Stable solutions of a system of two connected Chua cells

We investigate a nonlinear chain of two Chua oscillators and its stable solutions. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 11, pp. 1567–1569, November, 1998.     

Laws of Influence of Structural Characteristics on the Strength and Crack Resistance of Aging Metallic Materials

The structural characteristics (the volume fraction, size, and shape of and the distance among hardening-phase particles) of aging alloys and steels, which define the behavior of the critical stress intensity factor during thermal hardening, are determined using the structural-mechanical approach we have developed. It is experimentally demonstrated for maraging steels that our approach is capable of proving the correlations of strength, plasticity, and crack- resistance with the structural characteristics, which were varied by changing the chemical composition of steel and thermokinetic aging conditions__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 94–101, January 2005.     

On self-adjoint operators generated by nonhomogeneous elliptic problems with discontinuous boundary conditions and conjugation conditions

We construct and study self-adjoint operators corresponding to problems mentioned in the title. We describe a correlation between domains of definition of fractional powers of these operators and Sobolev spaces. We state new results on the solvability of several problems for nonlinear parabolic equations which have not yet been studied.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 3, pp. 374–381, March, 1991.     

A one-dimensional Schrödinger operator with point interactions on Sobolev spaces

A one-dimensional Schrödinger operator with point interactions on Sobolev spaces is studied on the basis of the extension theory of nondensely defined operators.     

Soliton attraction law

Soliton coordinates are determined for the Korteweg — de Vries equation. In this case, the center of mass of solitons moves uniformly. The two-soliton attraction law is established.Published in Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 5, pp. 686–688, May, 1995.The principal results of this paper were presented at the Congress of Mathematical Physics, July 1994 [2].     

Structural approach to enhance the fracture resistance of high-strength metallic materials

The paper proposes an approach to form (by special heat treatment) a structure and phase composition of martensitic steel that would enhance its ductility in the high-strength state. A correlation is experimentally established between the stability of fracture resistance and ductility in linear and plane stress states. The behavior of the scatterband of the ultimate strength with increase in the degree of ductility is analyzed. The possibility of predicting the ultimate strength from the lower edge of its scatterband is demonstrated with an example of a circular cylindrical shell __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 8, pp. 68–78, August 2006.     

Thermal oxidative destruction of complexes of heterocyclic N-oxides with Zn(II)tetra-phenylporphyrin

Thermogravimetry, differential thermal analysis and differential scanning calorimetry were applied for investigation of molecular complexes of heterocyclic N-oxide with zinc(II)tetraphenylporphyrin. The kinetic characteristics of the process of the thermal oxidative destruction for individual compounds and their molecular complexes have been calculated. The obtained results indicate that the complex formation of ZnTPhP with heteroaromatic N-oxides leads to an increase of the thermal stability both the metalloporphyrin and the ligands. It has been shown that the stability of the molecular complexes of ZnTPhP with heteroaromatic N-oxides depends on basicity of the coordinated ligand.     

Molecular complexes of 4-nitropyridine and 4-nitroquinoline <Emphasis Type="Italic">N</Emphasis>-oxides with boron trifluoride and hydrogen chloride as intermediates in S<Subscript>N</Subscript>Ar reactions

Complexation of 4-nitropyridine N-oxides with ν- (BF₃, HCl) and π-acceptors (tetracyanoethylene, chloranil, 2,3-dichloro-5,6-dicyano-1,4-benzoquinone, 7,7,8,8-tetracyanoquinodimethane) activates the nitro group to nucleophilic replacement by chlorine. Adducts formed by 4-nitropyridine and 4-nitroquinoline N-oxides with boron trifluoride and hydrogen chloride were studied by IR spectroscopy. It was shown that these complexes belong to the n,ν type and that the donor-acceptor interaction therein involves the oxygen atom of the N-oxide group.     

X-ray crystal structure and magnetic and photophysical properties of novel copper(II) N-oxide adduct [(4-MPyO)2(CuCl2)2(H2O)(C2H5OH)] (4-MPyO = 4-(4-methoxystyryl)pyridine N-oxide)

A new mixed adduct, (4-MPyO)2(CuCl2)2(H2O)(C2H5OH) [where 4-MPyO is the 4-(4-methoxystyryl)pyridine N-oxide], was obtained for the first time. It has been characterized by X-ray studies, IR, electronic absorption, and emission spectra, lifetime measurements, and variable-temperature magnetic susceptibility measurements in the range 80-300 K. The single-crystal X-ray diffraction shows that the geometry around both of the copper(II) ions can be described as a tetragonal pyramid with a trapezoidal base at the corners of which are two oxygen atoms of N-oxide and two chlorine atoms. The oxygen atoms of either water or ethanol are at the apex of the pyramid. Besides that, two molecules of the adduct form a double-hydrogen-bonded superdimer in which they are connected to each other through hydrogen bonds of the O-H...Cl type as formed between the chlorine atoms and ethanol molecule (Cl...O 3.22 A). The copper(II) atoms are antiferromagnetically coupled within a dimeric unit, and a singlet-triplet separation of 2 J value (1100 cm(-1)) is greater than the value expected from Hatfield's rule for the bridging angles Cu-O-Cu equal 108.9 degrees and 110.2 degrees . By means of the PM3-calculated values of vertical excitation energies, the ligand-to-metal charge-transfer (LMCT) and the metal-to-ligand charge-transfer transitions in the unresolved experimental absorption spectra of I have been revealed. From the large Stokes shift value of emission spectra in solvents of different polarity (more than 6500 cm(-1) in acetonitrile), the charge-transfer (CT) nature of the emissive (LMCT) state of I has been concluded. Biexponential decay of the excited complex in acetonitrile and frozen propanol suggests that the two different CT conformers (0.8, 4.12 ns and 1.99, 15.2 ns, respectively) are present in the excited state in solution while only one CT form is indicated by a monoexponential decay (9.0 micros) in the solid.