absolute class field

absolute class field的基本解释

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绝对类域

与absolute class field相关的网络例句 [注：此内容来源于网络，仅供参考]

The definition of the absolute value for a fuzzy number is obtained.Furthermore,a lot ofproblems,such as absolute integrability,bounded variation and absolute continuity,arepresented and discussed.The representation theorem of the absolute values of fuzzy num-bers is established.It plays an important role in discussing the problems conceming theabsolute value.The relation between the absolute integrability and integrabili-ty is discussed,and the following result is obtained:aintegrable fuzzy-number-valued function is absolutely integrable iff it is integrable.The relation between theabsolute integrability and the absolute continuity of the primitive for fuzzy-number-valuedfunctions is dealt with.It is also pointed out that a fuzzy number valued function is ab-solutelyintegrable if and only if its integral primitive is fuzzy absolutely continuous.

提出了模糊数绝对值的概念并讨论了与绝对值相关的一系列问题，如绝对可积性、有界变差性、绝对连续性等，给出了模糊数绝对值的定义以及表示定理，该表示定理在涉及绝对值问题的讨论中起非常重要的作用；讨论了绝对可积与可积之间的关系，得到了结论：可积的模糊数值函数绝对可积的充要条件是该模糊数值函数可积；给出了模糊数值函数绝对可积与其积分原函数绝对连续性之间的关系，指出模糊数值函数绝对可积的充要条件是其原函数模糊绝对连续。

The main contributions of the second part of this dissertation are focused on the cryptographic properties of logical functions over finite field, with the help of the properties of trace functions, and that of p-polynomials, as well as the permutation theory over finite field: The new definition of Chrestenson linear spectrum is given and the relation between the new Chrestenson linear spectrum and the Chrestenson cyclic spectrum is presented, followed by the inverse formula of logical function over finite field; The distribution for linear structures of the logical functions over finite field is discussed and the complete construction of logical functions taking on all vectors as linear structures is suggested, which leads to the conception of the extended affine functions over finite field, whose cryptographic properties is similar to that of the affine functions over field GF (2) and prime field F〓; The relationship between the degeneration of logical functions and the linear structures, the degeneration of logical functions and the support of Chrestenson spectrum, as well as the relation between the nonlinearity and the linear structures are discussed; Using the relation of the logical functions over finite field and the vector logical functions over its prime field, we reveal the relationship between the perfect nonlinear functions over finite field and the vector generalized Bent functions over its prime field; The existence or not of the perfect nonlinear functions with any variables over any finite fields is offered, and some methods are proposed to construct the perfect nonlinear functions by using the balanced p-polynomials over finite field.

重新定义了有限域上逻辑函数的Chrestenson线性谱，考察了新定义的Chrestenson线性谱和原来的Chrestenson循环谱的关系，并利用一组对偶基给出了有限域上逻辑函数的反演公式；给出了有限域上随机变量联合分布的分解式，并利用随机变量联合分布的分解式对有限域上逻辑函数的密码性质进行了研究；给出了有限域上逻辑函数与相应素域上向量逻辑函数的关系，探讨了它们之间密码性质的联系，如平衡性，相关免疫性，扩散性，线性结构以及非线性度等；讨论了有限域上逻辑函数各类线性结构之间的关系，并给出了任意点都是线性结构的逻辑函数的全部构造，由此引出了有限域上的"泛仿射函数"的概念；考察了有限域上逻辑函数的退化性与线性结构的关系、退化性与Chrestenson谱支集的关系；给出了有限域逻辑函数非线性度的定义，利用有限域上逻辑函数的非线性度与相应素域上向量逻辑函数非线性度的关系，考察了有限域上逻辑函数的非线性度与线性结构的关系；利用有限域上逻辑函数与相应素域上向量逻辑函数的关系，揭示了有限域上的广义Bent函数与相应素域上的广义Bent函数的关系，以及有限域上的完全非线性函数与相应素域上向量广义Bent函数之间的关系；给出了任意有限域上任意n元完全非线性函数存在性与否的完整证明，并利用有限域上平衡的p-多项式的性质给出了有限域上完全非线性函数的一些基本构造方法。

And to let us see, that even absolute power, where it is necessary, is not arbitrary by being absolute, but is still limited by that reason, and confined to those ends, which required it in some cases to be absolute, we need look no farther than the common practice of martial discipline: for the preservation of the army, and in it of the whole common-wealth, requires an absolute obedience to the command of every superior officer, and it is justly death to disobey or dispute the most dangerous or unreasonable of them; but yet we see, that neither the serjeant, that could command a soldier to march up to the mouth of a cannon, or stand in a breach, where he is almost sure to perish, can command that soldier to give him one penny of his money; nor the general, that can condemn him to death for deserting his post, or for not obeying the most desperate orders, can yet, with all his absolute power of life and death, dispose of one farthing of that soldier's estate, or seize one jot of his goods; whom yet he can command any thing, and hang for the least disobedience; because such a blind obedience is necessary to that end, for which the commander has his power, viz.

让我们看看，即使在绝对权力有必要的地方，也不会因为权力的绝对而变得肆意，而仍然受那个原因和目的的限制，在某些情况下要求权力是绝对的，我们只要看看军事纪律的普遍应用：为保护军队——这是与整个共同体一致的——要求对上级军官绝对的服从，这些命令即使非常危险或没有理由，不服从或表示异议也可以处死；然而我们知道，一个士官，他可以命令一个士兵冲向炮口，或坚守阵地，在这种情况下几乎必死，但是他也不能命令士兵交给他一个便士；一个将军，可以因士兵擅离岗位或没有遵守不顾一切的命令而处死，然而他也不能用他对生死的绝对权力而处置或夺走那个士兵一丁点儿的财产；虽然他能够对士兵下任何命令，稍不服从即可处死；因为对那个目的而言，这样的盲目服从是必要的，为着那个目的，即保护其余的人，指挥者拥有这种权力；但是处置士兵的财产与此无关。良好的人性，恰当的理性，和对上帝的信仰。

与absolute class field相关的网络解释 [注：此内容来源于网络，仅供参考]

absolute class field：绝对类域

给出的定义后来被改称为绝对类域(absolute class field).高木证明了:代数数域k的任何阿贝尔扩张K均可表示成k上的类域.此定理通常被称为是类域论的基本定理或主定理.1920年9月25日高木贞治在法国斯特拉斯堡举行的世界数学家大会(9月22日