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
01 Jun 2021
TL;DR: In this paper, the analysis of divisor functions is studied in the context of Ramanujan's differential equations, and solutions suitable to tackle this singularity are developed and the problem is transformed into an analysis of a dynamical system.
Abstract: Properties of divisor functions $$\sigma _k(n)$$
, defined as sums of k-th powers of all divisors of n, are studied through the analysis of Ramanujan’s differential equations. This system of three differential equations is singular at $$x=0$$
. Solution techniques suitable to tackle this singularity are developed and the problem is transformed into an analysis of a dynamical system. Number theoretical consequences of the presented dynamical system analysis are then discussed, including recursive formulas for divisor functions.
TL;DR: In this paper, a special class of effective divisors which has properties similar to that of the case where $D$ is ample was proposed and the authors studied this divisor.
Abstract: Let $X$ be a smooth projective surface defined over the complex number field and let $D$ be an effective divisor on $X$. In this paper we will propose a special class of effective divisors which has some properties similar to that of the case where $D$ is ample and we will study this divisor.
TL;DR: A fundamental result of this work is that under the nonrestrictive condition, (N, M)=1, the algorithms defined in finite integer and complex integer rings are as intensive computationally as the corresponding algorithms define in rational and complex rational number systems only in the worst case.
Abstract: In this work, we present and analyze a number theoretic approach to computing one-dimensional cyclic convolution of sequences defined in finite integer and complex integer rings. A fundamental result of this work is that under the nonrestrictive condition, (N, M)=1, the algorithms defined in finite integer and complex integer rings are as intensive computationally as the corresponding algorithms defined in rational and complex rational number systems only in the worst case. They simplify considerably for a large number of cases of importance in digital signal processing.
Patent•
17 Nov 2004
TL;DR: In this article, the authors proposed a kind of divider whose divisor is 15i 2n, which uses different adder, and-gate or not gate to form the divider, the input end is the binary dividend, one output end forms the binary quotient of the dividing result, and another end output the binary remainder of dividing.
Abstract: The invention is a kind of divider whose divisor is 15i‡2n. The character lies in: it uses different adder, and-gate or not gate to form the divider, the input end is the binary dividend, one output end forms the binary quotient of the dividing result, and another end output the binary remainder of the dividing. The divider can carry on division whose divisor is 15i‡2n, the dividend is 0-1272n +2n -1, (n=0, 1, 2, 3®®n). The divider is simple, the cost is low.
Patent•
NEC1
TL;DR: In this paper, an error correcting circuit corrects bit errors in a received codeword by making a difference detecting circuit (13) detect a degree difference between a higher and a lower degree polynomial.
Abstract: of EP0619654Using a Euclidean algorithm for error correction, an error correcting circuit corrects bit errors in a received codeword by making a difference detecting circuit (13) detect a degree difference between a higher and a lower degree polynomial. When the difference is equal to one, a dividing circuit (11) is supplied in a first stage of the algorithm with the higher and the lower degree polynomials as a dividend and a divisor polynomial. When the difference is greater than one, the difference is decremented by one to provide an amount of shift, responsive to which a shifting circuit (15) shifts coefficients of the lower degree polynomial to higher degree terms to provide a shifted polynomial. In the first stage, the shifted polynomial is used as the divisor polynomial. Preferably, an error number is calculated. From an error location polynomial, an error location number is detected. Only when the error location number coincides with the error number, the bit errors are correctable.