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.
Papers published on a yearly basis
Papers
More filters
Patent•
08 Aug 1991
TL;DR: In this article, the inverse element of a divisor is calculated by multiplying the divident and the inverse elements of the divisors while converting one of them to a matrix expression, and then the quotient x/y is calculated in the vector expression.
Abstract: PURPOSE:To make a circuit scale compact and to accelerate calculation speed by calculating the inverse element of a divisor out of a divident and the divisor expressed by a vector with (m) bits on a finite field GF (2 ) by vector expression and multiplying the divident and the inverse element of the divisor while converting one of them to a matrix expression. CONSTITUTION:When a quotient x/y of two elements (x) and (y) on the finite field GF (2 ) is calculated, at first, an inverse element y of the first element (y) is generated with the vector expression by an inverse element generating circuit 3 and afterwards, multiplier circuits 1 and 2 convert the second element (x) to the matrix expression and multiply this element (x) in the matrix expression and the inverse element y in the vector expression. Then, the quotient x/y is calculated in the vector expression. In comparison with a conventional circuit using a ROM as three conversion tables, the circuit scale of the inverse element generating circuit 3 becomes about 1/3 and the inverse element generating circuit 3 is used only once. Thus, the circuit scale of the multiplier circuit on the finite field GF (2 ) is made compact and the calculation speed can be accelerated.
TL;DR: In this paper, the authors studied the properties of weak mutually unbiased bases in the phase space of quadratic systems with variables in the Euclidean plane and showed that there is a duality between the weak mutually-neutral bases and the maximal lines through the origin.
Abstract: Quantum systems with variables in ${\mathbb Z}(d)$ are considered. The properties of lines in the ${\mathbb Z}(d)\times {\mathbb Z}(d)$ phase space of these systems, are studied. Weak mutually unbiased bases in these systems are defined as bases for which the overlap of any two vectors in two different bases, is equal to $d^{-1/2}$ or alternatively to one of the $d_i^{-1/2},0$ (where $d_i$ is a divisor of $d$ apart from $d,1$). They are designed for the geometry of the ${\mathbb Z}(d)\times {\mathbb Z}(d)$ phase space, in the sense that there is a duality between the weak mutually unbiased bases and the maximal lines through the origin. In the special case of prime $d$, there are no divisors of $d$ apart from $1,d$ and the weak mutually unbiased bases are mutually unbiased bases.
Posted Content•
TL;DR: In this paper, it was shown that when the right hand side of the complex Monge-Amp\{e}re equation is in some weighted space for p_0 > 2n, it has a classical solution.
Abstract: We consider the complex Monge-Amp\'{e}re equation on complete K\"{a}hler manifolds with cusp singularity along a divisor when the right hand side $F$ has rather weak regularity. We proved that when the right hand side $F$ is in some \emph{weighted} $W^{1,p_0}$ space for $p_0 > 2n$, the Monge-Amp\'{e}re equation has a classical $W^{3,p_0}$ solution.
KEK1
TL;DR: In this article, the relation between instanton counting on ALE spaces and BPS state counting on a toric Calabi-Yau threefold was studied, and it was shown that the character of affine SU(N) algebra naturally arises in wallcrossings of D4-D2-D0 states.
Abstract: We study the relation between the instanton counting on ALE spaces and the BPS state counting on a toric Calabi-Yau three-fold We put a single D4-brane on a divisor isomorphic to AN−1-ALE space in the Calabi-Yau three-fold, and evaluate the discrete changes of BPS partition function of D4-D2-D0 states in the wall-crossing phenomena In particular, we find that the character of affine SU(N) algebra naturally arises in wallcrossings of D4-D2-D0 states Our analysis is completely based on the wall-crossing formula for the d = 4,N = 2 supersymmetric theory obtained by dimensionally reducing the CalabiYau three-fold
Posted Content•
TL;DR: For the Dirichlet divisor problem, asymptotic upper bounds for integrals of the type = √ √ 0^T\Delta^k(t)|\zeta(1/2+it)|^{2m}dt \qquad(k,m\in\Bbb N) were established in this article, which complements the results of Ivi c-Zhai [Indag. Math. 2015].
Abstract: Let $d(n)$ be the number of divisors of $n$, let $$ \Delta(x) := \sum_{n\le x}d(n) - x(\log x + 2\gamma -1) $$ denote the error term in the classical Dirichlet divisor problem, and let $\zeta(s)$ denote the Riemann zeta-function. Several upper bounds for integrals of the type $$ \int_0^T\Delta^k(t)|\zeta(1/2+it)|^{2m}dt \qquad(k,m\in\Bbb N) $$ are given. This complements the results of the paper Ivi\'c-Zhai [Indag. Math. 2015], where asymptotic formulas for $2\le k \le 8,m =1$ were established for the above integral.