谈谈北京大学藏秦简《鲁久次问数于陈起》的一些抄写特点

北京大学藏秦简《鲁久次问数于陈起》是一篇很重要的数学文献。根据《史记·秦始皇本纪》和里耶秦简"同文字方"的记载,可知该篇用"者"字表示{诸},用"吏"字表示{事},用"鼠"字表示{予},用"民"而不用"黔首",体现了战国晚期秦国抄本的特点。该篇"■"、"单"、"弋"、"见"等字的写法都保留了战国古文的字形特点,"料"字则是楚文字"■"字的误抄。该篇底本是用战国楚文字抄写的,文中出现"也"、"殹"并用的现象。

汉英问数法比较及其类型学考察

汉英两种语言中都有提问具体和抽象对象、离散对象以及事物、动作或行为等的某一个属性或特征的数量的问数法。但是汉语中提问大数目和小数目所用的问数法有区分,但英语中没有不同;汉语中存在不同问数法跟量词关系不同的情况,而英语中不存在这种情况;英语的问数法存在提问可数和不可数对象之分,汉语中无此区分。从这些共性和差异可以管窥不同语言问数法的类型学特征。

秦九韶“大衍总数术”中问数化定数算法解析

秦九韶在"大衍总数术"中化问数为定数有两条途径:一是将诸问数直接两两连环求等;一是将诸问数先求总等,存一(位)约众(位),然后再连环求等。连环求等时的根本原则是"约奇弗约偶",其中的"奇"、"偶"系指等数的个数的单、双。"约奇弗约偶"就是在化约时约含有奇数个等数的问数而不约含有偶数个等数的问数,目的是使约后的两数互素。如果化约后得到的两数不互素,即属有续等的情形,此时要用"以续等约彼则必复乘此"的方法再次化约。若约后仍有续等,则要继续用此方法化约,直至求得定数。诸问数的排列顺序以及求等化约的先后次序不会影响计算结果的正确性。两种求定数的途径异曲同工,秦氏的算法是具有一般性的通法。

《鲁久次问数于陈起》中的“音律-历法生成论”及其宇宙图像

《鲁久次问数于陈起》是汉代以前关于数为何重要并有益社会之讨论的最详细文献,应以“音律-历法生成论”来理解全篇内容。首先,陈起对自然要素的叙述顺序,符合先秦以“岁”为旨归的“历法生成论”,同时加入了音律要素。音律要素有自身的生成序列,借助《汉书·律历志》,并配合战国秦汉时期从以律管定音扩大到黄钟作为度量衡标准的历史过程,我们得以理解以度数为旨归的“音律生成论”的基本形态,这也解释了简文中音律与日常用数、百事经纪的关系。同时,对五音生律法和十二律生律法的讨论,解释了音律生成论中五和六的关系,为“数”具象化时出现的奇、偶数搭配提供了基础。而参照出土日书和式盘实物,本文为简文还原出一幅式图或宇宙图像,借此,简文中提到的所有“数”都得到了合理关联;由于占岁时和占病祟都是这种宇宙图像的功能,因此简文中提到的“瘳与死毕有数”和“以卜天下”也都得到了相应理解。

数的宇宙生成论:《鲁久次问数于陈起》与《蒂迈欧》比较研究

本文致力于比较北大秦简《鲁久次问数于陈起》(以下简称《陈起》)与柏拉图对话《蒂迈欧》,以此为例考察中国早期与古希腊基于数的宇宙生成论之异同。首先,本文将分别论述二者中音律与宇宙生成论核心要素(如行星与恒星运动、年月日周期的形成及宇宙结构)的关系。其次,本文关注二者从音律(纯比例)逐级创生(一维到二维到三维)的方式:在《陈起》中,该过程是以黄钟律作为嘉量的方式渗入到日常生活中的,而在《蒂迈欧》中,该过程则表达为平面与立体几何的构造。二者差异在于数之地位不同:《陈起》中,数内在于日常生活,但《蒂迈欧》中,数则超越于具体事物(位于具体事物与理念之间)。最后,本文进一步探究这一差异背后的原因并说明:柏拉图宇宙生成论的主要工作是解释哲学家如何能够藉助理解天的秩序来认识更高的理念世界的绝对秩序,同时以该秩序来理解自然界和人之生命的秩序;而在早期中国宇宙论中,没有超越于天之外的秩序,圣人贤臣之特质正在于能认识到这些隐含在自然秩序中的音律数和历法数,并将它们要么通过度量衡的方式带入百事经纪,要么通过具象化的宇宙图像,带入与个人生活相关的择日占卜或与国家行为相关的祭祀礼仪。

