bioremediation of domestic wastewater toward the biorefinery are briefly discussed.     

Imaging of small molecules in tissue sections with a new intermediate-pressure MALDI linear ion trap mass spectrometer

We describe a new intermediate-pressure MALDI linear ion trap mass spectrometer and its capabilities for imaging mass spectrometry. The instrument design is described and is characterized in terms of four performance issues (1) MALDI performance at intermediate pressure; (2) analysis of samples on non-conductive and conductive glass slides; (3) critical importance of tandem mass spectrometry (both MS² and MS³) for identification of analyte species and imaging of isobaric species; (4) capability for repeated analysis of the same tissue section. Application of the new instrument to imaging phospholipids in rat brain sections is described in detail.