We answer a question due to A. Myasnikov by proving that all expected ranks occur as the ranks of intersections of finitely generated subgroups of free groups. Mathematics Subject Classification (2000): 20E05 Let F be a free group. Let H and K be nontrivial finitely generated subgroups of F . It is a theorem of Howson [1] that H ∩K has finite rank. H. Neumann proved in [2] that rank(H ∩K)− 1 ≤ ...

The truncated singular value decomposition (TSVD) is a popular method for solving linear discrete ill-posed problems with small to moderately sized matrix A. This replaces the A by closest Ak of low rank k, and then computes minimal norm solution system equations rank-deficient so obtained. modified TSVD (MTSVD) improves method, replacing that closer than in unitarily invariant has same spectra...

Let P1, ..., Pk be a collection of disjoint point sets in < 2 in general position. We prove that for each 1 ≤ i ≤ k we can find a plane spanning tree Ti of Pi such that the edges of T1, ..., Tk intersect at most (k − 1)(n− k) + (k)(k−1) 2 , where n is the number of points in P1 ∪ ...∪Pk. If the intersection of the convex hulls of P1, ..., Pk is non empty, we can find k spanning cycles such that...

This paper describes an algorithm to compute the envelope of a set of points in a plane, which generates convex or non-convex hulls that represent the area occupied by the given points. The proposed algorithm is based on a k-nearest neighbours approach, where the value of k, the only algorithm parameter, is used to control the “smoothness” of the final solution. The obtained results show that t...

Consider a nite non-vertical, and non-degenerate straight-line segment s = s0; s1] in the Euclidian plane E 2. We give a method for constructing the boundary of the upper convex hull of all the points with integral coordinates below (or on) s, with abscissa in x(s0); x(s1)]. The algorithm takes O(log n) time, if n is the length of the segment. We next show how to perform a similar construction ...

Let R be a commutative local k-algebra of Krull dimension one, where k is field. α automorphism R, and define S to the skew polynomial algebra R[θ;α]. We offer, under some additional assumptions on criterion for have injective hulls all simple S-modules locally Artinian - that is, satisfy property (⋄). It easy well known if finite order, then has this property, but in order get when infinite we...

Abstract Define the k -th Radon number $$r_k$$ r k of a convexity space as smallest (if it exists) for which any set points can be partitioned into parts whose convex hulls intersect. Combining recent abstract fractional Helly theorem Holmsen and Lee with earlier method...

Hard-chine boats are usually intended for high-speed regimes where they operate in the planing mode. These often designed to be relatively light, but there special applications that may occasionally require fast heavily loaded. In this study, steady-state hydrodynamic performance of nominal-weight and overloaded hard-chine hulls calm water is investigated with computational fluid dynamics solve...