难解的

By taking advantage of the non-conjugate transformation and multiple variant equations on braid group s, two intractable problems are proposed, and the hardness of these problems comes from the enlarged amount of va.

辫子群是一种新兴的适用于量子计算机时代的公钥密码平台，辫子群上已知的用于公钥密码系统的一些难解问题和基于这些难解问题的公钥加密算法都受到不同程度的攻击。

It is difficult to get the analytic solution of difference equation by using traditional methods with computer.

摘要利用传统方法很难在计算机上实现差分方程的解析解求解，本文提出了一种获得差分方程解析解的线性算法，该算法的基础是完全线形变化法。

The value of market esoterica to the consumer of investment advice is a different story.

这当然是股市秘籍存在的价值，但就我个人的看法，投资成功不是靠晦涩难解的公式、计算机运算或是股票行情板上股票上下的跳动，相反地投资人要能成功，惟有凭借着优异的商业判断同时避免自己的想法、行为，受到容易煽动人心的市场情绪所影响，以我个人的经验来说，要能够免除市场诱惑，最好的方法就是将格拉厄姆的市场先生理论铭记在心。

The value of market esoterica to the consumer of investment advice is a different story. In my opinion, investment success will not be produced by arcane formulae, computer programs or signals flashed by the price behavior of stocks and an investor will succeed by coupling good business judgment with an ability to insulate his thoughts and behavior from the super-contagious emotions that swirl about themarketplace.

这当然是股市秘籍存在的价值，但就我个人的看法，投资成功不是靠晦涩难解的公式、计算机运算或是股票行情板上股票上下的跳动，相反地投资人要能成功，惟有凭借着优异的商业判断同时避免自己的想法、行为，受到容易煽动人心的市场情绪所影响，以我个人的经验来说，要能够免除市场诱惑，最好的方法就是将格拉厄姆的市场先生理论铭记在心。

It is found that the later is better than the former greatly, due to the fact that accurate solution by gaussian elimination is zero error. But zero error is ideal situation and it is difficult to reach in practice. So all we can do is to search an optimal solution under many restriction conditions, and the optimal can represent the solution of the question better.

咎其原因，高斯消元法是求解问题的精确解，而在实际生产科研工作中，这种理想状况是很难达到的，因此，遗传算法在多个约束条件下寻找当前最优解作为问题的解，才具有实际意义。

The second-order linear homogeneous differential equations in differential equation theory occupies an important position, but the second order differential equation has no general solution method, most of the solutions of these equations is difficult to obtain analytical expressions and even some impossible to obtain the solution of the form, and the second order differential equation solving is divided into homogeneous and inhomogeneous problems.

二阶线性齐次微分方程在微分方程理论中占有重要位置，但二阶变系数微分方程却没有一般的求解方法，大多数这类方程很难求得解的分析表达式甚至有的根本不可能求得其解的分析形式，并且二阶变系数微分方程的求解又分为齐次的和非齐次的问题。

In his Culture and Anarchy , Matthew Arnold writes,"The great men of culture are those who have had a passion for diffusing, for making prevail, for carrying from one end of society to the other, the best knowledge, the best ideas of their time; who have laboured to divest knowledge of all that was harsh, uncouth, difficult, abstract, professional, exclusive; to humanise it, to make it efficient outside the clique of the cultivated and learned, yet still remaining the best knowledge and thought of the time, and a true source, therefore, of sweetness and light."

马修·阿诺德在《文化和无政府状态》一书中这样描述："伟大的文化人是这样一些人，他们具有一种激情，要将他们时代最好的知识、最好的思想从社会的一端传播和搬运到社会的另一端，使之流行不衰；他们殚精竭虑，要为知识去除一切粗糙的、粗野的、难解的、抽象的、专业的和孤傲的成分，要把它人性化，使它在绅士和学者的圈子之外，也见成效，与此同时，又保留了时代最好的知识和思想，因而成为甜美和光明的真正源泉。"

Turing Machines, A Brief Introduction to the Undecidability, Intractability and Complexity of Problems.

图灵机，问题的不可解性、难解性和复杂性等计算理论初步知识。

Solid geometry is difficult for middle school students to learn.

立体几何的学习是中学生学习难点之一，主要体现在图形难"看"、概念难懂、定理难用、习题难解。

If you will try to form a notion of yourself, of the sort of a something that you suspect to inhabit and partially to control your flesh and blood body, you will encounter a walking bundle of superfluities: and when you mentally have put aside the extraneous things—your garments and your members and your body, and your acquired habits and your appetites and your inherited traits and your prejudices, and all other appurtenances which considered separately you recognize to be no integral part of you,—there seems to remain in those pearl-colored brain-cells, wherein is your ultimate lair, very little save a faculty for receiving sensations, of which you know the larger portion to be illusory.

确实，一个容易上当受骗的认知，暂时地生存于一堆难解的奥秘里，这真不是一个可羡的处境。但是，这个人生——这个我执著依恋的人生——不会再来。与此同时，我常听人谈起&真理&，他们甚至为自己的对真理的了解大下赌注：但我更愿与&善戏谑的彼拉多&为伍，响应他丢弃的至今未被解答的关于什么是真理的疑问。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。