查询词典 the remainder

Liber Abaci emphasizes summed-up algorithm, but does not pay attention to the form of propositions derived, and it mainly reflects the tendency of practical algorithms, such as principal method from India and the algebraic knowledge from the Arab. In Liber Abaci it is found some problems similar to ancient Chinese mathematics like pursuit problems, drainage problems, business problems, hundred fowls problems, remainder problems, indeterminate problems, as well as some Algorithm—fraction addition and subtraction,the compound rule of three, the method Elchataym and the method of Excess and Deficit, and so on.

在系统梳理《计算之书》数学内容过程中，笔者发现《计算之书》中存有与中国古代数学中相似的实用算题，如：追及问题、排水问题、经商问题、百鸡问题、剩余问题、不定问题等，以及和中算一致的算法：分数算法、多率法和重今有术、第二类"Elchataym算法"和盈不足术等。

It includes the basic structural theory of groups; groups'actions on sets and the applications of these actions; the basic structures of rings; the properties of uniquely factorized domains; the Chinese Remainder; the extensions of fields; finite fields with applications; the Galois theory with applications.

主要内容包括群的基本结构理论、群在集合上的作用及其应用、环的基本结构和因子分解理论、中国剩余定理、域的扩张理论、有限域及其应用、Galois 理论及其应用。

The author mainly realized the method of generating the large random numbers and judging the prime number using Lehmann means,then three pairs of secure key with different lengths (256 bits,512 bits,1024 bits) was generated to meet the demand of different security grade. In encryption module,modular multiplication arithmetic of large number was realized adopting addition chaining. In decryption module,extended Euclid was used to get inverse,and the Chinese remainder theorem was used to realize decryption,which increased the speed of decryption greatly.

作者主要实现了大随机数的生成、采用整除小素数和勒曼测试法判定素数，可以生成三种不同长度的密钥对(256位、512位、1024位)来满足不同的加密安全等级的需求；加密模块中，选用了二进制序列的乘法方法，实现了大数模幂乘运算；解密模块中，引用了扩展的欧几里德法求逆元，并采用中国剩余定理实现解密过程，大大提高了解密速度。

It turns out that the modulus of the RSA cryptosystem is easy to factor if the the ratio of the two prime factors of the modulus can be well approximated by a small fraction.(3) A fast public-key encryption scheme is developed by using the Chinese remainder theorem.

2找到了RSA公钥密码算法的一类弱密钥，指出如果RSA数的两个素因子的比值能够被一个小分数有效逼近的话，则RSA数是容易分解的。

In this paper, the relationship between the linear complexity and the 2-adic complexity is investigated based on the Chinese Remainder Theorem and some other related theories in the number theory, and the existence of N-periodic sequences that simultaneously achieve the maximum 2-adic complexity and a great k-error 2-adic complexity is proved.

文中借助数论中的中国剩余定理等相关理论研究了二元序列的2-adic复杂度与线性复杂度的关系，证明了具有最大2-adic复杂度以及较大k错2-adic复杂度的N周期序列的存在性，给出了具有这种性质的周期序列的数目的下界。

The Chinese Remainder Theorem is one of the greatest achievements in the Chinese traditional mathematics,which is on the theory of congruence of first degree. It's from the problem of the "Wu Buzhishu" in the Chinese classical mathematical work Sunzisuanjing.

"中国剩余定理"是中国传统数学中关于一次同余式理论的一项杰出成就，它源于中国数学典籍《孙子算经》中的"物不知数"问题，秦九韶在《数书九章》(1247)中将这一问题发展为求解一次同余式组的一般方法，称为"大衍总数术"。

The second chapter is the goal and technical analysis of introduction. After that, I carried on the craft analysis of the production type determination, and the semifinished, and the craftroute formulation, and the processing remainder determination, and so on. It is general about seven aspects.

第二章开始阐述了本课题的目的意义和技术分析，之后着重从生产类型的确定、毛坯的分析、工艺路线的制定、加工余量的确定、各工序工艺装备的确定、切削用量的确定、工序时间的计算等七个方面进行工艺分析。

One out of three potential inductees was rejected by the Army doctors for physical reasons — a telling remainder of the effects of the Depression on the American people.

每三个应征者中，就有一人因为身体原因被军医淘汰——这现象可以说是经济大萧条*对人民影响结果。

Methods: 458 postmenopausal endometrial polyps were all treated by transcervical recection of polyp,and diagnosed by pathology.The presence of ER,PR, Bcl-2 and Ki-67 were detected by immunohistochemical staining.Following up these cases, 160 cases recured in three months to three years after treatment.These recurrence were treated by large dose mifepristone.After three months, 55 cases remainder EP were detected by hysteroscopy and treated by TCRP,then detected the presence of above receptors in the same way.

绝经后子宫内膜息肉患者458例，均接受宫腔镜下子宫内膜息肉切除术，术后病理诊断均为子宫内膜息肉，并采用免疫组化法检测子宫内膜息肉中雌、孕激素受体及Ki-67、Bcl-2的表达；随访以上患者，术后3个月～3年复发160例，均予大剂量米非司酮口服治疗，3个月后行宫腔镜检查，有残余息肉者55例，再行TCRP，并采用免疫组化法检测子宫内膜息肉中雌、孕激素受体及Ki-67、Bcl-2的表达。

A pool of water near some ruined walls was the only remainder of the deep ditches; and here stood a magnificent old tree with overhanging branches- that was the genealogical tree.

那座老邸宅也不见了，现在只剩下一个长方形的水潭，两边立着一些断垣残壁。这就是那条壕沟的遗址。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。