A continuous decomposition of the Menger curve into pseudo-arcs

It is proved that the Menger universal curve admits a continuous decomposition into pseudo-arcs with the quotient space homeomorphic to .

     

一维光子晶体结构参数对禁带带隙的影响研究

采用平面波法(PWM)计算一维光子晶体的带隙结构。分别就构造一维光子晶体结构的高低折射膜层的介电常数及填充比(高折射膜层的厚度与晶体周期长度的比值)对禁带带隙宽度的影响作出分析。通过最小二乘曲线和曲面拟合得到带宽与介电常数或带宽与填充比的函数关系图，以确定最佳的禁带带宽，从而设计一维光子晶体的周期结构。对高低折射膜层为GaAs/空气组成的一维光子晶体，介电常数比约为13/1，当填充比为0.16时，计算得禁带带宽为0.2564×2πc/Λ，禁带的中心频率为0.3478×2πc/Λ，与实验数据吻合。     

一种简便的计算层析系统X射线硬化校正方法

以实物拍摄为依据,用一种最简便的修正方法解决计算机X射线层析术成像时由于硬化效应引起的切片图灰度失真问题。用高性能数字X射线机FAXITRON MX-20(射线管焦点20μm,探测板灰度等级16位)对不同厚度的物体进行透射成像,测得对应的透射光强度,并利用新创的指数拟合法得到理想的拟合曲线,由此推导硬化效应的指数校正公式;最后利用实验室的微型计算机层析设备进行扇形束扫描,并逆投影重建生成计算层析断层图像,验证了该校正方法的实用性。该指数拟合法的误差不到常用的二阶多项式拟合法的1/3,对物体计算层析重构,硬化校正以前有明显的“杯状”伪迹,切片灰度不均匀,用指数法修正以后该伪迹消失,切片灰度均匀。     

Excess molar heat capacity of isobutyric acid–water binary liquid mixtures near and far away from the critical temperature

The heat capacity of the liquid–liquid mixture isobutyric acid–water has been measured for the first time near and far away from its critical point using an adiabatic calorimeter. The measurements were performed at atmospheric pressure, in the one phase region as a function of three temperatures: (1) T − T_C = 0.055 °C, (2) T − T_C = 3.055 °C, (3) T − T_C = 8.055 °C and of the composition X in acid (IA). The heat capacity C_p decreases rapidly when X increases at the used temperatures. Near the critical composition, C_p is not affected by the correlation of the concentration fluctuations.

The molar excess heat capacity of the system under investigation was analysed along the phase diagram and considered as a structural transformation effect.     

The dual bases for the Bézier-Said-Wang type generalized Ball polynomial bases and their applications

A unifying representation for the existing generalized Ball bases and the Bernstein bases are given. Then the dual bases for the Bézier-Said-Wang type generalized bases (BSWGB for short) are presented. The Marsden identity and the mutual transformation formulas between Bézier curve and Bézier-Said-Wang type generalized curve (BSWGB curve) are also given. These results are very useful for the applications of BSWGB curves and their popularization in CAGD. Numerical examples are also given to show the effectiveness of our methods.     

Relation of structure to performance characteristics of monolithic and perfusive stationary phases

Commercially available polymer-based monolithic and perfusive stationary phases were evaluated for their applicability in chromatography of biologics. Information on bed geometry, including that from electron microscopy (EM), was used to interpret and predict accessible volumes, binding capacities, and pressure drops. For preparative purification of biologics up to at least 7 nm in diameter, monoliths and perfusive resins are inferior to conventional stationary phases due to their low binding capacities (20–30 g/L for BSA). For larger biologics, up to several hundred nanometers in diameter, calculations from EM images predict a potential increase in binding capacity to nearly 100 g/L. The accessible volume for adenovirus calculated from the EM images matched the experimental value. While the pores of perfusive resins are essentially inaccessible to adenovirus under binding conditions, under non-adsorbing conditions the accessible intrabead porosity is almost as large as the interbead porosity. Modeling of breakthrough curves showed that the experimentally observed slow approach to full saturation can be explained by the distribution of pore sizes.     

Visco-penalization of the sum of two monotone operators

A new type of approximating curve for finding a particular zero of the sum of two maximal monotone operators in a Hilbert space is investigated. This curve consists of the zeros of perturbed problems in which one operator is replaced with its Yosida approximation and a viscosity term is added. As the perturbation vanishes, the curve is shown to converge to the zero of the sum that solves a particular strictly monotone variational inequality. As an off-spring of this result, we obtain an approximating curve for finding a particular zero of the sum of several maximal monotone operators. Applications to convex optimization are discussed.     

On S-Shaped Bifurcation Curves for a Class of Perturbed Semilinear Equations

By making use of bifurcation analysis and continuation method, the authors discuss the exact number of positive solutions for a class of perturbed equations. The nonlinearities concerned are the so-called convex-concave functions and their behaviors may be asymptotic sublinear or asymptotic linear. Moreover, precise global bifurcation diagrams are obtained.     

Supersimplicity and quadratic extensions

An elliptic curve over a supersimple field with exactly one extension of degree 2 has an s-generic point. A. Martin-Pizarro would like to express his gratitude to the organisation of the Florida Logic year, in which he took part. Martin-Pizarro research was supported by a DFG-Forschungsstipendium MA3310/1-1. F. O. Wagner is a Membre junior de l’Institut Universitaire de France. Work done during the semester on Model Theory and Applications in Algebra and Analysis at the Isaac Newton Institute for the Mathematical Sciences, whose hospitality is gratefully acknowledged.     

Some inverse problems in rheology leading to integral equations

Two inverse problems of the integral type, which are of the general importance to rheology, are discussed. The first of them is the possibility of calculating the molecular weight distribution (MWD) from the flow curve and the second one is the interrelation between creep and relaxation functions. It was shown that the first problem is incorrect and any solution is unstable in respect to minor experimental errors. It means that the general solution of this problem is impossible in principle and only estimations of the width of unimodal MWD can be received from the curvature of the flow curve. The possibility of the correct calculation of the creep function exists in case the relaxation curve being approximated by the sum of exponential members. But the approximation of the relaxation curve within the experimental accuracy is the necessary, but not sufficient condition for the correct solution of this integral inverse problem, because not every mode of approximation leads to the satisfactory prediction of creep function.Delivered as the Courtaulds Lecture at the Golden Jubilee Conference of the British Society of Rheology and Third European Rheology Conference, Edinburgh, 3–7 September, 1990.