Abstract In this paper we studied the analytic invariants of spherically symmetric space-time by considering various quadruples orthogonal unit vectors α i , β and then some results have been developed there upon. Further it is noticed that, for K spsq = rprq rsrs pqpq 0, p ≠ q r s p, q, r, 1, 2, 3,4, quadruple ( ) vector yield flat geometry if only ρ 5 0. Also pqps 0 g qq psps + ss 0; s, 1; 2;...

A Diophantine m-tuple with the property D(n), where n is an integer, is defined as a set of m positive integers with the property that the product of its any two distinct elements increased by n is a perfect square. It is known that if n is of the form 4k + 2, then there does not exist a Diophantine quadruple with the property D(n). The author has formerly proved that if n is not of the form 4k...

The Delaunay triangulation (DT) is one of the most common and useful triangulations of point sets P in the plane. DT is not unique when P is degenerate, specifically when it contains quadruples of co-circular points. One way to achieve uniqueness is by applying a small (or infinitesimal) perturbation to P . We consider a specific perturbation of such degenerate sets, in which the coordinates of...

Recently, the W3C Linking Open Data effort has boosted the publication and inter-linkage of large amounts of RDF datasets on the Semantic Web. Various ontologies and knowledge bases with millions of RDF triples from Wikipedia and other sources, mostly in e-science, have been created and are publicly available. Recording provenance information of RDF triples aggregated from different heterogeneo...

This thesis presents a framework of a passively replicated transaction manager. By integrating transactions and replication, two well known fault tolerance techniques, the framework provides high availability for transactional systems and better support for non-deterministic execution for replicated systems. A prototype Java implementation of the framework, based on Jgroup/ARM and Jini, has bee...

We prove quantitative versions of the Balog–Szemerédi–Gowers and Freiman theorems in the model case of a finite field geometry F2 , improving the previously known bounds in such theorems. For instance, if A ⊆ F2 is such that |A + A|6 K |A| (thus A has small additive doubling), we show that there exists an affine subspace H of F2 of cardinality |H | K−O( √ K ) |A| such that |A ∩ H |> (2K )−1|H |...

Periods, eccentricities, and masses in hierarchical stellar systems inform us on the formation early evolution of these fascinating objects. To complement multiplicity statistics nearby solar-type stars, 19 new spectroscopic orbits inner subsystems 15 hierarchies (10 triples 5 quadruples) are determined based high-resolution echelle spectra collected during several years. While previous papers ...