区域插值

在CAD,CAGD及工程技术中,曲面片之间的连接和光滑过渡是一个众所周知的重要问题,如二片Bezier曲面或Coons 曲面在交线处一般是不光滑的(如图1.1实线部分),因此要设计一张过渡曲面C(虚线部分)来光滑拼接这二张曲面,又如工程技术中,     

新题征展(69)

A 题组新编 1.已知ABCD为空间四边形,分别求下列情况下两对角线AC、BD所成的角:     

碳氢化合物/阻燃剂混合工质替代HCFC22的研究

为推进碳氧化合物(HCs)自然工质的安全应用,本文尝试引入阻燃组元,组成以自然工质为主体,环境特性、 安全性和循环性能俱佳的HCs/阻燃剂混合工质。对阻燃组元的选择原则和性能进行了探讨,通过理论循环分析,得出了 CO2/HC1270/R13I1等6种HCFC22替代物。     

Near-field lithography on the azobenzene polymer liquid crystal films

In this article, we reported near-field research on azobenzene polymer liquid crystal films using scanning near-field optical microscopy (SNOM). Optical writing and subsequently topographic reading of the patterns with subwavelength resolution were carried out in our experiments. Nanometer scale dots and lines were successfully fabricated on the films and the smallest dot diameter is about 120 nm. The width of the line fabricated is about 250 nm. This method is also a choice for nanolithography. The mechanism of the surface deformation on the polymer films was briefly analyzed from the viewpoint of gradient force in the optical near field. The intensity distribution of the electric field near the tip aperture was numerically simulated using finite-difference time-domain (FDTD) method and the numerical simulation results were consistent with the experimental results.     

关于逆向Pedoe不等式及其应用

本文给出著名的Pedoe不等式之逆向不等式(3),并利用它得出著名的Oppenheim不等式之逆向不等式(12)。此外,本文还给出正定厄米特矩阵的Minkouski不等式之逆向不等     

综合题新编选登

题 1 2 7　过点 (0 ,1)的直线l与曲线C :y =x+1x (x >0 )交于相异两点 ,设曲线C在这两点处的切线分别为l1与l2 ,求l1与l2 交点的轨迹 .解　设直线l与曲线C交于点M (x1,y1) ,N(x2 ,y2 ) ,l1与l2 交于点P(x ,y) ,直线l的斜率为k ,方程为 y =kx +1.对 y =x +1x求导 ,得 :y′ =1- 1x2 .则 y′|x =x1=1- 1x21,y′|x =x2 =1- 1x21.故直线l1的方程为y - (x1+1x1) =(1- 1x12 ) (x -x1) ,即 y =(1- 1x12 )x +2x1(1)同理 ,可求得l2 的方程为y =(1- 1x22 )x +2x2(2 )(1) - (2 )得 (1x22 - 1x12 )x +2x1- 2x2=0 .由于x1≠x2 ,解得x =2x1x2x1+x2(3)由 …     

常曲率空间中有限点集的两类几何不等式

应用距离几何的理论与方法,研究了n维常曲率空间中有限点集的一些几何度量之间关系,建立了常曲率空间中有限点集的两类几何不等式,推广了已有的结果.     

静电纺空气过滤用PET/CTS抗菌复合纳米纤维膜的制备

采用静电纺丝法制备PET/CTS复合纳米纤维膜,并在纤维膜表面吸附一层纳米银,进一步增加纤维膜的抗菌性能.以扫描电镜(SEM)对不同配比PET/CTS所制备的纤维膜的微观形貌进行表征,结果显示w(CTS)/w(PET)为12.5%时,纤维形貌较好,平均直径为405 nm.分别对不同厚度的PET/CTS纤维膜进行力学性能、透气性能以及空气过滤性能测试,结果表明纺丝时间为7 h时,纤维膜具有较好的性能,其弹性模量为48.15 MPa、断裂伸长率183.30%、拉伸断裂应力2.11 MPa、拉伸强度2.49 MPa、拉伸屈服应力1.23 MPa、最大力1.38 N,阻气值为3.99 k Pa·S/m,过滤效率为99.55%,压降为621.32 Pa.吸附银离子实验表明,最佳GA交联浴配比为GA(vol%)=3.5%.紫外可见光谱(UV)及透射电镜(TEM)表征证明,有10 nm左右纳米银生成.抑菌实验表明,载银PET/CTS复合纳米纤维膜对金黄色葡萄球菌(S.a.)和大肠杆菌(E.coli.)的杀菌率分别为99.97%和99.99%.     

吡唑类化合物的合成研究进展

吡唑类化合物是一类重要的药物合成中间体,在抗肿瘤、抗病毒、抗抑郁等领域发挥着重要作用。本文综述了吡唑类衍生物的合成方法,包括1,3-亲电化合物与肼类的环化、1,3-偶极体系的环加成等。     

BURNING OF SINGLE CARBON PARTICLE APPROACHED BY ACTIVATION ENERGY ASYMPTOTICS

The method of activation energy asymptotics is used to treat the combustion of a singlecarbon particle in quiescent gas mixture with high temperature.Both heterogeneousreactions 2C+O_2→2CO,C+CO_2→2CO and homogeneous reaction2CO+O_2 (?) 2CO_2 are considered.It is shown that the burning of the particle principallyis carried out during a diffusion-limited period.Four brief and complex periods throughwhich the history of the particle evolves from a heat-up period to the diffusion-limited periodare described.A comparison between results of activation energy asymptotics and e(?)numerical solutions is given.The agreement is considered satisfactory.