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 paper, a combinatorial identity which is closely related to the multi-dimensional integral of the divisor function was found, which was used to determine the finite dual of the group algebra of infinite dihedral group.
Abstract: In this note, we find a combinatorial identity which is closely related to the multi-dimensional integral $\gamma_{m}$ in the study of divisor functions. As an application, we determine the finite dual of the group algebra of infinite dihedral group.
3 citations
TL;DR: In this article, the phase mismatch parameters in all possible FWM products in a dispersion-managed fiber (DMF) link become integer multiples of a common divisor and that, if this divisors coincides with an integer multiple of π radian, the Q-penalty caused by FWM can be quenched in theory.
3 citations
TL;DR: In this paper, it was shown that the number of infinitary harmonic numbers not exceeding x is less than 2.2 x 1/2 2 (1+e)log x/log log x for any e > 0 and x > n 0 (e).
Abstract: The infinitary divisors of a natural number n are the products of its divisors of the , where p y is an exact prime-power divisor of n and (where y α = 0 or 1) is the binary representation of y . Infinitary harmonic numbers are those for which the infinitary divisors have integer harmonic mean. One of the results in this paper is that the number of infinitary harmonic numbers not exceeding x is less than 2.2 x 1/2 2 (1+e)log x/log log x for any e > 0 and x > n 0 (e). A corollary is that the set of infinitary perfect numbers (numbers n whose proper infinitary divisors sum to n ) has density zero.
3 citations
Patent•
01 Aug 2014
TL;DR: In this article, a fast integer divider circuit with a plurality of adders is described, where each adder subtracts a multiple of the divisor from the current value in the partial remainder register.
Abstract: Embodiments disclosed pertain to apparatuses, systems, and methods for fast integer division. Disclosed embodiments pertain to an integer divide circuit to divide a dividend by a divisor and produce multiple quotient bits per iteration. In some embodiments, the fast integer divider may include a partial remainder register initialized with the dividend. Further, the fast integer divider circuit may include a plurality of adders, where each adder subtracts a multiple of the divisor from the current value in the partial remainder register. A logic block coupled to each of the adders, determines multiple quotient bits at each iteration based on the subtraction results.
3 citations
TL;DR: In this article, it was shown that if the zero divisor graph of a finite commutative ring with identity is planar, then the graph has a planar supergraph with a Hamiltonian cycle.
Abstract: Let $R$ be a finite commutative ring with identity. We form the zero divisor graph of $R$ by taking the nonzero zero divisors as the vertices and connecting two vertices, $x$ and $y$, by an edge if and only if $xy=0$. We establish that if the zero divisor graph of a finite commutative ring with identity is planar, then the graph has a planar supergraph with a Hamiltonian cycle. We also determine the book thickness of all planar zero divisor graphs.
3 citations