Euclid’s algorithm for computing the greatest common divisor of 2 numbers is considered to be the oldest proper algorithm known ([10]). This algorithm can be amplified naturally in various ways. The GCD problem for more than two numbers is interesting in its own right. Thus, we can use Euclid’s algorithm recursively to compute the GCD of more than two numbers. Also, we can do a constructive com...

PURPOSE To investigate longitudinal changes in goblet cell density (GCD) in contact lens (CL) wearers who do and do not develop symptoms of dry eye (DE). METHODS Sixty healthy individuals fitted with daily disposable hydrogel CLs and 23 age-balanced non-CL-wearing controls underwent assessment using the 5-item dry eye questionnaire, noninvasive tear film break-up time measurement, ocular surf...

Extended gcd calculation has a long history and plays an important role in computational number theory and linear algebra. Recent results have shown that finding optimal multipliers in extended gcd calculations is difficult. We present an algorithm which uses lattice basis reduction to produce small integer multipliers x1, . . . , xm for the equation s = gcd (s1, . . . , sm) = x1s1 + · · · + xm...

The paper presents a new fast k-ary reduction for integer GCD. It enjoys powerful properties and improves on the running time of the quite similar integer GCD algorithm of Kannan et al. Our k-ary reduction also improves on Sorenson's k-ary reductionn14] and thus favorably matches We-ber's algorithmm15]. More generally, the fast k-ary reduction also provides a basic tool for almost all the best ...

All rings are assumed to be commutative with identity. A generalized GCD ring (G-GCD ring) is a ring (zero-divisors admitted) in which the intersection of every two finitely generated (f.g.) faithful multiplication ideals is a f.g. faithful multiplication ideal. Various properties of G-GCD rings are considered. We generalize some of Jäger’s and Lüneburg’s results to f.g. faithful multiplication...

In this letter, generalized gamma distribution (GCD) is introduced as a new statistical model of spectral distribution to be applied to the likelihood ratio test performed in voice activity detection (VAD). A gradient-based on-line algorithm is proposed to estimate the parameters of GCD according to the maximum likelihood criterion. Experimental results show that the VAD algorithm implemented b...

A heuristic algorithm, GCDHEU, is described for polynomial GCD computation over the integers. The algorithm is based on evaluation at a single large integer value (for each variable), integer GCD computation, and a single-point interpolation scheme. Timing comparisons show that this algorithm is very efficient for most univariate problems and it is also the algorithm of choice for many problems...

RESUMO Objetivo Testar a variável da hereditariedade familiar para gagueira crônica do desenvolvimento (GCD) como preditora de efeito direto no desfecho fluência fala em crianças. Métodos Participaram estudo 200 crianças, 2 12 anos, ambos os gêneros, sem distinção raça e nível sócio-econômico-cultural, que apresentaram queixa GCD, outras intercorrências linguagem e/ou audição, período cinco ano...

Fast generation of a large prime is important to enhance security. However, primality test of prime generation takes long time. Therefore, primality tests are combined to speed up. A combination of trial division and Miller-Rabin test (TD combined test hereafter) is the most popular combination. GCD operation and Miller-Rabin test combination (GCD combined test hereafter) is also popular and ea...