The Affine partitioning framework, which unifies many useful program transforms such as unimodular transformations, loop fusion, fission, scaling, reindexing, and statement reordering, has been proved to be successful in automatic discovery of the loop-level parallelization in programs. The affine partition algorithm was improved from the aspects of compile-time and runtime efficiency in this p...

The generalized conjunction/disjunction function (GCD) is a continuous logic function of two or more variables that integrates conjunctive and disjunctive properties in a single function. It is used as a mathematical model of simultaneity and replaceability of inputs. Special cases of this function include the full (pure) conjunction, the partial conjunction, the arithmetic mean, the partial di...

Statistical modeling is at the heart of many engineering problems. The importance of statistical modeling emanates not only from the desire to accurately characterize stochastic events, but also from the fact that distributions are the central models utilized to derive sample processing theories and methods. The generalized Cauchy distribution (GCD) family has a closed-form pdf expression acros...

The stress-activated protein kinase Gcn2 regulates protein synthesis by phosphorylation of translation initiation factor eIF2α, from yeast to mammals. The Gcn2 kinase domain (KD) is inherently inactive and requires allosteric stimulation by adjoining regulatory domains. Gcn2 contains a pseudokinase domain (YKD) required for high-level eIF2α phosphorylation in amino acid starved yeast cells; how...

In this paper, we study the transfer of some $t$-locally properties which are stable under localization to $t$-flat overrings an integral domain $D$. We show that $D,$ $D[X],$ $D\langle X\rangle,$ $D(X)$ and $D[X]_{N_v}$ simultaneously P$v$MDs (resp., Krull, G-GCD, Noetherian, Strong Mori). A complete characterization when a pullback is P$v$MD GCD, Mori, Mori) given. As corollaries, investigate...

This paper considers the computation of greatest common divisor (GCD) dt1,t2(x,y) three bivariate Bernstein polynomials that are defined in a rectangular domain, where t1(t2) is degree when it written as polynomial x(y) whose coefficients y(x). The Sylvester resultant matrix and its subresultant matrices used for degrees GCD. It shown there four forms these they differ their computational prope...

in this study, a new and ecient approach is presented for numerical solution offredholm integro-dierential equations (fides) of the second kind on unbounded domainwith degenerate kernel based on operational matrices with respect to generalized laguerrepolynomials(glps). properties of these polynomials and operational matrices of integration,dierentiation are introduced and are ultilized to r...

Euclid’s algorithm gives the greatest common divisor (gcd) of two integers, gcd(a, b) = max{d ∈ Z | d|a, d|b} If for simplicity we define gcd(0, 0) = 0, we have a function gcd : Z× Z −→ N with the following properties: Lemma 1 For any a, b, c, q ∈ Z we have: (i) gcd(a, b) = gcd(b, a). (ii) gcd(a,−b) = gcd(a, b). (iii) gcd(a, 0) = |a|. (iv) gcd(a− qb, b) = gcd(a, b). Proof. Trivial; for (iv) use...

We consider a generalization of the gcd-sum function, and obtain its average order with a quasi-optimal error term. We also study the reciprocals of the gcd-sum and lcm-sum functions.

In this paper we analyze a slight modification of Jebelean’s version of the k-ary GCD algorithm. Jebelean had shown that on n-bit inputs, the algorithm runs in O(n) time. In this paper, we show that the average running time of our modified algorithm is O(n/ logn). This analysis involves exploring the behavior of spurious factors introduced during the main loop of the algorithm. We also introduc...