For upper semicontinuous finite-dimensional set-valued mappings with either convex closed or aspheric closed values we prove the existence of special continuous e -approximations that point-wise converge to a Borel measurable selector of the set-valued mapping as e tends to zero. For convex-valued case the convergence holds on the entire domain while for aspheric-valued case — on a certain coun...

Stock valuation is very important for fundamental investors to select undervalue stocks to earn excess profit. However, it may be difficult to use stock valuation results because different models generate different estimates on the same stock. This suggests that the value of a stock should be multi-valued rather than single-valued. We therefore develop a multi-valued stock valuation model based...

Multi-valued networks provide a simple yet expressive qualitative state based modelling approach for biological systems. In this paper we develop an abstraction theory for asynchronous multi-valued network models that allows the state space of a model to be reduced while preserving key properties of the model. The abstraction theory therefore provides a mechanism for coping with the state space...

We consider a generalized equation governed by strongly monotone and Lipschitz single-valued mapping maximally set-valued in Hilbert space. are interested the sensitivity of solutions w.r.t. perturbations both mappings. demonstrate that directional differentiability solution map can be verified using operator resolvent mapping. The result is applied to quasi-generalized equations which we have ...

A program called MVSIS has been developed which optimizes multi-level multi-valued networks (MV networks). We describe what such a network is and the capabilities contained in MVSIS. MVSIS is modeled after SIS, which synthesizes binary multi-level networks, but the logic network of MVSIS is such that all variables can be multivalued each with its own range. Included in MVSIS are almost all the ...

To understand the function of genetic regulatory networks in the development of cellular systems, we must not only realise the individual network entities, but also the manner by which they interact. Multi-valued networks are a promising qualitative approach for modelling such genetic regulatory networks, providing an interesting compromise between the simplicity of Boolean models and more deta...

When ƒ is single-valued we know that continuity is equivalent to the assertion that A, B closed imply f (A), f~(B) closed. When ƒ is multi-valued we take this as a definition of continuity. I t does not follow, as in the single-valued case, that f~~(B) is open if B is open. These definitions include both a single-valued map ( = continuous function) and its inverse. In this note we show that cer...

The main contributions of this paper is twofold. First, our primary concern to suggest a new iterative algorithm using the P-?-proximal-point mapping technique and Nadler?s for finding approximate solutions system generalized multi-valued nonlinear variational-like inclusions. Under some appropriate conditions imposed on parameters mappings involved in inclusions, strong convergence sequences g...

Landmark based heuristics are among the most accurate current known admissible heuristics for cost optimal planning. Disjunctive action landmarks can be considered as at-least-one constraints on the actions they contains. In many planning domains, there are many critical propositions which have to be established for a number of times. Previous landmarks fail to express this kind of general card...