论数学与哲学的关系（二）

本文通过微积分初期的矛盾，即所谓第二次数学危机及其解决过程的长期而激烈的争论，无穷小分析，极限思想等资料阐明了数学与哲学，数学语宗教的关系是。     

极限与无穷小辨析

极限与无穷小是微积分中的基本概念,是整个微积分学的理论基础.极限是运动与静止的统一;极限可以被看作是函数变换器;极限是连接有限与无限的桥梁.极限与无穷小有着密切的关系,借助于极限,可以深刻地理解无穷小的本质.反过来,无穷小思想也是对极限思想的补充.深刻地理解极限和无穷小的实质,对学习微积分是十分必要的.     

无穷小与微分的思考

数学中的无穷对象和过程,本质上都是双相无穷,是潜无穷与实无穷的对立统一。本文通过分析无穷小的两种面貌——潜无穷小和实无穷小,揭示了无穷小与极限、导数、微分、不定积分、定积分的关系,并阐述了这些基本概念间的关系,给出了某些概念的几何意义。     

非标准分析中的微积分

通常所说的《数学分析》是属于柯西体系的微积分理论,它是在实数连续统的基础上,运用极限方法即ε—δ方法建立起来的.这种理论比十七、十八世纪牛顿、莱布尼兹等人的微积分理论前进了一大步.一百多年来,柯西的这一套体系已成为微积分基本理论的唯一体系,人们一提到微积分,自然就以这套体系为标准,所以通常称柯西体系的《数学分析》为“标准分析”.标准分析是在实数域R上讨论的,无穷小、无穷大作为变量的极限.无穷小作为以零为极限的一种特殊变量,这种概念导致了不可避免的自相矛盾:如若无穷小的距离大于零,那么若干个距离势必拥有有效长度,然而在标准分析中不管     

什么是微分及其本质?——学习马克思《数学手稿》体会之二

自从微积分这门学科于十七世纪后半叶问世以来,关于它的基本概念及理论基础问题引起了长期的争论。最近几年以来,我国数学界很多人认真学习马克思的数学手稿,努力运用辩证唯物主义批判数学领域里的唯心主义和形而上学,热烈开展对微积分基本概念及理论基础问题的讨论。究竟什么是微分其及本质?什么是无穷小量、极限和导数的本质?     

试论极限思想与微积分的逻辑辩证关系

微分和积分,本质上都是极限。只有把握了极限思想,才能真正体会微积分的基本知识、基本理论和基本技能,培养辩证唯物主义观。     

无穷小的认识过程初探

微积分是高等数学的基本组成部分,它不仅在高等数学中占有重要地位,而且也是现代化建设和高科技发展不可缺少的有效工具。而无穷小是微积分理论的最基本概念之一,在微积分理论体系中,无穷小是一个必须要弄清楚的概念。然而,人们对无穷小的认识却经历了一个漫长的过程。直到十八世纪,仍然没有较完善的解释无穷小概念。无穷小是什么？无穷小究竟究竟能不能是零？我们怎样确切地描述它？这些问题引起了数学界乃至哲学界的争论长达一个半世纪。无穷小问题至关重要,若其不能解决,极限概念就无法建立,微积分理论就不会完善。到十九世纪二十年代,无穷小概念才有了比较合理的解释。为了更好地学习微积分理论,掌握现代化科学文化知识,我们有必要了解无穷小的历史。     

建立微积分理论代数基础的尝试

为了使微积分理论建立在代数基础上。从微积分中彻底取消无穷小和极限概念，笔者对此进行了初步的尝试，用代数方法推导出了微积分的公式。     

无穷小和与差逐项等价替换的探讨

无穷小整体等价替换对求未定式“0(0)”型极限很有帮助，但现行各高数教材中均告诫不可用无穷小代数和逐项等价替换来求极限，否则会导致错解.该文通过例题探讨在满足相应条件下，即对前者理论稍加推广，无穷小和与差逐项等价替换用以求极限同前者一样有效，并分析了导致“失效”与“错解”的潜在原因.     

