Topic
Divisor
About: Divisor is a research topic. Over the lifetime, 2462 publications have been published within this topic receiving 21394 citations. The topic is also known as: factor & submultiple.
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TL;DR: In this article, the local structure of Mori contractions was studied under the assumption that there exists a reduced divisor such that $K_X+S$ is plt and anti-ample.
Abstract: We study the local structure of Mori contractions $f\colon X\to Z$ of relative dimension one under an additional assumption that there exists a reduced divisor $S$ such that $K_X+S$ is plt and anti-ample.
01 Jan 2009
TL;DR: In this article, a self-contained proof for an n 2 3 lower bound for the number of pairs (a, b) of elements with ab 6 ba in every non-commutative group of size n was given.
Abstract: Lipton and Zalcstein presented a constant time algorithm for testing if a group is abelian in 12 However, the reference only contains a short abstract without proof In this paper, we give a self contained proof for an n 2 3 lower bound for the number of pairs (a, b) of elements with ab 6 ba in every non-commutative group of size n It implies a constant time randomized algorithm that tests if a group of n elements is commutative Our lower bound for the number of non-commutative pairs (a, b) (ab 6 ba) in a non-commutative group of size n has a generalized format (p 1)(q 1)n 2 pq , where p > 1 is the least integer divisor of n, and q > p is the second least integer divisor of n
Posted Content•
TL;DR: In this paper, the properties of the sequences {PdCn} and {qd(n)}, and prove that the Makowski and Schinzel conjecture hold for the sequences of {pd(n)} and {Qd( n)}.
Abstract: Let n be a positive integer, Pd(n) denotes the product of all positive divisors of n, qd(n) denotes the product of all proper divisors of n. In this paper, we study the properties of the sequences {PdCn)} and {qd(n)}, and prove that the Makowski &. Schinzel conjecture hold for the sequences {pd(n)} and {qd(n)}.
01 Jan 2018
TL;DR: In this paper, it was shown that the Grobner basis of any binomial ideal is a lattice ideal, and that the lattice ideals are exactly those which are saturated.
Abstract: In this chapter we introduce the main topic of this book: binomials and binomial ideals. Special attention is given to toric ideals. These are binomial ideals arising from an integer matrix which represents the exponent vectors of the monomial generators of a toric ring. It will be shown that the toric ideal IA attached to the matrix A is graded if and only if A is a configuration matrix. Furthermore, it will be shown that an arbitrary binomial ideal is a toric ideal if and only if it is a prime ideal. Then we study the Grobner basis of a binomial ideal and show that its reduced Grobner basis consists of binomials. We introduce Graver bases and show that the reduced Grobner basis of a binomial ideal is contained in its Graver basis. Naturally attached to a lattice \(L\subset {\mathbb Z}^n\) (i.e. a subgroup of the abelian group \({\mathbb Z}^n\)) there is a binomial ideal IL, called the lattice ideal of L. It will be shown that the saturation of any binomial ideal is a lattice ideal, and that the lattice ideals are exactly those which are saturated. The ideal generated by the binomials corresponding to the basis vectors of a basis of the lattice L is called a lattice basis ideal. Its saturation is the lattice ideal IL. The chapter closes with an introduction to Lawrence ideals and to squarefree divisor complexes.
Patent•
10 Apr 1991
TL;DR: In this article, a simple configuration was proposed to execute display precise arithmetic operation through simple configuration by obtaining the quotient by converting a divisor into a reciprocal and multiplying a dividend by it.
Abstract: PURPOSE:To execute display precise arithmetic operation through simple configuration by obtaining the quotient by converting a divisor into a reciprocal and multiplying a dividend by it, and simultaneously, executing the arithmetic operation by bit-shifting the divisor and the dividend according to the absolute value of the divisor. CONSTITUTION:The table of the reciprocal of input data is formed previously in one area of a ROM 5, and simultaneously, the table of the reciprocal of the data obtained by bit-shifting the input data is formed previously in another area. The absolute value of divisor data from a RAM 1 is discriminated by an ALU 3, and when this absolute value is larger than a prescribed value, the divisor data is shifted by prescribed number of bits, and is converted by using other area of the ROM 5. Simultaneously with this, this converted data and the data obtained by shifting the dividend data from the RAM 1 by prescribed number of bits are multiplied by a multiplier 7, and the quotient is obtained. Thus, the highly precise divisional arithmetic operation can be executed through the simple configuration.