Theories of mathematics education: European perspectives, commentaries and viable research directions

We briefly comment on different perspectives on (1) the role of mathematics education theories, (2) the issue of plurality and healthy heterogeneity versus consolidation; (3) underlying inquiry systems or the implicit role of philosophy in theories of mathematics education. This paper also outlines developments within the European research scene on theory usage in mathematics education research, which complement the discussion at the 29th PME research forum in Melbourne.     

Optimal investment,consumption and proportional reinsurance under model uncertainty

This paper considers the optimal investment, consumption and proportional reinsurance strategies for an insurer under model uncertainty. The surplus process of the insurer before investment and consumption is assumed to be a general jump–diffusion process. The financial market consists of one risk-free asset and one risky asset whose price process is also a general jump–diffusion process. We transform the problem equivalently into a two-person zero-sum forward–backward stochastic differential game driven by two-dimensional Lévy noises. The maximum principles for a general form of this game are established to solve our problem. Some special interesting cases are studied by using Malliavin calculus so as to give explicit expressions of the optimal strategies.     

Dynamic analysis of a turbidostat model with the feedback control

In this paper, a mathematical model with impulsive state feedback control is proposed for turbidostat system. The sufficient conditions of existence of positive order one periodic solution are obtained by using the existence criteria of periodic solution of a general planar impulsive autonomous system. It is shown that the system either tends to a stable state or has a periodic solution, which depends on the feedback state, the control parameter of the dilution rate and the initial concentration of microorganism and substrate. By investigating the periodic solution, the period and the initial point of the periodic solution are given. The results show that turbidostat with impulsive state feedback control tends to an order one periodic solution.     

平板几何迁移算子的特征值问题

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单位圆内代数体函数的充满圆及Borel半径

研究了单位圆内具有有限个分支点的代数体函数,并用覆盖曲面的几何方定义了他们的级和Borel半径,得到了在单位圆内大于1的有穷级代数体函数必存在充满圆及Borel半径.     

Blow-up and global solutions for quasilinear parabolic equations with Neumann boundary conditions

Using the upper and lower solution techniques and Hopf's maximum principle, the sufficient conditions for the existence of blow-up positive solution and global positive solution are obtained for a class of quasilinear parabolic equations subject to Neumann boundary conditions. An upper bound for the ‘blow-up time’, an upper estimate of the ‘blow-up rate’, and an upper estimate of the global solution are also specified.     

Correlation functions for multi-matrix models and quaternion determinants

Using a close relationship to the Brownian motion model of random matrices, multi-matrix models in quantum field theory are analyzed. In the case many hermitian matrices are connected in a chain and one of them has a restricted (real symmetric, self dual real quaternion or antisymmetric hermitian) symmetry, the multi-matrix multi-level correlation functions are shown to have quaternion determinant forms.     

图模型及其在统计建模中的应用

图模型是近年来兴起的一个新的统计研究方向,主要借助拓扑图的直观形式对多维概率分布进行统计推断和因果分析。本文对图模型的基本概念、原理、建模及应用进行了简单介绍。     

稀疏过程的三特征的联合分布函数

本文考虑一类人寿保险,保费到达为Po isson过程,索赔到达为p-稀疏过程,我们推导三特征的联合分布函数;破产时间,破产概率,破产前的盈余,破产赤字,并由这联合分布得破产概率的显示表达式.     

Some Calculations on Link Polynomials from 2-Parameter Quantum Groups

Starting with the link invariant G (p,q,z) , a skein relation is introduced which enables us to calculate the polynomial starting with G (p,q,z) = 1, for the unknot. The relation between G (p,q,z) and the known 2-variable link invariant K (l,m) is shown. Then the polynomial of some common knots is calculated, also it is shown that this invariant failed to distinguish the Birmans pairs as well as Jones invariant.