A New Method to Construct Integrable Coupling System for Burgers Equation Hierarchy by Kronecker Product

It is shown that the Kronecker product can be applied to construct a new integrable coupling system of soliton equation hierarchy in this paper. A direct application to the Burgers spectral problem leads to a novel soliton equation hierarchy of integrable coupling system. It indicates that the Kronecker product is an efficient and straightforward method to construct the integrable couplings.     

Time-Resolved FTIR Study on the Reaction of CHCl2 with NO2

采用时间分辨傅立叶变换红外发射光谱(TR-FTIR)研究了环境化学中重要的氯代甲基CHCl2和NO2分子的反应. 通 过0.5 cm-1高分辨的TR-FTIR发射光谱观察到四种振动激发态产物CHClO、NO、CO和HCl,进而推测出CHCl2+NO2反应三个相应的产物通道. 其中,CO是CHCl2+NO2反应中首次观测到的产物,而HCl则是明确肯定存在的初级反应产物.     

相干态表象在量子相空间分布函数中的应用

利用相干态表象和IWOP技术导出了自由热态密度矩阵的正规乘积形式,进而根据相干态表象下的Wigner函数定义重构了自由热态和热相干态的Wigner函数.结果表明利用相干态表象下的Wigner函数定义和算符的正规乘积形式可以方便简捷重构一些量子态的Wigner函数.     

双模坐标-动量积分型投影算符及其在量子光学中的应用

引进了幺正的双模坐标-动量积分型投影算符,利用有序算符内的积分（IWOP）技术分析了其变换特性,并导出了其正规乘积展开式.然后利用该积分型投影算符对角化了双模耦合量子谐振子体系的哈密顿量,从而求出了体系的本征能级与本征波函数.最后讨论了特例情形. 关键词： 积分型投影算符 有序算符内的积分技术 坐标-动量耦合     

线性空间C[a,b]上的线性相关性研究

研究了线性空间C[a,b]上的线性相关性,给出了衡量C[a,b]上n个函数线性相关性程度的量以及线性相关的充分必要条件.     

Optimal overlapping and functional interaction in product development

Overlapping of development stages and interaction between different functions are regarded as important strategies for reducing development lead time. However, overlapping typically requires additional costs for rework and functional interaction increases communication time. This paper presents an analytical model to improve project performance by balancing the positive and negative effects of overlapping and functional interaction. We first investigate the progress of downstream development, which is essential to derive the optimal overlapping policies. We find that the downstream progress increases over time when the upstream evolution is fast or linear, but it is indefinite when the upstream evolution is slow. Then, we present optimal overlapping policies taking into account the complexity of downstream progress. The impact of different project properties, such as the dependency between development stages and the opportunity cost of time, on overlapping policies is discussed. Finally, we derive the optimal functional interaction strategy when the optimal overlapping is followed. The methodology is illustrated with a case study at a handset design company.     

A stability property for locally uniformly rotund renorming

It is proved that C(K,E) (the space of all continuous functions on a Hausdorff compact space K taking values in a Banach space E) admits an equivalent locally uniformly rotund norm if C(K) and E do so. Moreover, if the equivalent LUR norms on C(K) and E are lower semicontinuous with respect to some weak topologies, the LUR norm on C(K,E) can be chosen to be lower semicontinuous with respect to an appropriate weak topology. As a consequence we prove that if X and Y are two Hausdorff compacta and C(X), C(Y) admit equivalent (pointwise lower semicontinuous) LUR norms, then so does C(X×Y).