Characteristics and structures of weak efficient surfaces of production possibility sets

This paper studies the characteristics and structure of the weak surface of the production possibility set. We apply techniques and methods of transferring a polyhedral cone from its intersection form to its sum form, identify an intersection representation of the production possibility set. We give the structure theorem of weak surface of the production possibility set, which includes three complementary slackness conditions. We define the input weak efficiency and output weak efficiency for different DEA models according to the representation of the intersection form. It investigates the characteristics of the weak surfaces, and proves the structure theorems of input weak DEA efficiency and output weak DEA efficiency. The structure theorems establish weighted combination of inputs and outputs that are weak DEA efficient. Numerical examples are provided for illustration.     

良序套张量积的代数中的强不可约算子

设Ｈ为复的可分无限维Ｈｉｌｂｅｒｔ空间，称有界线性算子Ｔ为强不可约的，如果与Ｔ可交换的幂等算子只有０和Ｉ．王宗尧、蒋春澜、纪有清等人证明了在任何一个套的套代数中都存在大量的强不可约算子，并且找到了它们的酉轨道闭包．本文考虑有限个套的张量积的代数中强不可约算子的存在性问题。证明了：对复平面上任何一个连通完备集σ、总存在一个对角算子Ｎ和它的一个范数可以任意小的紧摄动Ｔ＝Ｘ＋Ｋ，使得Ｔ是一个强不可约算子、Ｔ在有限个良序套的张量积的代数中，并且σ（Ｔ）＝σｌｒｅ（Ｔ）＝σ（Ｎ）＝σｌｒｅ（Ｎ）＝σ进一步，文章还对具有单点谱的算子和良序套与正交补为良序套的张量积的代数进行了讨论，得到了一些结果．     

Thermal conductance for single wall carbon nanotubes

We report a theoretical analysis of the phonon thermal conductance, κ(T), for single wall carbon nanotubes (SWCN). In a range of low temperatues up to 100 K, κ(T) of perfect SWCN is found to increase with temperature, approximately, in a parabolic fashion. This is qualitatively consistent with recent experimental measurements where the tube-tube interactions are negligibly weak. When the carbon-carbon bond length is slightly varied, κ(T) is found to be qualitatively unaltered which implies that the anharmonic effect does not change the qualitative behavior of κ(T). Received 12 June 2001     

Synthesis,characterization, and micellization of an epoxy‐based amphiphilic diblock copolymer of ϵ‐caprolactone and glycidyl methacrylate by enzymatic ring‐opening polymerization and atom transfer radical polymerization

Amphiphilic diblock copolymer polycaprolactone‐block‐poly(glycidyl methacrylate) (PCL‐b‐PGMA) was synthesized via enzymatic ring‐opening polymerization (eROP) and atom transfer radical polymerization (ATRP). Methanol first initiated eROP of ?‐caprolactone (?‐CL) in the presence of biocatalyst Novozyme‐435 under anhydrous conditions. The resulting monohydroxyl‐terminated polycaprolactone (PCL–OH) was subsequently converted to a bromine‐ended macroinitiator (PCL–Br) for ATRP by esterification with α‐bromopropionyl bromide. PCL‐b‐PGMA diblock copolymers were synthesized in a subsequent ATRP of glycidyl methacrylate (GMA). A kinetic analysis of ATRP indicated a living/controlled radical process. The macromolecular structures were characterized for PCL–OH, PCL–Br, and the block copolymers by means of nuclear magnetic resonance, gel permeation chromatography, and infrared spectroscopy. Differential scanning calorimetry and wide‐angle X‐ray diffraction analyses indicated that the copolymer composition (?‐CL/GMA) had a great influence on the thermal properties. The well‐defined, amphiphilic diblock copolymer PCL‐b‐PGMA self‐assembled into nanoscale micelles in aqueous solutions, as investigated by dynamic light scattering and transmission electron microscopy. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5037–5049, 2007     

On the uniqueness of the foliation of spheres of constant mean curvature in asymptotically flat 3-manifolds

In this note we study constant mean curvature surfaces in asymptotically flat 3-manifolds. We prove that, outside a given compact subset in an asymptotically flat 3-manifold with positive mass, stable spheres of given constant mean curvature are unique. Therefore we are able to conclude that the foliation of stable spheres of constant mean curvature in an asymptotically flat 3-manifold with positive mass outside a given compact subset is unique.

     

重离子治疗计划系统的构想

对重离子柬治癌的优势进行简要的回顾，并着重介绍了用于重离子放射治疗的治疗计划系统。治疗计划系统是一套软件系统，不同的硬件设施应有与其相匹配的软件系统，即治疗计划系统。在此基础上，针对兰州重离子加速器的特点提出一些关于治疗计划系统方面的构想。After a brief review concerning the advantages of heavy ions in radiotherapy, more interests are concentrated on treatment planning system （TPS） for heavy ion radiotherapy. Compared to the hardware devices such as accelerator and beam delivery system, the TPS is a set of software system, and different therapy facilities require their corresponding TPSs. Based on the specialities of the Heavy Ion Research Facility in Lanzhou （HIIRFL）, some suggestions on the TPS for tumor therapy at HIRFL finally are given.     

The Generalized West Decomposition of Operators and Other Compact Perturbation Problems

This paper introduces the concept of the generalized Riesz operators and the concept of the generalized West decomposition of a general operator which generalizes the definition of the West decomposition of Riesz operators, and proves that the following three statements are equivalent on a general Banach space： （a） Every generalized Riesz operator has the generalized West decomposition; （b） Every operator makes strong Stampfli theorem true; Every operator has Apostol＇s compact correction.     

Initial study on the structure and photoluminescence properties of SiC films doped with Al

SiC films doped with aluminum (Al) were prepared by the rf-magnetron sputtering technique on p-Si substrates with a composite target of a single crystalline SiC containing several Al pieces on the surface. The as-deposited films were annealed in the temperature range of 400-800 °C under nitrogen ambient. The thin films have been characterized by X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR) and scanning electron microscopy (SEM). The results show that the introduction of Al into films hinders crystalline formation process. And with the increase of annealing temperature, more Si particles are formed in the films, which strongly affect the optical absorption properties. The photoluminescence (PL) spectra of the samples show two peaks at 370 nm and 412 nm. The intensities of the PL peaks are evidently improved after Al doped. We attribute the origin of the two PL peaks to a kind of Si-related defect centres. The obtained results are expected to have important applications in modern optoelectronic devices.     

拟南芥胚的不同区域对MeV离子辐照的响应

利用不同能量的质子在大气环境中辐照拟南芥的含水种子，能量从1.1MeV到6.5MeV.根据模拟计算结果，相应能量的离子对种子的损伤区域分别为胚的浅层、胚的一半和整个胚.本实验中，具有较高能量的质子可以完全均匀地作用于拟南芥生长、发育及遗传密切相关的胚茎端分生组织，而能量较低的质子则不能直接作用于茎端分生组织.实验所用质子注量范围为4×10⁹ions/cm²—1×10¹⁴ions/cm².实验结果显示，虽然拟南芥种子的发芽率和幼苗存活率随离子注量增加都呈现下降的趋势，但对应于不同的胚损伤区域，即在不同的入射质子能量条件下，注量曲线具有各自的特征.实验结果显示，拟南芥种子中除了胚茎端分生组织作为对离子辐照敏感的辐射主靶外，茎端分生组织之外的胚区域可能作为离子辐射次靶，影响到最终的辐射生物学效应. 关键词： 离子辐照 拟南芥 胚区域 生物效应