Cohomology Splittings of Stiefel Manifolds

The complex Stiefel manifolds admit a stable decomposition asThom spaces of certain bundles over Grassmannians. The purposeof the paper is to identify the splitting in any complex orientedcohomology theory.     

Why to consider environmental pollution in cholera modeling?

We propose a deterministic model to study the impact of environmental pollution on the dynamics of cholera. We consider both human to human and human‐environment‐human transmission modes in our model. We obtain the expression for the basic reproduction number of the proposed model. The study of our model reveals that environmental pollution plays a significant role in the spread of cholera and should not be ignored. Although various dimensions of cholera has been studied using mathematical models but scanty efforts have been made to understand impact of environmental pollution on this disease. Through this study, we try to bridge this gap.     

Universal moduli spaces of surfaces with flat bundles and cobordism theory

For a compact, connected Lie group G, we study the moduli of pairs (Σ,E), where Σ is a genus g Riemann surface and E→Σ is a flat G-bundle. Varying both the Riemann surface Σ and the flat bundle leads to a moduli space , parametrizing families Riemann surfaces with flat G-bundles. We show that there is a stable range in which the homology of is independent of g. The stable range depends on the genus of the surface. We then identify the homology of this moduli space in the stable range, in terms of the homology of an explicit infinite loop space. Rationally, the stable cohomology of this moduli space is generated by the Mumford-Morita-Miller κ-classes, and the ring of characteristic classes of principal G-bundles, H^∗(BG). Equivalently, our theorem calculates the homology of the moduli space of semi-stable holomorphic bundles on Riemann surfaces.We then identify the homotopy type of the category of one-manifolds and surface cobordisms, each equipped with a flat G-bundle. Our methods combine the classical techniques of Atiyah and Bott, with the new techniques coming out of Madsen and Weiss's proof of Mumford's conjecture on the stable cohomology of the moduli space of Riemann surfaces.     

An Efficient and Simple One-Pot Synthesis of Novel 2-Amino-5-aza-6-(dinitrilomethylene)-4,7,7-trimethylbicyclo[2.2.2]octane-1,3-dicarbo-nitrile and its Crystal Structure

Abstract  

The title compound was prepared by the reaction of 4-methyl-pent-3-en-2-one and malononitrile, at room temperature, in the presence of indium-triflate and triethylamine. The structure of the molecule was established by spectral analysis and X-ray diffraction studies. The compound crystallizes in the monoclinic space group C2/c with unit cell parameters: a = 14.269 (2), b = 10.141 (2), c = 19.743 (3) ?, β = 95.523(4)°, Z = 8. The crystal structure was solved by direct methods and refined to R = 0.0526 for 2,690 observed reflections. The isoquinuclidine rings adopt boat conformation. The molecules in the unit cell are arranged in layers. The crystal structure is stabilized by N–H⋯N interactions.     

Upon the influence of the post-arc current on the low voltageswitching process in vacuum

The paper presents one stage of the scientific research, performed for the investigation of the post-arc (p.a.) current within low voltage switching process in vacuum, when interrupting short-circuit currents of high values. A large power equipment, supplied by the mains and providing an accurate reproduction of the processes, concerning the short circuit phenomenon (U=1.5 kV; I=100 kA) was used. An experimental model, which can reproduce the switching conditions of the power circuit-breaker in vacuum, was available as well. The influence of an axial magnetic field on the p.a. current and the switching process was also explored