A trace class operator inequality

In this note, we generalize the inequality about the trace of positive semidefinite matrix trk(AB)?k(trA)k(trB) to Hilbert space, and obtain a relevant inequality about positive trace class operator.     

迭代的计算与估计

对高次多项式函数这类非线性映射给出了一般 n次迭代的一个计算结果 ,还讨论了一维欧氏空间中一些非多项式型映射的迭代 .在二维欧氏空间中 ,我们给出了几类特殊的非线性迭代的结果 .对于一些难以精确计算迭代表达式的映射 ,我们给出了其迭代的估计 .     

Synthesis and optoelectronic properties of silole‐containing polyfluorenes with binary structures

2,5‐Bis(2‐bromofluorene‐7‐yl)silole was prepared by a modified one‐pot synthesis with a reverse addition procedure, from which novel silole‐containing polyfluorenes with binary random and alternating structures (silole contents between 4.5 and 25% and high M_w up to 509 kDa were successfully synthesized. The well‐defined repeating unit of the alternating copolymer comprises a terfluorene and a silole ring. Optoelectronic properties including UV absorption, electrochemistry, photoluminescence (PL), and electroluminescence (EL) of the copolymers were examined. The different excitation energy transfers from fluorene to silole of the copolymers in solution and in the solid state were compared. The films of the copolymers showed silole‐dominant green emissions with high absolute PL quantum yields up to 83%. EL devices of the copolymers with a configuration of ITO/PEDOT/copolymer/Ba/Al displayed exclusive silole emissions peaked at around 543 nm and the highest EL efficiency was achieved with the alternating copolymer. Using the alternating copolymer and poly(9,9‐dioctylfluorene) as the blend‐type emissive layer, a maximum external quantum efficiency of 1.99% (four times to that of the neat film) was realized, which was a high efficiency so far reported for silole‐containing polymers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 756–767, 2007     

Generalized optical logic elements - GOLEs

A Generalized Optical Logic Element or GOLE is device that performs any of the 16 Boolean logic operations on signals in an optical beam with very fast switching among functions. The advantages of a generalized or universal gate in manufacturing are obvious. Extremely flexible functioning becomes possible if the GOLE functionality is switched in response to earlier computations. Likewise Field Programmable Gate Arrays or FPGAs can be used to fix the GOLE functions, making one of the most powerful and flexible processor units ever designed - called a Field GOLE. Such systems can be made in bulk optics to utilize Spatial Light Modulator or SLM capabilities, but integrated optics on silicon will be the choice for most applications. GOLEs can be generalized in several ways to become Fredkin gates and generalized Fredkin gates. They can also be cascaded similarly to electronic gates.     

On Basic Constraint Qualifications for Infinite System of Convex Inequalities in Banach Spaces

The BCQ and the Abadie CQ for infinite systems of convex inequalities in Banach spaces are characterized in terms of the upper semi-continuity of the convex cones generated by the subdifferentials of active convex functions. Some relationships with other constraint qualifications such as the CPLV and the Slate condition are also studied. Applications in best approximation theory are provided.     

Interface solution for writing-induced nano-deformation of slider body

Writing-induced nano-deformation of slider body becomes a big concern when the mechanical spacing between the head and disk is continuously reduced to achieve higher magnetic recording areal density. Reduced head–disk spacing increases the risk of head/disk contact and causes the thermal instability in head–disk interface (HDI). This paper reports authors’ efforts towards exploration of interface solutions for writing-induced instability in ultra-low head–disk spacing magnetic system. Multi-shallow step structure with optimized rail position is analyzed and a new femto slider with such structure is explored. The results of numerical simulation indicate that the multi-shallow step structure is an effective approach in reducing the flying height change caused by the writing-induced nano-deformation of the slider body.     

脉冲激光偏振方向对氮分子高次谐波的影响——基于含时密度泛函理论的模拟

采用含时密度泛函方法,结合赝势模型和电子交换相关作用的广义梯度近似,模拟了氮分子在超强飞秒激光脉冲作用下的高次谐波产生现象,并研究了激光脉冲偏振方向对氮分子高次谐波的影响.结果表明氮分子的高次谐波谱具有典型原子谐波谱的特征;谐波谱强度随着θ(激光偏振方向与分子轴向夹角)的增大而减小.这与J.Itatanl在Nature上报道的实验结果基本一致.     

单脉冲和多脉冲飞秒激光对单层光学薄膜的损伤

 利用掺钛的蓝宝石飞秒激光系统输出的单脉冲和多脉冲飞秒激光(中心波长800 nm，脉宽50 fs，靶面聚焦直径Ф 40 μm)，分别对BK7玻璃基底上厚约500 nm的单层HfO₂和单层ZrO₂薄膜进行辐照，得到了这两种薄膜在1-on-1和1 000-on-1测试方法下的激光损伤阈值。实验发现，两种方法下HfO₂单层膜的阈值均比ZrO₂单层膜的阈值高。从简化的Keldysh多光子离化理论出发，认为HfO₂薄膜材料的带比ZrO₂的宽是导致上述结果的主要原因。同时，同一种薄膜的多脉冲下的阈值比单脉冲下的低，原因是多脉冲下，飞秒激光对光学薄膜的损伤存在累积效应。