主观几何学初步探讨*

此处的所谓“主观几何学”是指使用数学的语言和方法,研究抽象了的客观形体和其观察记录之间的关系的学科.当观察记录的过程中考虑主观因素(如观察器的位置,人体视觉系统的功能等)的影响时,便带来了许多不同于通常几何学的特点.本文给出基本假设;建议球面观察记录;研究了抽象的客观形体及其观察记录之间的基本对应关系以及给出应用上述理论的例子.我们期望主观几何学的研究将影响或连系于视觉系统生理学,应用光学等研究,并在测量、导航和仿生学等中得到应用.     

Fredholm第一种积分方程Ax=y的表示定理和一次迭代定理*

本文给出两个定理.表示定理指出:若具有界L₂核的Fredholm第一种积分方程Ax=y有唯一解,则其中,一次迭代定理指出:可由公式=x₀+g₀A*(y-Ax₀)一次迭代求得的充分和必要条件是满足下列条件之一:
     

BASIC EQUATIONS, THEORY AND PRINCIPLE OF COMPUTATIONAL STOCK MARKET (Ⅰ)──BASIC EQUATIONS

IntroductionComputationaleconomicwillbethetendencyofmodemeconomicanalysis,nevedhelessthereisalongwaytoachievethelevelofcomputationalmathematicsandcomputationalmechanicsatpresent.Stockmarketisasensiblebarometermeasuredtheweatherofmarketeconomicactivities.Althoughtherearemanypapersoncomputationaleconomic(forexampleRefs.[l,2])butpaperconcernedwithstockmarketisrarelyseen.InChina,mostpublicationsonstockmarket(forexampleRefs.[3~5])arequotationdata,predicationoftendency,skillsorexperiencesforgainin…     

金融衍生产品的力学方法分析（Ⅱ）—期权市场价格基本方程

类似固体力学建立基本方程方法，根据期权特点，采用一些假设，建立期权市场价格基本方程：hv0(t)=m1vo^-1(t)-n1vo(t) F,式中h,m1,n1,F为常数，主要假设有：期权市场价格vo(t)的升降由市场供求决定；影响v0(t)的因素如行使价，期限，波幅等用正或反比关系；买和卖用相反规律。文中给出不同情况下基本方程的解，并和期货市场价基本方程的解vf(t)相比较，以及用隐函数存在定理证明vf与v0(t)存在一一对应关系，为研究期货vf对期权价vo(t)的影响提供理论依据。     

圆柱嵌入半空间的三维问题的一个简便的积分方程解法

将由Mindlin集中力组成的轴对称载荷沿弹性半空间z轴[0,L]内分布,并迭加Boussinesq的解,就能使边界条件为1.Z=0,r≠0,σz=τrz=02.0≤z≤L,U(e,z)=a-e,(1≥e/a≈1)3.P=-2π[a∫Lτry(a,z)dz ∫0arσ(r,L)dr](1)的圆柱嵌入半空间的三维问题归结为一Fredholm第一种积分方程.本文给出了Fredholm第一种积分方程近似解误差估计的一个定理. 将本文所论述的方法,用于桩的分析,较R.Butterfield等人的方法为优越,即所得到积分方程是一维非奇异的、能考虑初应力的影响、不需要预先假定沉陷函数,并且考虑了可压缩桩中的三维应力状态.     

嵌在倾斜半空间的轴向受力刚性桩的线载荷积分方程法的分析

嵌在表面水平的弹性半空间的桩或杆他人已做了许多工作。但嵌在表面倾斜的半空间的桩或杆与半空间表面夹角非直角情形的分析则未见到。在基楚工程中常遇见这类情形,如斜坡的桩,或码头,桥墩,海洋结构等的斜桩等。这类轴向受力的三维非轴对称问题宜用作者提出的线载荷积分方程法来分析。本短文分析嵌在小斜度弹性半空间轴向受力刚性桩的铅垂位移(沉陷)。所用的假设是:半空间是均匀各向同性的;轴向受力后桩仍保持铅垂状态;桩为中等长度(20≤L/D≤80,见图1)。为计算简便,只考虑桩一土表面上x_1=0线上的点的铅垂方向位移的相容性。据文献[7],忽略桩的径向位移的相容性对于计算的沉陷值的影响是不大的。图1表示本问题及其座标;图2为本文所用的基本虚载荷。     

FORMULAE OF FORCE AT A POINT IN THE INTERIOR OF A HALF SPACE WITH SHEAR MODULUS LINEARLY VARIED WITH DEPTH

According to a lemma and an assumption, this paper presents formulae of force at apoint in the interior of a half space with Poisson＇s ratio v=constant and shear modulus Glinearly varied with depth. These formulae can be used as an approximate basic solutionwhen the integral equation method is employed for the analysis of piles and othergeotechnical engineering problems.     

ANALYSIS OF FINANCIAL DERIVATIVES BY MECHANICAL METHOD (Ⅱ)-BASIC EQUATION OF MARKET PRICE OF OPTION

1　ＴｈｅＰｒｅｓｅｎｔＳｔａｔｅ ,ｔｈｅＳｉｇｎｉｆｉｃａｎｃｅａｎｄｔｈｅＭｅｔｈｏｄｓｏｆＯｐｔｉｏｎＲｅｓｅａｒｃｈＡｎｏｐｔｉｏｎｉｓａｒｉｇｈｔｏｆｓｅｌｅｃｔｉｏｎ .Ｔｈｅｒｅａｒｅｔｗｏｓｅｌｅｃｔｉｏｎｓｆｏｒｐｕｒｃｈａｓｉｎｇａｎｏｐｔｉｏｎ :ｉ.ｅ .,ｔｏｅｘｅｒｃｉｓｅｉｔｏｒｎｏｔｔｏｅｘｅｒｃｉｓｅｉｔ.Ｔｏａｂｕｙｅｒ,ｐｕｒｃｈａｓｉｎｇａｎｏｐｔｉｏｎｉｓｕｓｅｄｆｏｒｈｅｄｇｉｎｇｏｒｆｏｒｍａｋｉｎｇｐｒｏｆｉｔｓｆｒｏｍｓｐｅｃｕｌａｔｉｏｎ .Ｔｏａｓｅｌｌ…     

ANALYSIS OF FINANCIAL DERIVATIVES BY MECHANICAL METHOD (Ⅰ)-BASIC EQUATION OF PRICE OF INDEX FUTURES

Similar to the method of continuum mechanics, the variation of the price of index futures is viewed to be continuous and regular. According to the characteristic of index futures, a basic equation of price of index futures was established. It is a differential equation, its solution shows that the relation between time and price forms a logarithmic circle. If the time is thought of as the probability of its corresponding price, then such a relation is perfectly coincided with the main assumption of the famous formula of option pricing, based on statistical theory, established by Black and Scholes, winner of 1997 Nobel’ prize on economy. In that formula, the probability of price of basic assets (they stand for index futures here) is assummed to be a logarithmic normal distribution. This agreement shows that the same result may be obtained by two analytic methods with different bases. However, the result, given by assumption by Black-Scholes, is derived from the solution of the differential equation.