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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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Posted Content
TL;DR: In this article, Mumford and Hausen compared the fan of the toroidal embedding with a polyhedral divisor on a curve, and showed that the fan can be used to construct a torus on a normal affine variety.
Abstract: Given an effective action of an (n−1)-dimensional torus on an n- dimensional normal affine variety, Mumford constructs a toroidal embedding, while Altmann and Hausen give a description in terms of a polyhedral divisor on a curve. We compare the fan of the toroidal embedding with this polyhedral divisor.

20 citations

Posted Content
TL;DR: In this article, Castravet and Tevelev this article studied effective divisors on Ω(n, n) -overline{M}_{0,n}, focusing on hypertree divisor classes.
Abstract: We study effective divisors on $\overline{M}_{0,n}$, focusing on hypertree divisors introduced by Castravet and Tevelev and the proper transforms of divisors on $\overline{M}_{1,n-2}$ introduced by Chen and Coskun. Results include a database of hypertree divisor classes and closed formulas for Chen--Coskun divisor classes. We relate these two types of divisors, and from this construct extremal divisors on $\overline{M}_{0,n}$ for $n \geq 7$ that furnish counterexamples to the conjectural description of the effective cone of $\overline{M}_{0,n}$ given by Castravet and Tevelev.

20 citations

Journal ArticleDOI
TL;DR: In this article, the authors provided quasi-periodic solutions for completely resonant non-linear wave equations in one and two spatial dimensions and with periodic boundary conditions in an invariant subspace, where no small divisor problem arises.
Abstract: We provide quasi-periodic solutions with two frequencies $\omega\in \mathbb R^2$ for a class of completely resonant non-linear wave equations in one and two spatial dimensions and with periodic boundary conditions. This is the first existence result for quasi-periodic solutions in the completely resonant case. The main idea is to work in an appropriate invariant subspace, in order to simplify the bifurcation equation. The frequencies, close to that of the linear system, belong to an uncountable Cantor set of measure zero where no small divisor problem arises.

20 citations

Patent
Freiman Charles1, Wang Chung Chian1
29 Jan 1968
TL;DR: In this paper, a high speed, high capacity binary digital division system utilizing a composite of table lookup and iteration techniques is presented. But it does not consider the use of carry-save adder circuits.
Abstract: A system and method for digital division employing a composite of table lookup and iteration techniques. A stored logic table is used which generates a factor M which when multiplied against the divisor, provides a new divisor in a predetermined range close to unity in value. Both the divisor and the dividend are then multiplied by the factor M, the capacity of the table lookup determining the maximum difference of the new divisor from unity. The arrangement is such that, depending upon the difference between the new divisor and unity, a selected number of new partial quotient digits is directly determined from a selected number of digits in newly generated partial remainders. By generating quotient digits in successive groups, only a few iterations are needed to divide one long number by another. Successive division steps entail merely the generation of new partial products, and derivation of the difference of these partial products from the previous partial remainder. By arranging the significant portion of the new divisor to be a negative quantity in a preferred form of system, only adder circuits need by employed. A high speed, high capacity binary digital division system utilizing these techniques is further arranged to utilize carry-save adder circuits to utilize carry and sum quantities without introducing carry propagation delays, and otherwise minimize operating cycle time.

20 citations

Journal ArticleDOI
TL;DR: Gomez-Perez and Sadornil as discussed by the authors showed that the nth iterate of f has a square-free divisor of degree of order at least n 1+o(1) as n→∞ (uniformly in q).
Abstract: D. Gomez-Perez, A. Ostafe, A.P. Nicolas and D. Sadornil have recently shown that for almost all polynomials f∈Fq[X] over the finite field of q elements, where q is an odd prime power, their iterates eventually become reducible polynomials over Fq. Here we combine their method with some new ideas to derive finer results about the arithmetic structure of iterates of f. In particular, we prove that the nth iterate of f has a square-free divisor of degree of order at least n1+o(1) as n→∞ (uniformly in q).

20 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20222
2021157
2020172
2019127
2018120
2017140