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Search Results: 1 - 10 of 539204 matches for " A. V. Sobolev "
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The investigation of the kinetics of hydrochemical oxidation of metal sulphides with the aim of determination of the optimal conditions for the selective extraction of molybdenum from ores
Lutsik V.,Sobolev A.
Journal of Mining and Metallurgy, Section B : Metallurgy , 2005, DOI: 10.2298/jmmb0501033l
Abstract: The kinetics of the oxidation of molybdenyte, pyrite and sphalerite in solutions of nitric acid, hydrogen peroxide, and sodium hypochlorite was studied by the rotating disk method. The influence of the molar concentration of reagent, pH of solution, temperature, disk rotation frequency, and duration of measurements on the specific rate of hydrochemical oxidation of sulpfides was determined. The kinetic models allowing to calculate the dissolution rate of sulphides when these parameters change simultaneously were obtained. The conditions of kinetically and diffusion-controlled processes were detected. The details of mechanism of the studied processes were revealed. The nature of intermediate solid products, the reasons and the conditions of their formation as well as the character of their influence on the kinetics of dissolution processes were determined. The probable schemes of interactions corresponding to the observable kinetic dependences were offered. The conditions of the effective and selective molybdenum leaching directly from ore without its concentration were found.
Wiener-Hopf operators in higher dimensions: the Widom conjecture for piece-wise smooth domains
A. V. Sobolev
Mathematics , 2013, DOI: 10.1007/s00020-014-2185-2
Abstract: We prove a two-term quasi-classical trace asymptotic formula for the functions of multi-dimensional Wiener-Hopf operators with discontinuous symbols. The discontinuities occur on the surfaces which are assumed to be piece-wise smooth. Such a two-term formula was conjectured by H. Widom in 1982, and proved by A. V Sobolev for smooth surfaces in 2009.
On Hankel-type operators with discontinuous symbols in higher dimensions
A. V. Sobolev
Mathematics , 2011, DOI: 10.1112/blms/bdr113
Abstract: We obtain an asymptotic formula for the counting function of the discrete spectrum for Hankel-type pseudo-differential operators with discontinuous symbols.
Bethe-Sommerfeld conjecture for periodic operators with strong perturbations
L. Parnovski,A. V. Sobolev
Mathematics , 2009, DOI: 10.1007/s00222-010-0251-1
Abstract: We consider a periodic self-adjoint pseudo-differential operator $H=(-\Delta)^m+B$, $m>0$, in $\R^d$ which satisfies the following conditions: (i) the symbol of $B$ is smooth in $\bx$, and (ii) the perturbation $B$ has order less than $2m$. Under these assumptions, we prove that the spectrum of $H$ contains a half-line. This, in particular implies the Bethe-Sommerfeld Conjecture for the Schr\"odinger operator with a periodic magnetic potential in all dimensions.
Schr?dinger operator on homogeneous metric trees: spectrum in gaps
A. V. Sobolev,M. Solomyak
Mathematics , 2001, DOI: 10.1142/S0129055X02001235
Abstract: The paper studies the spectral properties of the Schr\"odinger operator $A_{gV} = A_0 + gV$ on a homogeneous rooted metric tree, with a decaying real-valued potential $V$ and a coupling constant $g\ge 0$. The spectrum of the free Laplacian $A_0 = -\Delta$ has a band-gap structure with a single eigenvalue of infinite multiplicity in the middle of each finite gap. The perturbation $gV$ gives rise to extra eigenvalues in the gaps. These eigenvalues are monotone functions of $g$ if the potential $V$ has a fixed sign. Assuming that the latter condition is satisfied and that $V$ is symmetric, i.e. depends on the distance to the root of the tree, we carry out a detailed asymptotic analysis of the counting function of the discrete eigenvalues in the limit $g\to\infty$. Depending on the sign and decay of $V$, this asymptotics is either of the Weyl type or is completely determined by the behaviour of $V$ at infinity.
Quasi-conformal mappings and periodic spectral problems in dimension two
E. Shargorodsky,A. V. Sobolev
Mathematics , 2001,
Abstract: We study spectral properties of second order elliptic operators with periodic coefficients in dimension two. These operators act in periodic simply-connected waveguides, with either Dirichlet, or Neumann, or the third boundary condition. The main result is the absolute continuity of the spectra of such operators. The corner stone of the proof is an isothermal change of variables, reducing the metric to a flat one and the waveguide to a straight strip. The main technical tool is the quasi-conformal variant of the Riemann mapping theorem.
On the spectrum of an "even" periodic Schroedinger operator with a rational magnetic flux
N. D. Filonov,A. V. Sobolev
Mathematics , 2013,
Abstract: We study the Schr\"odinger operator on $L_2(\mathbb R^3)$ with periodic variable metric, and periodic electric and magnetic fields. It is assumed that the operator is reflection symmetric and the (appropriately defined) flux of the magnetic field is rational. Under these assumptions it is shown that the spectrum of the operator is absolutely continuous. Previously known results on absolute continuity for periodic operators were obtained for the zero magnetic flux.
