大数定律MATLB随机模拟的规律性

第二作者等用一个哲学公式及0.9规格化了收敛过程,从而形象化地解释了概率论与随机计算中的若干定理,使模拟的数值规律化.基于数学软件MATLB进行了大数定律的随机模拟,直观形象地展示了1/n∑_(i=1)~nX_i到数学期望μ的收敛过程,与第二作者等的哲学公式相吻合,从而有助于学生理解和掌握大数定律.     

An approach for solving a fuzzy multiobjective programming problem

In this paper we present a new approach, based on the Nearest Interval Approximation Operator, for dealing with a multiobjective programming problem with fuzzy-valued objective functions.     

Approximation numbers of Sobolev embeddings—Sharp constants and tractability

We investigate optimal linear approximations (approximation numbers) in the context of periodic Sobolev spaces H^s(T^d)$H^s\left({\mathbb{T}}^d\right)$ of fractional smoothness s>0$s>0$ for various equivalent norms including the classical one. The error is always measured in _L2(T^d)$L_2\left({\mathbb{T}}^d\right)$. Particular emphasis is given to the dependence of all constants on the dimension d$d$. We capture the exact decay rate in n$n$ and the exact decay order of the constants with respect to d$d$, which is in fact polynomial. As a consequence we observe that none of our considered approximation problems suffers from the curse of dimensionality. Surprisingly, the square integrability of all weak derivatives up to order three (classical Sobolev norm) guarantees weak tractability of the associated multivariate approximation problem.     

一致有界树指标马氏链的层频率的强大数定律

利用一致有界树指标马氏链的强大数定律,给出了一致有界树指标马氏链的关于状态和状态序偶出现的层频率的强大数定律.     

基于最小偏差和优势度的区间数互补判断矩阵排序法

针对决策信息以区间数互补判断矩阵形式给出的多目标决策问题。首先,给出相对优势度的概念和区间数加性一致性互补判断矩阵的判定定理。其次,建立一个目标规划模型,通过求解该模型得到区间数互补判断矩阵的权重向量,并利用各权重向量的总体相对优势度对方案进行排序,提出了基于最小偏差和优势度的区间数互补判断矩阵排序法。方法的核心是对数值型互补判断矩阵排序方法的拓展。最后,通过实例说明方法的可行性和有效性。     

基于概念图的大数定律教学

介绍概念图的内涵及其基本理论,并将其应用于概率论中关于＂大数定律＂的教学过程,通过学生小组合作制作概念图,以及师生合作完善概念图,来帮助学生理清脉络、加深理解,教学实践效果良好.     

A Generalization of Weak Law of Large Numbers

Kolmogorov's weak law of large numbers for i.i.d. random variables is generalized to a larger class distributions and to a wide class of normalizing sequences. The result is extended to maximal sums of negatively associated identically distributed random variables.     

An integrable semi-discrete equation and combinatorial numbers with their combinatorial interpretations

A Hankel type determinant solution for an integrable semi-discrete equation is presented. As an application, the relations between the solution and combinatorial numbers are discussed, which lead to new combinatorial numbers. The so-called Motzkin-like numbers are obtained, and the corresponding combinatorial interpretation is given. Additionally, it is also shown that some lattice paths have connections with the special solution.     

Criteria for Componentwise Linearity

We establish characteristic-free criteria for the componentwise linearity of graded ideals. As applications, we classify the componentwise linear ideals among the Gorenstein ideals, the standard determinantal ideals, and the ideals generated by the submaximal minors of a symmetric matrix.     

Lyubeznik Table of Sequentially Cohen–Macaulay Rings

We prove that sequentially Cohen–Macaulay rings in positive characteristic, as well as sequentially Cohen–Macaulay Stanley–Reisner rings in any characteristic, have trivial Lyubeznik table. Some other configurations of Lyubeznik tables are also provided depending on the deficiency modules of the ring.