Let G be a finite group, and let N(G) be the set of conjugacy class sizes of G. By Thompson’s conjecture, if L is a finite non-abelian simple group, G is a finite group with a trivial center, and N(G) = N(L), then L and G are isomorphic. Recently, Chen et al. contributed interestingly to Thompson’s conjecture under a weak condition. They only used the group order and one or two special conjugacy class sizes of simple groups and characterized successfully sporadic simple groups (see Li’s PhD dissertation). In this article, we investigate validity of Thompson’s conjecture under a weak condition for the alternating groups of degrees p+1 and p+2, where p is a prime number. This work implies that Thompson’s conjecture holds for the alternating groups of degree p + 1 and p + 2., Alireza Khalili Asboei, Reza Mohammadyari., and Obsahuje seznam literatury
In this review we present immunohistochemical methods for visualization of capillaries and muscle fibres in thick muscle sections. Special attention is paid to the procedures that preserve good morphology. Applying confocal microscopy and virtual 3D stereological grids, or tracing of capillaries in virtual reality, length of capillaries within a muscle volume or length of capillaries adjacent to a muscle fibre per fibre length, fibre surface area or fibre volume can be evaluated by an unbiased approach. Moreover, 3D models of capillaries and muscle fibres can be produced. Comparison of the developed methods with counting capillary profiles from 2D sections is discussed and the reader is warned that counting capillary profiles from 2D sections can underestimate the capillary length by as much as 75 percent. Application of the described 3D methodology is illustrated by the anatomical remodelling of capillarity during acute denervation and early reinnervation in the ra t soleus and extensor digitorum longus muscles., I. Eržen, J. Janáček, L. Kubínová., and Obsahuje bibliografii a bibliografické odkazy
The complete mitochondrial genome (mitogenome) of Spilarctia robusta (Lepidoptera: Noctuoidea: Erebidae) was sequenced and analyzed. The circular mitogenome is made up of 15,447 base pairs (bp). It contains a set of 37 genes, with the gene complement and order similar to that of other lepidopterans. The 12 protein coding genes (PCGs) have a typical mitochondrial start codon (ATN codons), whereas cytochrome c oxidase subunit 1 (cox1) gene utilizes unusually the CAG codon as documented for other lepidopteran mitogenomes. Four of the 13 PCGs have incomplete termination codons, the cox1, nad4 and nad6 with a single T, but cox2 has TA. It comprises six major intergenic spacers, with the exception of the A+T-rich region, spanning at least 10 bp in the mitogenome. The nucleotide composition of the genome is greatly A+T biased (81.09%), with a negative AT skewness (-0.007), indicating the presence of fewer As than Ts, similar to other Noctuoidea. The A+T-rich region is 343 bp long, and contains some conserved regions, including an "ATAGA" motif followed by a 19 bp poly-T stretch, a microsatellite-like (AT)9 and a poly-A element, a characteristic shared with other lepidopteran mitogenomes. Phylogenetic analysis, based on 13 PCGs using Maximum likelihood methods revealed that S. robusta belongs to the superfamily Noctuoidea., Yu Sun, Sen Tian, Cen Qian, Yu-Xuan Sun, Muhammad N. Abbas, Saima Kausar, Lei Wang, Guoqing Wei, Bao-Jian Zhu, Chao-Liang Liu., and Obsahuje bibliografii
In this paper we characterize totally umbilic hypersurfaces in a space form by a property of the extrinsic shape of circles on hypersurfaces. This characterization corresponds to characterizations of isoparametric hypersurfaces in a space form by properties of the extrinsic shape of geodesics due to Kimura-Maeda.
The concept of a 0-distributive poset is introduced. It is shown that a section semicomplemented poset is distributive if and only if it is 0-distributive. It is also proved that every pseudocomplemented poset is 0-distributive. Further, 0-distributive posets are characterized in terms of their ideal lattices.
We present three characterizations of n-dimensional Archimedean copulas: algebraic, differential and diagonal. The first is due to Jouini and Clemen. We formulate it in a more general form, in terms of an n-variable operation derived from a binary operation. The second characterization is in terms of first order partial derivatives of the copula. The last characterization uses diagonal generators, which are "regular'' diagonal sections of copulas, enabling one to recover the copulas by means of an asymptotic representation.
In this paper we obtain two new characterizations of completeness of a normed space through the behaviour of its weakly unconditionally Cauchy series. We also prove that barrelledness of a normed space $X$ can be characterized through the behaviour of its weakly-$\ast $ unconditionally Cauchy series in $X^\ast $.
Let $R$ be a commutative ring and $\mathcal {C}$ a semidualizing $R$-module. We investigate the relations between $\mathcal {C}$-flat modules and $\mathcal {C}$-FP-injective modules and use these modules and their character modules to characterize some rings, including artinian, noetherian and coherent rings.
We investigate the structure and properties of $TL$-sub-semihypergroups, where $T$ is an arbitrary triangular norm on a given complete lattice $L$. We study its structure under the direct product and with respect to the fundamental relation. In particular, we consider $L=[0,1]$ and $T=\min $, and investigate the connection between $TL$-sub-semihypergroups and the probability space.