期权标的资产波动率的重构方法

在B lack-Scho les公式中,波动率σ是一个非常重要的参数.并且在诸如股票、利率、股指期货等标的资产的交易市场中,人们往往希望知道标的资产未来价格的波动率,从而知道该资产的未来风险结构.但一般来说,由于事件还没有发生,人们对σ的未来走向很难预测.但可以运用B lack-Scho les的理论框架,从期权市场获取的信息去重构标的资产价格的波动率.论文使用的是基于T ikhonov正则化的数值微分方法,利用Dup ire公式去重构标的资产的未来预期波动率.相对于其他方法,该算法更加快速有效,并且能识别标的资产的预期风险突变.     

对流扩散方程的一些单调性差分格式

本文分析了逆风格式、格式和修正Dennis格式随网格Reynolds数变化的性质,构造了相应的半隐差分格式,它们具有无条件稳定性和无条件单调性。数值例子说明这些格式可以计算高Reynolds的定态流动问题。     

高阶导数的插值公式

本文我们得到一种插值公式,它通过一系列点,且满足该点列上的初始高阶导数值.最后还给出这种插值公式的误差估计.     

关于Delta算子的广义Taylor公式的余项估计

本文对哑演算中Ｒｏｔａ提出的至今尚未解决的广义Ｔａｌｏｒ公式的余项估计问题进行了研究。获得了Ｄｅｌｔａ算子关于一般函数的一个不同于Ｌａｇｒａｎｇｅ型的结果,并解决了二阶Ｄｅｌｔａ算子的余项估计问题。     

Some inequalities involving π and an application to Hilbert's inequality

Some inequalities involving π are proved. As an application, we give some strengthened Hilbert's inequalities.     

Recursion Formulas to Find Solutions of Some Nonlinear Evolution Equations

New recursion formulas are obtained for finding solutions of some nonlinear evolution equations.     

关于奇异夸克物质的性质

基于以前的工作,导出了新的奇异夸克质量公式,并用于研究奇异夸克物质的性质,得到与MIT袋模型类似的结果.而且发现,新公式导致与以前有所不同的结果,即声速随能量密度的增加而趋向于极端相对论情况的速度减慢.     

Trace formula in noncommutative geometry and the zeros of the Riemann zeta function

We give a spectral interpretation of the critical zeros of the Riemann zeta function as an absorption spectrum, while eventual noncritical zeros appear as resonances. We give a geometric interpretation of the explicit formulas of number theory as a trace formula on the noncommutative space of Adele classes. This reduces the Riemann hypothesis to the validity of the trace formula and eliminates the parameter of our previous approach.     

DYNAMICAL EXPLANATION ON TOROFLUX'S PHENOMENA

本文分析了流动环特殊现象的力学原理。流动环是由细长钢带缠绕形成的环状螺旋玩具,具有瞬间几何形态突变和绕圆柱物体运动时迅速旋转两种独特现象。文中利用封闭曲杆的拓扑学规律确定其曲率和扭率,用于计算和比较流动环两种平衡状态的弹性变形势能。证实流动环的形态突变源于最小弹性势能原理。以组成流动环的单个圆环为分析对象,且考虑邻近圆环的牵拉效应。分析了流动环下落时相对圆柱体的滚动过程,以解释旋转现象的产生原因。导出了流动环下落旋转的角加速度公式。理论计算结果与实验数据较好吻合。     

Calculation of the light intensity distribution reflected by a planar corner-cube retroreflector array with the size of centimeter and above

The light intensity distribution (LID) reflected by a planar corner-cube retroreflector array with the size of centimeter and above (PCCRA) is calculated based on the Collins formula, coordinate transformation matrixes and vector algebra. The expression can be used for the PCCRAs with different parameters and different complex optical systems described by ABCD matrix. The expression indicates that the LID of a PCCRA is much different from a single corner-cube retroreflector (CCR) with equivalent aperture. Computer simulations are applied to explain the expression clearly. The results show that the LID of the PCCRA is more homogeneous than the single CCR with equivalent aperture under circumstances of both normal incident light and oblique incident light. In addition, the expression is proved by comparing the simulation result of the PCCRA only comprising a single CCR and the previous experimental result.