Divisibility of class numbers of imaginary quadratic function fields by a fixed odd number

In this paper we find a new lower bound on the number of imaginary quadratic extensions of the function field $\mathbb{F}_{q}(x)$ whose class groups have elements of a fixed odd order. More precisely, for q, a power of an odd prime, and g a fixed odd positive integer ≥?3, we show that for every ε?>?0, there are $\gg q^{L(\frac{1}{2}+\frac{3}{2(g+1)}-\epsilon)}$ polynomials $f \in \mathbb{F}_{q}[x]$ with $\deg f=L$ , for which the class group of the quadratic extension $\mathbb{F}_{q}(x, \sqrt{f})$ has an element of order g. This sharpens the previous lower bound $q^{L(\frac{1}{2}+\frac{1}{g})}$ of Ram Murty. Our result is a function field analogue which is similar to a result of Soundararajan for number fields.     

AN EXPLICIT FINITE VOLUME SPATIAL MARCHING METHOD FOR REDUCED NAVIER–STOKES EQUATIONS

This paper develops a spatial marching method for high-speed flows based on a finite volume approach. The method employs the reduced Navier– Stokes equations and a pressure splitting in the streamwise direction based on the Vigneron strategy. For marching from an upstream station to one downstream the modified five-level Runge–Kutta integration scheme due to Jameson and Schmidt is used. In addition, for shock handling and for good convergence properties the method employs a matrix form of the artificial dissipation terms, which has been shown to improve the accuracy of predictions. To achieve a fast rate of convergence, a local time-stepping concept is used. The method retains the time derivative in the governing equations and the solution at every spatial station is obtained in an iterative manner. The developed method is validated against two test cases: (a) supersonic flow past a flat plate; and (b) hypersonic flow past a compression corner involving a strong viscous–inviscid interaction. The computed wall pressure and wall heat transfer coefficients exhibit good general agreement with previous computations by other investigators and with experiments.     

One Pot Reduction of Imines Generated in-situ from Aldehydes and Amines by the NaBH4-InCl3 System

A combination of sodium borohydride and a catalytic amount of indium（Ⅲ） chloride in acetonitrile reduces imines formed in-situ from aldehydes and amines to the corresponding functionalised secondary and tertiary amines in moderate to good yields. Noteworthy is that highly chemoselective reactions were achieved in the presence of other functional groups such as halogens, carbon-carbon double bonds and hydroxyl groups.     

VIBRATION CHARACTERISTICS OF SLOTTED SHAFTS

The dynamics of asymmetric rotors has been investigated in the literature. However, considering the importance in the practical fields, the vibration characteristics of slotted shafts are not studied in detail. It needs more attention particularly with the emerging of new materials, such as composites for shafts. The present study aims at the analysis of the slotted shafts including the compensatory inertia slots. Also, the slotted composite shaft has been modelled based on first order shear deformation theory using finite element method with shell elements. Different materials such as, Boron epoxy, Carbon epoxy and Graphite epoxy have been tried for various stacking sequences. The slot parameters, stacking sequences and material properties have found to influence to great extent on the vibrational characteristics of rotors. The results are compared with those of isotropic slotted shaft.     

Group graded associated ideals with flat base change of rings and short exact sequences

This paper deals with the study of behaviour of G-associated ideals and strong Krull G-associated ideals with flat base change of rings and behaviour of G-associated ideals with short exact sequences over rings graded by finitely generated abelian group G.     

ChemInform Abstract: H-Bridged Structures for Tetrahedranes A4H4 (A: C,Si, Ge,Sn, and Pb).

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.     

ChemInform Abstract: Boron Analogues of Cyclopropenium Cation: B3H+ 6, the First Three- Membered Nonplanar 2π Aromatic.

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.