Let R be an associative ring not necessarily with identity element. For any x, y ∈ R. Recall that R is prime if xRy = 0 implies x = 0 or y = 0, and is semiprime if xRx = 0 implies x = 0. Given an integer n ≥ 2, R is said to be n−torsion free if for x ∈ R, nx = 0 implies x = 0.An additive mapping d : R → R is called a derivation if d(xy) = d(x)y + yd(x) holds for all x, y ∈ R, and it is called a...

A bstract We derive analytically the terms of maximal transcendentality planar 2- and 3-point functions single-trace chiral primary operators $$ \mathcal{N} N = 2 SQCD on ℝ 4 , to all orders in ’t Hooft coupling. These results prove two conjectures we formulated previous work. Furthermore, also provide an exp...

The basic Schema Theorem for genetic algorithms is modiied for a grammatically-based learning system. A context-free grammar is used to deene a language in which each sentence is mapped to a tness value. The derivation trees associated with these sentences are used to deene the structure of schemata. The eeect of crossover and mutation on schemata is described. A schema theorem is developed whi...

Establishing authenticity and independence of documents in relation to others is not a new problem, but in the era of hyper production of e-text it certainly gained even more importance. There is an increased need for automatic methods for determining originality of documents in a digital environment. The method of n-gram overlap is only one of several methods proposed by the literature and is ...

In this paper, we study the generalized derivation of a Lie sub-algebra algebra polynomial vector fields on $\mathbb{R}^n$ where $n\geq1$, containing all constant and Euler field, under some conditions sub-algebra.

Let M be a 2-torsion free prime Γ-ring satisfying the condition a α b β c=a β b α c,∀a,b,c∈M and α,β∈Γ, U be an admissible Lie ideal of M and F=(f i ) i∈N be a generalized higher (U,M)-derivation of M with an associated higher (U,M)-derivation D=(d i ) i∈N of M. Then for all n∈N we prove that [Formula: see text]. Mathematics Subject Classification (2010): 13N15; 16W10; 17C50.

In the papers [1, 2, 4–6, 8] the similarities and differences between systems of sequents and systems of natural deduction for some fragments of intuitionistic logic were presented. The main goal of almost all of these papers was to study the connection between cut-free derivations and normal derivations. It is a well-known property that the natural deduction image of a cut-free derivation is a...

We present the derivation of a solution to a LISP programming exercise. The derivation is in three steps. First, an ineecient solution is given. Second, the quintessence of a more eecient solution is captured in a number of equalities. Third, an ecient solution is derived from the ineecient o n e b y a n umber of transformation steps, each of which is justiied by the equalities.

Pool Resolution for propositional CNF formulas is introduced. Its relationship to state-of-the-art satis ability solvers is explained. Every regular-resolution derivation is also a pool-resolution derivation. It is shown that a certain family of formulas, called NT (n) has polynomial sized pool-resolution refutations, whereas the shortest regular refutations have an exponential lower bound. Thi...

In this paper, we propose a new algorithm for the derivation of a protocol specification in Pr/T-nets, which is the specification of communicating N entities (N can be given), from a given service specification in Pr/T-nets and an allocation of the places of the service specification to the N entities. Our algorithm decomposes each transition of the service specification into a set of communica...