The article deals with spaces the geometry of which is defined by cyclic and anticyclic algebras. Arbitrary multiplicative function is taken as a fundamental form. Motions are given as linear transformation preserving given multiplicative function.
A real matrix is a G-matrix if is nonsingular and there exist nonsingular diagonal matrices and such that , where denotes the transpose of the inverse of . Denote by a diagonal (signature) matrix, each of whose diagonal entries is or . A nonsingular real matrix is called -orthogonal if . Many connections are established between these matrices. In particular, a matrix is a G-matrix if and only if is diagonally (with positive diagonals) equivalent to a column permutation of...
PageRank is a ranking method that assigns scores to web pages using the limit distribution of a random walk on the web graph. A fibration of graphs is a morphism that is a local isomorphism of in-neighbourhoods, much in the same way a covering projection is a local isomorphism of neighbourhoods. We show that a deep connection relates fibrations and Markov chains with restart, a particular kind of Markov chains that include the PageRank one as a special case. This fact provides constraints on the...
For , it is said that is g-tridiagonal majorized by (and it is denoted by ) if there exists a tridiagonal g-doubly stochastic matrix such that . In this paper, the linear preservers and strong linear preservers of are characterized on .
A new technique for query reformulation that assesses the relevance of retrieved documents using weight propagation is proposed. The technique uses a Guided Local Search (GLS) in conjunction with the latent semantic indexing model (to semantically cluster documents together) and Lexical Matching (LM). The GLS algorithm is used to construct a minimum spanning tree that is later employed in the reformulation process. The computations done for Singular Value Decomposition (SVD), LM and the minimum...