On the solvability of boundary value problems for quasilinear ultraparabolic equations in some mathematical models of the dynamics of biological systems

Under consideration is the problem of modeling some population dynamics. Mathematically, it reduces to studying the solvability of a nonlocal boundary value problem for quasilinear ultraparabolic equations with astronomical time t and biological time (age) a. Some theorems of existence and uniqueness are proved for regular solutions to this problem.     

Heterospin biradicals based on new piperidineoxyl-substituted 3,6-di-<Emphasis Type="Italic">tert</Emphasis>-butyl-<Emphasis Type="Italic">o</Emphasis>-benzoquinone

A nucleophilic addition reaction of 4-hydroxy-2,2,6,6-tetramethylpiperidine-1-oxyl (OH-TEMPO) to 3,6-di-tert-butyl-o-benzoquinone was used to obtain a new sterically hindered o-benzoquinone (1) containing 2,2,6,6-tetramethylpiperidineoxyl functional group, which was characterized by IR spectroscopy, mass spectrometry, elemental analysis, and X-ray diffraction. A one-electron reduction of 1 with potassium and thallium is an efficient method for the generation of earlier unknown heterospin biradicals 5a and 5b, respectively, containing nitroxide and o-semiquinone radical centers. Analysis of the hyperfine structure of the ESR spectra of biradicals 5a and 5b in solution showed that they belong to the group of heterospin biradicals with strong (J >> a) and fast exchange interaction between the radical centers.     

Novel structurally characterized o-semiquinonato PCP-pincer nickel complexes

Structural study of dialkyl (PCP)-pincer o-semiquinonato nickel complexes indicated sloped relative positions of bi- and tri-dentate ligands. It became bright confirmation of propositions made on the base of their EPR spectra followed by molecular modelling.     

Solvability of the Inverse Problem of Finding Thermal Conductivity

We study the inverse problem of finding the coefficient of thermal conductivity of the heat equation (along with the solution). As the overdetermination condition we take the values of the solution at the final time. Existence of a regular solution is proven.     

Oxidation of aromatic compounds: XVI. Radical cations derived from acetylenic compounds with electron-withdrawing groups: Reactions and ESR parameters

One-electron oxidation of aryl-substituted acetylenes ArC≡CX where X is an electron-withdrawing group gives different products, depending on the X substituent. Acetylenic substrates with medium-strength electron-withdrawing substituents, X = CO₂R, COAr, COR, PO(OEt)₂, give rise to tetrasubstituted ethenes X(ArCO)C=C(COAr)X. Compounds with strong electron-withdrawing groups (X = COCF₃, COCO₂R, CN) are converted into furan derivatives. Probable mechanisms of transformations of ArC≡CX radical cations into the final products are discussed. Radical cations derived from disubstituted acetylenes were characterized by ESR spectroscopy.     

Boundary Problems for Parabolic Equations with Degenerate Boundary Condition of the Third Kind

Doklady Mathematics - The solvability of initial-boundary value problems for linear parabolic equations of the second order with a degenerate boundary value condition of the third kind is studied....