几个数学题目

下面所谈的几个数学题目,都是大家所熟知的,我觉得它们还有一定底兴趣,因而把它们以及它们的解法谈一下,也许可以作为中学里科学小组的参考材料。第一个问题已知圆上三点A,B,C。求作此圆的一个内接三角形A′B′C′使得这个三角形的三条平分角线恰好与圆分别交于已知点A,B,C。如果单纯借助于平面几何的知识去解这个问题也许是比较困难的,但如果利用一点初中代数的知识,那么这个问题就变得很容易了。我们在圆上先画一个内接三角形A′B′C′,然后作这个三角形的三条平分角线,分别交圆于A,     

一类三阶非线性分布时滞动力方程的振动结果

研究一类三阶非线性分布时滞动力方程的振动性,通过构造广义Riccati变换得到一类新的广义Riccati不等式,利用积分平均技巧等方法,建立了保证该方程一切解均振动或收敛于0的若干新的振动结果,推广和改进了近期文献的相关结论,并给出了若干例子。     

Baseline drift effect on the performance of neutron and γ ray discrimination using frequency gradient analysis

Frequency gradient analysis (FGA) effectively discriminates neutrons and γ rays by examining the frequency-domain features of the photomultiplier tube anode signal. This approach is insensitive to noise but is inevitably affected by the baseline drift similar to other pulse shape discrimination methods. The baseline drift effect is attributed to factors such as power line fluctuation, dark current, noise disturbances, hum, and pulse tail in front-end electronics. This effect needs to be elucidated and quantified before the baseline shift can be estimated and removed from the captured signal. Therefore, the effect of baseline shift on the discrimination performance of neutrons and γ rays with organic scintillation detectors using FGA is investigated in this paper. The relationship between the baseline shift and discrimination parameters of FGA is derived and verified by an experimental system consisting of an americium-beryllium source, a BC501A liquid scintillator detector, and a 5 GSample/s 8-bit oscilloscope. The theoretical and experimental results both show that the estimation of the baseline shift is necessary, and the removal of baseline drift from the pulse shapes can improve the discrimination performance of FGA.     

Third-Order Optical Nonlinearity in Novel Porphyrin Dimers

We investigate the third-order optical nonlinearities in four novel porphyrin dimers （dimers A to D） and a monomeric porphyrin H2 CPTPP measured by using the single-beam z-scan technique with a pulsed Q-switched Nd：YAG nanosecond laser at 532nm. All the samples show strong excited state absorption （ESA） and high value of Х^（3） in the ns domain at this wavelength. We perform a comparison between dimer A and its monomer H2 CPTPP in their third-order optical nonlinearity, and discuss the relationships between the values of Х^（3） and the different bridging groups for all the dimers.     

Al2O3/SnO2 Co-Nanoparticle Modified Grafted Collagen for Improving Thermal Stability and Infrared Emissivity

Al2O3/SnO2 co-nanoparticles were prepared with a modified sol-gel technique followed by a thermal treatment process. With these co-nanoparticles the grafted collagen-Al2O3/SnO2 nanocomposites were obtained using a supersonic dispersion method. X-ray diffraction, FT-IR analysis, transmission electron microscopy, TGA/DTA and infrared emissivity test were performed to characterize the resulting nanoparticles and nanocomposites, respectively. The Al2O3/SnO2 co-nanoparticles showed a narrow distribution of size between 20-40 nm and could be uniformly absorbed on the tri-helix scaffolds of the grafted collagen without any aggregation. The nanocomposites possessed better thermal stability and substantially lower infrared emissivity than the grafted collagen and Al2O3/SnO2 co-nanoparticles with an increase of degradation temperature from 39 to 210 ℃ and a decrease of infrared emissivity from 0.850 of the grafted collagen and 0.708 of the Al2O3/SnO2 co-nanoparticles to 0.424, which provided a potential application of the nanocomposites to areas such as photoelectronics.     

工业CT技术及其NDT应用

ＣＴ（Ｃｏｍｐｕｔｅｄ Ｔｏｍｏｇｒａｐｈｙ）,即计算机层析成像技术或计算机断层扫描技术,是一种高新技术．它是物理学和计算机科学的发展产物,或者说,它是核物理学与现代图像理论相结合而产生的一门边缘学科．ＣＴ技术最引人注目的应用是在医学临床诊断领域,被人们称作医用ＣＴ（ＭＣＴ）,用于对人体的病灶作断层扫描,尔后以图像方式分析和确定病状．对此,医用ＣＴ已是家喻户晓,成为临床医学诊断不可或缺最为有效的手段．如今,医用ＣＴ已发展到了第五代,即超高速动态三维ＣＴ．因此,ＣＴ技术被公认为是２０世纪后期最伟大…     

Numerical investigation of three-dimensional viscous incompressible flows in divergent curved channels and turbulent model study

In order to make the numerical calculation of viscous flows more convenient for the flows in channel with complicated profile governing equations expressed in the arbitrary curvilinear coordinates were derived by means of Favre density- weighted averaged method, and a turbulent model with effect of curvature modification was also derived. The numerical calculation of laminar and turbulent flows in divergent curved channels was carried out by means of parabolized computation method. The calculating results were used to analyze and investigate the aerodynamic performance of stator cascades in compressors preliminarily.     

高三数学首轮复习“四为主七环节”教学模式

搞好高三数学首轮复习,是搞好整个高三数学复习的关键．毫无疑问,实现这一教学任务的主阵地在课堂．为了改变目前高三数学首轮复习课堂教学中存在的“或机械地使用现存资料,或对新授的知识进行简单的重复再现”;“以讲代练,堂上老师灌,作业模仿做”等倾向,进一步优...     

配方(下)

５　求抛物线的顶点、焦点、焦距和准线设ｌ是一条确定的直线,Ｆ是一个确定的点,距离ｌ和Ｆ等远的点的轨迹叫抛物线,为了描述抛物线,在平面上建立坐标系,设Ｆ点到直线ｌ的距离等于ｐ;再设Ｆ点的坐标是（０,１２ｐ）,直线ｌ的方程是ｙ＝－１２ｐ．那么抛物线上一点（ｘ,ｙ）就应该满足条件（ｘ－０）２＋（ｙ－ｐ２）２＝（ｙ＋ｐ２）．化简上式,得　ｙ＝１２ｐｘ２．（１３）（１３）就叫抛物线的方程,ｌ叫准线,Ｆ叫它的焦点,ｐ叫它的焦距,直线ｘ＝０是它的对称轴,而对称轴和抛物线的交点（０,０）叫它的顶点;图３　抛物线…     

酶法测定葡萄糖

利用已糖激酶、６－磷酸葡萄糖脱氢酶偶联而催化葡萄糖反应的原理,通过还原型烟酰胺腺嘌呤二核苷酸磷酸的吸光度变化率得出 酶促反应速度,采用标准曲线法了葡萄糖的含量。检出限为７×１０＾－７ｍｏｌ／Ｌ。