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 ...

A two-dimensional depth-integrated theory is derived for the gravity-driven free surface flow of cohesionless granular avalanches over complex shallow basal topography. This is an important extension of the one-dimensional Savage–Hutter theory. A simple curvilinear coordinate system is adopted, which is fitted to the ‘mean’ downslope chute topography. This defines a quasi-two-dimensional refere...

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...

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 numerical simulation of steady and unsteady two-dimensional flows past cylinder with dimples based on highly accurate pseudospectral method is the subject of the present paper. The vorticity and streamfunction formulation of two-dimensional incompressible NavierStokes equations with no-slip boundary conditions is used. The system is formulated on a unit disk using curvilinear body fitted coor...

Adaptive mesh refinement (AMR) computations are complicated by their dynamic nature. The development of solvers for realistic applications is complicated by both the complexity of the AMR and the geometry of realistic problem domains. The additional complexity of distributed memory parallelism within such AMR applications most commonly exceeds the level of complexity that can be reasonable main...

In this paper a new method for calculating of electric fields intensity around or inside any arbitrary shape electrode systems or conductors with the same or different configuration have been presented. As we know that in design and construction of a high voltage equipment, analysis of electric field intensity around and or inside that equipment has very important role therefore, according to p...