Positive solutions and pattern formation in a diffusive tritrophic system with Crowley–Martin functional response

Nonlinear Dynamics - In the present work, we have studied a diffusive tritrophic food chain model in which the species at each trophic level interact in accordance with Crowley–Martin...     

PVP Assisted Shape-Controlled Synthesis of Self-Assembled 1D ZnO and 3D CuO Nanostructures

Self-assembled one-dimensional (1D) zinc oxide (ZnO) rods and three-dimensional (3D) cupric oxide (CuO) cubes like nanostructures with a mean crystallite size of approximately 33 and 32 nm were synthesized through chemical route in the presence of polyvinylpyrrolidone (PVP) under mild synthesis conditions. The technique used for the synthesis of nanoparticles seems to be an efficient, inexpensive and easy method. X-Ray diffraction patterns confirmed well crystallinity and phase purity of the as prepared samples, followed by the compositional investigation using Fourier Transform Infrared (FT-IR) spectroscopy. The formation of ZnO nanorods and CuO nanocubes like structures were through Scanning Electron Microscopy (SEM) images. The mechanism and the formation factors of the self-assembly were discussed in detail. It was clearly observed from results that the concentration of precursors and PVP were important factors in the synthesis of self-assembly ZnO and CuO nanostructures. These self-assembly nanostructures maybe used as novel materials in various potential applications.     

Dominant K-theory and integrable highest weight representations of Kac-Moody groups

We give a topological interpretation of the highest weight representations of Kac-Moody groups. Given the unitary form G of a Kac-Moody group (over C), we define a version of equivariant K-theory, KG on the category of proper G-CW complexes. We then study Kac-Moody groups of compact type in detail (see Section 2 for definitions). In particular, we show that the Grothendieck group of integrable highest weight representations of a Kac-Moody group G of compact type, maps isomorphically onto , where EG is the classifying space of proper G-actions. For the affine case, this agrees very well with recent results of Freed-Hopkins-Teleman. We also explicitly compute for Kac-Moody groups of extended compact type, which includes the Kac-Moody group E₁₀.     

On the Topology of Kac–Moody groups

We study the topology of spaces related to Kac–Moody groups. Given a Kac–Moody group over $\mathbb C $ , let $\text {K}$ denote the unitary form with maximal torus ${{\mathrm{T}}}$ having normalizer ${{\mathrm{N}}}({{\mathrm{T}}})$ . In this article we study the cohomology of the flag manifold $\text {K}/{{{\mathrm{T}}}}$ as a module over the Nil-Hecke algebra, as well as the (co)homology of $\text {K}$ as a Hopf algebra. In particular, if $\mathbb F $ has positive characteristic, we show that $\text {H}_*(\text {K},\mathbb F )$ is a finitely generated algebra, and that $\text {H}^*(\text {K},\mathbb F )$ is finitely generated only if $\text {K}$ is a compact Lie group . We also study the stable homotopy type of the classifying space $\text {BK}$ and show that it is a retract of the classifying space $\text {BN(T)}$ of ${{\mathrm{N}}}({{\mathrm{T}}})$ . We illustrate our results with the example of rank two Kac–Moody groups.     

An efficient one-pot synthesis of novel polysubstituted 4-amino-2,3-dihydropyridines

A convenient and efficient one-pot multi-component synthesis of novel polysubstituted 4-amino-2,3-dihydropyridines from carbonyl compounds, malononitrile and acetonitrile, using indium triflate is reported. Acetonitrile acts both as a solvent as well as a substrate.     

Bismuth triflate–L(−)‐proline catalyzed synthesis of chiral 2,5‐diaryl‐2,3‐dihydropyrano[2,3‐b]quinolin‐4‐ones

The synthesis of chiral (2R) 2,5‐diaryl‐2,3‐dihydropyrano[2,3‐b]quinolin‐4‐ones, was achieved, at ambient temperature, by the reaction of 3‐acetyl‐4‐aryl‐carbostyril and an aldehyde, in the presence of bismuth triflate–L(?)‐proline complex, formed in situ. The products were obtained in 62–78% yield with high enantioselectivity (72–96% ee). J. Heterocyclic Chem., (2011).     

Classifying spaces of Kač-Moody groups

We study the structure of classifying spaces of Kač-Moody groups from a homotopy theoretic point of view. They behave in many respects as in the compact Lie group case. The mod p cohomology algebra is noetherian and Lannes'T functor computes the mod p cohomology of classifying spaces of centralizers of elementary abelian p-subgroups. Also, spaces of maps from classifying spaces of finite p-groups to classifying spaces of Kač-Moody groups are described in terms of classifying spaces of centralizers while the classifying space of a Kač-Moody group itself can be described as a homotopy colimit of classifying spaces of centralizers of elementary abelian p-subgroups, up to p-completion. We show that these properties are common to a larger class of groups, also including parabolic subgroups of Kač-Moody groups, and centralizers of finite p-subgroups. Received: 15 June 2000 / in final form: 20 September 2001 / Published online: 29 April 2002     

Real Structures and Morava K-Theories

We show that real k-structures coincide for k=1,2 on all formal groups for which multiplication by 2 is an epimorphism. This enables us to give explicit polynomial generators for the Morava K(n)-homology of BSpin and BSO for n=1,2.