Efficient and widely applicable oxidation method of tribromomethyl carbinols with PCC

An efficient and widely applicable oxidation method of tribromomethyl carbinols in the presence of pyridinium chlorochromate has been developed with excellent yields up to 96%. This method was well applied for the oxidation of a variety of aromatic, aliphatic, and heterocyclic tribromomethyl carbinols.     

Green’s relations and regularity for semigroups of transformations that preserve order and a double direction equivalence

Let T _X be the full transformation semigroup on a set X,

Enhancing sound absorption using periodic micro-perforated structure with porous layer

To get desired sound absorption,we proposed a novel periodic composite structure comprised of micro-perforated plates(MPPs),porous materials and air cavities.The composite structure is then solved using an equivalent circuit model,with equivalent fluid porous model and Maa's theory.Distributed four-pole elements are used to handle structures which are not compact compared to the sound wavelength.The model procedures are validated and confirmed as satisfactory by published results and finite-element results.Analysis conducted on a single layer shows that,compared with traditional MPP,the porous addition can increase sound absorption in the low-to-medium frequency range;however,the advantage of porous materials in the high-frequency range is lost.Meanwhile,by arranging the porous materials in parallel and controlling their filling ratios,the absorption curve of the composite structure can be tuned.As to periodic composite structures,it is found that the influence of layer number N is mainly in the low-to-medium frequency range.When N varies,the half-absorption bandwidth increases over 40%(≥380 Hz) compared with a single layer.Compared with multi-layered MPPs,N=2 and N=4 produce an increase of bandwidth by 50%(≥400 Hz) and 30%(≥300 Hz) respectively.As N increases,the sound absorption is better but the enhancement weakens as it tends to the limit of the composite structure.These results show the potential enhancements that can be made to the traditional MPP,which can benefit the research on wideband noise reduction in the low-to-medium frequency range.     

The application of lightning forecasting based on surface electrostatic field observations and radar data

This paper presents an analysis of lightning forecasting based on atmospheric electrostatic field (EF), radar and lightning location data in Nanjing of China. The warning behavior with EF data in summer of 2009 was analyzed and the suitable EF warning indexes were determined. To improve EF warnings effect, a method of cloud-ground (CG) lightning nowcasting based on EF observations, radar data, etc. was proposed and the best radar forecasting index was selected in the paper. The experimental (2009) and independent test (2010) results show that POD is 82.7%, FAR is 14.6%, CSI is 72.4% and average lead time is 20.8 min.     

带电粒子在交变磁场中运动问题的分析策略

在解析带电粒子在交变磁场中运动的对称性和周期性特点的基础上,以2014年的两道高考题为例,阐述带电粒子在交变磁场中运动问题的分析思路.     

指数型二分性,Melnikov函数和异宿轨道

本文用不同于Ｐａｌｍｅｒ＾［２］的方法，讨论了非自治微分方程存在异宿轨道的条件。得到了已知文献中不同的一个Ｍｅｌｍｉｋｏｖ型的函数。     

Quasiperiodic solutions of the discrete Chen-Lee-Liu hierarchy

Using the Lax matrix and elliptic variables, we decompose the discrete Chen-Lee-Liu hierarchy into solvable ordinary differential equations. Based on the theory of the algebraic curve, we straighten the continuous and discrete flows related to the discrete Chen-Lee-Liu hierarchy in Abel-Jacobi coordinates. We introduce the meromorphic function ?, Baker-Akhiezer vector \(\bar \psi \) , and hyperelliptic curve ?_N according to whose asymptotic properties and the algebro-geometric characters we construct quasiperiodic solutions of the discrete Chen-Lee-Liu hierarchy.     

Converse Lyapunov theorems for nonautonomous discrete-time systems

This paper presents converse Lyapunov theorems for exponential stability of nonautonomous discrete-time systems with disturbances and free of disturbances, respectively. It is shown that Lyapunov functions exist for discrete-time systems if the systems are exponentially stable. Moreover, in the periodic case, we explicitly construct a Lyapunov function for systems with disturbances. Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 61, Optimal Control, 2008.     

Periodicity and area spectrum of black holes

The recent speculation of Maggiore that the periodicity of a black hole may be the origin of the area quantization law is confirmed. We exclusively utilize the period of motion of an outgoing wave, which is shown to be related to the vibrational frequency of the perturbed black hole, to quantize the horizon areas of a Schwarzschild black hole and a Kerr black hole. It is shown that the equally spaced area spectrum for both cases takes the same form and the spacing is the same as that obtained through the quasinormal mode frequencies. Particularly, for a Kerr black hole, the small angular momentum assumption, which is necessary from the perspective of quasinormal mode, is not employed as the general area spacing is reproduced.