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In this paper, we present new variants of some known fixed point theorems and new fixed point results for cyclic operators on ordered sets, on distance spaces, and on ordered distance spaces. Some results in terms of the fixed point structures are also presented. Our results include existence, uniqueness, convergence of successive approximations, well posedness of fixed point problems and the Ostrowsky property. We also identify some of the main research directions regarding cyclic operators and formulate several open problems for each of them. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of diagonal operator, we present the historical roots of diagonal operators and we give some fixed point theorems for this class of operators. Our approaches are based on the weakly Picard operator technique, difference equation techniques, and some fixed point theorems for multi-valued operators. Some applications to differential and integral equations are given. We also present some research directions. [ABSTRACT FROM AUTHOR]

Old geological maps are extremely important sources of information about the state of geological knowledge of a specific period. Using GIS techniques, the old geological data and concepts can be compared and analyzed together with modern ones. Thus, the aim of this work is to present some old Transylvanian geological maps from the second half of the nineteenth century, with special respect to their legend and topographic basis, as well as to discuss the georeferencing methods and results in order to incorporate them into a unified GIS database. The geological maps of this study are the followings: the geognostic map of the Habsburg Empire by Haidinger (Geognostische Uibersichts-Karte der Oesterreichischen Monarchie 1845); the geological map of Transylvania by Hauer et al. (General-Karte des Grossfürstenthums Siebenbürgen und der im Jahre 1861 mit dem Königreiche Ungarn vereinigten Theile 1863); the geological map of the Habsburg Empire by Hauer (Geologische Übersichts-Karte der Österreichisch−Ungarischen Monarchie nach den Aufnahmen der k. k. geologischen Reichsanstalt 1867-1871); the geological map of the Seklerland by Herbich (A Székelyföld földtani térképe 1878a). These maps were compiled using as topographic basis the map sheets of the 1st and 2nd Military Survey of the Habsburg Empire (later Austro-Hungarian Monarchy). [ABSTRACT FROM AUTHOR]

In the delimitation of flood-prone areas, particularly in areas that are difficult to access using traditional flight equipment, the most critical problem is the generation of a high-quality DEM of the major and minor riverbed, in order to obtain several hydraulic parameters (e.g., the surface of the drainage section, average water velocity) with equivalent accuracy. The chosen area for the case study represents one with the greatest history of hydrological risk factors in the Someşul Mic basin, given the extreme previous hydrological events that have taken place (e.g., in the year 1995) as well as the limited capacity of the river for upstream river flow, and to handle the volume of the flash floods. In this study, the use of UAV technology coupled with Leica MultiStation for validation made it possible to achieve this performance. Another advantage was the existence of the hydrometric station situated in the middle of the study area, the information from which was used for statistics, calibration of the measurements and validation of the results obtained (roughness of the riverbed, the debit with an overflow possibility). The hydraulic calculations performed on the 11 transverse profiles, conducted using the GIS terrain model, led to the high accuracy defining of the flood-prone areas corresponding to the flows in the major riverbed with probabilities of 1 and 5 %. Also highlighted on the 2D and 3D images were several civilian areas at risk in the case of extreme hydrological events, related to maximum flow. [ABSTRACT FROM AUTHOR]

In this paper, we will present some fixed set and fixed point theorems for nonself multivalued generalized contractions. We will discuss the cases of multivalued contractions, multivalued φ-contractions and multivalued Kannan contractions. Our results propose some existence, uniqueness and related properties of the multivalued fractal generated by iterative multifunction systems. The approach is based on some new properties proved for the multi-fractal operator induced by a nonself multivalued generalized contraction. Some open problems are also formulated. [ABSTRACT FROM AUTHOR]

Recently, due to more than a decade of magnetic measurements obtained from LEO (low Earth orbit) satellites, more robust global geomagnetic field models have been produced. Generally, these models are based on data selected on specific criteria, as night-side and quiet-time measurements to get the best possible description of the internal contributions and to minimise the ionospheric and magnetospheric effects. Despite recent efforts, the external fields contributions remain poorly modelled and clearly understood. Here, we propose to estimate the unmodelled signals mainly linked to the external magnetic fields. We compute residuals from the available day-time and night-time original CHAMP (CHAllenging Minisatellite Payload) satellite data and GRIMM-3 model. The post-processing of residuals and the residuals distribution for all geomagnetic field components offer us the possibility to investigate some of their specific features, important to be considered when internal field models are computed. [ABSTRACT FROM AUTHOR]