In this paper,The concept of a (∈,∈ ∨q)-fuzzy ideal in an ordered Abel-Grassmann groupoid is introduced. In partcicular, left regular ordered Abel-Grassmann groupoids are characterized by using the (∈ ,∈ ∨q)-fuzzy ideals.

We show that for logics that capture DSPACE(log n) over ordered structures, and for recursive probability distributions on the class of nite models of the signature, the 0{1 law and the convergence law hold if and only if certain boundedness conditions are satissed. As one of the applications , we consider the conjecture of Kolaitis and Vardi, stating that for arbitrary probability distribution...

Recent papers of Sharp [4] and Stephen [5] have shown that any finite topology with n points which is not discrete contains <(3/4)2” open sets, and that this inequality is best possible. We use the correspondence between finite TO-topologies and partial orders to find all non-homeomorphic topologies with n points and >(7/16)2” open sets. We determine which of these topologies are TO, and in the...

For a coequality q we say that it is regular coequality on set X ordered under the antiorder ̨ if there exists an anti-order on X=q such that the natural mapping W X ! X=q is a reverse isotone surjection of anti-ordered sets. The lattice of regular coequalities is described. 2000 Mathematics Subject Classification: 03F65, 06F05

We study the behavior of solutions for parametric equation $$-\Delta_{p}^{a_1} u(z)-\Delta_{q}^{a_2} u(z)=\lambda |u(z)|^{q-2} u(z)+f(z,u(z)) \quad \mbox{in } \Omega,\, \lambda >0,$$ under Dirichlet condition, where $\Omega \subseteq \mathbb{R}^N$ is a bounded domain with $C^2$-boundary $\partial \Omega$, $a_1,a_2 \in L^\infty(\Omega)$ $a_1(z),a_2(z)>0$ a.a. $z $p,q (1,\infty)$ and $\Delta_{p}^...

The Zap Q-learning algorithm introduced in this paper is an improvement of Watkins’ original algorithm and recent competitors in several respects. It is a matrix-gain algorithm designed so that its asymptotic variance is optimal. Moreover, an ODE analysis suggests that the transient behavior is a close match to a deterministic Newton-Raphson implementation. This is made possible by a two time-s...

Engineering analysis often involves the accurate numerical solution of boundary value problems in discrete form. Hierarchical quadtree (or octree) grid generation offers an efficient method for the spatial discretisation of arbitrary-shaped two- (or three-) dimensional domains. It consists of recursive algebraic splitting of sub-domains into quadrants (or cubes), leading to an ordered hierarchi...