Du Bois–Reymond Type Lemma and Its Application to Dirichlet Problem with the p(t)–Laplacian on a Bounded Time Scale

This paper is devoted to study the existence of solutions and their regularity in the p(t)–Laplacian Dirichlet problem on a bounded time scale. First, we prove a lemma of du Bois–Reymond type in time-scale settings. Then, using direct variational methods and the mountain pass methodology, we present several sufficient conditions for the existence of solutions to the Dirichlet problem.     

Stock market crashes are outliers

We call attention against what seems to be a widely held misconception according to which large crashes are the largest events of distributions of price variations with fat tails. We demonstrate on the Dow Jones Industrial Average that with high probability the three largest crashes in this century are outliers. This result supports the suggestion that large crashes result from specific amplification processes that might lead to observable pre-cursory signatures. Received and Revised: 30 November 1997 / Accepted: 8 December 1997     

“String” formulation of the dynamics of the forward interest rate curve

We propose a formulation of the term structure of interest rates in which the forward curve is seen as the deformation of a string. We derive the general condition that the partial differential equations governing the motion of such string must obey in order to account for the condition of absence of arbitrage opportunities. This condition takes a form similar to a fluctuation-dissipation theorem, albeit on the same quantity (the forward rate), linking the bias to the covariance of variation fluctuations. We provide the general structure of the models that obey this constraint in the framework of stochastic partial (possibly non-linear) differential equations. We derive the general solution for the pricing and hedging of interest rate derivatives within this framework, albeit for the linear case (we also provide in the appendix a simple and intuitive derivation of the standard European option problem). We also show how the “string” formulation simplifies into a standard N-factor model under a Galerkin approximation. Received: 30 January 1998 / Revised: 12 February 1998 / Accepted: 16 February 1998     

抗日根据地冬学运动的教师问题

抗日战争时期，抗日根据地冬学运动的轰轰烈烈发展使冬学教师短缺问题日益突出。根据地通过发动干部、选拔在校学生、动员当地知识分子和实行小先生与集体互相学习制等途径弥补了教师的空缺。但教师的选拔是严格的，并且必须经过一定的培训。在待遇差、条件极其艰苦的情况下，冬学教师们克服困难，出色地完成了民众教育与动员的任务。历史应该记住这些为抗战的胜利而在大后方无私奉献的冬学教师们。     

New Voronoi Diagram Algorithm of Multiply-Connected Planar Areas in the Selective Laser Melting

This paper studies the practical generation of Voronoi diagrams for multiply-connected planar areas bounded by line segments. The core of the algorithm was calculating Voronoi polygon of every Voronoi object in planar areas independently. The main approach had two steps. The first step was calculating all relevant bisectors of every Voronoi object. The second was combining obtained bisectors into completed Voronoi polygons individually. All code was implemented in Visual C++ platform. The resulting code was extensively tested in real-world data and its practical running time grew only linearly. Three statistical CPU-consumption charts had been drawn with the Voronoi diagrams computation data, and compared with other published codes for computing Voronoi diagrams. The algorithm was applied to compute offsetting of slice area consisting of large-scale line segments for the selective laser melting (SLM) trajectory scanning technology which is a kind of rapid prototyping (RP). The experimental results of offsetting for slice area based on Voronoi diagrams show that the approach is effective and simple for polygon offsetting problems. The method is helpful to those offsetting work and can provide more effective offsetting solution.     

浅谈发展农村职业教育的问题和建议

大力发展农村职业技术教育，是推动社会主义新农村建设的重要保证。因此，针对当前农村职业教育中存在的问题，我们应转变观念，一切从实际出发，统筹安排，整合现有的农村教育资源，利用城市文化教育资源反哺农村，以达到提高农民职业技术水平，推动新农村建设的目的。     

非线性退缩椭圆型方程Neumann问题正解的存在性

利用变形后的山路引理[1 ] ,研究了一类非线性退缩椭圆型方程Neumann问题正解的存在性与不存在性     

推覆体的几何学与四川龙门山推覆体模式

本文根据四川灌县、江油地区龙门山推覆体构造带的观察,结合国内外资料讨论推覆体的几何学特征和几何分类。作者首先根据推覆体沿主断层倾斜面顺向下滑和逆向上冲运动的性质,将推覆体划分为下滑推覆体和上冲推覆体两种基本类型;然后,根据推覆体与结晶岩体几何学的关系,并结合其与主断层面相对运动的性质又划分为单侧式推覆体和双侧式推覆体两大类和几个小类。作者从推覆体的发生、发展和演化过程探讨四川龙门山中北段推覆体模式。归类是初步的。在这些归类和龙门山推覆体模式分析中,对今后探索地壳上层滑脱构造的形成,模拟与这类构造有关的油气田区域是今后研究的努力方向。     

大别—桐柏山区植被分类初探

本文提出大别—桐柏山区自然植被分类的依据、原则和分类系统的单位及命名方法。根据野外考察资料分析,初步拟定了大别—桐柏山区自然植被分类系统方案,将其分为针叶林、阔叶林、竹林、灌丛植被、草丛植被、沼泽植被和水生植被7个植被型,在植被型下再分17个群系组和124个群系。     

论贵州山地高效节约型农业的发展途径及意义

从当代农业的特点、效益出发，结合贵州实际，提出了高效节约型农业研究的５点方向，明确了３个主要技术措施，具有一定的现实指导作用。