Given a set S of n points in the plane, we compute in time O(n) the total number of convex polygons whose vertices are a subset of S. We give an O(m n) algorithm for computing the number of convex k-gons with vertices in S, for all values k = 3; : : : ;m; previously known bounds were exponential (O(ndk=2e)). We also compute the number of empty convex polygons (resp., k-gons, k m) with vertices ...

Let D be a 1-dimensional Prüfer domain with exactly two maximal ideals. We completely determine the star operations and the semistar operations on D. Let G be a torsion-free abelian additive group. If G is not discrete, G is called indiscrete. If every non-empty subset S of G which is bounded below has its infimum inf(S) in G, then G is called complete. If G is not complete, G is called incompl...

Let M be a complete metric ANR-space such that for any metric compactum K the function space C(K,M) contains a dense set of Bing (resp., Krasinkiewicz) maps. It is shown that M has the following property: If f : X → Y is a perfect surjection between metric spaces, then C(X,M) with the source limitation topology contains a dense Gδ-subset of maps g such that all restrictions g|f(y), y ∈ Y , are ...

If a group Γ is generated by a finite subset 5, then one has the "growth function" gs, where gs(m) is the number of distinct elements of Γ expressible as words of length <m on 5. Roughly speaking, J. Milnor [9] shows that the asymptotic behaviour of gs does not depend on choice of finite generating set S c Γ, and that lower (resp. upper) bounds on the curvature of a riemannian manifold M result...

Given a von Neumann algebra M denote by S(M) and LS(M) respectively the algebras of all measurable and locally measurable operators affiliated with M. For a faithful normal semi-finite trace τ on M let S(M, τ) (resp. S0(M, τ)) be the algebra of all τ -measurable (resp. τ -compact) operators from S(M). We give a complete description of all derivations on the above algebras of operators in the ca...

For problems SAT and MAX SAT, local search algorithms are widely acknowledged as one of the most e ective approaches. Most of the local search algorithms are based on the 1ip neighborhood, which is the set of solutions obtainable by ipping the truth assignment of one variable. In this paper, we consider rip neighborhoods for r 2, and propose, for r = 2; 3, new implementations that reduce the nu...

We show that Szepietowski’s system of generators [8] for the mapping class group of the non-orientable surface is the minimal generating set by Dehn twists and Y -homemorphisms. Let Ng be a non-orientable surface which is a connected sum of g projective planes. We assume that g ≥ 4. Let M(Ng) be the group of isotopy class of homeomorphisms over Ng, i.e, the mapping class group of Ng. We introdu...

We develop a theory of stratified $LM$-filters which generalizes the theory of stratified $L$-filters. Our stratification condition explicitly depends on a suitable mapping between the lattices $L$ and $M$. If $L$ and $M$ are identical and the mapping is the identity mapping, then we obtain the theory of stratified $L$-filters. Based on the stratified $LM$-filters, a general theory of lattice-v...

in this paper, we give some new definitions of m-fuzzy metric spaces and we prove a common fixed point theorem for six mappings under the condition of weakly compatible mappings in complete m-fuzzy metric spaces.