Permanence as a principle of practice

The paper discusses Peano's argument for preserving familiar notations. The argument reinforces the principle of permanence, articulated in the early 19th century by Peacock, then adjusted by Hankel and adopted by many others. Typically regarded as a principle of theoretical rationality, permanence was understood by Peano, following Mach, and against Schubert, as a principle of practical rationality. The paper considers how permanence, thus understood, was used in justifying Burali-Forti and Marcolongo's notation for vectorial calculus, and in rejecting Frege's logical notation, and closes by considering Hahn's revival of Peano's argument against Pringsheim's reading of permanence as a logically necessary principle.     

基于主成分分析法的高性能波长计研究与实现

波长探测作为科学技术中的一个基本工具,在分析化学、生物传感和光学通信等众多领域具有重要作用。从多模光纤信号传输理论出发,在绝热、准直模型中建立基于模式干涉效应的强度干涉图像理论;实验测量时,在光纤尾端引入缓变（斜率约为0.01）锥形区域设计,保证收集到侧面辐射信号的同时,也近似满足理论模型和数值仿真结果。在搭建的显微共焦成像系统中,连续扫描窄带激光器进行干涉图像存储,经过区域选取、向量拼接以及奇异值分解等步骤得到由器件特性决定的校样矩阵。波长的探测过程共分为两个步骤：在工作带宽内纳米量级粗略扫描光波长得到粗略校准矩阵,一维待测信号强度图像与之进行内积相关性运算后,选取数值最高的波长值作为预估波长单元;在此基础上精细扫描得到精细校样矩阵,选取三个最大主成分并定义与波长欧氏距离最小值确定最终探测波长。采用内积相关性运算联合主成分分析法不仅可以将波长探测分辨率提高到20 pm、准确率达到96.7%,探测效率较其他光谱重建算法提高50倍。实验证实该波长计工作范围至少为400～700 nm,器件尺寸仅为π×(20 μm)2×0.5 mm。该器件在高性能、便携式和低成本方面较同类器件有较大提升,在光谱重建效率也集成了高效算法,能够广泛应用于光纤传输系统的波长实时探测。     

AC conductivity,structural, and dielectric properties of zinc supported on titanium dioxide: Facile synthesis and DFT calculation

We present a simple and systematic synthesis method of Zn doped TiO₂ (Zn/TiO₂) that is usually prepared with sophisticated preparation procedures. Zn/TiO₂ have been synthesized following a facile and efficient incipient wet impregnation method. The resulting Zn/TiO₂ has been characterized by X-ray diffraction, scanning electron microscopy, and energy-dispersive X-ray spectroscopy, which revealed the successful formation of the anatase phase and traces of the rutile phase. The existence of the rutile phase in smaller proportion was a clear sign of the Zn doping induced anatase-to-rutile phase transition. Sensible enhancement in the dielectric constant due to Zn addition has also been observed from experiment and approximate first-principle calculation. Thus, our results have significant impact on TiO₂ based semiconductor technology.     

造林方案的优化及其计算机辅助系统

本文以吉林省长白山某林区为背景，综合运用多元统计分析、多目标优化及计算机技术，对造林方案的优化及其计算机辅助系统的开发进行了探讨。     

Information theory approach in efficiency measurement

The current non–parametric method of measuring productive efficiency of input–output systems is generalized here in the stochastic case in terms of an information theory approach based on the concept of entropy. Use of maximum entropy as a method of finding the most probable distribution of the input–output data set and as a predictive criterion is illustrated for production systems with multiple inputs and outputs.     

Existence and Uniqueness of Stationary Solutions for 3D Navier–Stokes System with Small Random Forcing via Stochastic Cascades

We consider the 3D Navier–Stokes system in the Fourier space with regular forcing given by a stationary in time stochastic process satisfying a smallness condition. We explicitly construct a stationary solution of the system and prove a uniqueness theorem for this solution in the class of functions with Fourier transform majorized by a certain function h. Moreover we prove the following “one force—one solution” principle: the unique stationary solution at time t is presented as a functional of the realization of the forcing in the past up to t. Our explicit construction of the solution is based upon the stochastic cascade representation.     

关于圣文南原理的证明问题

本文证明线弹性体表面小域中作用的平衡力系在弹性体中的影响随到小域的距离而单调衰减,但不一定趋于零,就是说,平衡力系可能在无穷远点造成非零的影响,所以圣文南原理的传统提法并不能一般性的成立.     

Differential Games of inf-sup Type and Isaacs Equations

Motivated by the work of Fleming, we provide a general framework to associate inf-sup type values with the Isaacs equations. We show that upper and lower bounds for the generators of inf-sup type are upper and lower Hamiltonians, respectively. In particular, the lower (resp. upper) bound corresponds to the progressive (resp. strictly progressive) strategy. By the Dynamic Programming Principle and identification of the generator, we can prove that the inf-sup type game is characterized as the unique viscosity solution of the Isaacs equation. We also discuss the Isaacs equation with a Hamiltonian of a convex combination between the lower and upper Hamiltonians.     

扩张原理的一种新的表现形式

提出一种基于“模糊点”的模糊集合的分解定理，在此分解定理的基础上给出模糊扩张原理的一种新的表现形式。新的扩张原理与以往人们所提出的扩张原理是等价的，而表现形式更为直观、简便。同时，利用该扩张原理得到模糊复合函数以及多元模糊关系合成运算的合理解释。