We introduce in this paper a notion of continuity in digital spaces which extends the usual notion of digital continuity. Our approach uses multivalued maps. We show how the multivalued approach provides a better framework to define topological notions, like retractions, in a far more realistic way than by using just single-valued digitally continuous functions. In particular, we characterize t...

This paper describes an efficient simulator for state transition analysis of multivalued continuous-time neural networks, where the multivalued transfer function of neuron is regarded as a stepwise constant one. Use of stepwise constant method enables to analyse the state transition of the network without solving explicitly the differential equations. This method also enables to select the opti...

In the relational model of data the Fourth Normal Form condition guarantees the elimination of data redundancy in terms of functional and multivalued dependencies. For efficient means of data processing the industry standard SQL permits partial data and duplicate rows of data to occur in database systems. Here, the combined class of uniqueness constraints, functional and multivalued dependencie...

Coherent manipulation of spin ensembles is a key issue in the development of spintronics. In particular, multivalued spin switching may lead to new schemes of logic gating and memories. This phenomenon has been studied with atom vapours 30 years ago, but is still awaited in the solid state. Here, we demonstrate spin multistability with microcavity polaritons in a trap. Owing to the spinor natur...

8 Browder, F. E., "Strongly nonlinear parabolic boundary value problems," Amer. J. Math., in press. 9 Browder, F. E., "Nonlinear elliptic boundary value problems, II," Trans. Amer. Math. Soc., in press. 10 Browder, F. E., "Nonlinear equations of evolution," Ann. of Math., in press. 11 Browder, F. E., "On a theorem of Beurling and Livingston," Canad. J. Math., in press. 12 Browder, F. E., "Multi...

A connectionist model made up of a combination of RBF networks is proposed the model decomposes multivalued dependencies into local single valued functions theory and applications are presented

We extend the result on the equivalence between functional and multivalued dependencies in relational databases and a fragment of propositional logic. It is shown that this equivalence still holds for functional and multivalued dependencies in databases that support complex values via nesting of records and lists. The equivalence has several implications. Firstly, it extends a well-known result...

Functional dependencies (FDs) and multivalued dependencies (MVDs) play a fundamental role in relational databases where they provide semantics for the data and at the same time are the foundation for database design. Since XML documents are closely coupled with relational databases in that XML documents are typically exported and imported from relational databases, the study of FDs and MVDs in ...

In this paper, we introduce an iteration scheme for two multivalued maps in Kohlenbach hyperbolic spaces. This extends the single-valued iteration process due to Agarwal et al. (J. Nonlinear Convex Anal. 8(1):61-79, 2007). Using this new algorithm, we approximate common fixed points of two multivalued mappings through -convergence and strong convergence under some weaker conditions. A necessary...

This paper is concerned with the existence of mild solutions to a class of semilinear differential inclusions with nonlocal conditions. By using the fixed point theory for multivalued maps, we get some general results on nonlocal differential inclusions, which include some recent results on nonlocal problems as special cases. An example of partial differential equations is provided to illustrat...