The sodium salt of the single-isomer, chiral resolving agent, octakis(2,3-diacetyl-6-sulfo)-g-cyclodextrin (ODAS-gCD) has been used for the capillary electrophoretic separation of the enantiomers of alkylarylphosphates which carry a phosphorus-based stereogenic center. The effective mobilities and separation selectivities were measured at different ODAS-gCD and methanol concentrations to find t...

s t lcm lcm*2 lcm*4 gcd gcd/2 gcd/4 s t lcm lcm*2 lcm*4 gcd gcd/2 gcd/4 Table 1: Execution times (ms) for cyclic(s) to cyclic(t) redistribution on 32 processors. other block sizes t. Fig. 3 shows the total times in milliseconds for a cyclic(192) to cyclic(8) redistribution on 32 processors for increasing data sizes. This redistribution corresponds to the cyclic(Y t) to cyclic(t) case with Y = 2...

We formalize the notion of approximate GCD for univariate poly-nomials given with limited accuracy and then address the problem of its computation. Algebraic concepts are applied in order to provide a solid foundation for a numerical approach. We exhibit the limitations of the euclidean algorithm through experiments, show that existing methods only solve part of the problem and assert its worst...

The binary GCD algorithm, also known as Stein’s algorithm, is an algorithm that computes the greatest common divisor of two nonnegative integers. Stein’s algorithm uses simpler arithmetic operations than the conventional Euclidean algorithm; it replaces division with arithmetic shifts, comparisons, and subtraction. Although the algorithm was first published by the Israeli physicist and programm...

It is well known that an integral domain D is a UFD if and only if every nonzero prime ideal of D contains a nonzero principal prime. This is the so-called Kaplansky’s theorem. In this paper, we give this type of characterizations of a graded PvMD (resp., G-GCD domain, GCD domain, Bézout domain, valuation domain, Krull domain, π-domain).

A Gaze-Contingent Display (GCD) is developed in GLSL to compensate for scotomata (loss of retinal visual acuity) such as brought on by Age-related Macular Degeneration (AMD). The compensatory GCD introduces a magnification ring slaved to the viewer’s gaze point.

Extended gcd computation is interesting itself. It also plays a fundamental role in other calculations. We present a new algorithm for solving the extended gcd problem. This algorithm has a particularly simple description and is practical. It also provides reened bounds on the size of the multipliers obtained.

The Heuristic Polynomial GCD procedure (GCDHEU) is used by the Maple computer algebra system, but no other. Because Maple has an especially eecient kernel that provides fast integer arithmetic, but a relatively slower interpreter for non-kernel code, the GCDHEU routine is especially eeective in that it moves much of the computation into \bignum" arithmetic and hence executes primarily in the ke...

This paper is the second part of a new proof Bel’tyukov–Lipshitz theorem, which states that existential theory structure $$\left\langle {\mathbb{Z};0,1, + , - \leqslant ,|{\kern 1pt} } \right\rangle $$ decidable. We construct quasi-quantifier elimination algorithm (the notion was introduced in first proof) to reduce decision problem for ,{\text{GCD}}} positive {{{\mathbb{Z}}_{{ > 0}}};1,{{{\{ a...

the unitary cayley graph xn has vertex set zn = {0, 1,…, n-1} and vertices u and v areadjacent, if gcd(uv, n) = 1. in [a. ilić, the energy of unitary cayley graphs, linear algebraappl. 431 (2009) 1881–1889], the energy of unitary cayley graphs is computed. in this paperthe wiener and hyperwiener index of xn is computed.