以问导学,让教学变“喂”为“觅”——《求一个小数的近似数》教学案例与反思

曾听说过这样一个故事：一个农民买一头小猪回家喂养。因环境生疏小猪不肯吃食，农民就在喂食时，用汤匙撒少许盐放人食中，小猪便狼吞虎咽起来，久而久之，小猪养成这样一种习惯：撒一点盐吃一口，不撒盐则不吃。

The L_(p) Shephard problem on entropy of log-concave functions

this paper,we introduce the L_(p) Shephard problem on entropy of log-concave functions,a comparison problem:whether ∏_(p)f≤∏_(p)g implies that Ent(f)≥Ent(g),for 1≤p<n,and Ent(f)≤Ent(g),for n<p,where ∏_(p)f is the L_(p) projection body of a log-concave function f.Our results give a partial answer to this problem.

Database-oriented storage based on LMDB and linear octree for massive block model

Data organization requires high efficiency for large amount of data applied in the digital mine system. A new method of storing massive data of block model is proposed to meet the characteristics of the database, including ACID-compliant, concurrency support, data sharing, and efficient access. Each block model is organized by linear octree, stored in LMDB（lightning memory-mapped database）. Geological attribute can be queried at any point of 3D space by comparison algorithm of location code and conversion algorithm from address code of geometry space to location code of storage. The performance and robustness of querying geological attribute at 3D spatial region are enhanced greatly by the transformation from 3D to 2D and the method of 2D grid scanning to screen the inner and outer points. Experimental results showed that this method can access the massive data of block model, meeting the database characteristics. The method with LMDB is at least 3 times faster than that with etree, especially when it is used to read. In addition, the larger the amount of data is processed, the more efficient the method would be.

New signature scheme based on two cryptographic assumptions

In order to improve the security of the signature scheme, a digital signature based on two hard-solved problems is proposed. The discrete logarithm problem and the factoring problem are two well known hard- solved mathematical problems. Combining the E1Gamal scheme based on the discrete logarithm problem and the OSS scheme based on the factoring problem, a digital signature scheme based on these two cryptographic assumptions is proposed. The security of the proposed scheme is based on the difficulties of simultaneously solving the factoring problem and the discrete logarithm problem. So the signature scheme will be still secure under the situation that any one of the two hard-problems is solved. Compared with previous schemes, the proposed scheme is more efficient in terms of space storage, signature length and computation complexities.

MULTI-MATERIAL NUMERICAL SIMULATION OF MOVING SHOCK INTERACTING WITH CONSECUTIVE BUBBLES

Numerical simulations are performed on the interface with large deformation induced by the interaction between a moving shock and two consecutive bubbles. The high performance of the level set method for multi-material interfaces is demonstrated. Discontinuous Galerkin finite element method is used to solve Euleri- an equations. And the fifth-order weighted essentially non-oscillatory （WENO） scheme is used to solve the level set equation for capturing multi-material interfaces. The ghost fluid method is used to deal with the interfacial boundary condition. Results are obtained for two bubble interacting with a moving shock. The contours of the constant density and the pressure at different time are given. In the computational domain, three different cases are considered, i.e. two helium bubbles, a helium bubble followed by an R22 bubble in the direction of the moving shock, and an R22 bubble followed by a helium bubble. Computational results indicate that multi-mate- rial interfaces can be properly captured by the level set method. Therefore, for problems involving the flow of three different materials with two different interfaces, each interface separating two different materials can be similarly handled.

Question classification in question answering based on real-world web data sets

To improve question answering （QA） performance based on real-world web data sets,a new set of question classes and a general answer re-ranking model are defined.With pre-defined dictionary and grammatical analysis,the question classifier draws both semantic and grammatical information into information retrieval and machine learning methods in the form of various training features,including the question word,the main verb of the question,the dependency structure,the position of the main auxiliary verb,the main noun of the question,the top hypernym of the main noun,etc.Then the QA query results are re-ranked by question class information.Experiments show that the questions in real-world web data sets can be accurately classified by the classifier,and the QA results after re-ranking can be obviously improved.It is proved that with both semantic and grammatical information,applications such as QA, built upon real-world web data sets, can be improved,thus showing better performance.

Purchasing policy model based on components/parts unification

This paper presents a mathematical model for components/parts unification (CPU) policy. This model considers two components/parts that are functionally interchangeable but purchased from suppliers with different prices and quality characteristics. Because of the buyer's quality preference and suppliers' discount rates for bulky purchases, the model assists the procurement manager to determine how best to purchase the components/parts to meet its demand while minimizing the total acquisition costs.

