Solving the problem of contact equilibrium of a punch and an elastic body

The variational problem of contact equilibrium of a punch and an elastic body is considered. An equivalent formulation of the problem is given in variational inequality form. Existence and uniqueness of the solution is investigated in a particular case. A penalty method is proposed for approximate solution of the problem.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 56, pp. 97–103, 1985.     

ΓD‐convergence for a class of quasilinear elliptic equations in thin structures

We study the asymptotic behaviour of the solution of a stationary quasilinear elliptic problem posed in a domain Ω^(ε) of asymptotically degenerating measure, i.e. meas Ω^(ε) → 0 as ε → 0, where ε is the parameter that characterizes the scale of the microstructure. We obtain the convergence of the solution and the homogenized model of the problem is constructed using the notion of convergence in domains of degenerating measure. Proofs are given using the method of local characteristics of the medium Ω^(ε) associated with our problem in a variational form. Copyright © 2005 John Wiley & Sons, Ltd.     

Structure and properties of the Ti-Si-N nanocrystalline coatings synthesized in vacuum by the electroarc method

Phase composition, defect substructure, and mechanical properties of the Ti-Si-N coating deposited on metal and ceramic-metal substrates by electroarc sputtering of the Ti-Si composite cathode in an ionized nitrogen atmosphere are investigated by the methods of modern materials science. It is established that coatings so formed with a thickness of ∼1–3 μm are superhard (H_v ∼ 50 GPa), and have the nanocrystalline structure (with crystalline sizes D = 7 nm) based on titanium nitride δ-TiN. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 46–51, February, 2007.     

Mass-spectrometric study of 2- and 4-thiobarbituric acid derivatives

The mass spectra of 2- and 4-thiobarbituric acids and some of their close analogs at ionizing voltages of 70 and 14 eV are compared. Qualitative and quantitative differences in the behavior of these compounds under the influence of electron impact were established. It is shown that the position of the thione group in the ring and the tautomeric transformations have a substantial effect on the character of the fragmentation of the investigated compounds. The established fragmentation principles make it possible to distinguish the structural isomers in a series of 2- and 4-thiobarbituric acids from their mass spectra.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 4, pp. 529–535, April, 1976.     

Synthesis and regioselectivity of the [3,3]-sigmatropic rearrangement of substituted 2-allylthio- and 2-allylseleno-1,4-dihydropyridines

The reaction of 3-cyano-1,4-dihydropyridine-2-thiolates and the corresponding selenolates with allyl bromide gave 2-allylthio- and 2-allylseleno-3-cyano-1,4-dihydropyridines, which, upon heating in various solvents or in the solid state, undergo [3,3]-sigmatropic rearrangement to give 3-cyano-3-allyl-1,2,3,4-tetrahydropyridine-2-thiones and the corresponding selenones. The resultant pyridinethiones are alkylated by alkyl halides at the sulfur atom and are oxidized by iodine to give disulfides.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 8, pp. 1888–1895, August, 1991.     

ACID SODIUM SALT OF 1H-PYRAZOLE-3,4,5- TRICARBOXYLIC ACID: SYNTHESIS,CRYSTAL STRUCTURE AND FEATURES OF INTRAMOLECULAR BONDS

Journal of Structural Chemistry - The oxidation reaction of 3,3′,5,5′-tetramethyl-1H,1′H-4,4′-bipyrazole in the HNO3–Fe3+ system unexpectedly resulted in the formation...     

Membrane detection of nanogram amounts of formate dehydrogenase

A method for the detection of nanogram amounts of formate dehydrogenase on membranes was developed. The optimization of the method was carried out for determination of the best mediator concentration and tetranitrotetrazolium blue. It was found that 5-methyl-phenazil methosulfate is a more effective mediator than phenazine methosulfate. Different types of membranes were tested and it was shown that nitrocellulose membrane provides a low background and the highest sensitivity. Under optimal conditions the detection limit was 15 ng of the enzyme in the probe.     

Evidence for a magnetic collapse in the epsilon phase of solid oxygen

Solid oxygen is the only elementary molecular magnet. Under the very high pressure of 96 GPa oxygen transforms into a metal and a superconductor. Theory predicts a nonmagnetic state occurring before the transition into the superconducting xi phase. Nevertheless, until now there was no direct evidence of a magnetic collapse in high-pressure oxygen. For the first time direct information is provided on magnetic properties of the epsilon phase, which is sandwiched between the antiferromagnetic delta phase and the superconducting xi phase. We used magnetic neutron diffraction. The data show that the long-range magnetic order disappears at the delta-epsilon transition. The magnetic collapse occurs at P approximately equal to 8 GPa, far below the pressure of the insulator-metal (superconductor) transition. The collapse is preceded by a decrease in temperature of transition towards the long-range magnetically ordered state (T(LRO)) in the delta phase, at P = 7.6 GPa.     

Stability of iteration methods for maps with a linear contracting majorant

We study the computational stability for the iteration process of finding a fixed point of a mapping that has a linear contracting majorant, assuming that the errors that appear at every step of the iteration process are uniformly bounded. Bibliography: 4 titles. Translated fromObchyslyuval'na ta Prykladna Matematyka, No. 81, 1997, pp. 23–24.