共查询到20条相似文献,搜索用时 500 毫秒
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关于矩阵乘法的一个算法的时间复杂度 总被引:4,自引:1,他引:3
两个n阶非负整数方阵相乘,常规算法的时间复杂度为O(n3),文献[1]提出一个“运算次数”为O(n2)的“最佳”算法,本文根据算法分析理论得出此算法的时间复杂度不低于O(n3log2n),因而比常规算法的运算量还大. 相似文献
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有限可换主理想环上模理论可判定性及其复杂性 总被引:3,自引:1,他引:2
本文利用初等等价的工具,引用Ehenfeucht Game理论,证明了有限可换主理想环上模的理论是可判定的,并且判定过程的计算复杂性上界为2cn2. 相似文献
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关于矩阵乘法的一个改进算法的时间复杂度 总被引:2,自引:0,他引:2
两个n阶非负整数方阵相乘,常规算法的时间复杂度为O(n3),文献[1]提出一个“运算次数”为O(n2)的“最佳”算法,文献[2]对此算法做了进一步研究,提出三种改进策略.本文根据算法分析理论,得出改进后的算法的时间复杂度仍不低于O(n3logn),因而其阶仍高于常规算法的运算量的阶. 相似文献
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三角形重心的一个向量性质的另证及推广 总被引:1,自引:0,他引:1
文[1]类比文[2]用高等几何方法(仿射几何法)给出了三角形重心的另一个向量性质(即性质1).本文将给出性质1的初等证法并推广之. 相似文献
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该文给出了一些负相协随机变量的指数不等式.这些不等式改进了由Jabbari和Azarnoosh[4]及Oliveira[7] 所得到的相应的结果.利用这些不等式对协方差系数为几何下降情形, 获得了强大数律的收敛速度为n-1/2(log log n)1/2(log n)2.这个收敛速度接近独立随机变量的重对数律的收敛速度, 而Jabbari和Azarnoosh[4]在上述情形下得到的收敛速度仅仅为n-1/3(log n)5/3. 相似文献
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This paper is an elementary introduction to the theory of moduli spaces of curves and maps. As an application to enumerative geometry, we show how to count the number of bitangent lines to a projective plane curve of degree d by doing intersection theory on moduli spaces. 相似文献
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Yakov Varshavsky 《Geometric And Functional Analysis》2007,17(1):271-319
The goal of this paper is to generalize a theorem of Fujiwara (Deligne’s conjecture) to the situation appearing in a joint
work [KV] with David Kazhdan on the global Langlands correspondence over function fields. Moreover, our proof is more elementary
than the original one and stays in the realm of ordinary algebraic geometry, that is, does not use rigid geometry. We also
give a proof of the Lefschetz–Verdier trace formula and of the additivity of filtered trace maps, thus making the paper essentially
self-contained.
The work was supported by the Israel Science Foundation (Grant No. 555/04)
Received: May 2005 Accepted: August 2005 相似文献
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We analyze an elementary theorem of Euclidean geometry, the Droz-Farny Line Theorem, from the point of view of the foundations of geometry. We start with an elementary synthetic proof which is based on simple properties of the group of motions. The proof reveals that the Droz-Farny Line Theorem is a special case of the Theorem of Goormatigh which is, in turn, a special case of the Counterpairing Theorem of Hessenberg. An axiomatic analysis in the sense of Hilbert [14] and Bachmann [2] leads to a study of different versions of the theorems (e.g., of a dual version or of an absolute version, which is valid in absolute geometry) and to a new axiom system for the associated very general plane absolute geometry (the geometry of pencils and lines). In the last section the role of the theorems in the foundations of geometry is discussed. 相似文献
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Ziv Ran 《Israel Journal of Mathematics》1999,111(1):109-124
This paper gives a formula for the number of members of a given ‘nice’ family of rational curves on a surface passing through
the appropriate number of general points, expressing this number in terms of reducible members of the family. Similar formulae
have been obtained previously using methods of quantum cohomology, but the present method is by contrast completely elementary,
relying merely on some simple geometry on ruled surfaces. 相似文献
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Horst Szambien 《Journal of Geometry》1986,26(2):163-171
A concept of topological projective geometry is defined, which in contrast to the definitions given in [Mi] and [SÖ] does not contain any dimensional restrictions. Besides elementary properties it is shown in this paper that these topological geometries always possess a coordinatization over a uniquely determined topological division ring if the dimension is finite.Dedicated to Prof. Dr. Hanfried Lenz on his 70th birthday 相似文献
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空间曲面上的曲线论是初等微分几何的重要部分.作者提出了一种以外微分运算和向量计算为主要工具,可以进行有关曲面上曲线局部性质的定理机器证明的算法.该算法结合了曲面上的活动标架,曲面上曲线的测地标架和曲线自身的Frenet标架,在Maple 9下得到实现.对20个例子进行的测试表明,由该算法生成的自动证明简短可读. 相似文献
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Kai Johannes Keller Nikolaos A. Papadopoulos Andrés F. Reyes-Lega 《Mathematische Semesterberichte》2008,55(2):149-160
The aim of this paper is to give a simple, geometric proof of Wigner’s theorem on the realization
of symmetries in quantum mechanics that clarifies its relation to projective geometry. Although several
proofs exist already, it seems that the relevance of Wigner’s theorem is not fully appreciated in general.
It is Wigner’s theorem which allows the use of linear realizations of symmetries and therefore guarantees
that, in the end, quantum theory stays a linear theory. In the present paper, we take a strictly geometrical
point of view in order to prove this theorem. It becomes apparent that Wigner’s theorem is nothing else
but a corollary of the fundamental theorem of projective geometry. In this sense, the proof presented here
is simple, transparent and therefore accessible even to elementary treatments in quantum mechanics. 相似文献
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Kai Johannes Keller Nikolaos A. Papadopoulos Andrés F. Reyes-Lega 《Mathematische Semesterberichte》2008,47(10):149-160
The aim of this paper is to give a simple, geometric proof of Wigner’s theorem on the realization
of symmetries in quantum mechanics that clarifies its relation to projective geometry. Although several
proofs exist already, it seems that the relevance of Wigner’s theorem is not fully appreciated in general.
It is Wigner’s theorem which allows the use of linear realizations of symmetries and therefore guarantees
that, in the end, quantum theory stays a linear theory. In the present paper, we take a strictly geometrical
point of view in order to prove this theorem. It becomes apparent that Wigner’s theorem is nothing else
but a corollary of the fundamental theorem of projective geometry. In this sense, the proof presented here
is simple, transparent and therefore accessible even to elementary treatments in quantum mechanics. 相似文献