Study on synthesis of two-armed polymers containing a crown ether core and their self-assembly behaviors in selective solvents

A series of well-defined two-armed polymers containing a crown ether core, poly(stearyl methacrylate)-crown ether-poly(stearyl methacrylate) (PSMA-crown-PSMA), with different molecular weight were synthesized via atom transfer radical polymerization (ATRP). The resultant polymers were characterized by ¹H NMR and GPC. The self-assembly behaviors of this kind of polymer in selective solvents were studied by TEM, and it was found that polymers with different molecular weight can directly self-assemble into hollow spheres, solid spheres and a monolayer film with regular pores by varying molecular weight and water content. The possible molecular packing motels for their self-assembly behaviors were proposed.     

On critical cases of Sobolev's inequalities for Heisenberg groups

We prove some Trudinger-type inequalities and Brezis-Gallouet-Wainger inequality on the Heisenberg group, extending to this context the Euclidean results by T. Ozawa.     

LU和Cholesky分解的向前舍入误差分析

1引言LU分解可用于解可逆线性系统Ax=b．作为数值代数领域中的重要工具,其舍入误差分析一直为众多学者所关注．事实上,长方矩阵的LU分解也有着广泛的应用,如,确定矩阵数值秩的LU分解(RRLU)[5,7],解等式约束最小二乘问题的直接消去法[3]等问题中都涉及到长方矩阵的LU分解．当A∈Rm×n且秩r≤min{m,n},则在考虑A的LU分解时[4],一般需要确定置换阵∏L,∏R使得A(1):=∏L-A∏R的LU分解能持续qr步,这里当A为亏秩矩阵时,qr=r;否贝qr=r-1．在．A(1)的LU分解的第k(k≤qr)步,需执行如下Gauss消去过程:     

ON GROWTH FACTORS OF THE LU FACTORIZATION

In this article, we derive upper bounds of different growth factors for the LU factorization, which are dominated by A11(k)-1A12(k),A21(k)A11(k)-1, where A11(k), A12(k), A21(k), A22(k) are sub-matrices of A. We also derive upper bounds of growth factors for the Cholesky factorization. Numerical examples are presented to verify our findings.     

Improved Sobolev inequalities on groups of Iwasawa type in presence of symmetry

Let G be a simple Lie group of real rank one and N be in the Iwasawa decomposition of G. We prove a refined version of the Sobolev inequality on N in presence of symmetry.     

The heat kernel on H-type groups

In this paper we present an explicit calculation of the heat kernel for the sub-Laplacian on an H-type group by using irreducible unitary representations of and the heat kernel for the associated Hermite operator.

     

PVC membrane electrode based on triheptyl dodecyl ammonium iodide for the selective determination of molybdate(VI)

Novel polyvinyl chloride (PVC) membrane electrodes based on triheptyl dodecyl ammonium iodide have been developed. In the presence of 12.5 mM H₂O₂, these electrodes are capable of determining molybdate(VI) ion. The electrodes exhibit near-Nernstian responses over a wide concentration range (2.0 × 10⁻⁶ to 5.0 × 10⁻³ M). The proposed electrodes demonstrate satisfying selectivity for molybdate(VI) ion in the presence of a wide variety of anions other than iodide, and can be used in the pH range 5.0-7.0. Moreover, the electrodes show an average response time of 2-3 min and can be used over a period of 2 months without any significant deviation being observed. In the light of our results, the response mechanism of the electrode is discussed and HMoO₂(O₂)₂⁻ is suggested as the response ion. The proposed electrode has been used to measure molybdenum in ore samples, and the results were in agreement with those obtained by means of ICP analysis.     

圆形阵列无线传感器的鸟鸣声检测方法*

针对海岛湿地自然保护区鸟类等发声动物监测困难的问题,开发了基于物联网的圆形阵列无线传感器实时在线监测系统。鉴于保护区现场环境条件的特殊性,为保障传感器系统在野外长期稳定运行,需减少无鸣声数据的传输量来减轻系统负担,该文提出了基于子带能量谱熵比的动态双门限鸟类鸣声端点检测算法,对监测数据的有效鸣声段检测后实时回传到云平台。经过仿真和野外实测数据对比了不同信噪比下的鸣声检测性能,结果表明在暴风雨、风浪等海岛自然环境噪声下,鸟鸣声端点检测算法的准确率达90%以上,基本可实现海岛环境中的有效鸣声端点检测,提升了圆形阵列无线传感器系统的可靠性。