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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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TL;DR: In this article, the authors considered the problem of computing the maximal possible number of quadrplets for integers with certain extra conditions and obtained an explicit upper bound, which is close to the optimal.
Abstract: Consider the divisor sum $\sum_{n\leq N}\tau(n^2+2bn+c)$ for integers $b$ and $c$ which satisfy certain extra conditions. For this average sum we obtain an explicit upper bound, which is close to the optimal. As an application we improve the maximal possible number of $D(-1)$-quadruples.

1 citations

Journal ArticleDOI
TL;DR: In this article, positivity conditions for adjoint bundles of dimension k + tL with n-3 have been studied, where n is the number of non-degenerate quadratic singularities in the adjoint bundle.
Abstract: Let $(X,L)$ be a smooth polarized variety of dimension $n$. Let $A\in |L|$ be an effective irreducible divisor, and let $\Sigma$ be the singular locus of $A$. We assume that $\Sigma$ is a smooth subvariety of dimension $k\geq 2$, and codimension $c\geq 3$, consisting of non-degenerate quadratic singularities. We study positivity conditions for adjoint bundles $K_X+tL$ with $t\geq n-3$. Several explicit examples motivate the discussion.

1 citations

Patent
26 Jan 2006
TL;DR: In this paper, a remainder calculation processor and a processor capable of performing remainder calculation by a multiplication method was proposed to reduce the processing quantity of remainder calculation for an input value whose range is limited.
Abstract: PROBLEM TO BE SOLVED: To provide a remainder calculation processor and a remainder calculation processing method capable of performing remainder calculation by a multiplication method, and reducing the processing quantity of remainder calculation for an input value whose range is limited SOLUTION: When an integer whose range is limited is defined as a dividend and the integer of a fixed value is defined as a divisor, a dividend (103) is multiplied (104) by an invert (100) of a fixed point display divisor, and a decimal part is extracted from the multiplication result of the invert (106), and the extraction result of the decimal part is multiplied (108) by a divisor (107), and an integral part is extracted (110) as a division calculation result from a multiplication result (109) In this case, an error to be generated due to the cutoff of non-display digits is guaranteed by adding 1 to the least significant digit of the valid display digits of the invert (100) of the divisor (102) to perform the above arithmetic processing Also, the number of digits of the fixed point display decimal part is defined as the precisely guaranteed minimum number of digits, and when the decimal point is extracted (106), the decimal part is extracted by mask processing with the precisely guaranteed minimum number of bits COPYRIGHT: (C)2006,JPO&NCIPI

1 citations

Journal ArticleDOI
TL;DR: A proof for general k is presented, thereby generalizing the results in Yuster and giving the dimension of the space of k-magic sequences of length n for every k and n and over every field.

1 citations

01 Mar 2021
TL;DR: In this paper, the notion of mp-residuated lattices is introduced and investigated and it is shown that a residuated lattice is mp if and only if the set of its ω-filters is a sublattice of the lattice of its filters.
Abstract: In this paper, the notion of mp-residuated lattice, as a subclass of residuated lattices in which every prime filter contains a unique minimal prime filter, is introduced and investigated. For a residuated lattice A, the notion of ω-filter is introduced and it is shown that Ω(A), the set of ω-filters of A, is a bounded distributive lattice. Also, it is observed that γ(A), the set of coannulets of A, is a sublattice of Ω(A). Then for each prime filter P of A, the notion of the divisor filter D(P) as an important tool in investigating of minimal prime filters of A is introduced and it is proved that a prime filter P is minimal prime if and only if P=D(P). Finally, by the notion of ω-filters, as an extension of divisor filters, a fundamental characterization of mp-residuated lattices is given and it is shown that a residuated lattice is mp if and only if the set of its ω-filters is a sublattice of the lattice of its filters.

1 citations


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