Appendix: On parahoric subgroups

We give the proofs of some simple facts on parahoric subgroups and on Iwahori Weyl groups used in [T. Haines, The base change fundamental lemma for central elements in parahoric Hecke algebras, preprint, 2008; G. Pappas, M. Rapoport, Twisted loop groups and their affine flag varieties, Adv. Math. 219 (2008) 118–198; M. Rapoport, A guide to the reduction modulo p of Shimura varieties, Astérisque 298 (2005) 271–318].     

Normalizers of subsystem subgroups in finite groups of Lie type

Finite groups of Lie type form the greater part of known finite simple groups. An important class of subgroups of finite groups of Lie type are so-called reductive subgroups of maximal rank. These arise naturally as Levi factors of parabolic groups and as centralizers of semisimple elements, and also as subgroups with maximal tori. Moreover, reductive groups of maximal rank play an important part in inductive studies of subgroup structure of finite groups of Lie type. Yet a number of vital questions dealing in the internal structure of such subgroups are still not settled. In particular, we know which quasisimple groups may appear as central multipliers in the semisimple part of any reductive group of maximal rank, but we do not know how normalizers of those quasisimple groups are structured. The present paper is devoted to tackling this problem. Supported by RFBR (grant No. 05-01-00797) and by SB RAS (Young Researchers Support grant No. 29 and Integration project No. 2006.1.2). __________ Translated from Algebra i Logika, Vol. 47, No. 1, pp. 3–30, January–February, 2008.     

基于合意空间的模糊子群

利用合意空间(ConsensusSpace)理论给出了一个群的C模糊子群的定义.指出这种模糊子群实际上是基于t范(Tm范)的模糊子群.证明了Rosenfeld的模糊子群是C模糊子群,且每一个C模糊子群都与一类特殊的C模糊子群同构.从而为模糊子群提供了新的理论基础.     

The influence of heat and mass transfer on MHD peristaltic flow through a porous space with compliant walls

The present study investigates the effects of heat and mass transfer on peristaltic transport in a porous space with compliant walls. The fluid is electrically conducting in the presence of a uniform magnetic field. Analytic solution is carried out under long-wavelength and low-Reynolds number approximations. The expressions for stream function, temperature, concentration and heat transfer coefficient are obtained. Numerical results are graphically discussed for various values of physical parameters of interest.     

所有子群皆交换或正规的有限群

本文研究所有子群皆交换或正规的有限群. 我们获得了非幂零的情形的一个特征刻画, 也给出了幂零情形的一些性质.     

Geodesic ideal triangulations exist virtually

It is shown that every non-compact hyperbolic manifold of finite volume has a finite cover admitting a geodesic ideal triangulation. Also, every hyperbolic manifold of finite volume with non-empty, totally geodesic boundary has a finite regular cover which has a geodesic partially truncated triangulation. The proofs use an extension of a result due to Long and Niblo concerning the separability of peripheral subgroups.

     

One-pot synthesis of Claisen–Schmidt reaction through (E)-chalcone derivatives: Spectral studies in human serum albumin protein binding and molecular docking investigation

An efficient and environmentally benign one-pot multicomponent synthesis of E-chalcones was developed using a mild and reusable new boron nitride-sulphonic acid catalyst. The catalyst was prepared by activating the boron nitride surface with nitric acid, followed by a simple reaction with 3-mercaptopropyl trimethoxysilane. The catalyst was characterized and morphological properties were studied by Fourier transform infrared, X-ray diffraction, transmission electron spectroscopy, scanning electron microscopy, Brunauer–Emmett–Teller theory, and Raman spectroscopy techniques. The solid acid catalyst was recycled five times in a Claisen–Schmidt reaction to synthesize new chalcone derivatives, and X-ray crystallography was used to elucidate the structure of (E)-1-(anthracen-9-yl)-3-(2-(4-methylpiperazin-1-yl)quinolin-3-yl)prop-2-en-1-one. A fluorescence quench titration method was used to assess its binding ability with human serum albumin (HSA), while molecular docking was also performed to get a more detailed insight into their interaction at the binding site of HSA.     

Embeddable quantum homogeneous spaces

We discuss various notions generalizing the concept of a homogeneous space to the setting of locally compact quantum groups. On the von Neumann algebra level we recall an interesting duality for such objects studied earlier by M. Izumi, R. Longo, S. Popa for compact Kac algebras and by M. Enock in the general case of locally compact quantum groups. A definition of a quantum homogeneous space is proposed along the lines of the pioneering work of Vaes on induction and imprimitivity for locally compact quantum groups. The concept of an embeddable quantum homogeneous space is selected and discussed in detail as it seems to be the natural candidate for the quantum analog of classical homogeneous spaces. Among various examples we single out the quantum analog of the quotient of the Cartesian product of a quantum group with itself by the diagonal subgroup, analogs of quotients by compact subgroups as well as quantum analogs of trivial principal bundles. The former turns out to be an interesting application of the duality mentioned above.     

Characterizing sequences for precompact group topologies

Motivated from [31], call a precompact group topology τ on an abelian group G ss-precompact (abbreviated from single sequence precompact  ) if there is a sequence u=(_un)$\mathbf{u}=(u_n)$ in G such that τ is the finest precompact group topology on G   making u=(_un)$\mathbf{u}=(u_n)$ converge to zero. It is proved that a metrizable precompact abelian group (G,τ)$(G,\tau )$ is ss-precompact iff it is countable. For every metrizable precompact group topology τ on a countably infinite abelian group G there exists a group topology η such that η is strictly finer than τ   and the groups (G,τ)$(G,\tau )$ and (G,η)$(G,\eta )$ have the same Pontryagin dual groups (in other words, (G,τ)$(G,\tau )$ is not a Mackey group in the class of maximally almost periodic groups).     

Covariance operator estimation of a functional autoregressive process with random coefficients

We deal with the covariance and cross covariance operators estimation of a Hilbert space valued autoregressive process with random coefficients. We establish bounds for empirical estimators in mean square error and almost sure convergence in Hilbert–Schmidt norm. Consistent estimators of the eigenvalues are also derived.