The construction of an efficient tree structure should take into account parameters which can be optimised. Coverage of a node, "dead area" of a node and overlap between nodes are examples of such parameters. Taking these parameters under account is important since minimization of a node coverage leads to more precise searching within the tree, minimization of a node "dead area" reduces the num...

Using laser tweezers, we study colloidal interactions of solid microspheres in the nematic bulk caused by elastic distortions around the particles with tangential surface anchoring. The interactions overcome the Brownian motion when the interparticle separation r-->p is less than 3 particle diameters. The particles attract when the angle theta between r-->p and the uniform far-field director n0...

We consider an expression for the probability R=P(Y<X) where random variables X and Y denote strength stress, respectively. Our aim is to study effect of dependency between on R. assume that follow exponential distributions their modeled by a copula with parameter theta. obtain closed-form R Farlie-Gumbel-Morgenstern (FGM), Ali-Mikhail-Haq (AMH), Gumbel's bivariate copulas compute Gumbel-Hou...

We find identities between theta constants with rational characteristics evaluated at period matrix of R, a cyclic 3 sheeted cover of the sphere with 3k branch points λ1...λ3k. These identities follow from Thomae formula [BR]. This formula expresses powers of theta constants as polynomials in λ1...λ3k. We apply the representation of the symmetric group to find relations between the polynomials ...

The high data availability and the increasing number of GIS users have motivated the emergence of distributed algorithms to process spatial operations efficiently. They are based on distributed indexes for an high performance processing. Researches and ongoing work use R-trees as a distributed spatial structure for indexing and retrieval of geo objects. However, these indexes have shown a chall...

Motivated by the work of Leininger on hyperbolic equivalence of homotopy classes of closed curves on surfaces, we investigate a similar phenomenon for free groups. Namely, we study the situation when two elements g, h in a free group F have the property that for every free isometric action of F on an R-tree X the translation lengths of g and h on X are equal.

In a visualization system, one of the key issues is to optimize performance and visual fidelity. This is especially critical for large virtual environments where the models do not fit into the memory. In this paper, we present a novel structure called HDoV-tree that can be tuned to provide excellent visual fidelity and performance based on the degree of visibility of objects. HDoV-tree also exp...

We prove that if T is an R-tree with a minimal free isometric action of FN , then the Out(FN )-stabilizer of the projective class [T ] is virtually cyclic. For the special case where T = T+(φ) is the forward limit tree of an atoroidal iwip element φ ∈ Out(FN ) this is a consequence of the results of Bestvina, Feighn and Handel [6], via very different methods. We also derive a new proof of the T...

of D is an R-tree. (ii) There exists a tree (V, E ) whose vertex set V contains X, and an edge weighting C : E -i R that assigns a positive length C(e) to each edge e in E , such that D is the restriction of X to the shortest-path metric induced on V. (iii) There exists a map w : S(X) -i R>o from the set S(X) of all bi-partitions or splits of X into the set R ~ o of non-negative real numbers su...