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.

Unitary super perfect numbers

Abstract: We shall show that 9, 165 are all of the odd unitary super perfectnumbers. 1 Introduction We denote by σ(N) the sum of divisors of N. N is called to be perfectif σ(N) = 2N. It is a well-known unsolved problem whether or not anodd perfect number exists. Interest to this problem has produced manyanalogous notions.D. Suryanarayana [10] called N to be super perfect if σ(σ(N)) = 2N.It is asked in this paper and still unsolved whether there were odd superperfect numbers.A special class of divisors is the class of unitary divisors defined by Cohen[2]. A divisor d of n is called a unitary divisor if (d,n/d) = 1. Then we writed || n. We denote by σ ∗ (N) the sum of unitary divisors of N. Replacing σby σ ∗ , Subbarao and Warren [9] introduced the notion of a unitary perfectnumber. N is called to be unitary perfect if σ ∗ (N) = 2N. They provedthat there are no odd unitary perfect numbers. Moreover, Subbarao [8]conjectured that there are only finitely many unitary perfect numbers.Combining these two notions, Sitaramaiah and Subbarao [6] studiedunitary super perfect (USP) numbers, integers N satisfying σ

Divide circuit having high-speed operating capability

Abstract: A divide circuit which is adapted to obtain a quotient by using a dividend and a divisor, the dividend and the divisor being input signals of either quadruple logic or quadruple logic converted from binary logic, includes a unit for setting a candidate value of the quotient, a unit connected to the setting unit for multiplying the quotient candidate value by the divisor, and a unit connected to the multiplying unit for comparing a result obtained by the multiplying unit with the dividend.

Effective divisors on Hurwitz spaces and moduli of curves

Abstract: We discuss the transition from uniruledness to being of general type for moduli spaces of curves and Hurwitz spaces of covers. First, we construct and calculate the class of a virtual divisor on the moduli space of curves of genus 23, having slope less than that of the canonical divisor. Provided the virtual divisor in question is an actual divisor (which is implied by the Strong Maximal Rank Conjecture), it follows that M_{23} a variety of general type. Secondly, we prove the effectiveness of the canonical bundle of several Hurwitz spaces of degree k covers of the projective line from curves of genus 13

Connections on parahoric torsors over curves

Abstract: We define parahoric $\cG$--torsors for certain Bruhat--Tits group scheme $\cG$ on a smooth complex projective curve $X$ when the weights are real, and also define connections on them. We prove that a $\cG$--torsor is given by a homomorphism from $\pi_1(X\setminus D)$ to a maximal compact subgroup of $G$, where $D\, \subset\, X$ is the parabolic divisor, if and only if the torsor is polystable.