The Goodman–Nguyen relation within imprecise probability theory

The Goodman–Nguyen relation is a partial order generalising the implication (inclusion) relation to conditional events. As such, with precise probabilities it both induces an agreeing probability ordering and is a key tool in a certain common extension problem. Most previous work involving this relation is concerned with either conditional event algebras or precise probabilities. We investigate here its role within imprecise probability theory, first in the framework of conditional events and then proposing a generalisation of the Goodman–Nguyen relation to conditional gambles. It turns out that this relation induces an agreeing ordering on coherent or C-convex conditional imprecise previsions. In a standard inferential problem with conditional events, it lets us determine the natural extension, as well as an upper extension. With conditional gambles, it is useful in deriving a number of inferential inequalities.     

基于物元可拓法的轨道交通PPP项目风险评价研究

风险评价是风险控制的前提,风险控制对项目成功实施至关重要.文章通过文献查阅和专家访谈梳理了PPP(Public-Private-Partnership)项目风险,建立涵盖37条指标的轨道交通PPP项目风险指标体系,构建基于物元可拓法的风险评价模型,以呼和浩特轨道交通PPP项目为例,对其项目风险进行了评价,提供一种PPP项目风险事前事中评价的方法,给项目相关方的项目风险评价和管理提供参考.     

微分方程解的存在区间的确定

从六个方面说明了确定一阶微分方程解的存在区间的方法.     

Decidability of the representation extension property for finite semigroups

We prove that the decision problem of whether or not a finite semigroup has the representation extension property is decidable.     

Size of support of initial heat distribution in the 1D heat equation

The size of support of initial heat distribution is determined by the heat flow observed either at any fixed time or at any fixed position     

扩链法合成聚乳酸类生物降解材料

详细地综述了聚乳酸类生物降解材料的扩链法合成，特别是使用二异氰酸酯类、二恶唑淋类扩链剂的合成进展。参考文献37篇。     

Similarity of $$sgn x( - \tfrac{{d^2 }}{{dx^2 }} + c\delta )$$ Type Operators to Normal and Self-adjoint Operators

Mathematical Notes -     

基于传导变换的传导知识研究

基于传导变换的传导知识是一类重要的可拓知识.本文以传导变换和传导效应为基础,规定了传导度和传导知识的定义与类型,为研究传导知识的挖掘奠定理论基础.     

Schrödinger Operator Perturbed by Operators Related to Null Sets

We discuss the Schrödinger operator with positive singular perturbations given by operators which act in the space constructed by a positive measure supported by a null set. We construct examples when perturbations are given by the one-dimensional Laplacian on a segment.     

Hopf–Galois Extensions with Central Invariants and Their Geometric Properties

We set up a general framework to study representation theory of certain algebras whichusually appear in the study of restricted Lie algebras or various quantum objects at roots of unity.The object of the study is a Hopf–Galois extension with central invariants. It turns out that theseextensions possess some geometric properties which are close to those of principal bundles andFrobenius manifolds. We define Hopf–Galois extensions of not necessarily affine schemes andprove that the classification problem of such extensions leads to a stack.