Monitoring and analysis of deformations in the earth's crust engineering structures are among important issues geodesy. In order to monitor deformations, a geodetic network consisting reference object points is created general. Deformation research carried out by analyzing movements at points. Measurements for determination these can be made with classical techniques as well GNSS techniques. Th...

For a non-trivial connected graph G, a set S ⊆ V (G) is called an edge geodetic set of G if every edge of G is contained in a geodesic joining some pair of vertices in S. The edge geodetic number g1(G) of G is the minimum order of its edge geodetic sets and any edge geodetic set of order g1(G) is an edge geodetic basis. A connected edge geodetic set of G is an edge geodetic set S such that the ...

Geodesy is the science of the measurement and mapping of the Earth’s surface, and in this context it is also the science that defines and realizes coordinates and associated coordinate systems. Geodesy thus is the foundation for all applications of GNSS. This chapter presents the reference systems needed to describe coordinates of points on the Earth’s surface or in near space and to relate coo...

Dynamic datums, which account for crustal dynamics, are widely used in Australia and New Zealand, although in many cases users may not be aware that they are using such a datum. The most widely-used global dynamic datums in Australia and New Zealand are the International Terrestrial Reference Frame (ITRF) and the World Geodetic System 1984 (WGS84). The use of WGS84 presents particular challenge...

The Problem: Since the advent of satellite positioning users have been faced with the need to transform coordinates delivered by the satellite based systems to those based on the national geodetic system of the country or area concerned. Transformations between Co-ordinate Reference Systems based on different geodetic datums (sometimes colloquially referred to as “datum shifts”) used within oil...

Let G be a connected graph. For two vertices u and v in G, a u–v geodesic is any shortest path joining u and v. The closed geodetic interval IG[u, v] consists of all vertices of G lying on any u–v geodesic. For S ⊆ V (G), S is a geodetic set in G if ⋃ u,v∈S IG[u, v] = V (G). Vertices u and v of G are neighbors if u and v are adjacent. The closed neighborhood NG[v] of vertex v consists of v and ...

A new and efficient algorithm is presented for the coordinate transformation problem of massively three-dimensional networks formed, e.g., by the atoms of crystal fragments or molecular clusters. The new algorithm is based on a divide-and-conquer technique to perform iterative coordinate transformation, applicable even for three-dimensional networks, with linear scaling memory and near linear s...

This paper presents a new iterative algorithm as an upgrade to sufficient LMI conditions for the H∞ static-output-feedback (SOF) control of discrete-time systems. Based on an analysis of the structures of the coordinate transformation matrix and the Lyapunov matrix, the open question of how to fix the Lyapunov matrix structure raised by G. I. Bara and M. Boutayeb is replaced with the question o...