统计模型在中文文本挖掘中的应用

本文讨论了中文文本挖掘的三个问题:分词、关键词提取和文本分类。对分词问题,介绍了基于层叠隐马尔可夫模型的ICTCLAS分词法,以及将词与词之间的分隔视为缺失数据并用EM算法求解的WDM方法;对关键词提取问题,提出了贝叶斯因子法,并介绍了使用稀疏回归的CCS方法;对文本分类问题,介绍了根据关键词频率建立分类器的方法,以及先建立主题模型再根据主题概率建立分类器的方法。本文通过两组文本数据对上述方法进行比较,并给出使用建议。     

负二项分布随机变量数字特征的求解

本文给出了生产实践中被广泛应用的负二项分布的五种定义,研究了该分布对应随机变量的期望、方差等数字特征的求解,汇总了负二项分布与其它分布之间的关系.     

微积分与线性代数教学的渗透与融合

通过典型问题,探讨如何将《微积分》与《线性代数》两门不同的数学基础课程相互渗透与融合,从而揭示这两门课之间的密切联系,开阔学生思路,提高学生将所学知识融会贯通的能力.     

完整Coriolis力作用下带有外源强迫的非线性KdV方程

利用摄动方法,从描写既有Coriolis力垂直分量又含有水平分量的位涡方程出发,给出了近赤道非线性Rossby波所满足的具有外源强迫的非线性KdV方程,并利用Jacobi椭圆函数展开法,求解了改进后的非线性KdV方程的行波解及孤立波解.通过分析KdV方程的行波解,指出Coriolis力的水平分量和外源对Rossby波动的影响.     

Optimal mean–variance asset-liability management with stochastic interest rates and inflation risks

This paper considers an optimal asset-liability management problem with stochastic interest rates and inflation risks under the mean–variance framework. It is assumed that there are \(n+1\) assets available in the financial market, including a risk-free asset, a default-free zero-coupon bond, an inflation-indexed bond and \(n-2\) risky assets (stocks). Moreover, the liability of the investor is assumed to follow a geometric Brownian motion process. By using the stochastic dynamic programming principle and Hamilton–Jacobi–Bellman equation approach, we derive the efficient investment strategy and efficient frontier explicitly. Finally, we provide numerical examples to illustrate the effects of model parameters on the efficient investment strategy and efficient frontier.     

Isometries and additive mapping on the unit spheres of normed spaces

In this paper, we investigate isometric extension problem in general normed space. We prove that an isometry between spheres can be extended to a linear isometry between the spaces if and only if the natural positive homogeneous extension is additive on spheres. Moreover, this conclusion still holds provided that the additivity holds on a restricted domain of spheres.     

Ground State Solutions for a Quasilinear Schrödinger Equation

In this paper, we study the following quasilinear Schrödinger equation of the form

$$\begin{aligned} -\Delta u+V(x)u-\Delta (u^{2})u= g(x,u),~~~ x\in \mathbb {R}^N \end{aligned}$$

where V and g are 1-periodic in \(x_{1},\ldots ,x_{N}\), and g is a superlinear but subcritical growth as \(|u|\rightarrow \infty \). We develop a more direct and simpler approach to prove the existence of ground state solutions.

     

从几何直观的视角理解行列式

行列式理论是线性代数课程的一个重要内容.从平行四边形的有向面积、平行六面体的有向体积以及它们的几何直观性质引进低阶行列式的定义,可以帮助学习者从几何直观的角度更好地理解行列式的定义以及行列式的性质.克莱姆法则、矩阵乘积的行列式以及代数余子式等代数概念都可以进行几何直观的解释.     

Multi-recurrence and van der Waerden systems

We explore recurrence properties arising from dynamical approach to the van der Waerden theorem and similar combinatorial problems. We describe relations between these properties and study their consequences for dynamics. In particular, we present a measure-theoretical analog of a result of Glasner on multi-transitivity of topologically weakly mixing minimal maps. We also obtain a dynamical proof of the existence of a C-set with zero Banach density.     

Determination of lanthanum and cerium in cmsx-4 nickel-based superalloys by inductively coupled plasma mass spectrometryEI北大核心CSCD

CMSX-4 is the second-generation nickel-based single crystal superalloy used widely in the world. The oxidation resistance and corrosion resistance of CMSX-4 alloy can be improved by adding trace lanthanum (La), cerium (Ce) and other rare earth elements. A method for the simultaneous determination of La and Ce in CMSX-4 nickel-based superalloy by wet dissolution-inductively coupled plasma mass spectrometry was established. The sample was heated and dissolved under normal pressure by aqua regia and hydrofluoric acid, and the interference of fluorine ion was eliminated by using perchloric acid. The amount of dissolved acid and the digestion conditions were optimized. The limits of detection were 0.23 μg/g for La and 0.85 μg/g for Ce under optimized conditions. The spiked recoveries were 95.0%–98.9% with the relative standard deviations of 1.3%–3.9%, which can meet the requirements of accurate and rapid determination of La and Ce in CMSX-4 nickel-based superalloy. © 2023, Youke Publishing Co.,Ltd. All rights reserved.