On the continuous dependence of the solution of a boundary value problem on boundary conditions. Elements of p-regularity theory

The problem of the existence of a continuous dependence of the solution of a boundary value problem on a parameter is considered. In this paper, it is proved that, in the presence of the p-regularity property, there exists a solution that continuously depends on a small parameter. The main result of the paper is based on theorems representing different versions of the implicit function theorem. In the case of degenerate mappings, the theorems are used to analyze a boundary value problem with a small parameter. In the case of absolute degeneration, a -p-factor operator is found. The concept of the p-kernel of the operator is introduced, as well as the left and right inverse operators. Theorems are formulated that are special versions of the generalized Lyusternik theorem and the implicit function theorem in the degenerate case. An implicit function theorem is formulated and proved in the case of a nontrivial kernel.</jats:p

Conceptual model of geotechnical information system

Geological, geodynamical and hydrological research in Zagreb area resulted in several spatial data of different lineage, coordinate systems and resolution. The goal of this paper is the gathering of data in a unique geotechnical information system, which will br the basis for further analysis. We are using ArcGIS modules for spatial and geostatistical analysis. Geotechnical information systems can be used to prevent, mitigate and alleviate damage caused by the natural disasters such as eartquakes and landslides. However, the geotechnical data bases have not been utilized extensively. Examples of using the data bases this chapter for seismic hazards assessment, planning for new structures, ground water hydrology, disaster mitigation systems of gas pipelines, and infrastructure management systems are presented

Precise geodetic and hydrographic measurements in Karst areas

Recent advances in GPS-technology (GNSS) enable hydrographic surveyors to capture the topography of the bottom and the water surface with even more accuracy. Faculty of Geodesy, University of Zagreb, recently acquired the latest technology for performing the precise hydrographic surveying: Trimble R8 GNSS receiver that is going to be used with already used echo sounding equipment. The GSM signals are used for transmitting corrections from the base station to the rover. Thus, it is possible to use single-frequency DESO 14 for two-frequencies bathymetry through repeating the course of the vessel on exactly the same points with both transducers. It is expected that the new technology shall yield more accurate results and increase measurement speed, because the OTF times should be significantly shortened

Application of 3D terrestrial laser scanning in geodynamic monitoring

During last 10 years, geodesists from the Faculty of Geodesy, University of Zagreb, together with geologists and tectonicians established and performed a number of series of GPS-measurements on the Geodynamic Network of the City of Zagreb. The results of these campaigns emphasized the spots with higher level of geodynamic activity, resulting in damages on objects: houses, walls, churches. Therefore, the technology of threedimensional laser scanning has been employed in order to capture much more detailed picture of fast movements. In the first experimental phase of the project, only rapidly sliding areas are observed. The main hypothesis of proposed research is to check if the technology of precise laser scanning is able to produce comparable point clouds showing the movements of objects in the field. As an additional source of information, this research should contribute to the better understanding of the processes below the Earth surface

Geology, tectonics, geodesy and geodynamics of Croatia

This paper summarizes recent research activities on merging the geodetic, geologic and neotectonic evidence of geodynamics in Croatia. The area of the City of Zagreb, which is the boundary zone of Eastern Alps, Dinnarides and Pannonian Basin is included as well. It is shown here that the evidence for fractures of Eastern Adriatic differs from the previous hypotheses. This conclusion is derived from the results of various geodetic measurements: satellite positioning (GPS), astro-geodetic measurements of deflections of the vertical. These results are combined with geologic measurements and results of seismic activity studies in order to give more detailed and more accurate picture of the current situation in the tectonically very active region of Dinnarides. Several GPS-campaigns performed in the City of Zagreb area are examined as well. Due to the proximity of Croatian capitol, special attention has been paid to the effects of possible hazard on construction code

Geodesy, tectonics and geodynamics of Dinnarides

This paper summarises recent aetivities on merging the geodetic, geologic and neotectonic evidence of geodynamics in Croatian part of Dinnarides. The area of the City of Zagreb, which is the boundary zone of Eastern Alps, Dinnarides and Pannonian Basin is incIuded as well. It is shown here that the evidence for fractures of Eastern Adriatic differs from the previous hypotheses. This concIusion is derived from the results of various geodetic measurements: satellite positioning (GPS), astro-geodetic measurements of detlections of the vertical. These results are combined with geologic measurements and results of seismic activity studies in order to give more detailed and more accurate picture of the current situation in the tectonically very active region of Dinnarides. Several GPS-campaigns performed in the City of Zagreb area are examined as well. Due to the proximity of Croatian capitol, special attention has been paid to the effects of possible hazard on construction code