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1.
利用同余式、平方剩余、Pell方程的解的性质、递归序列证明了:不定方程x3-1=749y2仅有整数解(x,y)=(1,0). 相似文献
2.
Firoz Firozzaman Fahim Firoz 《International Journal of Mathematical Education in Science & Technology》2017,48(5):756-762
Understanding the solution of a problem may require the reader to have background knowledge on the subject. For instance, finding an integer which, when divided by a nonzero integer leaves a remainder; but when divided by another nonzero integer may leave a different remainder. To find a smallest positive integer or a set of integers following the given conditions, one may need to understand the concept of modulo arithmetic in number theory. The Chinese Remainder Theorem is a known method to solve these types of problems using modulo arithmetic. In this paper, an efficient remainder rule has been proposed based on basic mathematical concepts. These core concepts are as follows: basic remainder rules of divisions, linear equation in slope intercept form, arithmetic progression and the use of a graphing calculator. These are easily understood by students who have taken prealgebra or intermediate algebra. 相似文献
3.
Hsiu‐Fu Hsu Corresponding author Shih‐Jay Chien Hsiu‐Hui Chen Chien‐Hsing Chen Li‐Ya Huang Chung‐Hao Kuo 《Liquid crystals》2013,40(6):683-689
Liquid crystalline α,α′‐bis(4‐alkoxyphenylethynyl)oligothiophenes (bi‐ and ter‐thiophene) have been synthesized and their mesogenic behaviour and optical properties investigated. They all exhibited a nematic mesophase, and compounds with long alkoxy chains also showed lamellar phases. Increasing the number of thiophene units increased both the transition temperatures and the mesophase ranges. As for their optical properties, incorporating more thiophene units results in red‐shifted absorption and emission spectra, slightly enhanced quantum efficiency, and a larger Stoke's shift. Most importantly, in terms of the absorption and emission maxima, the incorporation of one 4‐alkoxyphenylethynyl moiety was found to be equivalent to adding one thiophene ring. 相似文献
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5.
We show that any connected regular graph with d+1 distinct eigenvalues and odd-girth 2d+1 is distance-regular, and in particular that it is a generalized odd graph. 相似文献
6.
NP-hardness of the recognition of coordinated graphs 总被引:1,自引:0,他引:1
A graph G is coordinated if the minimum number of colors that can be assigned to the cliques of H in such a way that no two cliques with non-empty intersection receive the same color is equal to the maximum number of cliques
of H with a common vertex, for every induced subgraph H of G. In previous works, polynomial time algorithms were found for recognizing coordinated graphs within some classes of graphs.
In this paper we prove that the recognition problem for coordinated graphs is NP-hard, and it is NP-complete even when restricted
to the class of {gem, C
4, odd hole}-free graphs with maximum degree four, maximum clique size three and at most three cliques sharing a common vertex.
F.J. Soulignac is partially supported by UBACyT Grant X184, Argentina and CNPq under PROSUL project Proc. 490333/2004-4, Brazil. 相似文献
7.
The exact Wigner function of a parametrically excited quantum oscillator in a phase-sensitive amplifying/attenuating reservoir is found for initial even/odd coherent states. Studying the evolution of negativity of the Wigner function we show the difference between the “initial positivization time” (IPT), which is inversely proportional to the square of the initial size of the superposition, and the “final positivization time” (FPT), which does not depend on this size. Both these times can be made arbitrarily long in maximally squeezed high-temperature reservoirs. Besides, we find the conditions when some (small) squeezing can exist even after the Wigner function becomes totally positive. 相似文献
8.
为减少城市交通拥挤,从交通量均分的角度出发,提出了综合反映道路网络局部和整体性质的k最优定向,并且利用奇度点配对的思想为定向问题设计了启发式算法。 相似文献
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10.
In the setting of ZF, i.e., Zermelo–Fraenkel set theory without the Axiom of Choice (AC), we study partitions of Russell‐sets into sets each with exactly n elements (called n ‐ary partitions), for some integer n. We show that if n is odd, then a Russell‐set X has an n ‐ary partition if and only if |X | is divisible by n. Furthermore, we establish that it is relative consistent with ZF that there exists a Russell‐set X such that |X | is not divisible by any finite cardinal n > 1 (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献