数量标号对偶变维数不动点算法和组合引理

本文给出一个数量标号的八面形变维数不动点算法，它是Ｌａａｎ和Ｔａｌｍａｎ算法的对偶形式。利用这算法，证明了比Ｆｒｅｕｎｄ组合引理更强的结果。另一方面，这算法可用于计算某些连续映射的零点，且具有跟踪连通零点集的功能。     

耗散孤立波方程的吸引子

本文研究耗散孤立波方程的长期动力学行为：吸引子的存在性、吸引子的几何结构、耗散系统参数扰动下动力行为、吸引子的分形维估计．     

Neural Computation of Wide Aperture Dimension of Optimum Gain Pyramidal Horn

A new method based on the multilayered perceptron neural network architecture for computing the wide aperture dimension of the pyramidal horn is presented. The computed wide aperture dimension is used in successfully designing optimum gain pyramidal horn. The other design parameters of the horn are determined from the simple and explicit analytical formulas. These formulas do not need the application of the iterative methods, and are not restricted to the high gain horn designs. The gain of a designed pyramidal horn is determined with no path length error approximation. Better accuracy with respect to the previous design methods is obtained for various pyramidal horn design examples.     

广义Fitz－Hugh－Nagumo方程组的整体吸引子及惯性流形

本文考虑广义Ｆｉｔｚ－Ｈｕｇｈ－Ｎａｇｕｍｏ方程组的初边值问题．去掉解属于某不变区域的限制，我们证明了初值属于Ｌ２情形下整体吸引子的存在性，并给出其维数估计．对二维情形证明了其惯性流形的存在性．我们的方法简化了Ｐ．Ｃｏｎｓｔａｎｔｉｎ等人的工作．     

Chaotic dynamics in agricultural markets

In a recent article, Chiarella [7] used a nonlinear supply curve with exactly one inflection point in the context of a cobweb model in order to make plausible that chaotic behaviour may result in such a model. There is, however, no exact proof under what conditions chaos can actually show up since Chiarella confines the analysis to a second order approximation to his difference equation. In a somewhat different model (a linear supply and a nonlinear demand curve which can be given a microeconomic foundation) we show that, under the formation of adaptive price expectations, the resulting adjustment mechanism can generate a wide range of dynamic behaviour (depending on the prevailing parameter constellations) such as stability, bifurcations with stable cycles of period 2, 4, 8, ... and, finally, aperiodic time paths, (i.e. we can show that period-3 cycles exist). In a second step, long historical time series of weekly price observations in German agricultural markets are scrutinized with regard to the hypothesis of nonlinearities. We study their correlation dimensions only recently employed by economists as a characteristic measure which allows, under certain conditions, to distinguish between deterministic chaos and random noise. Our results do not provide evidence to reject the hypothesis, although noise infection of the series cannot be ruled out.     

一类半鞅样本轨道的Fractal性质

本文用Ｈａｕｓｄｏｒｆｆ维数刻画了一类半这样本轨道的Ｆｒａｃｔａｌ性质，并由此研究了Ｂｒｏｗｎ运动与有界变差过程的碰撞问题．     

断裂表面的分形维数及其测量

本文介绍了作为表征断裂表面特征参数的分形维数的概念及其在非平面表面定量分析与微观断裂机制研究中的应用。具体介绍了测定断裂表面分形维数的各种实验方法,并对各种材料的实验结果和不同的观点进行了综述与讨论。     

Quantum cosmology inR 1×S 1×S n space time

Classical and quantum cosmological aspects for (n + 2) dimensional anisotropic spherically symmetric space-time with topology of (n + 1) spaceS ¹×S ⁿ have been studied. The Lorentzian field equations are reduced to an autonomous system by a change of field variables and are discussed near the critical points. The path integral expression for propagation amplitude is converted to a single ordinary integration over the lapse function by the usual technique and is evaluated in terms of Bessel functions.     

关于平面曲线的分形维数

关于平面曲线的分形维数邓冠铁（武汉华中理工大学教学系，武汉４３００７４）关键词分形维数，平面曲线，周期函数．分类号ＡＭＳ（１９９１）２８Ａ８０／ＣＣＬＯ１７４．１２为方便起见，采用如下定义和符号：设为平面上有界非空集，对ε＞０，用Ｇ（ε）＝｛（ｘ，ｙ...     

Fractal study of Ni–Cr–Mo alloy for dental applications: effect of beryllium

Different Ni-based alloys with various compositions were prepared by varying the amounts of beryllium. Effect of the amount of beryllium added to the alloy on its corrosion in an electrolyte solution of artificial saliva was investigated. Fractal dimension was used as a quantitative factor for surface analysis of the alloys before and after storage in the artificial salvia. The fractal dimensions of the electrode surfaces were determined by means of the most reliable method in this context viz. time dependency of the diffusion-limited current for a system involving “diffusion towards electrode surface”. The results showed that increase of the beryllium amount in the alloy composition significantly increases the alloy corrosion. It is accompanied by increase of the fractal dimension and roughness of the electrode surface, whereas a smooth and shiny surface is required for dentures. From the methodology point of view, the approach utilized for fractal analysis of the alloy surfaces (Au-masking of metallic surfaces) is a novel and efficient method for study of denture surfaces. Generally, this approach is of interest for corrosion studies of different metals and alloys, particularly where changes in surface structure have a significant importance.