线载荷积分方程法分析桩顶受任意荷载的弹性斜桩

嵌在各向同性均匀弹性半空间的弹性斜桩顶部,受任意荷载的位移和应力,可分解为在倾斜平面xOz及其法平面yOz内进行分析.将Mindlin力作为基本虚载荷,令集度为未知函数X(t)、Y(t)、Z(t),分别平行于x、y、z轴,的基本载荷沿桩轴t的[0,L]内分布,并在桩顶作用集中力Q_x,Q_y、Z,力偶矩M_y、M_x,根据弹性桩的边界条件,将问题归结为一组Fredholm-Volera型的积分方程.文中给出数值解.计算结果的精度可用功的互等定理来检查.     

UNIQUENESS OF SOLUTION OF FIELD POINT OF SINGULAR SOURCE OUTSIDE-REGION-DISTRIBUTION METHOD

IntroductionAmethod,inwhichaproblemissolvedbysingularsource(s)outside-region-distribution(s),wheretheboundaryconditionoftheproblemissatisfied,iscalled"SingularSourceOutside-Region-DistributionMethod"(SSORDM).Usnallynon-singularintegralequationisobtainedbysingularsource(s)outSide-region-distribunonconhnuously.Asanearlyuse,singUlarsourcedistribuhoncanbefoundinthemethodofsource-sinkdistributioninfluidmechanicsasisstatedin[I],however,noproblemwasreducedtoanintegralequationatthattime.Asforsol…     

The solution of elastostatic problems and the principles of minimum potential energy,minimum complementary work,under fuzzy boundary conditions

A Solution of elastostatic problem is defined on the basis of set theory and extended to the cases with fuzzy boundary conditions. Extension is also given for the principles of minimum potential energy and minimum complementary work with fuzzy boundary conditions. A quasisolution of an elastostatic problem is defined as an approximate solution with boundary conditions most close to the original. And the existance of quasisolution of an elastostatic problem can be proved on the basis of certain assumptions and the theorem of minimum elementary potential energy.     

Primary research on Subjectivity Geometry

The so-called Subjectivity Geometry herein is a course for studying the relationship between the abstracted object configuration and its observed record by means of mathematical methods and described by mathematical language. There are many features differing from the common geometry when the effects of the subjectivity (such as the position of the observer, the functions of the visual system of human) are taken into account during the observing-recording process. In this paper, some basic assumptions are made; spherical observing record is suggested; the fundamental relationship between the abstracted object configuration and its corresponding observed record is studied and an example of application of the above theory is presented. We anticipate that the study of subjectivity geometry will influence, or will be associated with the study of physiology of the visual system, applied optics etc., and will be useful in surveying, pilotage and imitative biology, etc. Supported by Scientific Foundation of South China University of Technology.     

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

The basic equation of market price of option is formulated by taking assumptions based on the characteristics of option and similar method for formulating basic equations in solid mechanics: hv ₀(t) = m ₁ v ₀ ^–1(t) – n ₁ v ₀(t) + F, where h, m ₁, n ₁, F are constants. The main assumptions are: the ups and downs of market price v ₀(t) are determined by supply and demand of the market; the factors, such as the strike price, tenor, volatility, etc. that affect on v ₀(t) are demonstrated by using proportion or inverse proportion relation; opposite rules are used for purchasing and selling respectively. The solutions of the basic equation under various conditions are found and are compared with the solution v _f (t) of the basic equation of market price of futures. Furthermore the one-one correspondence between v _f and v ₀(t) is proved by implicit function theorem, which forms the theoretic base for study of v _f affecting on the market price of option v ₀(t).     

计算股市的基本方程,理论和原理（Ⅲ）：基本理论

由基本方程导出两个理论：１．股票的价值理论３ｖ＊（ｔ）＝Ｖ＊（０）ｅｘｐ（ａｒ２＊ｔ）．２。股能守恒理论,将股能定义为股价ｖ及其导数ｖ的二次函数Х＝Ａｖ＾２＋Ｂｖｖ＋Ｃｖ＾２＋Ｄｖ,在基本方程约束下,将问题归结为沿最优路径的约束优化问题,应用Ｌａｇｒａｎｇｅ乘数,变分法Ｅｕｌｅｒ方程可证Х对任何ｖ、ｖ问题归结为沿最优路径的约束优化问题。应用Ｌａｇｒａｎｇｅ乘数,谱分法Ｅｕｌｅｒ方程可证Х对任何ｖ、     

计算股市的基本方程,理论和原理（I）——基本方程

本采用网络模型和类似于固体力学的方法论来研究计算股市。建立四个基本的联立方程,即：利率－流通量方程;股票买入、卖出方程;股价变化率方程;以及利率、股价及股价变化率方程。中着重讨论利率－流通量方程的解及其简单应用,包括时间离散化时股市网络用Ｂａｎａｃｈ收缩映射定理证明最终趋向平衡状态,以及银行减息引起资金流动按指数型式衰减等。     

PRIMARY RESEARCH ON SUBJECTIVITY GEOMETRY

The so-called“Subjectivity Geometry ”herein is a course for studying the relationshipbetween the abstracted object configuration and its observed record by means ofmathematical methods and described by mathematical language.There are many featuresdiffering from the common geometry when the effects of the subjectivity (such as theposition of the observer,the functions of the visual system of human) are taken into accountduring the observing-recording process.In this paper ,some basic assumptions are made;spherical observing record is suggested:the fundamental relationship between theabstracted object configuration and its corresponding observed record is studied and anexample of application of the above theory is presented.We anticipate that the study ofsubjectivity geometry will influence,or will be associated with the study of physiology of thevisual system,applied opties etc.,and will be useful in surveying,pilotage and imitativebiology,etc.     

ASYMMETRIC DYNAMIC INSTABILITY OF AXISYMMETRIC POLAR DIMPLING OF THIN SHALLOW SPHERICAL SHELLS

If the parameterε~2 ,which measures the thickness-to-rise of the shell,is small,theaxisymmetric polar dimpling of shallow spherical shell due to quadratic pressuredistribution is dynamic instability,i.e.,a small perturbation can change it to an asymmetricpolar dimple mode.In two cases,the problem can he reduced to an eigenvalue problemTw_n=c_nw_n,where T can approximately be reduced to a Sturm-Liouville operator ifε~2《1.The existence of at least one real eigenvalue of T,which means that the axisymmetricpolar dimpling is dynamically unstable,is proved by spectral theorem or Hilbert theorem.Furthermore,an eigenfunction,which represents one of the asymmetric modes of theunstable dimple shell,belonging to an eigenvalue of T,is found.