Finite groups with subnormal second or third maximal subgroups

In the paper, the precise structure of finite groups all of whose second (or all of whose third) maximal subgroups are subnormal is established.     

On an efficient splitting‐based method for solving the diffusion equation on a sphere

A novel numerical approach for solving the diffusion problem on a sphere is suggested. By using operator splitting, we develop a new method that allows constructing finite difference schemes of the second and fourth approximation orders in the spatial variables. Both schemes properly ensure the balance of mass and the energy dissipation in the L₂ ‐norm. The schemes are very cheap from the computational standpoint. Numerical results demonstrate the skillfulness of the approach in describing the diffusion dynamics on a sphere. It is shown the method can directly be extended to nonlinear diffusion problems.© 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 331–352, 2012     

Finite groups in which every 3-Maximal subgroup commutes with all maximal subgroups

The structure of finite groups in which every 3-maximal subgroup commutes with all maximal subgroups is described.     

Structure of finite groups with <Emphasis Type="Italic">S</Emphasis>-quasinormal third maximal subgroups

We study finite groups whose 3-maximal subgroups are permutable with all Sylow subgroups.     

Solubility in the PrCl<Subscript>3</Subscript>-SmCl<Subscript>3</Subscript>-HCl-H<Subscript>2</Subscript>O System at 25°C

The solubility in the PrCl₃-SmCl₃-HCl-H₂O quaternary water-salt system was studied at 25°C along the 40% hydrochloric acid section (a system with solid solutions and discontinuity). The composition of the discontinuity point was as follows: PrCl₃ · 7H₂O, 2.33; SmCl₃ · 6H₂O, 0.11; HCl, 40.05; and H₂O, 57.51 wt %.     

Misfit disclination dipoles in nanocrystalline films and coatings

A theoretical model is proposed for describing the special physical micromechanism of misfit stress relaxation in nanocrystalline (NC) films and coatings. According to this model, under certain conditions, grain boundary sliding occurs in NC films and coatings, which is accompanied by the formation of an ensemble of disclination dipoles (rotational defects). These dipoles produce elastic stress fields, which partially compensate misfit stresses in NC films and coatings. Using the proposed model, it is shown that the nucleation of disclination dipoles in a film (coating) can significantly decrease the total energy of the film/substrate composite for the AlN/6H-SiC and GaN/6H-SiC systems over a wide range of structural parameter values.     

Mechanism of Hardening of Ultrafine-Grained Aluminum after Annealing

Physics of the Solid State - A theoretical model is proposed that describes the hardening mechanism of ultrafine-grained aluminum obtained by high pressure torsion after low-temperature annealing....     

Spectral approximation in the numerical stability study of nondivergent viscous flows on a sphere

The accuracy of calculating the normal modes in the numerical linear stability study of two-dimensional nondivergent viscous flows on a rotating sphere is analyzed. Discrete spectral problems are obtained by truncating Fourier's series of the spherical harmonics for both the basic flow and the disturbances to spherical polynomials of degrees K and N, respectively. The spectral theory for the closed operators [1], and embedding theorems for the Hilbert and Banach spaces of smooth functions on a sphere are used to estimate the rate of convergence of the eigenvalues and eigenvectors. It is shown that the convergence takes place if the basic state is sufficiently smooth, and the truncation numbers K and N of Fourier's series for the basic flow and disturbances tend to infinity keeping the ratio N/K fixed. The convergence rate increases with the smoothness of the basic flow and with the power s of the Laplace operator in the vorticity equation diffusion term. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:143–157, 1998