随机数在随机事件与概率教学中的应用探索

本文对在随机事件与概率中的常见问题提出了一种新的借助于计算机实现的解决思路,即通过机器自动产生随机数后构建相应的数学模型,再通过编程计算得到最后结果。该方法既为概率论的教学带来了创新性思维,也为当前的教师提出了新的挑战。     

直觉梯形模糊几何集成算子及其在群决策中的应用

文章首先定义了直觉梯形模糊数及其运算法则,基于这些运算法则,给出了直觉梯形模糊几何集成算子,即直觉梯形模糊加权几何(IT-WG)算子、直觉梯形模糊有序加权几何(IT-OWG)算子以及直觉梯形模糊混合几何(IT-HG)算子。在此基础上,提出了在属性权重已知的情形下专家评价值以直觉梯形模糊信息给出的多属性群决策方法。最后以产品最优设计方案的选择为实例进行分析,所得结果验证了该方法的有效性。     

Optimal reinsurance under general law-invariant risk measures

In recent years, general risk measures play an important role in risk management in both finance and insurance industry. As a consequence, there is an increasing number of research on optimal reinsurance decision problems using risk measures beyond the classical expected utility framework. In this paper, we first show that the stop-loss reinsurance is an optimal contract under law-invariant convex risk measures via a new simple geometric argument. A similar approach is then used to tackle the same optimal reinsurance problem under Value at Risk and Conditional Tail Expectation; it is interesting to note that, instead of stop-loss reinsurances, insurance layers serve as the optimal solution. These two results highlight that law-invariant convex risk measure is better and more robust, in the sense that the corresponding optimal reinsurance still provides the protection coverage against extreme loss irrespective to the potential increment of its probability of occurrence, to expected larger claim than Value at Risk and Conditional Tail Expectation which are more commonly used. Several illustrative examples will be provided.     

等比级数在函数展开成幂级数中的应用

函数的幂级数展开是高等数学的教学重点之一,在解决函数的幂级数展开的问题中,等比级数起着重要的作用。文章介绍了利用等比级数将函数展开成幂级数的常见情形,并给出了具体的例子。     

数字化成图软件在公路线形设计上的应用研究

本文试图通过对地形、地籍数字化成图软件功能的改进,包括公路线形设计、纵横断面图的绘制和设计、土石方的计算与调配,以及各种数据表格的自动输出等,实现操作轻松快捷、简单准确,满足公路设计单位的需要,提高工作效率。     

一类新的反Smarandache几何级数周期行列式

本文定义了一类新的反Smarandache几何级数周期行列式,并利用初等数论的方法和行列式的性质,对这类行列式进行了研究,给出了它们的通项公式。     

关于曲线积分和曲面积分教学中几个难点的突破

加强曲线、曲面积分概念讲解,标准化曲线、曲面积分的计算程序,沟通有关积分之间关系,以消除学生 对斯托克斯等公式的深奥感,有效地突破了曲线、曲面积分教学中的几个难点。     

Arithmetic versus geometric mean estimators: Setting discount rates for capital budgeting

This paper addresses an issue central to the estimation of discount rates for capital budgeting: should the geometric mean or arithmetic mean of past data be used when estimating the discount rate? the use of the arithmetic mean ignores estimation error and serial correlation in returns. Unbiased discount factors have been derived that correct for both these effects. In all cases, the corrected discount rates are closer to the arithmetic than the geometric mean.     

On Social Statement Spaces

In this fundamental draft we shall introduce the concept of social propositional spaces as a general notion of social science and in particular language, logic and methodology. This should help us bridge an old gap between extension and cognition, or said in more specific words, between space as conceived in mathematics or physics and space as is brought in by social location, by the meaning of predicates, their explanation and logic. ¹ We shall not rely on the idea of factor analysis where some “main components” are fit into the data. Because the notion of euclidean normalization and orthogonality, in this context, is a bit artificial. We first show how combinatorial manifolds of statements can be represented in finite vector spaces over the Galois field F₂. This space which we denote as logic statement space can be spanned by generators of alternating codes. In this way the old concepts of truth tables and interaction attributes can be linked to informatics and in particular code theory and geometry. Extending the logic statement space onto a real vector space by mapping units of the finite rings onto units of the real rings we obtain logistic statement spaces. It turns out that vectors in logistic statement spaces represent cross-tables of logits connected with logistic regression analysis. As a completion of the theory we show that the logit is the first derivative of entropy with respect to probability.     

基于格规约辅助的MIMO系统GMD-TH预编码方案

现有的GMD-TH(Geometric Mean Decomposition-Tomlison Harashima)预编码方案在发射 端未对获得MIMO（Multiple-Input-Multiple-Output）信道增益矩阵优化,因而 其误码率和分集增益无法获得令人满意的效果。为此,在原有MIMO系统GMD-TH预编码的基础 上,提出一种基于格规约辅助的GMD-TH预编码方案。该方案采用基于格规约的算法对信道 矩阵进行优化,经过优化的信道矩阵其列向量之间具有更好的正交性并且向量的长度更短, 并且采用优化的信道矩阵提高了GMD-TH预编码MIMO系统的分集增益。仿真结果表明：相比于 传统的线性预编码方案,该预编码方案有效地提高了MIMO分集增益,相同误码率下,信噪 比降低3 dB以上,具有实用价值。