We consider the entailment problem in the fragment of first-order logic (FOL) composed of existentially closed conjunctions of literals (without functions), denoted FOL(∃,∧,¬a). This problem can be recast as several fundamental problems in artificial intelligence and databases, namely query containment for conjunctive queries with negation, clause entailment for clauses without functions and qu...

A Z-graded Lie bracket { , }P on the exterior algebra Ω(M) of differential forms, which is an extension of the Poisson bracket of functions on a Poisson manifold (M,P ), is found. This bracket is simultaneously graded skew-symmetric and satisfies the graded Jacobi identity. It is a kind of an ‘integral’ of the Koszul-Schouten bracket [ , ]P of differential forms in the sense that the exterior d...

Under what conditions does there exist a group homomorphism near an approximate group homomorphism? This question concerning the stability of group homomorphisms was posed by Ulam 1 . The case of approximately additive mappings was solved by Hyers 2 on Banach spaces. In 1950 Aoki 3 provided a generalization of the Hyers’ theorem for additive mappings and in 1978 Th. M. Rassias 4 generalized the...

We consider vector lattices endowed with locally solid convergence structures, which are not necessarily topological. show that such a is defined by the to 0 on positive cone. Some results unbounded modification were only available in partial cases generalized. Order characterized as strongest monotone nets converge their extremums (if they exist). partially characterize sublattices order restr...

The relation of existence of a homomorphism on the class of all relational structures of a fixed type is reflexive and transitive; it is a quasiorder. There are standard ways to transform a quasiorder into a partial order – by identifying equivalent objects, or by choosing a particular representative for each equivalence class. The resulting partial order is identical in both cases. Properties ...

Let Fg denote the closed orientable surface of genus g. What is the least order finite group, Gg, for which there is a homomorphism ψ : π1(Fg) → Gg so that no nontrivial simple closed curve on Fg represents an element in Ker(ψ)? For the torus it is easily seen that G1 = Z2 × Z2 suffices. We prove here that G2 is a group of order 32 and that an upper bound for the order of Gg is given by g . The...

Regular homomorphisms of oriented maps essentially arise from a factorization by a subgroup of automorphisms. This kind of map homomorphism is studied in detail, and generalized to the case when the induced homomorphism of the underlying graphs is not valency preserving. Reconstruction is treated by means of voltage assignments on angles, a natural extension of the common assignments on darts. ...

‎the aim of this paper is to study distribution of ratios of generalized order statistics from pareto distribution. parameter estimation of pareto distribution based on generalized order statistics and ratios of them have been obtained. inferences using method of moments and unbiased estimator have been obtained to develop point estimations. consistency of unbiased estimator has been illustrate...