Showing papers by "Hellenic Military Academy published in 2015"

Universal Taylor series on convex subsets of

Abstract: We prove the existence of holomorphic functions defined on any open convex subset, whose partial sums of the Taylor developments approximate uniformly any complex polynomial on any convex compact set disjoint from , and on denumerably many convex compact sets in which may meet the boundary . If the universal approximation is only required on convex compact sets disjoint from, then may be chosen to be smooth on , that is . Those are generic universalities.

Hopf hypersurfaces in pseudo-Riemannian complex and para-complex space forms

Abstract: The study of real hypersurfaces in pseudo-Riemannian complex space forms and para-complex space forms, which are the pseudo-Riemannian generalizations of the complex space forms, is addressed. It is proved that there are no umbilic hypersurfaces, nor real hypersurfaces with parallel shape operator in such spaces. Denoting by J be the complex or para-complex structure of a pseudo-complex or para-complex space form respectively, a non-degenerate hypersurface of such space with unit normal vector field N is said to be Hopf if the tangent vector field JN is a principal direction. It is proved that if a hypersurface is Hopf, then the corresponding principal curvature (the Hopf curvature) is constant. It is also observed that in some cases a Hopf hypersurface must be, locally, a tube over a complex (or para-complex) submanifold, thus generalizing previous results of Cecil, Ryan and Montiel.

Systemic geopolitical modeling. Part 1: prediction of geopolitical events

Abstract: We give two general mathematical models predicting geopolitical events into a geopolitical system according to Mazis’ lakatosian formulation methodology for a Systemic Geopolitical Analysis. To this end, we consider weighted geopolitical indices and their measurements. When the weighted geopolitical indices, as well as the related geopolitical measurements take values in different times and different geographical points, then they form two sets in the four-dimensional Euclidean space. The distance between these sets can be considered as a measure for assessing the occurrence or not of a geopolitical event. To this direction, we give general frameworks of two algorithms for determining the time moments and geographical points at which is expected the appearance of peculiar geopolitical events.

The normal Jacobi operator of real hypersurfaces in complex hyperbolic two-plane Grassmannians

Abstract: The aim of this paper is to introduce the notion of normal Jacobi operator of real hypersurfaces in complex hyperbolic two-plane Grassmannians. Furthermore, results concerning real hypersurfaces in complex hyperbolic two-plane Grassmannians whose normal Jacobi operator satisfies conditions of parallelism will be given.

Security and Formation of Network-Centric Operations

Abstract: After giving definitions and background information of key terms, we report and analyze the multi-layer graph model of network centric operations (NCOs), and we mention its advantages. Moreover, we investigate security problem of NCOs by applying methods of vertex pursuit games. Finally, in Sect. 6 we take up with the problem of network centric warfare strategic formation.

A New Condition on the Structure Jacobi Operator of Real Hypersurfaces in Non-flat Complex Space Forms

Abstract: In this paper a new condition for the Lie derivative of the structure Jacobi operator of real hypersurfaces in non-flat complex space forms is introduced A classification theorem for real hypersurfaces in non-flat complex space forms, whose structure Jacobi operator satisfies this condition and at the same time the commuting condition of the shape operator with the structure Jacobi operator, is presented Furthermore, three-dimensional real hypersurfaces in non-flat complex space forms, whose structure Jacobi operator satisfies the new condition, are classified