高维情形的Routh定理

本文研究了n维欧氏空间En中n维单形的体积有关问题.利用距离几何的理论与解析方法,建立了n维情形的Routh定理,作为其特例建立了n维情形的Ceva定理.     

巧消元解＂华约＂自主招生题

2011年“华约”自主招生落下帷幕,考生谈论中都指出,有道题,涉及解方程,会做,但在有限的时间我们都很难做到底．真是如此吗？根据考生回忆,笔者尝试分析这道题到底有什么玄机,给出不同解法,并评析其优劣,以飨读者,不妥之处望读者批评指正．为此,先将题目摘抄如下．     

A simulation study of a dual-plate in-room PET system for dose verification in carbon ion therapy

During carbon ion therapy, lots of positron emitters such as 11C, 15O, 11C are generated in irradiated tissues by nuclear reactions, and can be used to track the carbon beam in the tissue by a positron emission tomography （PET） scanner. In this study, an dual-plate in-room PET scanner has been designed and evaluated based on the GATE simulation platform to monitor patient dose in carbon ion therapy. The dual-plate PET is designed to avoid interference with the carbon beamline and with patient positioning. Its performance was compared with that of four-head and full-ring PET scanners. The dual-plate, four-head and full-ring PET scanners consisted of 30, 60, 60 detector modules, respectively, with a 36 cm distance measurements. Each detector module consisted of a between directly opposite detector modules for dose deposition 24~24 array of 2 mm×2 mm×18 mm LYSO pixels coupled to a Hamamatsu H8500 PMT. To estimate the production yield of positron emitters, a 10 cm×15 cm×15 cm cuboid PMMA phantom was irradiated with 172, 200, 250 MeV/u 12C beams. 3D images of the activity distribution measured by the three types of scanner are produced by an iterative reconstruction algorithm. By comparing the longitudinal profile of positron emitters along the carbon beam path, it is indicated that use of the dual-plate PET scanner is feasible for monitoring the dose distribution in carbon ion therapy.     

HIRFL装置主动式点扫描束流配送系统的Monte Carlo模拟优化

为获得适用于HIRFL 装置主动式点扫描束流配送系统配送的碳离子束,利用Monte Carlo (MC) 工具SHIELD-HIT12A 研究了配送距离和微型脊形过滤器结构周期对治疗室等中心处束斑半高宽(FWHM) 和剂量平坦度的影响。模拟研究发现:束流配送距离越短,束斑FWHM越小,但剂量平坦度越差;微型脊形滤器结构周期是影响剂量平坦度的关键因素,周期越小,剂量平坦度越好。通过模拟研究得出:在HIRFL装置重离子治疗终端将真空窗设置在距等中心距离小于125 cm 时,采用结构周期为2 mm微型脊形过滤器可以满足主动式点扫描照射对束斑FWHM和剂量平坦度的要求。To obtain carbon ion beams suitable for the active spot scanning beam delivery system at the Heavy Ion Research Facility in Lanzhou (HIRFL), the Monte Carlo program SHIELD-HIT12A was used to study the influences of beam delivery distance and structure period of mini ridge filter on full width at the half maximum (FWHM) of beam spot and dose flatness at the isocenter of the treatment room. The present simulation study shows that the shorter was the beam delivery distance, the smaller was the FWHM of beam spot, but the worse was the dose flatness. The structure period of mini ridge filter was a key factor to account for the dose flatness at the isocenter. The smaller was the structure period of mini ridge filter, the better was the dose flatness. Based on the simulation results, we conclude that 2 mm structure period for a mini ridge filter statisfies the requirements on the FWHM of beam spot and dose flatness at the isocenter for the active spot scanning beam delivery system at HIRFL when the distance between the vacuum window and the isocenter is set shorter than 125 cm in the nozzle.     

低阻抗大面积二极管的研制

采用高纯石墨环状阴极和有机玻璃绝缘子,研制了一套低阻抗大面积二极管系统。使用理论计算和数值模拟方法对二极管进行优化设计,在保证绝缘要求的同时,尽量优化二极管轴向长度和内外筒距离以减小二极管的回路电感。实验结果表明,优化后的二极管能在200 kV左右的电压上稳定工作,绝缘结构未发生击穿现象;实验中最高输出电压为213 kV,电流为221 kA,特性阻抗约为1 ,电流密度为8 kA/cm2,脉宽(FWHM)为50 ns。     

FeCl3催化羰基化合物的还原卤代反应

在甲基二氯硅烷作用下, FeCl₃能催化羰基化合物(醛、酮)的还原氯代反应, 得到相应的氯代产物; 在甲基二氯硅烷、PBr₃或NaI作用下, FeCl₃可以催化羰基化合物(醛、酮)的还原溴代或碘代反应, 分别以良好的收率得到相应的溴代烷或碘代烷.     

竹胶板-薄壁钢管约束收尘石粉混凝土组合柱轴压性能

提出一种新型的竹胶板-薄壁钢管复合约束收尘石粉混凝土组合柱(BSDCC),对10根BSD-CC试件进行轴压试验,考察试件的破坏特点和形态,调查收尘石粉混凝土的含量率和强度、试件长细比、截面组合与拉杆约束方式、拉杆间距比对试件承载能力和变形的影响规律.结果表明,BSD-CC试件的受压破坏形态主要为试件中部约束拉杆之间竹胶...     

高效液相色谱法测定平胃丸中橙皮苷的含量

提出了高效液相色谱法测定平胃丸中橙皮苷含量的方法。采用Hypersil BDS C18(200mm×4.6mm,5μm)色谱柱;以甲醇-乙酸-水(35+4+61)混合溶液为流动相,流量1mL.min-1,检测波长为283nm,橙皮苷的质量浓度与峰面积在8.08～121.2mg.L-1范围内呈线性关系。方法用于平胃丸中橙皮苷的测定,平均回收率为101.1%,相对标准偏差(n=9)为1.2%。     

非贵金属催化酮的不对称硅氢加成反应的研究进展

手性二级醇作为手性药物、香料等的原料,主要通过不对称加氢来制备.近来通过不对称硅氢加成的方法来制备手性醇的方法,由于其温和的反应条件及相对低廉的催化剂成本而受到广泛关注.介绍了近年来锌、铁、铜、钛等非贵金属催化剂催化潜手性酮的不对称硅氢加成反应的研究进展.     

傅里叶变换红外光谱法检测脑肿瘤

应用傅里叶变换红外光谱法检测了28例液氮冻存的离体脑肿瘤样本及其残留物(将脑肿瘤样本从ATR的ZnSe晶片上取下,样本在ZnSe晶片上沾染后留下的物质).结果发现,神经鞘瘤和神经上皮组织肿瘤(如星形细胞瘤等)的主要特征吸收峰存在明显差异,因此可从各个特征吸收峰的峰位、峰形及不同谱峰强度比的变化来初步鉴别脑肿瘤的性质,脑肿瘤组织样品残留物的红外光谱也可反映不同性质脑肿瘤的差异.与脂类糖蛋白以及核酸相关的谱带变化分析表明,通过特征峰强比(I1460cm-1/I1400cm-1,I1160cm-1/I1120cm-1和I1160cm-1/I1080cm-1)来鉴别肿瘤的性质与病理诊断结果的符合率超过85%.