Bush连续不可微函数的分形性质

本文对用递推关系确定的Bush连续不可微函数,找出了迭代函数系(IFS),从而得到它的级数表达式和所具有的自仿射分形的有关性质.最后还计算出函数图象的Hausdorff 维数的准确值.     

一类4阶Feigenbaum映射的拟极限集

讨论一类4阶Feigenbaum映射的拟极限集及其Hausdorff维数, 并证明对任意t∈(0,log_3^1/2+12), 总存在一类具有简单轨 的4阶非单谷Feigenbaum映射， 它有一个以t为Hausdorff维数的拟极限集.     

Study of the pulsed laser vapor doping of Si(1 0 0) with KrF excimer laser and BCl3 gas

The properties of pulsed laser vapor doping on p-Si(1 0 0) with a KrF (248 nm) excimer pulsed laser (248 nm) and BCl₃ gas are reported in this paper. The doped samples are characterized by the resistance measured using a four-probe method, since the sheet resistance changes with the carrier concentration of the sample. The doping effects with the variation of laser energy density, pulse number, and the pressure of BCl₃ were investigated in terms of the sheet resistance. In this way, the optimized parameters were obtained and used for the positive heavy doping on p-Si(1 0 0) and p-Si(1 1 1). Then, using a square mesh under the above conditions, an image doping was completed. Finally, the metal–semiconductor Ohmic contacts were realized by plating Ag and Cu films on the doped surface.     

高维电报方程的对称周期解

讨论n维电报方程的对称周期解．利用Schauder不动点定理，在非共振条件下给出了一个存在性定理．     

基于分形维数的液体爆炸分散中界面破碎形态研究

通过对爆炸抛撒图象的处理,得到液体界面的曲线.采用盒维数的计算方式,计算界面曲线的分形维数.通过对各时刻液体界面分形维数的变化研究,分析爆炸抛撒近场阶段的变化过程,同时观察到蘑菇状尖顶的出现与破碎,以及空化区域的形成和消失现象。     

同轴双无衍射光的理论与实验

提出同轴双无衍射光的概念。如果两束汇聚角略有不同的同轴无衍射光同时存在，则它们相互之间叠加干涉后产生一种纵向呈周期变化的光场结构，这是一种新的光束空间分布，这种光束在横向仍是一种同心环光斑，可用于精密对准。而在不同纵向位置，这些同心环的强度分布是不同的，且是周期性变化的。同轴双无衍射光的轴向周期性可用于沿光束传播方向的定位。文中提出了双环缝法、分段圆锥透镜法、正弦相位环光栅法等实现同轴双无衍射光的理论与实验方法，分析了同轴双无衍射光的横向与纵向传播的衍射光斑特性，理论计算与实验测量的结果基本相符合。     

一类递归集的Hausdorff维数及Bouligand维数

本文给出递归集的Ｈａｕｓｄｏｒｆｆ维数的下界估计，并由此确定了一类递归集的维数，所获结果包含并推广了Ｂｅｄｆｏｒｄ，Ｄｅｋｋｉｎｇ及文志英、钟红柳等人的有关结果。     

Zeroth-order phase transitions and Zipf law quantization

From the standpoint of thermodynamic averaging of fission microprocesses, we investigate the origin of radioactive release in an NPP after an accident or after resource depletion. The genesis of the NPP release is interpreted as a new thermodynamic phenomenon, a zeroth-order phase transition. This problem setting results in a problem in probabilistic number theory. We prove the corresponding theorem leading to quantization of the Zipf law for the frequency of a zeroth-order phase transition with different values of the jump of the Gibbs thermodynamic potential. We introduce the notion of hole dimension. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 1, pp. 118–142, January, 2007.     

Testing for additivity with B-splines

Regression splines are often used for fitting nonparametric functions, and they work especially well for additivity models. In this paper, we consider two simple tests of additivity: an adaptation of Tukey's one degree of freedom test and a nonparametric version of Rao's score test. While the Tukey-type test can detect most forms of the local non-additivity at the parametric rate of O(n-1/2), the score test is consistent for all alternative at a nonparametric rate. The asymptotic distribution of these test statistics is derived under both the null and local alternative hypotheses. A simulation study is conducted to compare their finite-sample performances with some existing kernel-based tests. The score test is found to have a good overall performance.     

Towards the synthesis of MAX-phase functional coatings by pulsed laser deposition

Pulsed laser deposition with a Nd:YAG laser was used to grow thin films from a pre-synthesized Ti₃SiC₂ MAX-phase formulated ablation target on oxidized Si(1 0 0) and MgO(1 0 0) substrates. The depositions were carried out in a substrate temperature range from 300 to 900 K, and the pressure in the deposition chamber ranged from vacuum (10⁻⁵ Pa) to 0.05 Pa Argon background pressure. The properties of the films have been investigated by Rutherford backscattering spectrometry for film thickness and stoichiometric composition and X-ray diffraction for the crystallinity of the films. The silicon content of the films varied with the energy density of the laser beam. To suppress especially the silicon re-sputtering from the substrate, the energy of the incoming particles must be below a threshold of 20 eV. Therefore, the energy density of the laser beam must not be too high. At constant deposition energy density the film thickness depends strongly on the background pressure. The X-ray diffraction measurements show patterns that are typical of amorphous films, i.e. no Ti₃SiC₂ related reflections were found. Only a very weak TiC(2 0 0) reflection was seen, indicating the presence of a small amount of crystalline TiC.