Let tt : (V, E, W ) be a finite, connected, weighted graph without loops and multiple edges. In a weighted graph each arc is assigned a weight by the weight function W : E +. A u v path P in tt is called a weighted u v geodesic if the weighted distance between u and v is calculated along P . The strength of a path is the minimum weight of its arcs, and length of a path is the number of edges in...

[1] Space-geodetic techniques can detect elastic deformation of the Earth caused by atmospheric pressure loading (ATML). However, it has not yet been demonstrated whether these surface displacements should be accounted for at the time of reduction of the observations or by applying time-averaged values to the coordinates after the analysis of the observations. An analysis of the power spectral ...

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...

A brief Note compiled by: Prof. Madhav N. Kulkarni, IIT Bombay Since the inception of the Very Long Baseline Interferometry (VLBI) system in 1967, this radio interferometry technique has revolutionised the fields of geodesy, geodynamics and astrometry. With the unprecedented precision and resolution made possible by VLBI various tasks such as geodetic positioning, reference frames interconnect...

Buckley and Harary introduced several graphical invariants related to convexity theory, such as the geodetic number of a graph. These invariants have been the subject of much study and their determination has been shown to be NP -hard. We use the probabilistic method developed by Erdös to determine the asymptotic behavior of the geodetic number of random graphs with fixed edge probability. As a...

We show that for every integer k ≥ 2 and every k graphs G1, G2, . . . , Gk, there exists a hull graph with k hull vertices v1, v2, . . . , vk such that link L(vi) = Gi for 1 ≤ i ≤ k. Moreover, every pair a, b of integers with 2 ≤ a ≤ b is realizable as the hull number and geodetic number (or upper geodetic number) of a hull graph. We also show that every pair a, b of integers with a ≥ 2 and b ≥...

Classic convexity can be extended to graphs in a natural way by considering shortest paths, also called geodesics: a set S of vertices of a graph is convex if it contains all the vertices lying in some geodesic with endpoints in S and the convex hull of a set S of vertices is the minimum convex set containing S. Farber and Jamison [9] characterized the graphs such that every convex set is the c...

Due to the relative lack of empirical field data, the response of very small glaciers (here defined as being smaller than 0.5 km2) to current atmospheric warming is not fully understood yet. Investigating their mass balance, e.g. using the direct glaciological method, is a prerequisite to fill this knowledge gap. Terrestrial laser scanning (TLS) techniques operating in the near infrared range c...

the simple method for height determination is spirit leveling. the leveled height differences are path-dependent. ergo height from spirit leveling is not unique. the problem can be solved by converting the path-dependent leveled height differences into unique path-independent height differences (vanicek and krakiwsky, 1986). the difference between the potentials of two close equipotential surfa...