算术的

These constructional methods can be used to treat many problems, the numerical results show that the given interval extension has smaller excessive width relative to the range of the functions over a domain. For univariate differentiable functions, the definition of interval slope is extended from the first order to high order according to their differentiability, and iterative formula of high-order interval slope computation is also developed.

对多元函数，在不要求函数的可微性及有关Lipschitz常数的条件下，给出了分量函数区间展开的斜率算术运算规则；利用函数局部凸或凹的运算特点，通过递归计算建立了多元函数区间扩张的构造方法。

Based on the foregoing strategy, we choose Inverse Modified Discrete Cosine Transform and Polyphase Synthesis Filterband of the MP3 decoder by an ASIC implementation. Moreover, to further reduce the hardware cost, we use CORDIC-based calculations and merging some arithmetic operations to replace the original ones of IMDCT and PSF.

基於前述的原则及由运算量的统计分析，我们选定「反转修正式离散余弦转换(Inverse Modified Discrete Cosine Transform， IMDCT)」与「多相位合成滤波频带(Polyphase Synthesis Filterband， PSF)」使用ASIC方式实现，同时为了有效降低这两个模组的硬体成本，我们导入「座标轴旋转数位计算机」及合并运算方式取代原始算术运算，使得新的计算式有效降低原IMDCT约74%之乘法及约49%加法运算，而在多相位合成滤波频带的反离散余弦转换也有降低约33.4%之乘法及约24.6%之加法运算。

In a circle,when an isogon unlimited number of margin increase, the limits of its perimeter is circumference, and its size limited is the area of the circle.

（《九章算术》方田章圆田术刘徽注）这就是说，圆内接正多边形的边数无限增加的时候，它的周长的极限是圆周长，它的面积的极限是圆面积。

Thirdly, the problems of institution investor'optimal liquidation strategy and optimal liquidation time were investigated with the conditions that the price of risky asset followed arithmetic Brown motion and liquidation velocity was limited. The problems involved the following scenes: price impact function was linear expression of liquidation velocity which was boundary closed set with an isolated point; price impact function was stochastic; price impact function was nonlinear.

接着，当风险资产的价格服从算术布朗运动，且对投资者的变现速度做出限制时，研究机构投资者的最优变现策略和最优变现时间问题，其中包括：价格冲击函数为变现速度的线性函数，变现速度是一带有孤立点的有界闭集；价格冲击是随机形式；价格冲击是变现速度的非线性函数。

Considering that the trade's price impact function includes the trade size and the liquidity discount of security market at that time,under the assumption that the risky asset's price follows the arithmetic Brown motion,and based on the none-shape,L shape or U shape of intraday liquidity patterns,this paper introduced the Lagrange equation of motion and the method of Frobenius,and found out the optimal intraday liquidation strategies of large security positions.

考虑到交易的价格影响是该时刻的交易量与市场流动性折扣的函数，假设风险资产价格服从算术布朗运动，以及分别在不考虑日内流动性模式，考虑L形和U形日内流动性模式的基础上，采用拉格朗日运动方程以及Frobenius方法，得到了大额风险头寸的日内最优变现策略。

The three states are transformed via two-dimension liquid crystal element and polarizators, and ternary arithmetic operation and ternary logic al calculus completed directly in this way.

三值光计算机用相互垂直的两个线偏振光和零光强三个独立的光状态表示信息；用二维液晶器件和偏振器实现此三个状态间的转换；采用三进制算术运算；直接处理三值逻辑运算；拥有巨大的数据位数(容易超过10~4位)；具有光运算、光传送、电控制等结构特色，具有很强的空间、时间并行性。

An opportunity, however, presented itself: being required to work out from data supplied to him the ''défflement'' of a proposed fortress (an operation then only performed by a long arithmetical process), Monge, substituting for this a geometrical method, obtained the result so quickly that the commandant at first refused to receive it - the time necessary for the work had not been taken; but upon examination the value of the discovery was recognized, and the method was adopted.

但是一个机会出现了：蒙日需要根据数据计算一个设计中的要塞的枪炮布置（通常需要很长的算术过程来完成），他用了一个几何的方法来代替，如此迅速地得到了结果，以至于司令官一开始拒绝接受-因为一般完成工作所需的时间还没有过去；但是检查发现的价值被认可了，而且该方法被采纳了。

The implementation processes of those two algorithms on smart card with cryptographic coprocessor are explained separately. The implementation process of RSA includes modular exponentiation and modular multiplication. The process of ECC includes the selection of base field and coordinates, scalar multiplication and field operation.

本文分别阐述了两者在带有加密协处理器的智能卡平台上的实现过程，包括RSA算法中模幂运算、模乘运算的实现；ECC算法中基域的选择、坐标系的选择、标量乘法和域算术运算的实现。

The subject area, therefore, provides a challenge for students of social science, geography, economics, planning, engineering or mathematics and other numerate disciplines, who wish to broaden their studies into other disciplines and to solve practical problems in this wider context....

的主题领域，因此，提供了一个社会科学，地理，经济，规划，工程或数学和其他学科的算术，谁希望扩大到其他学科的研究，以解决这个更广泛的方面实际困难的学生的挑战。。。。

It was supposed that the dynamic moving process of the stock price and the return was driven by Geometry Brownian Motion and the lognormal distribution respectively. Takinginto account the riskneutral environment, we got a closedform analytical formula for deferred arithmetic asian options by the method of Taylor expansion of the stochastic integral formula within the terminal payoff. Furthermore, with the series definition of the definite integral, we transferred the continuous problem into a discrete one which is simpleenough to figure out. Meanwhile we tested the accuracy of the formula with the Monte Carlo simulation as a benchmark and the result shows that the formula can be utilized to price the related financial derivatives.

在标的价格服从几何布朗运动、收益服从对数正态分布的前提下，通过风险中性定价原理，对到期损益中的随机积分进行任意次Taylor近似，并由级数定义将此连续问题离散化，给出了延期算术平均亚式期权封闭形式的解析定价公式，并与Monte Carlo模拟得到的价格作为标尺对得到的公式进行精确性检验，结果表明，所得公式可以应用到金融实务中对此类衍生品定价中。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。