This paper presents a regularization theory for numerical computation of polynomial greatest common divisors and a convergence analysis, along with a detailed description of a blackbox-type algorithm. The root of the ill-posedness in conventional GCD computation is identified by its geometry where polynomials form differentiable manifolds entangled in a stratification structure. With a proper r...

Giant colonic diverticulum (GCD), defined as a diverticulum larger than 4 cm, is a rare entity that is generally a manifestation of colonic diverticular disease. Because of its rarity and its variable and non-specific presentation, the diagnosis of GCD depends mainly on imaging findings. Knowledge of the spectrum of radiographic and CT features of the GCD is important in making the correct diag...

The problem of approximating the greatest common divisor(GCD) for polynomials with inexact coefficients can be formulated as a low rank approximation problem with a Sylvester matrix. In this paper, we present an algorithm based on fast Structured Total Least Norm(STLN) for constructing a Sylvester matrix of given lower rank and obtaining the nearest perturbed polynomials with exact GCD of given...

For two normal edge-transitive Cayley graphs on groups H and K which have no common direct factor and gcd(|H/H ′|, |Z(K)|) = 1 = gcd(|K/K′|, |Z(H)|), we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive. c ⃝ 2014 IAUCTB. All rights reserved.

The t-class semigroup of an integral domain is the semigroup of the isomorphy classes of the t-ideals with the operation induced by ideal t-multiplication. This paper investigates ring-theoretic properties of an integral domain that reflect reciprocally in the Clifford or Boolean property of its t-class semigroup. Contexts (including Lipman and Sally-Vasconcelos stability) that suit best t-mult...

We survey properties of the gcd-sum function and of its analogs. As new results, we establish asymptotic formulae with remainder terms for the quadratic moment and the reciprocal of the gcd-sum function and for the function defined by the harmonic mean of the gcd’s.

The present paper analyses and presents several improvements to the algorithm for finding the (a, b)-pairs of integers used in the k-ary reduction of the right-shift k-ary integer GCD algorithm. While the worst-case complexity of Weber’s “Accelerated integer GCD algorithm” is O (

The aim of this paper is to extend the truth value table oflattice-valued convergence spaces to a more general case andthen to use it to introduce and study the quantale-valued fuzzy Scotttopology in fuzzy domain theory. Let $(L,*,varepsilon)$ be acommutative unital quantale and let $otimes$ be a binary operationon $L$ which is distributive over nonempty subsets. The quadruple$(L,*,otimes,varep...

In this paper we perform a further investigation for r-gcd-sum and r-lcm-sum functions. By making use of the properties generalization Euler’s φ-function, Abel’s identity elementary arguments, derive asymptotic formulas average function, function their generalizations. Moreover, also study sums reciprocals r-gcd r-lcm.