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However, The RH remains a basically unproved conjecture to this day.

然而,黎曼假设至今始终是一个紧绷为获得证明的猜想。

Some of the oldest open problems in mathematics relate to the abundancy index of a number. Are there infinitely many perfect numbers? Does there exist an odd perfect number? Does there exist an odd multiply perfect number? Such questions have been considered for well over two millennia by the likes of Euclid, Fermat, Descartes, Mersenne, Legendre, and Euler.

暑期的数学研究已渐渐步入正轨,今天上午和导师讨论的时候提出了第一个conjecture,说是虽然6和12的倍数的abundancy index比较高,但是如果把两个相邻的数字相乘,他们乘积的abundancy index总体来说会甚至更高。

The Agnatic Union of the kindred in ancient Roman law, and a multitude of similar indications, point to a period at which all the ramifying branches of the family tree held together in one organic whole; and it is no presumptuous conjecture, that, when the corporation thus formed by the kindred was in itself an independent society it was governed by the eldest male of the oldest line.

古罗马法中亲属的宗法联合体以及大量类似的征兆,说明在有一个时期中家族所有的各支系都团结在一个有机的整体中;当亲属这样形成的集团本身就成为一个独立社会时,这个集团是由最老亲系的最长男性管理的;这自非狂妄的臆测。

In this paper we show that graphs K6,3,2*(k-6),1*4 (k ≥ 6) is chromatic choosable and hence Ohba's conjecture is true for the graphs K6,3,2*(k-6),1*4 and all complete k-partite subgraphs of them.

在本文我们证明图K6,3,2*(k-6),1*4(k≥6)是色可选择的,从而对图K6,3,2*(k-6),1*4(k≥6)和它们的所有完全k-部子图证明了Ohba猜想成立。

This dissertation investigates the construction of pseudo-random sequences (pseudo-random numbers) from elliptic curves and mainly analyzes their cryptographic properties by using exponential sums over rational points along elliptic curves. The main results are as follows:(1) The uniform distribution of the elliptic curve linear congruential generator is discussed and the lower bound of its nonlinear complexity is given.(2) Two large families of binary sequences are constructed from elliptic curves. The well distribution measure and the correlation measure of order k of the resulting sequences are studied. The results indicate that they are "good" binary sequences which give a positive answer to a conjecture proposed by Goubin et al.(3) A kind of binary sequences from an elliptic curve and its twisted curves over a prime field F_p. The length of the sequences is 4p. The "1" and "0" occur almost the same times. The linear complexity is at least one-fourth the period.(4) The exponential sums over rational points along elliptic curves over ring Z_ are estimated and are used to estimate the well distribution measure and the correlation measure of order k of a family of binary sequences from elliptic curves over ring Z_.(5) The correlation of the elliptic curve power number generator is given. It is proved that the sequences produced by the elliptic curve quadratic generator are asymptotically uniformly distributed.(6) The uniform distribution of the elliptic curve subset sum generator is considered.(7) We apply the linear feedback shift register over elliptic curves to produce sequences with long periods. The distribution and the linear complexity of the resulting sequences are also considered.

本文研究利用椭圆曲线构造的伪随机序列,主要利用有限域上椭圆曲线有理点群的指数和估计讨论椭圆曲线序列的密码性质——分布、相关性、线性复杂度等,得到如下主要结果:(1)系统讨论椭圆曲线-线性同余序列的一致分布性质,即该类序列是渐近一致分布的,并给出了它的非线性复杂度下界;(2)讨论两类由椭圆曲线构造的二元序列的&良性&分布与高阶相关性(correlation of order κ),这两类序列具有&优&的密码性质,也正面回答了Goubin等提出的公开问题;(3)利用椭圆曲线及其挠曲线构造一类二元序列,其周期为4p(其中椭圆曲线定义在有限域F_p上),0-1分布基本平衡,线性复杂度至少为周期的四分之一;(4)讨论了剩余类环Z_上的椭圆曲线的有理点的分布估计,并用于分析一类由剩余类环Z_上椭圆曲线构造的二元序列的伪随机性;(5)讨论椭圆曲线-幂生成器序列的相关性及椭圆曲线-二次生成器序列的一致分布;(6)讨论椭圆曲线-子集和序列的一致分布;(7)讨论椭圆曲线上的线性反馈移位寄存器序列的分布,线性复杂度等性质。

I guess this to accord with people basically to work to this environmental conjecture, see on fabaceous valve net like them in that way, simple, orderly, businesslike.

我猜这基本符合人们对这个工作环境的揣测,一如他们在豆瓣网上看到的那样,简单,有序,有效率。

According to these characteristics we conjecture that the ability of reabsorption water from the primary urine of the kidney in Felis bieti is stronger than that of the Felis lynx these characteristics maybe result from Felis bieti and Felis lynx's adaptation to their specific habitat .

由此推测荒漠猫肾的重吸收能力较猞猁强,这可能与其生活环境和食性相适应。

In Chapter 4, we will consider the conjecture from a different angle and prove some analogous results of Harman.

在第四章,我们改变探讨猜想的观点,与实数情况中Harman的部分结果相似。

By using the perturbations of infalling null dust and of both outgoing and infallingnull dust in theSitter black hole geometry,respectively,wecheck a conjecture to the Cauchy-horizon stability given by Helliwell and Konkowski.

由于黑洞的柯西视界稳定性与宇宙监督假定有紧密联系,所以它一直是广义相对论中的一个重要研究课题。

This study used microsatellite markers attempts to:(1) discover the genetic variation among sampling populations and reconstruct the phylogeographic scenario;(2) confirm the direction of gene flow (3) conjecture the causation and time of introgressive hybridization.

本文的研究发现两种石鸡之间具有显著的遗传分化(Fst=0.2979,Rst=0.1942,Neis D_A=3.016)。8个微卫星位点在大石鸡88个样本扩增出40个等位基因,在石鸡64个样本扩增出35个等位基因。

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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。

Closes the eye, the deep breathing, all no longer are the dreams as if......

关闭眼睛,深呼吸,一切不再是梦想,犹如。。。。。。