引理

The paper prices bond and bond option, analyzing dynamic interest rate, regime-switching and option pricing. According to the affection of regime-switching to interest rate derivative pricing, the paper deduces the partial differential equation of bond pricing with Ito lemma, and obtains characteristic function and recursion equation of bond option.

从利率动态变化、结构转换和期权定价三个方面进行分析，对结构转换下的债券和债券期权进行定价，考虑了结构转换对利率衍生物定价的影响，利用Ito引理获得债券定价的偏微分方程，并得到债券期权定价的特征函数与递归等式。

Intuitively, once a member gets to the vicinity of another member, then the repulsive force will be in effect and the conditions of Lemma 2 will not be satisfied anymore.

凭直觉，一旦会员愈附近另一位议员的话，斥力将在效应和条件引理2不会感到满意了。

In order to make the prior estimate of solution and calculate the upper right derivative of V along the solution, we employ some transformation techniques on fraction.

全文内容分为五章：第一章主要介绍了研究工作的意义、背景及本文主要工作和文中所要用到的一些引理。

In this paper, by using the notable Mountain Pass Lemma of critical point theory, some sufficient conditions for the existence and multiplicity of periodic and subharmonic solutions to a class of second order nonlinear functional difference equations with Jacobi operators are obtained.

论文研究了一类具有Jacobi算子类型的二阶非线性泛函差分方程(1)的周期解和次调和解的存在性与多重性。首先将方程（1）的解的存在性问题转化为某个泛函临界点的存在性问题，然后验证此泛函满足著名的山路引理的条件，从而得到论文的主要结论。

When the parameters are unknown, based on the Lyapunov theory, corresponding controller and the adaptive law of parameters are designed to suppress chaos to any unstable equilibrium by the adaptive control strategy. The asymptotical stability of chaos control is guaranteed in theory by lemma of Barbalat.

当该混沌系统的参数未知时，基于Lyapunov稳定性理论，利用自适应控制策略，设计了相应的非线性控制器和参数自适应律将混沌系统的轨道控制到其任意一个平衡点，并借助Barbalat引理，从理论上证明保证了混沌控制的渐近稳定性。

This paper deals with the existence and multiplicity for one elliptic problems with p-Laplacian and an asymptotic linear equation by variational methods, especially the Mountain pass Lemma.

本文主要利用变分法，特别是山路引理研究了一类P阶Laplace方程和渐近线性椭圆方程解的存在性及多解性。

By using the above lemma, the traffic network equi-librium problem is equivalent to a variational inequality problem.

正是这个引理，使得交通网络中的均衡问题同一个变分不等式等价。

Existence theorems for optimal elements are proved with the aid of Zorn's lemma and the scalarization theory.

借助于 Zorn 引理和标量化定理证明了最优元的存在性定理。

In this paper, by Zorn lemma and cone theory, the existence of the random fixed points for discontinuous increasing operators was discussed and the existence theorems of random fixed point were obtained.

本文利用Zorn引理和锥理论，研究了不连续随机算子的随机不动点的存在性问题，得到了几个有关不连续随机增算子的随机不动点定理。

This paper using Zorn Lemma, we get new fixed point theorems for noncom-pact and non monotone operators on Fully regular cones, all the results we get are new.

本文运用Zorn引理，得出了全正则锥上的非紧非单调算子的不动点的存在性结果，这些结论是全新的。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新