On the Interaction of Two Finite-Dimensional Quantum Systems

Interaction of quantum system S ^a described by the generalised × eigenvalue equation A| _s =E _s S ^a | _s (s=1,...,) with quantum system S ^b described by the generalised n×n eigenvalue equation B| _i = _i S ^b | _i (i=1,...,n) is considered. With the system S ^a is associated -dimensional space X ^a and with the system S ^b is associated an n-dimensional space X _n ^b that is orthogonal to X ^a . Combined system S is described by the generalised (+n)×(+n) eigenvalue equation [A+B+V]| _k = _k [S ^a +S ^b +P]| _k (k=1,...,n+) where operators V and P represent interaction between those two systems. All operators are Hermitian, while operators S ^a ,S ^b and S=S ^a +S ^b +P are, in addition, positive definite. It is shown that each eigenvalue _{k i} of the combined system is the eigenvalue of the × eigenvalue equation . Operator in this equation is expressed in terms of the eigenvalues _i of the system S ^b and in terms of matrix elements _s |V| _i and _s |P| _i where vectors | _s form a base in X ^a . Eigenstate | _k ^a of this equation is the projection of the eigenstate | _k of the combined system on the space X ^a . Projection | _k ^b of | _k on the space X _n ^b is given by | _k ^b =( _k S ^b –B)^–1(V– _k P})| _k ^a where ( _k S ^b –B)^–1 is inverse of ( _k S ^b –B) in X _n ^b . Hence, if the solution to the system S ^b is known, one can obtain all eigenvalues _{k i} } and all the corresponding eigenstates | _k of the combined system as a solution of the above × eigenvalue equation that refers to the system S ^a alone. Slightly more complicated expressions are obtained for the eigenvalues _{k i} } and the corresponding eigenstates, provided such eigenvalues and eigenstates exist.     

Threshold electron impact excitation of Cl2

A high resolution electron impact threshold spectroscopy technique was used to examine the excitation of Cl₂ in the 2–14 eV region. This study complements previous photon absorption and emission measurements, because it is capable of detecting transitions which are optically forbidden. In the region up to 7.5 eV, broad dissociative structures are correlated with optically active valence states, although relative intensities in the threshold spectrum differ considerably and indicate a substantial contribution from the optically forbidden transitions. At 7.46 eV a series of 5 equidistant sharp peaks is detected and interpreted as arising from the² π _g Feshbach resonance, which differs from the ground state positive ion Cl ₂ ⁺ by a pair of Rydberg electrons: (4sσ)². The decay channels responsible for the appearance of the resonance in a threshold spectrum are discussed and it is suggested that they include several valence states of the (2431) and (2341) configurations, whose potential energy curves cross the Cl ₂ ^? ,²π_g curve in the region of energy at which the resonance state is formed. At higher incident electron energies and up to ionisation, Rydberg states predominate, starting with (2430) 4s^3,1 π _g states detected for the first time. The absence of broad peaks above 8 eV and the irregular appearance of Rydberg bands is consistent with the strong Rydberg-valence configuration mixing proposed by Peyerimhoff and Buenker. Where our resolution permits comparison, good general agreement is found with recent synchrotron radiation absorption measurements of optically allowed transitions.     

Experimental and computational studies of trialkylaluminum and alkylaluminum chloride reactions with silica

