We consider the system of equations governing an incompressible immiscible two-phase flow within an heterogeneous porous medium made of two different rock types. Since the capillary pressure function depends on the rock type, the capillary pressure field might be discontinuous at the interface between the rocks. We introduce multivalued phase pressures to give a sense to the transmission condit...

Machine learning on linked data is strongly dependent on the selection of high quality data features to achieve good results and build reusable and generalizable models. In this work, we explore the problem of representing multivalued relations in a suitable form for machine learning while keeping the human comprehensibility of the resulting model. Specifically, we propose the use of a binary v...

We consider five different types of systems of generalized vector quasi-equilibrium problems and establish relationships among them by using different kinds of generalized pseudomonotonicities. We prove the existence of their solutions under lower semicontinuity for a family of multivalued maps involved in the formulation of these problems. The existence of solutions of these problems is also i...

in this paper,  we introduce the notion of  generalized multivalued  $f$- weak contraction and we prove some fixed point theorems related to introduced  contraction for multivalued mapping in complete metric spaces.  our results extend and improve the results announced by many others with less hypothesis. also, we give some illustrative examples.

In order to expand the simulation scale of smart substation, a simulation model of the inlet-outlet line unit, as described by the 0/108 S conductance for multivalued coefficients pre-storage is presented in this paper. As a part of orders decomposition, the address conversion circuit for multivalued coefficients can reduce the computational burden of processing elements. For the convenience of...

The existence of martingale selectors for a multivalued supermartin-gale with continuous parameter is proved.We also prove the weak regularity of multivalued supermartingales.Using the regularity of Banach-valued martingales,we show a multivalued supermartingale has a cadlag modiication under Kuratowski convergence. x1. Introduction Multivalued martingales and supermartingales with discrete par...