• equation : n. 1. 平衡，均衡；平均，相等。2. 【數學】方程式，等式。3. 【天文學】（時）差；均分，等分。4. 【化學】反應式。
1. 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

該方法綜合利用spa 、 dpa攻擊手段和rsa - crt演算法原理，將rsa演算法的大數分解難題轉化為以私鑰p或q為解的二次方程，最終獲取演算法私鑰值。
2. The limit cycles for type equation of quadratic differential systems

類方程的極限環
3. This program calculates the root ( s ) of the quadratic equation with very common and simple algorithms

這個程序能用非常普通和簡單的演算法來計算一個二次方程的根。
4. Quadratic equation solver - this program calculates the root ( s ) of the quadratic equation with very common and simple algorithms

這個程序能用非常普通和簡單的演算法來計算一個二次方程的根。
5. Simple and quadratic equation and some skills of operation in algebra may come from babylon

級進行對比分析，得到一些初步認識： 《代數學》中所討論的一次和二次方程以及某些運算技巧可能源於巴比倫。
6. Basing on the statistical inaming t ' heory ( slt ), the thesis discusses the svm problems in linearly separable case, lineariy non - separable case and non - linear separable case, and induces a convex quadratic programming ( qp ) problem with an equation constrain and non - equation constrains. then one program on solving the op problem is proposed

概述了統計學習理論的主要內容，推導了支持向量機方法在文本線性可分、線性不可分和非線性可分情況下實現分類的數學公式，將學習問題轉化為一個在等式約束和不等式約束下的凸二次優化問題，總結了求解的過程。
7. The quadratic nonlinear term and the cubic nonlinear term that coexist in equation ( 1 ), thus causes difficulty in studying this sort of system through the analytical method and correspondingly makes the solution of analytical expression of homoclinic orbit or heteroclinic orbit in hamilton system extremely difficult

二次非線性項和三次非線性項共同存在於方程（ 1 ）中，使得用解析方法研究這類系統的難度增大，對應hamilton系統中的同宿軌道或異宿軌道的解析表達式的求解相當困難。
8. 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

通過研究混合泥質砂巖有效介質通用hb電阻率模型的求解方法，表明模型導出的關于s _ （ wt ）的方程是一個一元二次方程，可用求根公式求解，解法非常簡單。
9. 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

花拉子米討論一元二次方程時所採用的算術解法與幾何論證相結合的方法似乎是受希臘人推崇幾何學的觀念的影響，但經過仔細分析，認為他的幾何證明本質上區別于歐幾里得的「幾何代數」 ，而與中國古代的「出入相補原理」更相像。
10. The discussion of the fourth kind of quadratic equation, the use of " rule of three ", the calculation of number r and some terms algebra can be found in indian classics introduced to arab and some of these mathematical knowledge maybe comes from china ( such as " rule of three " )

花拉子米對第四種二次方程的討論，使用的「三率法」 ，對圓周率的計算以及某些術語可以在早期傳入阿拉伯的印度典籍中找到出處，而在這些數學知識中有一些可能是遠源於中國的（比如「三率法」 ） 。
11. 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

文章首先討論了網路安全基本問題、網路安全協議和密碼學；對相關數學理論進行了研究，特別是給出了一種新的求解gf （ 2 ~ m ）上二次方程的矩陣法，而它是選取橢圓曲線上的隨機點的關鍵步驟，和ieeep1363的方法相比，它有易於軟體實現、效率高等優點，在國內外相關文獻上還未見到更好的求解方法；接著討論了橢圓曲線的基本運算，進而給出了在gf （ 2 ~ m ）上選取安全曲線及基點的步驟；文章還設計了橢圓曲線加密系統的加解密方案，討論了橢圓曲線系統的安全性問題。最後文章就koblitz曲線加密系統進行了軟體實現。
12. Quadratic integrability and boundeness of solutions about a class of second order time lag differential equation

二階滯后型微分方程解的有界性與平方可積性
13. 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

並得出相關的規律： 1 ） n個頂點q條邊的單二連通分支圖的平均交叉數aac （ n ， q ）可近似地表示為q的二次多項式， 2 ）在給定頂點數n與邊數q的單二連通分支圖中圍長較大的圖的平均交叉數大於圍長較小的圖的平均交叉數， 3 ）在給定頂點數n與邊數q的單二連通分支圖中當n為奇數或r n / 2時， r正則圖的平均交叉數大於非r正則圖的平均交叉數。
14. Stability aalysis of the characteristic difference scheme based on the local quadratic interpolation of convective - diffusion equation

對流擴散方程基於局部二次插值特徵差分格式的穩定性分析
15. Equation ( 1 ) is the dynamic equation that contains quadratic nonlinear term and cubic non - linear term

方程（ 1 ）是含有二次非線性項和三次非線性項的動力學方程。
16. Massive simulation experiments have proved the correctness and possibility of the fitting algorithm of quadratic surface which is based on general equation

大量的模擬數據實驗表明，本文提出的基於一般化方法的標準二次曲面擬合演算法的正確性和可行性。
17. Jacobi transformation is used to find correlations among coefficients. then a method to transform general quadratic surface to formal quadratic surface equation is introduced. the location, direction and size of quadratic surface are obtained

論述了運用jacobi變換方法來處理系數相關性問題，實現了二次曲面的一般方程的求取，並探討了將通用系數形式轉化為標準二次曲面方程的方法，從而求得二次曲面在空間的位置、方向和大小。
18. The bifurcation problems of type equation of quadratic differential systems

類方程的分支問題
19. 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

通過對攝像機內參數的合理假設，避免了一般使用kruppa方程標定時的非線性和多義性，並最終將固定內參數下的標定問題簡化為一個二次方程的求解。
20. 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

對于兩層框架，通過求解一個一元二次代數方程得到各柱柱端的轉動約束；對於三層框架，通過求解一個一元三次代數方程，得到各柱柱端的轉動約束。進而由傳統公式或規范附表得到各柱的計算長度系數值。