非高斯噪声驱动下一维双稳系统的逻辑操作

本文以成功率作为逻辑随机共振的测度, 主要研究了非高斯噪声激励下一维双稳系统的逻辑随机共振现象, 并用平均首次通过时间的方法对此现象的机理进行了解释. 研究结果表明: 只有在适当的噪声强度带或关联时间带上, 成功率才会达到共振峰值. 通过对系统参数进行优化, 提高了系统实现逻辑操作的可靠性. 关键词： 逻辑随机共振 一维双稳系统 非高斯噪声 平均首次通过时间     

几类群的混合自由积分解

讨论了有限实现群的混合自由积分解问题,证明了所有有限实现群皆可表示为其生成元个数不超过2的若干子群的混合自由积,并给出了 SL_n(Z)的具体的分解定理.     

Mixed integer programming for a special logic constrained optimal control problem

Integrating logical constraints into optimal control problems is not an easy task. In fact, optimal control problems are usually continuous while logical constraints are naturally expressed by integer (binary) variables. In this article we are interested is a particular form of an LQR optimal control problem: the energy (control L² norm) is to be minimized, system dynamic is linear and logical constraints on the control use are to be fulfilled. Even if the starting continuous problem is not a complicated one, difficulties arise when integrating the additional logical constraints. First, we will present two different ways of modeling the problem, both of them leading us to Mixed Integer Problems. Furthermore, algorithms (Generalized Outer Approximation, Benders Decomposition and Branch and Cut) are applied on each model and results analyzed. We also present a Benders Decomposition algorithm variant that is adapted to our problem (taking into account its particular form) and we will conclude by looking at the optimal solutions obtained in an interesting physical example: the harmonic spring.     

对我国证据开示制度的改进

建立完善的控辩双方证据开示制度,是国家法制建设的需要。我国司法实践当中证据开示制度存在不足,需要依据必要的原则进行改进。建立证据开示制度,对我国刑事诉讼意义深远。     

积逻辑系统中的广义重言式

讨论积逻辑系统中的广义重言式理论 ,给出积逻辑系统中子代数和广义重言式的一系列性质。本文的主要结果表明 ,在几个重要的逻辑系统中 ,标准积逻辑系统具有最简单的广义重言式结构 ,而在推理过程中 ,它具有较差的真值传递性。     

On a family of connectives for fuzzy sets

In this paper we find the general solution of the functional equation $\text{S}{}^1\text{(T(x, y), T(x, N(y))) = x}$, where $\text{S}{}^1$ is a t-conorm, T is a t-norm and N is a strong negation on the unit interval. In particular the result yields a family of connectives for fuzzy sets.     

Statistical issues in measurement

Measurement theories are traditionally couched in algebraic terms, which makes them unsuitable for statistical testing. A probabilistic recasting of these theories is proposed here. It is observed then that an axiom of probabilistic measurement has typically the form of a logical polynomial, the structure of which induces a particular partition of the parameter space, giving rise to a calss of statistical problems for which the null hypothesis is a union of convex polyhedrons. This is a consequence of the fact that a logical polynomial can always be rewritten in normal form, that is, as a disjunction of conjunctions. A likelihood ratio method is worked out in a couple of exemplary cases. One of these examples provides a test of transitivity, a property which lies at the heart of ordinal measurement.     

现代追求与传统情结——牟宗三对中国传统文化的解读

牟宗三对中国化与西方现代化的内在精神有着深刻独特的解析，面对西方现代化的强大冲击,他继续执守儒家心性论的立场，通过对“心性本体”的重新诠释，试图以自己的方式保住这一本体，并实现传统与现代的融合。但他的“良知坎陷说”最终并没有真正跳出传统儒家道德中心主义的立场。     

A Structure Theorem for Free Temporal Algebras

In this paper an algebraic version for temporal algebras of the logical filtrations for modal and temporal logics is analysed. A structure theorem for free temporal algebras and also some results with regard to the variety of temporal algebras are obtained.     

在列率域上的特征函数

在随机系统的分析中,许多问题可以借助特征函数得出简单的解法。本文是模拟 Fourier分析,引出 Walsh(沃尔什)分析。首先引入二进导数的概念,并用数学期望的概念来定义 Walsh 特征函数,对所对应的 Walsh 特征函数,经过 Gibbs 导数运算子,导出了矩的概念和性质,而且介绍了矩的计算法。同时也导出了研究函数的二进(逻辑)导数的 Walsh 变换结果。本文仅对一个随机变量的情况进行研究。