Probability and exams: The work of Antonio Bordoni

The Italian mathematician Antonio Bordoni is mainly known for his adherence to the Lagrangian approach to the foundations of calculus and for his role in creating an important school of mathematics. In this paper, I consider his less known work on the application of probability to design exams and analyze their outcomes. Within this framework, he obtained in 1837, as Mondésir and Poisson, the result that would lead Catalan to formulate his “new principle” of probability (Jongmans and Seneta, 1994). Moreover, in 1843, Bordoni also gave an early complete proof of the finite rule of succession.     

关于广义(α,β)-度量的若干Ricci曲率性质

本文研究了广义(α,β)-度量的Ricci曲率和Ricci曲率张量.首先,在一定条件下,本文给出了强Einstein广义(α,β)-度量的一个等价刻画.进一步,得到了广义(α,β)-度量是Ricci-齐次Finsler度量的一个充分必要条件.     

一阶导数形式不变性

针对数学教材中由导数基本公式到复合函数求导法则过渡形式不一致现象,提出一阶导数的一致形式、修订复合函数求导法则、给出导数基本公式的一般形式.     

On the convergence of general stationary iterative methods for range‐Hermitian singular linear systems

General stationary iterative methods with a singular matrix M for solving range‐Hermitian singular linear systems are presented, some convergence conditions and the representation of the solution are also given. It can be verified that the general Ortega–Plemmons theorem and Keller theorem for the singular matrix M still hold. Furthermore, the singular matrix M can act as a good preconditioner for solving range‐Hermitian linear systems. Numerical results have demonstrated the effectiveness of the general stationary iterations and the singular preconditioner M. Copyright © 2009 John Wiley & Sons, Ltd.     

Hausdorff dimension and measure of a class of subsets of the general Sierpinski carpets

In this paper we study a class of subsets of the general Sierpinski carpets for which two groups of allowed digits occur in the expansions with proportional frequency. We calculate the Hausdorff and Box dimensions of these subsets and give necessary and sufficient conditions for the corresponding Hausdorff measure to be positive and finite.     

Jeu de taquin and a monodromy problem for Wronskians of polynomials

The Wronskian associates to d linearly independent polynomials of degree at most n, a non-zero polynomial of degree at most d(n−d). This can be viewed as giving a flat, finite morphism from the Grassmannian Gr(d,n) to projective space of the same dimension. In this paper, we study the monodromy groupoid of this map. When the roots of the Wronskian are real, we show that the monodromy is combinatorially encoded by Schützenberger's jeu de taquin; hence we obtain new geometric interpretations and proofs of a number of results from jeu de taquin theory, including the Littlewood-Richardson rule.     

NORMALITY CRITERIA FOR FAMILIES OF MEROMORPHIC ALGEBROID FUNCTIONS

By using the definition of Hausdorff distance, we prove some normality criteria for families of meromorphic algebroid functions. Some examples are given to complement the theory in this article.     

非线性中立型延迟积分微分方程一般线性方法的稳定性分析

本文研究求解R(α,β₁,β₂,γ)类非线性中立型延迟积分微分方程的一般线性方法的数值稳定性,获得了代数稳定的一般线性方法稳定及渐近稳定的条件,最后的数值试验验证了所获理论的正确性.       

带有约束的增长曲线模型中回归系数线性估计的可容许性与泛容许性(英文)

本文研究了参数受约束的增长曲线模型中多元回归系数线性估计的可容许性和泛容许性.利用线性估计类中的八种最优标准和圣函数,得到了在三个等价了类中线性估计可容许以及回归系数线性估计泛容许的充要条件.本文的结论推广了覃红等人的工作.     

A numerical approach for solving an extended Fisher-Kolomogrov-Petrovskii-Piskunov equation

In the present paper a numerical method, based on finite differences and spline collocation, is presented for the numerical solution of a generalized Fisher integro-differential equation. A composite weighted trapezoidal rule is manipulated to handle the numerical integrations which results in a closed-form difference scheme. A number of test examples are solved to assess the accuracy of the method. The numerical solutions obtained, indicate that the approach is reliable and yields results compatible with the exact solutions and consistent with other existing numerical methods. Convergence and stability of the scheme have also been discussed.