A family of anisotropic integral operators and behaviour of its maximal eigenvalue
B. S Mityagin,A. V. Sobolev
Mathematics , 2011, DOI: 10.4171/JST/19
Abstract: We study the family of compact integral operators $\mathbf K_\beta$ in $L^2(\mathbb R)$ with the kernel K_\beta(x, y) = \frac{1}{\pi}\frac{1}{1 + (x-y)^2 + \beta^2\Theta(x, y)}, depending on the parameter $\beta >0$, where $\Theta(x, y)$ is a symmetric non-negative homogeneous function of degree $\gamma\ge 1$. The main result is the following asymptotic formula for the maximal eigenvalue $M_\beta$ of $\mathbf K_\beta$: M_\beta = 1 - \lambda_1 \beta^{\frac{2}{\gamma+1}} + o(\beta^{\frac{2}{\gamma+1}}), \beta\to 0, where $\lambda_1$ is the lowest eigenvalue of the operator $\mathbf A = |d/dx| + \Theta(x, x)/2$. A central role in the proof is played by the fact that $\mathbf K_\beta, \beta>0,$ is positivity improving. The case $\Theta(x, y) = (x^2 + y^2)^2$ has been studied earlier in the literature as a simplified model of high-temperature superconductivity.
Interacción térmica recubrimiento-sustrato en la proyección a alta velocidad (HVOF) de partículas (polvo) de WC-Co
Sobolev, V. V.,Guilemany, J. M.,Calero, J. A.
Revista de Metalurgia , 1995,
Abstract: The mathematical simulation of the thermal interaction between a 34CrMo4 (UNS-G41350) steel substrate and a coating formed by the droplets of WC-12 % Co powder particles during HVOF spraying is undertaken. Analysis of the heat transfer processes permitted the investigation of the temperature evolution, coating solidification, substrate fusion and solidification, particular features of the thermal interactions between the substrate and the coating as well as between the successive coating layers. The analysis has also permitted to estimate the optimal conditions of the substrate and the coating structure formation. The obtained results were used in subsequent articles to predict the structure parameters, which agree with the experimental data. Se utiliza la simulación matemática para establecer la interacción térmica entre un substrato y un recubrimiento obtenido mediante proyección térmica de alta velocidad, HVOF. El substrato es un acero 34CrMo4(UNS-G41350) y el recubrimiento está formado por la solidificación de gotas semifundidas de partículas de polvo de WC-12 % Co. El análisis del proceso de transferencia de calor permite la investigación de la evolución de la temperatura, la solidificación del recubrimiento, la fusión y posterior solidificación del substrato, las características peculiares de la interacción térmica entre el substrato y la primera capa de recubrimiento, así como con las diferentes capas sucesivas, y la estimación de las condiciones óptimas para la formación de la estructura del substrato y del recubrimiento. Los resultados obtenidos se han utilizado en posteriores artículos para predecir parámetros estructurales que están, por su parte, en concordancia con los datos experimentales.
Modelizacion de la formación de recubrimientos de WC-Co por proyección HVOF sobre sustratos de cobre
Sobolev, V. V.,Guilemany, J. M.,Calero, J. A.
Revista de Metalurgia , 1997,
Abstract: Present paper deals with the mathematical simulation of the heat transfer between a WC-Co coating and a copper substrate during HVOF spraying. This modelling includes the investigation of temperature variation, coating solidification, melting and subsequent solidification in the substrate interfacial region and specific features of the substrate-coating thermal interaction. The results obtained are used for modelling of the development of the coating structure and adhesion during HVOF spraying of the WC-Co powder on a copper substrate. Two types of substrate were considered: smooth (polished) and rough. Variations of solidification times, solidification velocity, thermal gradient and cooling velocity in the coating and substrate interfacial region are studied. Development of the amorphous and crystalline structures in the coating and of the crystalline structure in the substrate interfacial region is discussed. Behaviour of the crystal size and intercrystalline distance with respect to the thermal spray parameters and morphology of the substrate surface is analyzed. Optimal conditions for the formation of fine and dense crystalline structure are determined. Structural changes in the solid state of the substrate occurring because of heating and rapid cooling are considered. Mechanical and thermal mechanisms of development of the substrate-coating adhesion are discussed. Results obtained agree well with experimental data. En el presente trabajo se ha investigado la simulación matemática de la transferencia de calor entre un recubrimiento de WC-Co y un sustrato de cobre durante la proyección HVOF. Este modelo incluye el estudio de la variación de termperatura, solidificación del recubrimiento, la fusión y posterior solidificación en la región interfacial del sustrato, y caracerísticas especiales de la interacción térmica sustrato- recubrimiento. Los resultados obtenidos han sido utilizados en la modelización del desarrollo de la estructura del recubrimiento y la adherencia durante la proyección HVOF de polvos de WC-Co en un sustrato de cobre. Se han considerado dos tipos de sustrato: sustrato con superficies pulida y rugosa. Se han estudiado las variaciones de los tiempos de solidificación, de la velocidad de solidificación, del gradiente térmico, y de la velocidad de enfriamiento en el recubrimiento y en la región interfacial del sustrato. Se discute el desarrollo de las estructuras amorfas y cristalinas en el recubrimiento y de la estructura cristalina en la zona interfacial del sustrato. Asimismo, se estudia el comportamiento del tama o de los cristales
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