In a quadratic number field Q(√ D ), D a squarefree integer, with class number 1 any algebraic integer can be decomposed uniquely into primes but for only 21 domains Euclidean algorithms are known. It was shown by Cohn [5] that for D ≤ – 19 even remainder sequences with possibly non-decreasing norms cannot determine the GCD of arbitrary inputs. We extend this result by showing that there does...

Corticofugal pathways originating in auditory cortex innervate most subcortical auditory nuclei in the ascending pathway [Auditory Neurosci. 1 (1995) 287-308; J. Comp. Neurol. 371 (1996) 15-40]. Our goal is to determine if these projections arise from the same neurons or if different neurons project to each of the separate structures. We also seek to identify the layers and fields of auditory c...

Relativistic integral representation in terms of experimental neutron– proton scattering phase shifts alone is used to compute the charge form factor of the deuteron GCd(Q ). The results of numerical calculations of |GCd(Q)| are presented in the interval of the four–momentum transfers squared 0 ≤ Q ≤ 35 fm−2. Zero and the prominent secondary maximum in |GCd(Q)| are the direct consequences of th...

In this paper, we count cycles in a generalized Kautz digraph GK (n; d). Let n = pd such that d| ,p. Also let gl = gcd(d − (−1)l; n). We show that if one of the following conditions holds: • p6 √ d7 d+1 and k6 logd n+ 1, • √ d7 d+1 ¡p¡d (d+ 1) and k6 logd ( n 3 √ p2(d+1) ) + 10 3 , • d(d+ 1)¡p and k6 logd ( n d+1 ) then the number of cycles of length k in GK (n; d) is given by 1 k ∑ l | k ( k l...

New Result EREW PRAM: Compute gcd(x, y) with probability 1 − o(1) in O(n log log n/ log n) time using n6+ processors. [16] Reduction Our inputs are integers x, y with x ≥ y > 0. • Choose a prime bound B > 0, and assume p | x or p | y implies p > B. • Choose a at random, 1 ≤ a ≤ y − 1. • Compute r := ax mod y. • Remove all prime divisors ≤ B from r producing s. Thus P (r/s) ≤ B. We use (x, y) → ...

One can prove the following three propositions: (1) For all natural numbers m, n holds gcd(m,n) = gcd(m, n + m). (2) For all natural numbers k, m, n such that gcd(k, m) = 1 holds gcd(k,m · n) = gcd(k, n). (3) For every real number s such that s > 0 there exists a natural number n such that n > 0 and 0 < 1 n and 1 n ¬ s. In this article we present several logical schemes. The scheme Fib Ind conc...

A number of social insect species have recently been shown to have genetically influenced caste determination (GCD), challenging the conventional view that caste determination should be strictly environmental. To date, GCD has been found in phylogenetically isolated species; examples of GCD being present in multiple species of a genus are lacking. Through crossing experiments of neotenic (juven...

The integration of information across sensory modalities enables sound to be processed in the context of position, movement, and object identity. Inputs to the granule cell domain (GCD) of the cochlear nucleus have been shown to arise from somatosensory brain stem structures, but the nature of the projection from the spinal trigeminal nucleus is unknown. In the present study, we labeled spinal ...

for two normal edge-transitive cayley graphs on groups h and k which have no common direct factor and gcd(jh=h ′j; jz(k)j) = 1 = gcd(jk=k ′j; jz(h)j), we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.