a mapping $f:v^n longrightarrow w$, where $v$ is a commutative semigroup, $w$ is a linear space and $n$ is a positive integer, is called multi-additive if it is additive in each variable. in this paper we prove the hyers-ulam stability of multi-additive mappings in 2-banach spaces. the corollaries from our main results correct some outcomes from [w.-g. park, approximate additive mappings i...

We introduce a scheme to simplify a multi-valued network using redundancy removal techniques. Recent methods [1], [2] for binary redundancy removal avoid the use of state traversal. Additionally, [2] finds multiple compatible redundancies simultaneously. We extend these powerful advances in the field of binary redundancy removal to perform redundancy removal for multi-valued networks. First we ...

MOTIVATION The size, dimensionality and the limited range of the data values make visualization of single nucleotide polymorphism (SNP) datasets challenging. The purpose of this study is to evaluate the usefulness of 3D VizStruct, a novel multi-dimensional data visualization technique for analyzing patterns in SNP datasets. RESULTS VizStruct is an interactive visualization technique that redu...

We prove the existence of solutions for third-order nonconvex state-dependent sweeping process with unbounded perturbations of the form: −A x 3 t ∈ N K t, ẋ t ; A ẍ t F t, x t , ẋ t , ẍ t G x t , ẋ t , ẍ t a.e. 0, T , A ẍ t ∈ K t, ẋ t , a.e. t ∈ 0, T , x 0 x0, ẋ 0 u0, ẍ 0 υ0, where T > 0, K is a nonconvex Lipschitz set-valued mapping, F is an unbounded scalarly upper semicontinuous convex set-v...

In this paper, the chaotic behavior of a set-valued mapping F : X → 2 , where X is a compact space, is investigated. The existence of the generalized shadowing property in the hyperspace 2 is proved. Based on the generalized shadowing property of the set-valued mappings F and the assumption of the existence of an unstable chain recurrent point of the mapping F , it is shown that the Bernoulli s...

Let I be a finite or infinite index set, let X be a topological space, and let Yi, φNi i∈I be a family of FC-spaces. For each i ∈ I, letAi : X → 2i be a set-valued mapping. Some new existence theorems of maximal elements for a set-valued mapping and a family of set-valued mappings involving a better admissible set-valuedmapping are established under noncompact setting of FC-spaces. Our results ...

Multi-Valued Symbolic Model-Checking: Fairness, Counter-Examples, Running Time Arie Gurfinkel Master of Science Graduate Department of Computer Science University of Toronto 2003 Multi-valued model-checking is an effective technique for reasoning about systems with incomplete or inconsistent information. In particular, it is well suited for reasoning about abstract, partial, and feature-based s...