Limit correlation functions at zero for fixed trace random matrix ensembles

The limit as N → ∞ of the eigenvalue correlation function is studied in a neighborhood of zero for N × N Hermitian matrices chosen at random from the Hilbert-Schmidt sphere of an appropriate radius. Dyson’s famous sin π(t₁ − t₂)/π(t₁ − t₂)-kernel asymptotic is extended to this class of matrix ensembles. Bibliography: 9 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 341, 2007, pp. 68–80.     

The exterior magnetic field for the multilayer ellipsoidal model of the brain

The magnetic induction field in the exterior of an ellipsoidallyinhomogeneous, four-conducting-layer model of the human headis obtained analytically up to its quadrupole approximation.The interior ellipsoidal core represents the homogeneous brainwhile each one of the shells represents the cerebrospinal fluid,the skull and the scalp, all characterized by different conductivities.The inhomogeneities of these four domains, together with theanisotropy imposed by the use of the ellipsoidal geometry, providethe most realistic physical and geometrical model of the brainfor which an analytic solution of the biomagnetic forward problemis possible. It is shown that in contrast to the spherical model,where shells of different conductivity are magnetically invisible,the magnetic induction field in ellipsoidal geometry is stronglydependent on the conductivity supports. The fact that sphericalshells of different conductivity are invisible has enhancedthe common belief that the biomagnetic forward solution doesnot depend on the conductivity profiles. As we demonstrate inthe present work, this is not true. Hence, the proposed multilayeredellipsoidal model provides a qualitative improvement of therealistic interpretation of magnetoencephalography (MEG) measurements.We show that the presence of the shells of different conductivitycan be incorporated in the form of the dipole vector for thehomogeneous model. Numerical investigations show that the effectsof shell inhomogeneities are almost as sound as the level ofMEG measurements themselves. The degenerate cases, where eitherthe differences of the conductivities within the shells disappear,or the ellipsoidal geometry is reduced to the spherical one,are also considered.     

First example of the cascade acylation/IMDAV/ene reaction sequence,leading to N-arylbenzo[f]isoindole-4-carboxylic acids possessing anti-viral activity

The reaction between readily accessible N-aryl-3-phenylallylamines and maleic anhydride led to unexpected products – polysubstituted hydrogenated benzo[f]isoindole-4-carboxylic acids. This transformation proceeds through a previously unknown sequence of steps: N-acylation of the allylamine with maleic anhydride, intramolecular Diels-Alder reaction of the vinylarene in the intermediate N-maleamide, and Alder-ene reaction of the products of the previous two steps. Selected benzo[f]isoindoles displayed antiviral activity.     

Comparative Reactivity of Cyclocarbonate Groups of Oligomeric Triglycerides Based on Soybean Oil and Model Compounds in the Reactions of Nonisocyanate Urethane Formation

A comparative study of kinetic patterns has been carried out for the reaction of cyclocarbonate groups of oligomers and model compounds with n-butylamine in dimethylsulfoxide. The objects of study were ethylene carbonate, monofunctional 4-(2-ethylhexyloxymethyl) cyclocarbonate, trifunctional tricyclocarbonate of polyoxypropylene triol, and an oligomer based on soybean oil triglycerides with an average functionality of ~4.5. The most active compound is ethylene carbonate, whereas cyclocarbonate groups of the oligomer based on soybean oil triglycerides exhibit the lowest reactivity. All the reactions studied proceed via two parallel reaction pathways involving one and two amine molecules, respectively, and the second pathway contributes more to the observed rate of urethane formation. The dependence of the activation energy of aminolysis on the inductive effect of substituents in the model 4,5-substituted 1,3-dioxolane-2-ones has been established by DFT quantum chemical calculations.     

Synthesis of condensed pregnano[17,16-<Emphasis Type="Italic">d</Emphasis>]triazolines under high pressure

Condensed pregnano[17,16-d]triazolines were produced in 1,3-dipolar cycloaddition of 16-dehydropregnenolone acetate with organic azides at 10 kbar. The structure of the synthesized compounds was determined by using two-dimensional NMR spectroscopy (¹H—¹H COSY, NOESY, HSQC, and HMBC).     

Synthesis of [3H]-cycloalkanoprogesterones (pregna-d'-pentaranes) and study of their interaction with a progesterone receptor

In order to search target organs and to study the mechanism of the action of steroids with separated biological functions, tritium-labeled pregna-d'-pentaranes were synthesized by an original procedure, and their interaction with a progesterone receptor was investigated. The uterine progesterone receptor was shown to be the only specific binding protein for these compounds. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1532–1535, August, 1997.     

Kinetics of hydrolysis of five-membered <Emphasis Type="Italic">C</Emphasis>-nitroheterocycles: pyrazole,imidazole, 1,2,4-triazole,and isoxazole derivatives

Alkaline hydrolysis of mono-and dinitro derivatives of five-membered heterocycles, viz., pyrazole, imidazole, 1,2,4-triazole, and isoxazole, is accompanied by the elimination of the nitro group in the form of a nitrite anion. The hydrolysis kinetics was studied by the polarographic and photometric methods. The experimentally determined hydrolysis rate constants depend on the nature of the heterocycle. A possible mechanism for hydrolytic transformations of the compounds under study was proposed on the basis of the calculated thermodynamic parameters of the reaction (Δ G ^≠, ΔH ^≠, ΔS ^≠). Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2719–2725, December, 2005.