“微分”和“积分”二术语的来龙去脉

中国古代的传统数学中很早就有了"微分"和"积分"二术语,在中国古代传统数学著作《九章算术注》中就多次出现,其意义是无限分割和无穷叠加。而作为微积分理论中表示无穷小分析的"微分"和"积分"二术语则是在1859年的《代微积拾级》中首次出现。"微分"和"积分"二术语是中国数学家李善兰和西方传教士伟烈亚力合译时共同选用的。通过历史文献的梳理,得出"微分"和"积分"二术语的翻译可以说是李善兰翻译西方数学著作中名词意译的典范。     

Characterization of Ordovician carbonate reservoirs, southeastern Saskatchewan, Canada

The discovery of the prolific Ordovician Red River reservoirs in 1995 in southeastern Saskatchewan was the catalyst for extensive exploration activity which resulted in the discovery of more than 15 new Red River pools. The best yields of Red River production to date have been from dolomite reservoirs. Understanding the processes of dolomitization is, therefore, crucial for the prediction of the connectivity, spatial distribution and heterogeneity of dolomite reservoirs.The Red River reservoirs in the Midale area consist of 3～4 thin dolomitized zones, with a total thickness of about 20 m, which occur at the top of the Yeoman Formation. Two types of replacement dolomite were recognized in the Red River reservoir: dolomitized burrow infills and dolomitized host matrix. The spatial distribution of dolomite suggests that burrowing organisms played an important role in facilitating the fluid flow in the backfilled sediments. This resulted in penecontemporaneous dolomitization of burrow infills by normal seawater. The dolomite in the host matrix is interpreted as having occurred at shallow burial by evaporitic seawater during precipitation of Lake Almar anhydrite that immediately overlies the Yeoman Formation. However, the low δ18O values of dolomited burrow infills (-5.9‰～ -7.8‰, PDB) and matrix dolomites (-6.6‰～ -8.1‰, avg. -7.4‰ PDB) compared to the estimated values for the late Ordovician marine dolomite could be attributed to modification and alteration of dolomite at higher temperatures during deeper burial, which could also be responsible for its 87Sr/86Sr ratios (0.7084～0.7088) that are higher than suggested for the late Ordovician seawaters (0.7078～0.7080). The trace amounts of saddle dolomite cement in the Red River carbonates are probably related to "cannibalization" of earlier replacement dolomite during the chemical compaction.     

An Index mechanism for multi-scale view in spatial databases

There are numerous geometric objects stored in the spatial databases. An importance function in a spatial database is that users can browse the geometric objects as a map efficiently. Thus the spatial database should display the geometric objects users concern about swiftly onto the display window. This process includes two operations:retrieve data from database and then draw them onto screen. Accordingly, to improve the efficiency, we should try to reduce time of both retrieving object and displaying them. The former can be achieved with the aid of spatial index such as R-tree, the latter require to simplify the objects. Simplification means that objects are shown with sufficient but not with unnecessary detail which depend on the scale of browse. So the major problem is how to retrieve data at different detail level efficiently. This paper introduces the implementation of a multi-scale index in the spatial database SISP (Spatial Information Shared Platform) which is generalized from R-tree. The difference between the generalization and the R-tree lies on two facets: One is that every node and geometric object in the generalization is assigned with a importance value which denote the importance of them, and every vertex in the objects are assigned with a importance value,too. The importance value can be use to decide which data should be retrieve from disk in a query. The other difference is that geometric objects in the generalization are divided into one or more sub-blocks, and vertexes are total ordered by their importance value. With the help of the generalized R-tree, one can easily retrieve data at different detail levels.Some experiments are performed on real-life data to evaluate the performance of solutions that separately use normal spatial index and multi-scale spatial index. The results show that the solution using multi-scale index in SISP is satisfying.     

