Then he got out note - book and algebra and lost himself in quadratic equations , while the hours slipped by , and the stars dimmed , and the gray of dawn flooded against his window 然后他拿出笔记本和代数书，投入了二次方程式见时光悄悄溜走，星星渐渐隐敛。黎明的鱼肚白向他的窗户泻了下来。
After deriving swt from the model , we find out that the water saturation equation is a quadratic equation about swt , so its solution is very simple and obtained by using the standard quadratic - root formula 通过研究混合泥质砂岩有效介质通用hb电阻率模型的求解方法，表明模型导出的关于s _ ( wt )的方程是一个一元二次方程，可用求根公式求解，解法非常简单。
This condition comes down to the problem of finding the solution of a set of quadratic equations . the solution of this set of quadratic equations is a set of orthonormal vectors , which makes the equations more easily solved 具体使用这个判据时，虽然也要解方程组，但该方程组是一个二次齐次方程组，而且其解有较好对称性，因此该判据对很多态都可方便地使用。
The quadratic equation algorithm utilizes spa , dpa and principle of rsa - crt , converts the complicated prime factorization of a large composite number into finding the solution of a quadratic equation and gains the private key at last 该方法综合利用spa 、 dpa攻击手段和rsa - crt算法原理,将rsa算法的大数分解难题转化为以私钥p或q为解的二次方程,最终获取算法私钥值。
Through the reasonable assumption of intrinsic parameters , we can avoid the general nonlinear and ambiguity in solving kruppa equation . at last , the camera self - calibration can be simplified to solving a quadratic equation 通过对摄像机内参数的合理假设，避免了一般使用kruppa方程标定时的非线性和多义性，并最终将固定内参数下的标定问题简化为一个二次方程的求解。
In this paper , three correlative results are given : 1 ) the average crossing number of graph with n vertices and q edges can be signified approximately by quadratic equation of q . 2 ) the average crossing number of graphs with bigger girth is greater than that with smaller girth within given vertices and edges . 3 ) the average crossing number of r - regular graphs greater than that of non - regular graphs within given vertices and edges where n is odd or r < n / 2 并得出相关的规律： 1 ) n个顶点q条边的单二连通分支图的平均交叉数aac ( n , q )可近似地表示为q的二次多项式， 2 )在给定顶点数n与边数q的单二连通分支图中围长较大的图的平均交叉数大于围长较小的图的平均交叉数， 3 )在给定顶点数n与边数q的单二连通分支图中当n为奇数或r n / 2时， r正则图的平均交叉数大于非r正则图的平均交叉数。
The method for solving quadratic equation which combined arithmetic solution and geometry demonstration together by al - khw rizm probably is influenced by greek who praised highly geometry , but through analyzing carefully , his geometry seems different from " geometrical algebra " of euclid in essence , but is similar to chinese ancient mathematical method - out - in complementary - like principle 花拉子米讨论一元二次方程时所采用的算术解法与几何论证相结合的方法似乎是受希腊人推崇几何学的观念的影响，但经过仔细分析，认为他的几何证明本质上区别于欧几里得的“几何代数” ，而与中国古代的“出入相补原理”更相像。
In this thesis , the basic problem of network security , some correlative protocols and cryptology are discussed at first , math theory in point is also studied . especially , a sort of new matrix method of solving quadratic equation over gf ( 2m ) is given , which is the key of selecting random point over elliptic curves . no better solution has been found in related literature in the world . compared with ieee p1363 ' s method , it is easy to implement the software and obtain high efficiency , etc . then the basic operation of elliptic curve is debated and the steps of finding secure curve and basis point over gf ( 2m ) are presented . moreover , the encryption and decryption schemes of the ecc are designed and the security problem of ecc is also considered . in the end , ecc by koblitz curves are implemented 文章首先讨论了网络安全基本问题、网络安全协议和密码学；对相关数学理论进行了研究，特别是给出了一种新的求解gf ( 2 ~ m )上二次方程的矩阵法，而它是选取椭圆曲线上的随机点的关键步骤，和ieeep1363的方法相比，它有易于软件实现、效率高等优点，在国内外相关文献上还未见到更好的求解方法；接着讨论了椭圆曲线的基本运算，进而给出了在gf ( 2 ~ m )上选取安全曲线及基点的步骤；文章还设计了椭圆曲线加密系统的加解密方案，讨论了椭圆曲线系统的安全性问题。最后文章就koblitz曲线加密系统进行了软件实现。
On the research of power analysis attacks , the attack principles and operation methods of spa and dpa are introduced first , then the concrete algorithms to rsa and rsa - crt are investigated separately : the spa attacking algorithm for rsa is given and the dpa attacking algorithm for rsa is improved , three different algorithms which are based on the different preconditions are summarized ; the spa and dpa attacking algorithms for rsa - crt are presented , then a new attacking algorithm named quadratic equation algorithm is proposed based on the discussion before 在能量分析攻击方法研究中,首先介绍了spa 、 dpa的攻击原理和实施办法,之后分别针对rsa及rsa - crt算法进行讨论:给出了rsa的spa攻击算法,改进了dpa攻击rsa的现有方法,并依据不同前提归纳为三种具体算法;给出了spa攻击rsa - crt的算法,介绍了现有dpa攻击rsa - crt的余数猜想法,在此基础之上提出一种新的攻击算法? ?二次方程法。
A quadratic equation with one variable for two - story frames and a cubic equation with one variable for three - story frames are derived from which the rotational restraint provided to each column may be solved and the effective length factors can then be determined by the traditional formula or tables 对于两层框架，通过求解一个一元二次代数方程得到各柱柱端的转动约束；对于三层框架，通过求解一个一元三次代数方程，得到各柱柱端的转动约束。进而由传统公式或规范附表得到各柱的计算长度系数值。
