A characterization of the hypercyclically embedded subgroups of finite groups

A normal subgroup H of a finite group G is said to be hypercyclically embedded in G if every chief factor of G below H is cyclic. The major aim of the present paper is to characterize the normal hypercyclically embedded subgroups E of a group G by means of the embedding of the maximal and minimal subgroups of the Sylow subgroups of the generalized Fitting subgroup of E.     

Characterizations of $$sigma$$ -Solvable Finite Groups

Mathematical Notes - All the groups considered in this paper are finite, and $$G$$ always denotes a finite group; $$sigma$$ is a partition of the set $$mathbb{P}$$ of all primes, i.e.,...     

Grain boundary sliding and lattice dislocation emission in nanocrystalline materials under plastic deformation

A theoretical model is proposed to describe the physical mechanisms of hardening and softening of nanocrystalline materials during superplastic deformation. According to this model, triple interface junctions are obstacles to glide motion of grain boundary dislocations, which are carriers of grain boundary glide deformation. Transformations of an ensemble of grain boundary dislocations that occur at triple interface junctions bring about the formation of partial dislocations and the local migration of triple junctions. The energy characteristics of these transformations are considered. Pileups of partial dislocations at triple junctions cause hardening and initiate intragrain lattice sliding. When the Burgers vectors of partial dislocations reach a critical value, lattice dislocations are emitted and glide into adjacent grains, thereby smoothing the hardening effect. The local migration of triple interface junctions (caused by grain boundary sliding) and the emission of lattice dislocations bring about softening of a nanocrystalline material. The flow stress is found as a function of the total plastic strain, and the result agrees well with experimental data.     

Simultaneous high speed PIV and CH PLIF using R-branch excitation in the C2Σ+-X2Π (0,0) band

Simultaneous particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) utilizing R-branch transitions in the C-X (0,0) band were performed at a 10-kHz repetition-rate in a turbulent premixed flame. The CH lines at 310.690?nm (from the R-branch of the C-X band) used here have greater efficiency than A-X and B-X transitions, which allows for high-framerate imaging with low laser pulse energy. Most importantly, the simultaneous imaging of both CH PLIF and PIV is enabled by the use of a custom edge filter, which blocks scattering at the laser wavelength (below ～311?nm) while efficiently transmitting fluorescence at longer wavelengths. The Hi-Pilot Bunsen burner operated with a turbulent Reynolds number of 7900 was used to demonstrate simultaneous PIV and CH PLIF utilizing this filtered detection scheme. Instances where pockets of products were observed well upstream of the mean flame brush are found to be the result of out-of-plane motion of the flame sheet. Such instances can lead to ambiguous results when interpreting the thickness of reaction layers. However, the temporally resolved nature of the present diagnostics facilitate the identification and proper treatment of such situations. The strategy demonstrated here can yield important information in the study of turbulent flames by providing temporally resolved flame dynamics in terms of flame sheet visualization and velocity fields.     

Multiply\mathfrak{L} formations of finite groupsformations of finite groups

We study formations of finite groups. Gomel University, Gomel, Belorussia. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 52, No. 6, pp. 783–797, June, 2000.     

Estimates of n-diameters of some classes of functions analytic on Riemann surfaces

This study concerns the class A _K ^D of functions x analytic in a domain D of an open Riemann surface and satisfying there the inequality ¦x¦?1 with metric defined by the norm of the space C(K) of functions continuous on the compact subsetK ? D. The asymptotic formula $$\mathop {\lim }\limits_{n \to \infty } [d_n (A_K^D )]^{{1 \mathord{\left/ {\vphantom {1 n}} \right. \kern-\nulldelimiterspace} n}} = e^{ - 1/\tau } $$ is established, where D is a finitely connected domain of Carathéodory type,K ? D is a regular compact subset such thatd?k is connected, and τ = τ (D, K) is the flux of harmonic measure of the set ?D relative to the domaind?k through any rectifiable contour separating ?D and K.     

On Strongly Π-Permutable Subgroups of a Finite Group

Siberian Mathematical Journal - Let σ = {σi | i ∈ I} be some partition of the set of all primes ℙ,let ∅ ≠ Π ⊆ σ, and let G be a finite group. A set...