滚齿加工误差分析与检验组(之二)Ⅱ.齿轮的径向误差与检验项目

本文是“滚齿加工误差分析与检验组”一文的第二部分。这部分的主要内容是分析与研究滚齿加工时产生径向误差(亦称几何偏心)的原因,径向误差的合成方法、特征,径向误差与检验项目的关系、数学模型、几何意义。     

Optimal Investment Strategy in Safe-region on Consumption and Portfolio Problem

This paper investigates an optimal investment strategy on consumption and portfolio problem, in which the investor must withdraw funds continuously at a given rate. By analyzing the evolving process of wealth, we give the definition of safe-region for investment. Moreover, in order to obtain the target wealth as quickly as possible, using Bellman dynamic programming principle, we get the optimal investment strategy and corresponding necessary expected time. At last we give some numerical computations for a set of different parameters.     

Consistent loss prediction for a portfolio and its subportfolios

In the present paper, we consider a portfolio of risks consisting of two subportfolios, and we study the problem of whether or not the predictors based on the subportfolios are consistent with those based on the full portfolio. We study this aggregation problem for both the chain-ladder method and the additive method (or incremental loss ratio method). In the case of the chain-ladder method we extend results of Ajne and Klemmt, using the duality of the chain-ladder method applied to incremental losses; we also give a short proof for this duality, which was first observed by Barnett, Zehnwirth & Dubossarky. In the case of the additive method the aggregation problem has not been studied before and its solution is surprisingly simple.     

The proper distribution function of the deficit in the delayed renewal risk model

The main focus of this paper is to extend the analysis of ruin-related quantities to the delayed renewal risk models. First, the background for the delayed renewal risk model is introduced and a general equation that is used as a framework is derived. The equation is obtained by conditioning on the first drop below the initial surplus level. Then, we consider the deficit at ruin among many random variables associated with ruin. The properties of the distribution function (DF) of the proper deficit are examined in particular.     

计量经济学的几何直观化分析研究——直观几何方法及与巴伦坦图法的比较

计量经济学的回归分析,在传统上是用代数等式和矩阵的形式表述的。事实上,回归分析的几乎所有概念都可以在直观的几何框架内进行表述。与直观几何方法相比,传统的巴伦坦图存在一定的局限性和一些误导性错误,用几何图形法都可以得到有效解决,由此说明计量经济学一些基本概念通过几何原理图形化具有相应的作用和意义。     

The deficit at ruin in the stationary renewal risk model

Properties of the distribution of the deficit at ruin in the stationary renewal risk model are studied. A mixture representation for the conditional distribution of the deficit at ruin (given that ruin occurs) is derived, as well as a stochastic decomposition involving the residual lifetime associated with the maximal aggregate loss. When the individual claims have a phase-type distribution, the deficit at ruin is also of phase-type.     

A new method for automatic synthesis of tolerances for complex assemblies based on polychromatic sets

In computer-aided tolerance design (CAT), integrated design of dimensional and geometric tolerances is still one of the research hotspots. Polychromatic sets theory (PST) is a new mathematic tool, which is especially suitable for formal hierarchical structure models. Based on PST, in this article, a new hierarchical representation model for tolerance synthesis is presented to realise integrated design of dimensional and geometric tolerances. According to the inference relations between unified and individual colours of PST, the synthesis matrices of variational geometric constraints (VGC) are established in the VGC tier of the model, and the synthesis matrices of tolerance types are established in the tolerance type tier of the model. On this basis, the synthesis processes from the feature tier to the VGC tier and from the VGC tier to the tolerance type tier can be realised. VGCs, which are achieved by the synthesis matrices of VGCs, can be combined together to establish a well-constrained VGC network (VGCN). Tolerance types, which are achieved by the synthesis matrices of tolerance types, can be added to the well-constrained VGCN to construct a well-constrained tolerance network. An application example is given in the article to illustrate the synthesis steps.     

An effective method for constructing bounds for ruin probabilities for the surplus process perturbed by diffusion

In this paper, we first study orders, valid up to a certain positive initial surplus, between a pair of ruin probabilities resulting from two individual claim size random variables for corresponding continuous time surplus processes perturbed by diffusion. The results are then applied to obtain a smooth upper (lower) bound for the underlying ruin probability; the upper (lower) bound is constructed from exponentially distributed claims, provided that the mean residual lifetime function of the underlying random variable is non-decreasing (non-increasing). Finally, numerical examples are given to illustrate the constructed upper bounds for ruin probabilities with comparisons to some existing ones.     

零件设计中形位公差项目的选择

在进行零件设计时,正确选择形位公差项目及其公差值的确定是一项很慎重的工作,既要根据零件的使用性能和互换性要求,又要考虑生产率和成本的高低。本文仅对形位公差项目的选择进行初步的探讨。