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、     

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).     

主观几何中一组余弦定律方程的解*

本文讨论在主观几何应用例子[1]中出现的由余弦定理建立的一组六元二次带根式的代数方程的解.应用隐函数存在定理,本文证明这组方程存在有唯一的实解.把求解问题转化为无约束非线性优化问题,可以用已知的诸法来求解.文中给出了用下降法求解的数值例子.     

浅球薄壳轴对称极凹陷的非轴对称的动力不稳定性*

当壳厚-升高比ε2<<1时,由二次型载荷产生的轴对称极凹陷的浅球薄壳是动力不稳定的.微小的扰动足以使它变成非轴对称凹陷.在两种情形下,问题都可归结为特征值问题Tw_n=c_nw_n.其中T当ε2<<1时近似为一Sfrum-Liouville算子.本文用谱理论和Hilbert定理均可证明T至少存在一实的特征值;它意味着轴对称极凹陷是动力不稳定的.再进一步,本文还找出代表不稳定凹陷壳体的非轴对称变形的、属于一特征值的T的特征函数.     

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v*(t)=v(0)exp(ar₂t)。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φ=Av2+Bvv+Cv2+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?对任何v、v>守恒。文中给出应用这些方程和理论对股市走势作分析的一些判断并为深沪股市实际走势所验证。     

The solution of dynamic Point-Ring-Couple in an elastic space and its properties

The solution of dynamic Point-Ring-Couple at the origin,on z=0 plane,in an elastic space is presented and its properties are discussed.Let shocking loads be uniformly distributed,along the direction of circumference,at a circle,on z=0 plane,with radius a and centered at the origin.Then,the solution of our problem is obtained via integral calculation for a→0.When the intensity of this dynamic Point-Ring-Couple is varied with sinωt,the cones in the elastic space with apex at the origin and the z-axis be its symmetric axis,become zero stressed surfaces at any time instance.The solution of dynamic torsion problem of revolution solids with these cones as boundary under the application of torque varied with sinωt is found.     

一类带约束的二维弱奇异积分方程的一般解及其应用*

本文给出二维弱奇异积分方程作用着约束方程的比[1]为更一般的解P式中k和产是给出的连续函数;(s,φ)是原点在M(r,θ)的局部极坐标;(r,θ)是原点在O(0.0)的总体极坐标;F(r_*,θ)=c_*(常数)是研究域Q的边界围线?Q:g(ω)=F(r,θ)/[πkφ₀];g'=dg/dω,ω=N-r2sin2(θ+φ₀);φ₀,N为中值.[1]的(2.19)型的解仅为F(r,θ)=ω时上述解的特例.文中给出刚性圆锥和弹性半空间接触问题的解作为应用例子.此解较Love(1939)的解简明.     

Solution of A 2-D weak singular integral equation with constraint

In this paper, the solution of a 2-D weak singular integral equation of the first kind

动力点圆力偶作用于弹性全空间的解及其性质*

本文给出动力点圆力偶作用于弹性全空间原点的解,并讨论它的性质.将脉冲荷载沿以原点为心、α半径,在z=0平面上的圆周切向均匀分布,当a→0时经积分运算即得问题的解.当此动力点圆力偶的强度按sinωt变化时,在弹性全空间中以z轴为轴,原点为顶点的锥面在任何时刻均为零应力面.以这些锥面为边界的回转体受按sinωt而变化的扭矩作用的动力扭转问题的解可由本文的解得出.     

集中力作用于剪切模量沿深度线性变化的半空间的公式

根据一个引理和一个假设,本文绘出集中力作用于泊桑比v为常数和剪切模量G沿深度线性变化的半空间的公式.当用积分方程法分析桩和其它地学工程问题时,这些公式可以用作一近似的基本解.