Analysis of a Cavity Used for Medical Purposes with the Dyadic Green's Functions and the Moment method

The structure of a microwave radiator used for medical purposes is described. The dyadic Green's function and the method are used to analyze this Kind of multimode rectangular medium-filled cavity. The distribution of electromagnetic field intensity and the power density,as well as the temperature effect in the biological sample load are obtained.OPtimization of the size of cavity and the position of the input aperture have been performed with the computer to optimize the uniformity or microwave effect and the input VSWR.Necessary experiments were performed to compare the data obtained with theoretical analysis.

Analysis of radial basis function interpolation approach

The radial basis function （RBF） interpolation approach proposed by Freedman is used to solve inverse problems encountered in well-logging and other petrophysical issues. The approach is to predict petrophysical properties in the laboratory on the basis of physical rock datasets, which include the formation factor, viscosity, permeability, and molecular composition. However, this approach does not consider the effect of spatial distribution of the calibration data on the interpolation result. This study proposes a new RBF interpolation approach based on the Freedman＇s RBF interpolation approach, by which the unit basis functions are uniformly populated in the space domain. The inverse results of the two approaches are comparatively analyzed by using our datasets. We determine that although the interpolation effects of the two approaches are equivalent, the new approach is more flexible and beneficial for reducing the number of basis functions when the database is large, resulting in simplification of the interpolation function expression. However, the predicted results of the central data are not sufficiently satisfied when the data clusters are far apart.

The MKdV Equation with Nonuniformity Terms

In this paper, the MKdV equation with nonuniformity terms is discussed. It relates to the eigenvalue problem The evolution laws of scattering data for (1. 3) are derived and the inverse scattering solutions-soliton solutions of eq(1. 1) are obtained. In the end of the paper, the single soliton solution and Double soliton solution are discussed. The result extends the situation in [1].

ADAPTIVE GENETIC ALGORITHM BASED ON SIX FUZZY LOGIC CONTROLLERS

The performance of genetic algorithm(GA) is determined by the capability of search and optimization for satisfactory solutions. The new adaptive genetic algorithm(AGA) is built for inducing suitable search and optimization relationship. The use of six fuzzy logic controllers(6FLCs) is proposed for dynamic control genetic operating parameters of a symbolic-coded GA. This paper uses AGA based on 6FLCs to deal with the travelling salesman problem (TSP). Experimental results show that AGA based on 6FLCs is more efficient than a standard GA in solving combinatorial optimization problems similar to TSP.

Separation method for multi-source blended seismic data

Multi-source seismic technology is an efficient seismic acquisition method that requires a group of blended seismic data to be separated into single-source seismic data for subsequent processing. The separation of blended seismic data is a linear inverse problem. According to the relationship between the shooting number and the simultaneous source number of the acquisition system, this separation of blended seismic data is divided into an easily determined or overdetermined linear inverse problem and an underdetermined linear inverse problem that is difficult to solve. For the latter, this paper presents an optimization method that imposes the sparsity constraint on wavefields to construct the object function of inversion, and the problem is solved by using the iterative thresholding method. For the most extremely underdetermined separation problem with single-shooting and multiple sources, this paper presents a method of pseudo-deblending with random noise filtering. In this method, approximate common shot gathers are received through the pseudo-deblending process, and the random noises that appear when the approximate common shot gathers are sorted into common receiver gathers are eliminated through filtering methods. The separation methods proposed in this paper are applied to three types of numerical simulation data, including pure data without noise, data with random noise, and data with linear regular noise to obtain satisfactory results. The noise suppression effects of these methods are sufficient, particularly with single-shooting blended seismic data, which verifies the effectiveness of the proposed methods.

Accessing Web Heterogeneous Databases Based on CORBA

The future usage of heterogeneous databases will consist of the WWW and CORBA environments. The integration of the WWW databases and CORBA standards are discussed. These two techniques need to merge together to make distributed usage of heterogeneous databases user friendly. In an environment integrating WWW databases and CORBA technologies, CORBA can be used to access heterogeneous data sources in the internet. This kind of applications can achieve distributed transactions to assure data consistency and integrity. The application of this technology is with a good prospect.

A Class of Singularly Perturbed Nonlinear Shock Problems

Using the method of matched asymptotic expansions, the shock solutions for a class of singularly perturbed nonlinear problems are discussed. The relation of the shock solutions and their boundary conditions is obtained. And the known results are generalized.

New Approach to Linear Stackelberg Problems with Multiple Leaders-followers

In this paper, we study linear static Stac kelberg problems with multiple leaders-followers in which each decision maker wi thin his group may or may not cooperate. An exact penalty function method is dev eloped. The duality gaps of the followers’ problems are appended to the leaders’ objective function with a penalty. The structure leads to the decomposition of the composite problem into a series of linear programmings leading to an efficie nt algorithm. We prove that local optimality is reached for an exact penalty fun ction and illustrate the method with three examples. The model in this paper ext ends the stackelberg leader-follower model.