In this paper is considered the preservation of properties of the ring of coefficients R to the rings R[x] and R [[x]], where R[x] denotes the polynomials ring and R [[x]] is the power series ring. This study is carry out in the context of finite conductor rings; in particular, properties like GCD, G − GCD, coherence, quasi coherence and finite conductor are analized.

BACKGROUND A rare complication of diverticulosis of the colon is giant colonic diverticula (GCD). The condition was first described in English literature in 1953. METHODS A Medline search was undertaken for English, French and German language articles on 'giant colonic diverticula'. RESULTS A total of 135 patients were identified, presenting with a total of 155 GCD. With a complication rate...

We handle a problem to assign the starting offsets of a collision-free schedule in a certain form called a well-formed gcd notation. Each activity in an activity set recurs with its own period. If more than one activity occurs at the same time slot, it is a collision. If a schedule can be constructed as a well-formed gcd notation, the schedule is known to be collision-free. In this paper, we in...

A rational triangle has rational edge-lengths and area; a rational tetrahedron has rational faces and volume; either is Heronian when its edge-lengths are integer, and proper when its content is nonzero. A variant proof is given, via complex number GCD, of the previously known result that any Heronian triangle may be embedded in the Cartesian lattice Z; it is then shown that, for a proper trian...

The enzyme quinoprotein glucose dehydrogenase (GDH) catalyses the oxidation of glucose to gluconic acid by direct oxidation in the periplasmic space of several Gram-negative bacteria. Acidification of the external environment with the release of gluconic acid contributes to the solubilization of the inorganic phosphate by biofertilizer strains of the phosphate-solubilizing bacteria. Glucose deh...

A nonempty subset A of {1, 2, . . . , n} is said to be relatively prime if gcd(A) = 1. Nathanson [4] defined f(n) to be the number of relatively prime subsets of {1, 2, . . . , n} and, for k ≥ 1, fk(n) to be the number of relatively prime subsets of {1, 2, . . . , n} of cardinality k. Nathanson [4] defined Φ(n) to be the number of nonempty subsets A of the set {1, 2, . . . , n} such that gcd(A)...

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...

This paper proposed an efficient implementation of digital circuit based on the Euclidean Algorithm with modular arithmetic to find Greatest Common Divisor (GCD) of two Binary Numbers given as input to the circuit. Output of the circuit is the GCD of the given inputs. In this paper subtraction-based narrative defined by Euclid is described, the remainder calculation replaced by repeated subtrac...

In [3] and [5] the authors ask how many primes are of the form xY + yX, where gcd (x, y) = 1 and x, y 2: 2. Moreover, Jose Castillo (see [2]) asks how many primes are of the Smarandache form xil + X2 X3 + ... + Xn Xl , where n > 1, Xl, X2, ••• , Xn > 1 and gcd (Xl, X2, ••• , X n ) = 1 (see [9]). In this article we announce a lower bound for the size of the largest prime divisor of an expression...

The general fractional conformable derivative (GCD) and its attributes have been described by researchers in the recent times. Compared with other definitions, this presents a generalization of follows same derivation formulae. For electrical circuits, such as RLC, RC, LC, we obtain new class fractional-order differential equations using novel derivative, use GCD to depict circuits has shown be...