Reactions of trimethylaluminum, triethylaluminum, and diethylaluminum chloride and ethylaluminum dichloride with silica gel have been studied experimentally by infrared spectroscopy and elemental analysis. The silica gel was subjected to different pretreatments to alter surface functionalities prior to reaction. In all cases the extent of surface modification reaction follows the trend unmodified > 600 degrees C pretreated > hexamethyldisilazane (HMDZ) pretreated > 600 degrees C/HMDZ pretreated. All of the aluminum compounds studied completely react non-hydrogen-bonded silanols, while also reacting with hydrogen-bonded silanols and siloxanes. Primarily monomeric surface species result from the surface modification reaction. Ethylaluminum chlorides preferentially react with silanols through cleavage of the Al-C bond rather than the Al-Cl bond. Singly bonded Si(s)-O-AlCl(2) surface species are readily synthesized by reaction of ethylaluminum dichloride with HMDZ-pretreated silica gel. Bridged bonded (Si(s)-O)(2)-AlCl surface species are readily synthesized by reaction of diethylaluminum chloride with HMDZ-pretreated silica gel. Computational ab initio studies of the cluster Si(4)O(6)(OH)(4) as a model to study the reaction of monomeric and dimeric methylaluminum dichloride with a silica silanol are also described. Comparison of the potential energy surface (PES) of monomer and dimer indicates that the energetics favor monomer reaction, consistent with experimental results. The energy cost in the dimer reaction is primarily from cleavage of a bridged Al-Cl bond upon adsorption. This does not occur when the monomer adsorbs. A comparison of the PES for the two reaction pathways resulting from cleavage of either an Al-Cl or Al-C bond indicates that while the former reaction is slightly kinetically favored (E(a) = 23.1 kJ/mol for Al-Cl bond cleavage versus E(a) = 31.1 kJ/mol for Al-C bond cleavage), the latter is strongly thermodynamically favored with an overall free energy difference between the two reaction pathways of 135 kJ/mol favorable to Al-C bond cleavage. These reactions are thermodynamically controlled.     

Analytische Bestimmung von Niob,Tantal, Phosphor,Chlorid und 2,2-Dipyridyl in einigen Komplexverbindungen

Zusammenfassung Die analytische Bestimmung der Metalle, des Dipyridyls und der Chloride in Oxo-chloro-alkoxo-dipyridyl-Komplexverbindungen des Niobs und Tantals wurde beschrieben. Eine modifizierte Methode der Dipyridylanalyse, wie auch der Chloridbestimmung in Gegenwart von Dipyridyl wurde angegeben. Die radiometrische Metallbestimmung in Extraktionsverbindungen von Niob und Tantal mit Di-oktyl-methylenbis-phosphonsäure wurde dargelegt.

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Summary The analytical determination of metals, dipyridyl and chlorides in oxochloro-alkoxo-dipyridyl complex compounds of niobium and tantalum is described. A modified procedure of the dipyridyl analysis and also of the determination of chloride in the presence of dipyridyl is given. The radiometric determination of the metals in extraction compounds of niobium and tantalum with di-octyl-methylene-bis-phosphonic acid is discussed.

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Résumé On décrit le dosage des métaux, du dipyridyle et des chlorures dans les composés complexes oxo, chloro, alcoxo, dipyridyle, du niobium et du tantale. On indique une méthode modifiée pour le dosage de dipyridyle ainsi que pour la détermination des chlorures, en présence de dipyridyle. On décrit le dosage radiométrique des métaux dans les produits d'extraction du niobium et du tantale par l'acide di-octyl-méthylène-bis-phosphonique.

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Vorgetragen beim Symposium für analytische Chemie in Graz, 29. September bis 1. Oktober 1965.     

Kinetic determination of ultramicro amounts of copper

A new catalytic reaction is proposed and a kinetic method developed for the determination of ultramicro amounts of Cu(II) on the basis of its catalytic activity in oxidation of the 2-thiosemicarbazone of sodium 1,2-naphthoquinone-4-sulphonate by hydrogen peroxide in the presence of ascorbic acid. Under optimal conditions the sensitivity of the method is 0.25 ng/ml. The relative error is 4.8-18.2% for the concentration range 5-0.8 ng/ml. Most foreign ions do not change the rate of the catalysed reaction. Co(2+) and I(-) catalyse the reaction, Ni(2+) extensively inhibits it, and in the presence of EDTA only the uncatalysed reaction takes place.     

