We establish the existence of a best proximity pair for which the best proximity set is nonempty for a finite family of multimaps whose product is either an Ac -multimap or a multimap T : A → 2 such that both T and S ◦ T are closed and have the KKM property for each Kakutani multimap S : B → 2. As applications, we obtain existence theorems of equilibrium pairs for free n-person games as well as...

Memory plays a major role in Artificial Neural Networks. Without memory, Neural Network can not be learned itself. One of the primary concepts of memory in neural networks is Associative neural memories. A survey has been made on associative neural memories such as Simple associative memories (SAM), Dynamic associative memories (DAM), Bidirectional Associative memories (BAM), Hopfield memories,...

We claim that monomorphisms in Sets and Groups are the usual injective maps and homomorphisms. First, suppose that f : A → B is a set injection and that fg = gh. Then for all c ∈ C, we have f(g(c)) = f(h(c)) implies g(c) = h(c) by injectivitiy. Hence g = h. Conversely, suppose f : A → B is not an injection. Then let f(a) = f(a′) for some a 6= a′ ∈ A. Then let g(c) = a and h(c) = a′ for all c ∈ ...

3 MSDF syntax 4 3.1 Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.2 Datatype definitions . . . . . . . . . . . . . . . . . . . . . . . 6 3.3 Labels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.4 Semantic transitions . . . . . . . . . . . . . . . . . . . . . . . 10 3.5 Built-in operations on derived and parameterized sets . . . . . 14 3.6 Sequences ...

We consider the problem of computing the distance-dependent two-point function of general planar maps and hypermaps, i.e. the problem of counting such maps with two marked points at a prescribed distance. The maps considered here may have faces of arbitrarily large degree, which requires new bijections to be tackled. We obtain exact expressions for the following cases: general and bipartite map...

Much evidence indicates that the perirhinal cortex is involved in the familiarity discrimination aspect of recognition memory. It has been previously shown under selective conditions that neural networks performing familiarity discrimination can achieve very high storage capacity, being able to deal with many times more stimuli than associative memory networks can in associative recall. The cap...

Skewed-associative caches have been shown to statisticaly exhibit lower miss ratios than set-associative caches at equal associativity degrees. But for L1 caches, the performance of a four-way set-associative cache is known to be quite close to that of a 16-way set-associative cache. In this paper, we rst show that BTBs and L2 caches featuring long line size may beneet a lot from a high associa...