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.

Processor, control method thereof, and arithmetic processing program

Abstract: PROBLEM TO BE SOLVED: To provide a processor which can execute high radix division by a simpler processing procedure and a method for controlling the processor and a program. SOLUTION: A correction value calculation part 15 calculates the correction value of a loop count value based on a dividend zero count value based on a dividend A and a divisor zero count value based on a divisor B and the value of n. A correction loop count value calculation part 16 calculates a correction loop count value based on the dividend zero count value and the divisor zero count value and the correction value. A dividend shift part 17 shifts an absolute value of the dividend A only by the number of digits based on the dividend zero count value and the correction value, A divisor shift part 18 shifts an absolute value of the divisor B based on a divisor zero count value. A division loop operation part 20 performs a division arithmetic operation based on an output value from the dividend shift part 17, an output value from the divisor shift part 18, and the correction loop count value. COPYRIGHT: (C)2011,JPO&INPIT

Method and device for calculating a Montgomery conversion parameter

Abstract: A computation method for use in cryptography which employs the Montgomery modular multiplication algorithm. To speed up the computation process, an equivalence which gives the same remainder value as a divisor n is computed as a value relating to a Montgomery conversion parameter used in a Montgomery multiplication remainder operation. That is, the method calculates an equivalence H 0 = 2 m*k+1 (mod n) relating to a divisor n of 2 m*k+1 (step A), computes an equivalence H = 2 E(p, m, k) (mod n) of 2 E(p, m, k) (mod n) from H 0 by an REDC operation (step B), and performs a correction operation by H = REDC (H, G) n for g = 2 k*G/p, m, k ) when 2 P > mxk (step C).

Doubling construction of Calabi-Yau fourfolds from toric Fano fourfolds

Abstract: We give a differential-geometric construction of Calabi-Yau fourfolds by the `doubling' method, which was introduced in \cite{DY14} to construct Calabi-Yau threefolds. We also give examples of Calabi-Yau fourfolds from toric Fano fourfolds. Ingredients in our construction are \emph{admissible pairs}, which were first dealt with by Kovalev in \cite{K03}. Here in this paper an admissible pair $(\overline{X},D)$ consists of a compact Kahler manifold $\overline{X}$ and a smooth anticanonical divisor $D$ on $\overline{X}$. If two admissible pairs $(\overline{X}_1,D_1)$ and $(\overline{X}_2,D_2)$ with $\dim_{\mathbb{C}}\overline{X}_i=4$ satisfy the \emph{gluing condition}, we can glue $\overline{X}_1\setminus D_1$ and $\overline{X}_2\setminus D_2$ together to obtain a compact Riemannian $8$-manifold $(M,g)$ whose holonomy group $\mathrm{Hol}(g)$ is contained in $\mathrm{Spin}(7)$. Furthermore, if the $\widehat{A}$-genus of $M$ equals $2$, then $M$ is a Calabi-Yau fourfold, i.e., a compact Ricci-flat Kahler fourfold with holonomy $\mathrm{SU}(4)$. In particular, if $(\overline{X}_1,D_1)$ and $(\overline{X}_2,D_2)$ are identical to an admissible pair $(\overline{X},D)$, then the gluing condition holds automatically, so that we obtain a compact Riemannian $8$-manifold $M$ with holonomy contained in $\mathrm{Spin}(7)$. Moreover, we show that if the admissible pair is obtained from \emph{any} of the toric Fano fourfolds, then the resulting manifold $M$ is a Calabi-Yau fourfold by computing $\widehat{A}(M)=2$.

Motivic zeta functions and infinite cyclic covers

Abstract: We associate with an infinite cyclic cover of a punctured neighborhood of a simple normal crossing divisor on a complex quasi-projective manifold (assuming certain finiteness conditions are satisfied) a rational function in $K_0({\rm Var}^{\hat \mu}_{\mathbb{C}})[\mathbb{L}^{-1}]$, which we call {\it motivic infinite cyclic zeta function}, and show its birational invariance. Our construction is a natural extension of the notion of {\it motivic infinite cyclic covers} introduced by the authors, and as such, it generalizes the Denef-Loeser motivic Milnor zeta function of a complex hypersurface singularity germ.

The $${\mathbb {Q}}$$-Korselt set of $$\mathrm {pq}$$

Abstract: Let N be a positive integer, $${\mathbb {A}}$$ be a nonempty subset of $${\mathbb {Q}}$$ and $$\alpha =\dfrac{\alpha _{1}}{\alpha _{2}}\in {\mathbb {A}}{\setminus } \{0,N\}$$ . $$\alpha $$ is called an N-Korselt base (equivalently N is said an $$\alpha $$ -Korselt number) if $$\alpha _{2}p-\alpha _{1}$$ is a divisor of $$\alpha _{2}N-\alpha _{1}$$ for every prime p dividing N. The set of all Korselt bases of N in $${\mathbb {A}}$$ is called the $${\mathbb {A}}$$ -Korselt set of N and is simply denoted by $${\mathbb {A}}$$ - $$\mathcal {KS}(N)$$ . Let p and q be two distinct prime numbers. In this paper, we study the $${\mathbb {Q}}$$ -Korselt bases of pq, where we give in detail how to provide $${\mathbb {Q}}$$ - $$\mathcal {KS}(pq)$$ . Consequently, we finish the incomplete characterization of the Korselt set of pq over $${\mathbb {Z}}$$ given in [4], by supplying the set $${\mathbb {Z}}$$ - $$\mathcal {KS}(pq)$$ when $$q <2p$$ .