A computer generator for randomly layered structures

AcomputergeneratorforrandomlylayeredstructuresYUJia shun1,2,HEZhen hua2(1.TheInstituteofGeologicalandNuclearSciences,NewZealand;2.StateKeyLaboratoryofOilandGasReservoirGeologyandExploitation,ChengduUniversityofTechnology,China)Abstract:Analgorithmisintrod…     

海南岛地体及其毗邻陆缘晚中生代—新生代古地磁研究和构造演化

本文叙述了对海南岛及其毗邻大陆边缘白垩纪到第四纪地层岩石进行古地磁研究的全部工作过程。通过分析岩石中剩余磁矢量的磁偏角及磁倾角的变化,提出海南岛白垩纪以来经历的构造演化模式如下:早期伴随顺时针旋转而向南迁移,后期伴随逆时针转动并向北运移。联系该地区及邻区的地质、地球物理资料,对海南岛上述的构造地体运动提出以下认识:北部湾内早期有一拉张作用,主要是该作用使湾内地壳显著伸长减薄,形成北部湾盆地。从而导致了海南岛的早期构造运动,而海南岛后期的构造运动则主要是受南海海底扩张的影响。海南地体运动规律的阐明对于了解北部湾油气盆地的形成演化有重要的理论和实际意义。     

Exciton Seebeck in Molecular Systems

Various applications relevant to the exciton dynamics,such as the organic solar cell,the large-area organic light-emitting diodes and the thermoelectricity,are operating under temperature gradient.The potential abnormal behavior of the exicton dynamics driven by the temperature difference may affect the efficiency and performance of the corresponding devices.In the above situations,the exciton dynamics under temperature difference is mixed with     

Achieving Unusual States of Matter Under High Pressure

The elongation method,originally proposed by Imamura was further developed for many years in our group.As a method towards O(N)with high efficiency and high accuracy for any dimensional systems.This treatment designed for one-dimensional(ID)polymers is now available for three-dimensional(3D)systems,but geometry optimization is now possible only for 1D-systems.As an approach toward post-Hartree-Fock,it was also extended to     

《Chinese Science Bulletin》SUBJECT INDEX TO VOLUME 59(2014)

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An on-line scaling method for improving scalability of a database cluster

The explosive growth of the Internet and database applications has driven database to be more scalable and available, and able to support on-line scaling without interrupting service. To support more client's queries without downtime and degrading the response time, more nodes have to be scaled up while the database is running. This paper presents the overview of scalable and available database that satisfies the above characteristics. And we propose a novel on-line scaling method. Our method improves the existing on-line scaling method for fast response time and higher throughputs. Our proposed method reduces unnecessary network use, i.e. , we decrease the number of data copy by reusing the backup data. Also, our on-line scaling operation can be processed parallel by selecting adequate nodes as new node. Our performance study shows that our method results in significant reduction in data copy time.     

An improved R-tree based on childnode''s probability

R-Tree is a good structure for spatial searching. But in this indexing structure,either the sequence of nodes in the same level or sequence of traveling these nodes when queries are made is random. Since the possibility that the object appears in different MBR which have the same parents node is different, if we make the subnode who has the most possibility be traveled first, the time cost will be decreased in most of the cases. In some case, the possibility of a point belong to a rectangle will shows direct proportion with the size of the rectangle. But this conclusion is based on an assumption that the objects are symmetrically distributing in the area and this assumption is not always coming into existence. Now we found a more direct parameter to scale the possibility and made a little change on the structure of R-tree, to increase the possibility of founding the satisfying answer in the front sub trees. We names this structure probability based arranged R-tree (PBAR-tree).     

Integrating GIS Web services based on mediating architecture

The geographic information service is enabled by the advancements in general Web service technology and the focused efforts of the OGC in defining XML-based Web GIS service. Based on these models, this paper addresses the issue of services chaining,the process of combining or pipelining results from several interoperable GIS Web Services to create a customized solution. This paper presents a mediated chaining architecture in which a specific service takes responsibility for performing the process that describes a service chain. We designed the Spatial Information Process Language (SIPL) for dynamic modeling and describing the service chain, also a prototype of the Spatial Information Process Execution Engine (SIPEE) is implemented for executing processes written in SIPL. Discussion of measures to improve the functionality and performance of such system will be included.