共查询到19条相似文献,搜索用时 93 毫秒
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证明了由自由群整数环上一类元素确定的代数作用的遍历性,计算了Heisenberg群因子中特定元素的Fuglede-Kadison行列式值. 相似文献
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构造奇次同心幻方的一种方法 总被引:1,自引:0,他引:1
杨富锋 《数学的实践与认识》2006,36(5):192-199
幻方是古老的数学游戏,经过几个世纪的发展形成了很多有趣的构造方法.利用行列式的性质和变换得到了构造奇数阶同心幻方原基的一种方法,利用这种方法和排列组合都能得到任意奇数阶幻方的多种形式. 相似文献
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一、选择题 1.若abC>0,则|a|/a |b|/b |c|/c-|abc|/abc的值为( ) (A)2 (B)-2 (C)±2 (D)以上都不对 2.已知n是偶数,m是奇数,方程组:是整数、那么( ) (A)P、q都是偶数 (B)p、q都是奇数 (C)p是奇数,q是偶数 (D)p是偶数,q是奇数 3.设a、b都是整数。 (1)若a 5b是偶数,则a-3b也是偶数 (2)若a b能被3整除,则a、b都能被3整除 相似文献
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讨论了在与Borda投票规则相似的整数计分投票方法中,投票结果使备选方案集产生全排序(任意两个备选方案的总分值不同)的概率P的问题.给出了在一定假设条件下计算P值的相关公式;通过分析运行计算机程序得到的数据,讨论了P值关于整数计分投票问题的三个变量的单调性性质;最后根据P值函数的单调性性质,指出应如何设计和调整整数计分投票规则. 相似文献
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钻畏题 或毛用居卜省民 学期 反证法 初中三年级 2004一2005 学年度第二学期 训练目的 昧求 =l数 …粤一牌二为整数滋x=0:二- 二次函数y一a扩+bx+。的值都是奇 证:二次方程a扩+bx+。~O没有整数根. 一’证明士一。时,1夕一仑为奇数; x二l时,四于只十b七今为奇数,、 a十b为偶数.。、、州- 若a扩+bx+‘~O有整数根x。,则有 ax。2+bx。+c=0, (呼+b)x。’一b二。’+bx。+犷。; 添呱二缨鄂罐 巍蘸蘸蘸蘸蘸蘸蘸蘸蘸蘸潺 缪嘛狐赢 纂蘸薰矍翼 随堂测试 .证明:涯是无理数. 学生课后练习 1.已知自然数a、b、‘的公约数为1, 且az+夕~产,求证:‘必为奇数… 相似文献
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在国内外的数学竞赛题中,有一些题目的解法实际上只用到了整数的平方的某些性质,所涉及的知识是相当少的;但是,对于不习惯于利用这些性质的人,又会感到这些题目有一定的难度。本文打算通过一些例子,向中学生介绍这方面的解题方法。一、大家知道,所有的整数可以分为偶数和奇数两大类。偶数能表为2k的形式,奇数能表为2k 1的形式,这里k是整数。先看偶数的平方,由于(2k)~2=4k~2,可见任何偶数的平方能被4整除。再看奇数的平方,(2k 1)~2=4k~2 4k 1=4k~2(k 1) 1,由于k与k 1是相邻的两整数,故其中恰有一偶数,因此4k(k 1)能被 相似文献
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Saibal Mitra 《Journal of Combinatorial Theory, Series A》2009,116(1):30-43
We have obtained the exact asymptotics of the determinant . Inverse symbolic computing methods were used to obtain exact analytical expressions for all terms up to relative order L−14 to the leading term. This determinant is known to give weighted enumerations of cyclically symmetric plane partitions, weighted enumerations of certain families of vicious walkers and it has been conjectured to be proportional to the one point function of the O(1) loop model on a cylinder of circumference L. We apply our result to the loop model and give exact expressions for the asymptotics of the average of the number of loops surrounding a point and the fluctuation in this number. For the related bond percolation model at the critical point, we give exact expressions for the asymptotics of the probability that a point is on a cluster that wraps around a cylinder of even circumference and the probability that a point is on a cluster spanning a cylinder of odd circumference. 相似文献
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Answering a question of [BV] it is proved that the Picard bundle on the moduli space of stable vector bundles of rank two,
on a Riemann surface of genus at least three, with fixed determinant of odd degree is stable. 相似文献
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N. Budarina 《Lithuanian Mathematical Journal》2010,50(2):140-163
In 1999, Manjul Bhargava proved the Fifteen Theorem and showed that there are exactly 204 universal positive definite integral
quaternary quadratic forms. We consider primitive representations of quadratic forms and investigate a primitive counterpart
to the Fifteen Theorem. In particular, we give an efficient method for deciding whether a positive definite integral quadratic
form in four or more variables with odd square-free determinant is almost primitively universal. 相似文献
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Nikolai A. Volodin 《Journal of multivariate analysis》1999,70(2):202
In this paper exact formulae of the probability density function for the spherically symmetric distribution with marginal logistic are given. They are entirely different for odd and even dimensions. For an odd number of dimensions it is possible to express them by elementary functions but for an even number of dimensions, it is possible only by an infinite series of functions. These series, however, are very convenient for computations and could be useful in practice. 相似文献
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Peter J. Cameron 《Graphs and Combinatorics》1985,1(1):129-135
Cyclic automorphisms of the countable universal ultrahomogeneous graph are investigated using methods of Baire category and
measure theory. This leads to the study of random sumfree sets; it is shown that the probability that such a set consists
entirely of odd numbers is strictly positive, and bounds are given. 相似文献
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Ömer Eğecioğlu 《Annals of Combinatorics》2010,14(4):443-456
We show that the determinant of a Hankel matrix of odd dimension n whose entries are the enumerators of the Jacobi symbols which depend on the row and the column indices vanishes if and only
if n is composite. If the dimension is a prime p, then the determinant evaluates to a polynomial of degree p − 1 which is the product of a power of p and the generating polynomial of the partial sums of Legendre symbols. The sign of the determinant is determined by the quadratic
character of −1 modulo p. The proof of the evaluation makes use of elementary properties of Legendre symbols, quadratic Gauss sums, and orthogonality
of trigonometric functions. 相似文献
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Antonio Di Crescenzo Antonella Iuliano Barbara Martinucci 《Ricerche di matematica》2012,61(1):157-169
We consider a bilateral birth-death process characterized by a constant transition rate ?? from even states and a possibly different transition rate??? from odd states. We determine the probability generating functions of the even and odd states, the transition probabilities, mean and variance of the process for arbitrary initial state. Some features of the birth-death process confined to the non-negative integers by a reflecting boundary in the zero-state are also analyzed. In particular, making use of a Laplace transform approach we obtain a series form of the transition probability from state 1 to the zero-state. 相似文献
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Ana-Maria Castravet 《Proceedings of the American Mathematical Society》2007,135(12):3783-3788
A conjecture of Pukhlikov states that a smooth Fano variety of dimension at least 4 and index one is birationally rigid. We show that a general member of the linear system given by the ample generator of the Picard group of the moduli space of stable, rank 2 bundles with fixed determinant of odd degree on a curve of genus at least 3 is not birationally rigid.
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S. V. Sidorov 《Russian Mathematics (Iz VUZ)》2016,60(4):65-71
In this paper we consider the problem of similarity of matrices over integers and describe canonical representatives of the similarity classes of 2 × 2 matrices with zero trace and determinant equal an odd power of a prime number. 相似文献