An Improved Computing Method for Analysing the Spatial Resolved Reflectance from Biological Tissues

A mathematical expression of refiectance point-spread function, which is defined as the spatial distribution of light diffuse-reflected from bio-tissues irradiated by an infinitely narrow photon beam, is derived from the difusion approximation (DA) theory. With the introduction of reflectance point-spread function to describe the reflectance characteristics of bio-tissues, the convolution method is used to calculate the spatial resolved reflectance from dense and thick tissues irradiated by different photon beams. This is called the DA based convolution method and is used to calculate the responses of the semi-infinite bio-tissues irradiated by a Gaussian beam and a flat beam with different beam radius. The calculation results show that the DA based convolution method has much higher computing efficiency compared to the Monte Carlo method.     

高中《数学课程标准》中的“空间向量”

“向量”在中学数学中的地位日益显著．在最新的2002年《高中数学教学大纲》中，除了包含必修的“平面向量”，还在“直线、平面、简单几何体”中增添了新的(B)方案，“空间向量”在该方案中占有重要地位．而在新研制的高中《数学课程标准》(实验稿)(以下简称《标准》)中，“向量”的份量进一步加重，“平面上的向量”是必修的数学4中的重要内容，“空     

已获得苯的单个环状影像

IBM的科学家利用扫描隧道显微镜(STM)已获得清晰的六员环状苯的影像,外形很象用空间填充分子模型所得的图象,证实了化学家几十年来对苯的分子结构的认识是正确的。这是IBM在苏黎世的研究实验室1981年发明的一种技术,利用一支微细的探针在距样品表面约10?处进行扫描,当探针加有电压时,探针与样品间有电流通过,表面高低而引起的电流变化可灵敏地指示出表面间高度的差异。加州San Jose IBM Almaden研     

孔穴可用温度调制的亲油性大穴穴状体

意大利化学家E.Dalcanale等人最近合成了一种亲油性大灾穴状体(la和lb),这种穴状体的构象可用温度调制。温度在-60℃或以下时,以伸展型la(C_(2v)对称性)为主,温度高于5℃时,以器皿型件lb(C_(4v     

Ir~( 49)M壳层共振自电离速率

研究了对电子碰撞激发速率共振自电离速率的影响，并且计算了类镍铱离子３ｄ到４ｌ共振激发速率，其作用对研究Ｘ射线激光设计、高温等离子体等诸多应用都有很重要的影响。     

仿射极大曲面的Weierstrass公式及其应用

本文主订研究如何用Ｗｅｉｅｒｓｔｒａｓｓ公式构造仿射极大曲面；并应用Ｗｅｉｅｒｓｔｒａｓｓ公式证明Ａ＾３中不存在紧致无边的仿射极大曲面。     

Finite Integral Transform Solutions for Free Vibrations of Rectangular Thin Plates With Mixed Boundary Constraints北大核心CSCD

Analytical solutions, with unique research value, can serve as benchmarks for empirical formulas and numerical methods, a tool for rapid parameter analysis and optimization, and a theoretical basis for experimental designs. Conventional analytical methods, e.g., the Lévy solution method, are only applicable to mechanical problems of plates and shells with opposite simply-supported edges, which, however, may fail to obtain analytical solutions for the issues with complex boundary constraints. In recent years, the finite integral transform method for plate and shell problems was developed to deal with non-Lévy-type plates and shells, but it is still infeasible to solve the mixed boundary constrains-induced complex boundary value problems of higher-order partial differential equations. Herein, for the first time, the finite integral transform method was combined with the sub-domain decomposition technique to solve the free vibrations of rectangular thin plates with mixed boundary constraints. The rectangular plate was first divided into 2 sub-domains according to the mixed boundary constraints, and the 2 sub-domains were solved analytically with the finite integral transform method. Finally, the continuity conditions were introduced to obtain the analytical solution of the original problem. Based on the side spot-welded cantilever plates commonly used in engineering, the free vibration problem of a rectangular thin plate with 1 edge subjected to clamped-simply supported constraints and the other 3 edges free, was analyzed. The obtained natural frequencies and mode shapes are in good agreement with those from the finite element method as well as the solutions in literature, thus verifying the accuracy of the proposed method. The solution procedure of the finite integral transform method can be implemented based on the governing equations without any assumption of the solution form. Therefore, this strict analytical method is widely applicable to complex boundary value problems of higher-order partial differential equations for such mechanical problems of plates and shells. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

用胞映射方法讨论GKDV方程全局吸引域

本文用胞映射方法画出了GKDV方程未受扰系统和受扰系统的全局吸引域、r步吸引域。     

AM/AA/APEG/NANB共聚物的合成与性能研究

通过丙烯酰胺(AM),丙烯酸(AA),烯丙醇聚氧乙烯醚(APEG)和N,N-二烯丙基苄胺(NANB)制备共聚物P(AM/AA/APEG/NANB)。确定了最佳反应条件:m(AM)∶m(AA)=6.5∶3,APEG为5 wt%,NANB加量0.2 wt%,pH为7,反应温度40℃,引发剂0.4 wt%。通过IR和1H NMR确定了聚合物的分子结构,并对其进行性能测试。结果表明:2000 mg·L-1的AM/AA/APEG/NANB溶液具有较好的流变性能(120℃,粘度保留率:38.56%;1000 s-1,粘度保留率:17.93%)和抗盐性能(20 000 mg·L-1Na Cl,2000 mg·L-1Mg Cl2或Ca Cl2,粘度保留率分别为22.14%、18.34%和15.33%),且提高采收率可达16.12%。     

聚苯氧基磷酸联苯二酚酯/聚磷酸铵膨胀阻燃剂对环氧树脂阻燃性能影响研究

以聚苯氧基磷酸联苯二酚酯(PBPP)与聚磷酸铵(APP)组成复合阻燃剂,对环氧树脂(EP)进行阻燃改性.通过氧指数(LOI)、垂直燃烧(UL-94)、热失重(TGA)、锥形量热(CONE)和扫描电镜(SEM)等方法研究改性环氧树脂的阻燃性能和阻燃机理.结果表明,PBPP/APP体系对EP具有较好的阻燃性能,阻燃剂添加量为10%时能使环氧树脂的氧指数提高到29.6%,垂直燃烧等级达到UL94 V-0级,残炭量大大增加;平均热释放速率下降45.7%,热释放速率峰值下降51.0%,有效燃烧热平均值下降21.1%;TGA、CONE、SEM等综合分析显示了PBPP/APP改性后的环氧树脂比纯环氧树脂具有更高的热稳定性,燃烧后能够形成连续、致密、封闭、坚硬的焦化炭层,在聚合物表面产生有效覆盖、隔绝了氧气,改善了环氧树脂的燃烧性能.