We develop a level set method for the computation of multivalued physical observables (density, velocity, etc.) for the semiclassical limit of the Schrödinger equation. This method uses an Eulerian formulation and applies directly to arbitrary number of space dimensions. The main idea is to evolve the density near an n-dimensional manifold that is identified as the common zeros of n level set f...

where F : J ×Rn → (Rn) is a multivalued map, (Rn) is the family of all subsets of Rn, y0 ∈ Rn, and 0 ≤ t1 < t2 < ··· < tp ≤ b, p ∈ N, ck = 0, k = 1,2, . . . , p. The single-valued case of problem (1.1) was studied by Byszewski [5], in which a new definition of mild solution was introduced. In the same paper, it was remarked that the constants ck, k = 1, . . . , p, from condition (1.1b) can sati...

Let 2 be a finite set of join dependencies (JDs), multivalued dependencies (MVDs) and functional dependencies (IDS). To test whether .% implies an MVD X -+ Y or an PD X -+ A, the procedure in [ 31 first generates the dependency basis DEP( X) of X with respect to 2. Then, X + Y if and only if Y is the union of some elements in DEP( X) , and X -+ A if and only if A E DEP( X), and there is an PD V...

We present a complete finite axiomatization of the unrestricted implication problem for inclusion and conditional independence atoms in the context of dependence logic. For databases, our result implies a finite axiomatization of the unrestricted implication problem for inclusion, functional, and embedded multivalued dependencies in the unirelational case.

There is a well-known algorithm for determining when a decomposition ˆ {R1,R2, . . . ,Rm} of a database relation scheme has a lossless join with respect to a set of functional dependencies. We ®rst present a reformulation of this algorithm in terms of set closures. For the special case of mˆ 2, there is a well-known explicit condition for losslessness. Our formulation extends this result for ge...

Consider a relation schema with a set of dependency constraints. A fundamental question is what is the minimum space where the possible instances of the schema can be ”stored”. We study the following model. Encode the instances by giving a function which maps the set of possible instances into the set of words of a given length over the binary alphabet in a decodable way. The problem is to find...

This paper introduces a new definition of fuzzy multivalued dependency, called α-fmvd, on the basis of the αequality of tuples as defined in [1]. Next the definition is shown to be consistent, i.e., it reduces to that of classical multivalued dependency (mvd) when the choice parameter takes the value one. Finally, a set of sound and complete inference axioms have been designed and proved for th...

The existence of approximate fixed points and approximate endpoints of the multivalued almost I-contractions is established. We also develop quantitative estimates of the sets of approximate fixed points and approximate endpoints for multivalued almost I-contractions. The proved results unify and improve recent results of Amini-Harandi 2010 , M. Berinde and V. Berinde 2007 , Ćirić 2009 , M. Păc...