An implementation (in Maple) of the multivalued elementary inverse functions is described. The new approach addresses the difference between the single-valued inverse function defined by computer systems and the multivalued function which represents the multiple solutions of the defining equation. The implementation takes an idea from complex analysis, namely the branch of an inverse function, ...

In this paper, we present new fixed point results for nonlinear contractions (both single and multivalued) defined on subsets X (which may have empty interior) of a Fréchet space E. Some results for single-valued maps were presented in [2, 3] and the approach in these papers was based on constructing a specific map Fn (for each n∈N= {1,2, . . .}) whose fixed points converge to a fixed point of ...

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...

We present a method to incrementally voxelize triangles into a volumetric dataset with pre-filtering, generating an accurate multivalued voxelization. Multivalued voxelization allows direct volume rendering of voxelized geometry as well as volumes with intermixed geometry, accurate multiresolution representations, and efficient antialiasing. Prior voxelization methods either computed only a bin...

In this paper we study nonlinear second-order differential inclusions involving the ordinary vector p-Laplacian, a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and unifying and incorporates gradient systems, evolutionary variational inequalities and the classical boundary value problems, namely the Dirichlet, the Neumann and the p...

The transformation of a relational database schema into fourth normal form, which minimizes data redundancy, relies on the correct identification of multivalued dependencies. In this work, we study the learnability of multivalued dependency formulas (MVDF), which correspond to the logical theory behind multivalued dependencies. As we explain, MVDF lies between propositional Horn and 2-Quasi-Hor...

Data tables provide a convenient means of representation of descriptive information about objects. They serve also as standard input for data analysis tools or theories. In this paper we focus our attention upon the special class of data tables, namely multivalued information systems introduced by Z. Pawlak and E. Orłowska in the early 80s. The main idea presented in the paper is to interpret m...

Object-oriented Bayesian networks (OOBNs) facilitate the design of large Bayesian networks by allowing Bayesian networks to be nested inside of one another. Weak conditional independence has been shown to be a necessary and sufficient condition for ensuring consistency in OOBNs. Since weak conditional independence plays such an important role in OOBNs, in this paper we establish two useful resu...

The viscoelastic character of polymer solutions and melts gives rise to instabilities that are not seen in the flows of Newtonian liquids. In industrial applications such as coating and extrusion, these so-called “elastic” instabilities can impose a limitation on the throughput. Hence, it is important to understand, and if possible, to suppress them. The first instability we study is the phenom...

The fixed points theorems for Rhoades-type contraction mapping were investigated by many authors [1, 5, 8, 10, 13, 16, 22] and the more results on this fields can be found in [2, 4, 9, 11, 15, 23]. Hybrid fixed point theory for nonlinear single-valued and multivalued maps is a new development in the domain of contraction-type multivalued theory (see [3, 7, 10, 12, 14, 17, 18, 20] and references...