Eine kennzeichnende Eigenschaft der Zykel der Galileischen Ebene

Ohne Zusammenfassung     

Efficacy of Biologically Active Food Supplements for People with Atherosclerotic Vascular Changes

The current paper deals with the development of a new biologically active food supplement (BAFS) aimed at treating atherosclerosis. Since atherosclerosis is considered to be a disease of aging, the composition of the supplement includes such essential minerals as magnesium and potassium, which are commonly used to prevent atherosclerosis, as well as vitamins C, E and the B-group vitamins in order to address the needs of the elderly. The authors outline the supplement-manufacturing technology and discuss the clinical trial undertaken by patients, aged about 60 years, with peripheral atherosclerosis. The research methodology focuses on studying the effectiveness of the developed supplement by assessing the influence of the active ingredients on treating metabolic disorders. To establish the efficacy of the supplement, blood tests, ultrasound and physical examinations were applied. The combination therapy resulted in improved metabolism and an overall better performance of the cardiovascular system; therefore, the BASF can be recommended as part of combination therapy to prevent and treat atherosclerotic and age-related changes in blood vessels.     

Synthesis of Cobalt Bis(Dicarbollide)—Curcumin Conjugates for Potential Use in Boron Neutron Capture Therapy

A series of novel cobalt bis(dicarbollide)—curcumin conjugates were synthesized. Two conjugates were obtained through the nucleophilic ring-opening reaction of the 1,4-dioxane and tetrahydropyran derivatives of cobalt bis(dicarbollide) with the OH group of curcumin, and using two equiv. of the oxonium derivatives, two other conjugates containing two cobalt bis(dicarbollide) units per molecule were obtained. In contrast to curcumin, the conjugates obtained were found to be non-cytotoxic against both tumor and normal cell lines. The analysis of the intracellular accumulation of the conjugates by flow cytometry showed that all cobalt bis(dicarbollide)—curcumin conjugates entered HCT116 colorectal carcinoma cells in a time-dependent manner. New non-cytotoxic conjugates contain a large amount of boron atoms in the biomolecule and can potentially be used for further biological research into boron neutron capture therapy (BNCT).     

Analysis of Plant–Plant Interactions Reveals the Presence of Potent Antileukemic Compounds

A method to identify anticancer compounds in plants was proposed based on the hypothesis that these compounds are primarily present in plants to provide them with an ecological advantage over neighboring plants and other competitors. According to this view, identifying plants that contain compounds that inhibit or interfere with the development of other plant species may facilitate the discovery of novel anticancer agents. The method was developed and tested using Magnolia grandiflora, Gynoxys verrucosa, Picradeniopsis oppositifolia, and Hedyosmum racemosum, which are plant species known to possess compounds with cytotoxic activities. Plant extracts were screened for growth inhibitory activity, and then a thin-layer chromatography bioautography assay was conducted. This located the major antileukemic compounds 1, 2, 4, and 5 in the extracts. Once the active compounds were located, they were extracted and purified, and their structures were determined. The growth inhibitory activity of the purified compounds showed a significant correlation with their antileukemic activity. The proposed approach is rapid, inexpensive, and can easily be implemented in areas of the world with high biodiversity but with less access to advanced facilities and biological assays.     

Novel Inhibitors of 2′-O-Methyltransferase of the SARS-CoV-2 Coronavirus

The COVID-19 pandemic is still affecting many people worldwide and causing a heavy burden to global health. To eliminate the disease, SARS-CoV-2, the virus responsible for the pandemic, can be targeted in several ways. One of them is to inhibit the 2′-O-methyltransferase (nsp16) enzyme that is crucial for effective translation of viral RNA and virus replication. For methylation of substrates, nsp16 utilizes S-adenosyl methionine (SAM). Binding of a small molecule in the protein site where SAM binds can disrupt the synthesis of viral proteins and, as a result, the replication of the virus. Here, we performed high-throughput docking into the SAM-binding site of nsp16 for almost 40 thousand structures, prepared for compounds from three libraries: Enamine Coronavirus Library, Enamine Nucleoside Mimetics Library, and Chemdiv Nucleoside Analogue Library. For the top scoring ligands, semi-empirical quantum-chemical calculations were performed, to better estimate protein–ligand binding enthalpy. Relying upon the calculated binding energies and predicted docking poses, we selected 21 compounds for experimental testing.