Photon interaction studies using 241Am γ-rays

We have carried out some photon interaction measurements using 59.54 keV γ-rays from a ²⁴¹Am source. These include γ attenuation studies as well as photoelectric absorption studies in various samples. The attenuation studies have been made using leaf and wood samples, samples like sand, sugar etc., which contain particles of varying sizes as well as pellets and aqueous solutions of rare earth compounds. In the case of the leaf and wood samples, we have used the γ-ray attenuation technique for the determination of the water content in fresh and dried samples. The variation of the attenuation coefficient with particle size has been investigated for sand and sugar samples. The attenuation studies as well as the photoelectric studies in the case of rare earth elements have been carried out on samples containing such elements whose K-absorption edge energies lie below and close to the γ-energy used. Suitable compounds of the rare earth elements have been chosen as mixture absorbers in these investigations. A narrow beam good geometry set-up was used for the attenuation measurements. A well-shielded scattering geometry was used for the photoelectric measurements. The mixture rule was invoked to extract the values of the mass attenuation coefficients for the elements from those of the corresponding compounds. The results are consistent with theoretical values derived from the XCOM package.     

Viscoelasticity and birefringence of polyisoprene

The complex Young's modulus, E^*(ω), and the complex strain-optical coefficient, O^*(ω), which is the ratio of the birefringence to the strain, were measured for polyisoprene (PIP) over a frequency range of 1 ～ 130 Hz and a temperature range of 22 ～ ?100°C. The imaginary part of O^*, O″, was positive at low frequencies and negative at high frequencies. The real part, O′, was always positive and showed a maximum. The complicated behavior of O^* could be understood by the assumption that E^* = E_R^* + E_G^* and O^* = C_RE_R^* + C_GE_G^*, where E_R^* and E_G^* were complex quantities and C_R and C_G were constants. The C_R value, equal to the ordinary stress-optical coefficient measured in the rubbery plateau zone, was 2.0 × 10^?9 Pa^?1. The C_G value, defined as the ratio O″/E″ in the glassy zone, was ?1.1 × 10^?11 Pa^?1. The E_G^*, which was the major component of E^* in the glassy zone, showed almost the same frequency dependence as that of polystyrene and polycarbonate. The E_R^*, which was dominant in the rubbery zone, was described well by the bead-spring theory. The temperature dependence of the E_G^* was stronger than that of the E_R^*. This difference caused the breakdown of the thermorheological simplicity for E^* and O^* around the glass-to-rubber transition zone. © 1995 John Wiley & Sons, Inc.     

Chen’ s theorem in arithmetical progressions

LetN be a sufficiently large even integer and

纳米二氧化锆制备过程的DSC、TGA和XRD研究

用ＤＳＣ、ＴＧＡ和ＸＲＤ技术研究了在沉淀法制备纳米ＺｒＯ２的过程中，残留ＮＨ４Ｃｌ、ｐＨ值、滴加方式、以及结构稳定剂Ｙ２Ｏ３的添加量对结晶过程的影响。结果表明，残留ＮＨ４Ｃｌ使结晶化温度降低，使放热过程变为吸热过程。而ｐＨ值、滴加方式和结构稳定剂的添加对结晶过程无明显影响。     

钙钛矿型CaSiO_3解压缩和重压缩过程的分子动力学模拟

用分子动力学模拟方法 (MD)研究了 3 0 0K时钙钛矿型CaSiO3 ,从高压到负压的解压缩过程 .MD模拟获得的P V关系与实验数据相近 ,与已报道的MD模拟数据基本一致 ,所得体积模量也在实验数据分布范围内 .减压缩和重压缩的MD模拟数据与实验结果相似 .钙钛矿型CaSiO3 解压缩成非晶态时 ,存在两个结构破坏阶段 :破坏硅氧八面体和破坏钙氧二十面体 .当钙氧二十面体被破坏后 ,重压缩不能得到钙钛矿型结构 .只要钙氧二十面体未被破坏 ,重压缩可恢复钙钛矿型结构 .本研究得到的结果尚未见相关报道 .由MD模拟数据计算了CaSiO3 系统的红外光谱 ,分析这些数据可知钙钛矿型CaSiO3 解压缩非晶化是一个二阶软模相变 .研究表明钙钛矿型CaSiO3 结构存在一个等容的亚稳极限 ,其解压缩非晶化是一个受动力学控制的亚稳状态 .     

USING MEASURING METHOD TO FIND AREA OF ENCLOSED PLANE REGION AND VOLUME OF ENCLOSED SPACE REGION

Two simple methods to calculate the area and volume called improved square gridmethod and cube cutting method are proposed in this paper. For any plane curve orspace surface satisfying certain conditions, by our method, the error of measurement isof the second infinitive order of measuring unit (the side length of the square grid or theside length of the little cube) when the unit is small enough. And when some properties ofthe curve or the surface can be found or its varying bounds can be evaluated, it is pointedout, in order to make the error smaller than any given value, how small the length of themeasuring unit should be.     

Interval estimation of the critical value in a general linear model

Summary This paper concerns interval estimation of the critical value θ which satisfies under the general linear model,Y _i =μ(x _i )+ε _i (i=1,2,···), where for and the functional forms off _j ^′ s are known. From an asymptotic expansion it is shown that, under reasonable conditions, the limiting distribution of is normal. Thus in the large-sample case a confidence interval for θ can be obtained. Such a result is useful when one is interested in carrying out a retrospective analysis rather than designing the experiment (as in the Kiefer-Wolfowitz procedure). In Section 3 a sequential procedure is considered for confidence intervals with fixed width 2d. It is shown that, for a given stopping variableN, is also asymptotically normal asd→0. Thus the coverage probability converges to 1−α (preassigned) asd→0. An example of application in estimating the phase parameter in circadian rhythms is given for the purpose of illustration. Research partially supported by the NSF Grant DMS-8502346.     

Existence and uniqueness for nonlinear boundary value problems in kinetic theory

A boundary value problem for the stationary nonlinear Boltzmann equation in a slab has been examined in a weightedL space. It has been proved that the problem possesses a unique solution for boundary data small enough. The proof is based on the implicit function theorem. It has also been shown that for the linearized problem the Fredholm alternative applies.