On the lines of the binary gcd algorithm for rational integers, algorithms for computing the gcd are presented for the ring of integers in Q( √ d) where d ∈ {−2,−7,−11,−19}. Thus a binary gcd like algorithm is presented for a unique factorization domain which is not Euclidean (case d = −19). Together with the earlier known binary gcd like algorithms for the ring of integers in Q( √−1) and Q(√−3...

BACKGROUND AND PURPOSE There is recent evidence of various types of morphological changes in the hippocampus of a rodent model of medial temporal lobe epilepsy (mTLE). However, little is known about such changes in humans. We examined the histological changes [i.e., neuronal loss, cell genesis, and granule cell dispersion (GCD)] in surgical hippocampal specimens taken from patients with mTLE. ...

A generalized arithemtic numerical monoid is of the form S = 〈a, ah+d, ah+2d, . . . , ah+ xd〉 where the gcd(a, d) = 1 and a > x. Much is known for the arithmetic numerical monoid, when h = 1, due to known information for that specific monoid’s length set. Therefore, this paper will explore various invariants of the generalized arithmetic numerical monoid.

K. Bibak et al. [arXiv:1503.01806v1 [math.NT], March 5 2015] proved that congruence ax ≡ b (mod n) has a solution x0 with t = gcd(x0, n) if and only if gcd ( a, n t ) = gcd ( b t , n t ) thereby generalizing the result for t = 1 proved by B. Alomair et al. [J. Math. Cryptol. 4 (2010), 121–148] and O. Grošek et al. [ibid. 7 (2013), 217–224]. We show that this generalized result for arbitrary t f...

We present a derivation of Gosper's algorithm which permits generalization to higher-order recurrences with constant least and most significant coefficients. Like Gosper's algorithm, the generalized algorithm requires only 'rational' operations (such as gcd and resultant computations) but no factorization.

We present a derivation of Gosper's algorithm which permits generalization to higher-order recurrences with constant least and most signiicant coeecients. Like Gosper's algorithm, the generalized algorithm requires only "rational" operations (such as gcd and resultant computations) but no factorization.

The paper studies some properties of the ring of integer-valued quasi-polynomials. On this ring, theory of generalized Euclidean division and generalized GCD are presented. Applications to finite simple continued fraction expansion and Smith normal form of integral matrices with integer parameters are also given.

We present a parallel implementation of Schönhage’s integer GCD algorithm on distributed memory architectures. Results are generalized for the extended GCD algorithm. Experiments on sequential architectures show that Schönhage’s algorithm overcomes other GCD algorithms implemented in two well known multiple-precision packages for input sizes larger than about 50000 bytes. In the extended case t...

We present a new characterization of semi-bent and bent quadratic functions on finite fields. First, we determine when a GF (2)-linear combination of Gold functions Tr(x i+1) is semi-bent over GF (2), n odd, by a polynomial GCD computation. By analyzing this GCD condition, we provide simpler characterizations of semi-bent functions. For example, we deduce that all linear combinations of Gold fu...

ÐIn many scientific applications, dynamic array redistribution is usually required to enhance the performance of an algorithm. In this paper, we present a generalized basic-cycle calculation (GBCC) method to efficiently perform a BLOCK-CYCLIC(s) over P processors to BLOCK-CYCLIC(t) over Q processors array redistribution. In the GBCC method, a processor first computes the source/destination proc...