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GEM International Journal on Geomathematics Appendix A GEM International Journal on Geomathematics As already pointed out, the special importance of mathematics as a basic science that makes important contributions in technology, economy, and commerce has been increasingly acknowledged within the last few years. This process did not remain without effects on mathematics itself. New mathematical disciplines, such as scientific computing, financial and business mathematics, industrial mathematics, biomathematics, and also mathematics concerned with geoscientific problems, i.e., geomathematics, have complemented the traditional mathematical disciplines. Mathematics is the “raw material” for the models and the essence of each computer simulation. As the key technology, it translates images of the real world to models of the virtual world, and vice versa. GEM—International Journal on Geomathematics, ISSN: 1869–2672 (print version), ISSN: 1869–2680 (electronic version), https://www.springer.com/ mathematics/applications/journal/13137, was launched in August 2010 as a forum for peer-reviewed mathematical papers that 1. model the system Earth (geosphere, cryosphere, hydrosphere, atmosphere, bio- sphere), or 2. contain analytic, algebraic, and operator-theoretic methods necessary for the mathematical treatment of geoscientifically relevant problems, or 3. apply geospecific computational and numerical analysis methods, or 4. represent survey contributions characterizing the bridge between a geoscientifi- cally relevant research field and mathematics. A.1 GEM and Its Task and Objective The intent of the mathematical journal GEM is to deal with the qualitative and quan- titative properties of the current or possible structures of the system Earth. GEM provides concepts of scientific research concerning the system Earth. The research © The Author(s), under exclusive license to Springer Nature Switzerland AG 2019 93 W. Freeden et al., An Invitation to Geomathematics, Lecture Notes in Geosystems Mathematics and Computing, https://doi.org/10.1007/978-3-030-13054-1 94 A GEM International Journal on Geomathematics Earth‘ s System Mathematics (Gravitation, Magnetism, Deformation, etc.) Fluid Dynamics (Ocean, Atmosphere, etc.) Ill-Posed and GEM Inverse Problems Differential- and Integral Equations Constructive Approximation Numerical and Computational Methods Fig. A.1 Essential thematic structure of GEM object (cf. Fig. A.1), i.e., the system Earth, consists of a number of elements which represent individual systems themselves. The complexity of the entire system Earth is determined by interacting physical, biological, and chemical processes transforming and transporting energy, material, and information. It is characterized by natural, social, and economic processes influencing one another. All these aspects require a geoscientifically relevant type of mathematics. Geomathematics and its organ GEM have to be concerned with nothing more than the organization of the complexity of the system Earth. Descriptive thinking is required in order to clarify abstract complex situations. Correct simplifications of complicated interactions, exact thinking and formulations are needed, numerical realizations (modeling and simulation) should be given, etc. All in all, geomathematics represents the key science of the complex system Earth. Wherever there are data and observations to be processed, e.g., the diverse scalar, vectorial, and tensorial clusters of satellite A.3 GEM and Its Editorial Structure 95 and exploration data, we need geomathematics. Whenever modeling and simulation come into play for the system Earth, geomathematics is decisive. A.2 GEM As Scientific Bridge The specific task of geomathematics and its forum GEM is to build a bridge between mathematical theory and geophysical as well as geotechnical practice. The special attraction is based on the vivid communication between mathematicians more interested in model development, theoretical foundation, and the approximate as well as computational solution of problems, and engineers and physicists more familiar with measuring technology, methods of data analysis, implementation of routines, and software applications. A special feature is that geomathematics primarily deals with those regions of the Earth which are only insufficiently or not at all accessible for direct measurements (even by remote sensing methods). Inverse theories and methods are absolutely essential for the mathematical evaluation in these cases. Mostly, a physical field is measured in the vicinity of the Earth’s surface and/or satellite height, and it has then to be continued downward or upward by mathematical methods until one reaches the interesting depths or heights. For all these aspects GEM provides an adequate forum for scientific distribution among mathematically oriented people. A.3 GEM and Its Editorial Structure GEM is intended to publish peer-reviewed mathematical papers and survey articles of geoscientific relevance. The relevance does not include necessarily numerical applications to a real data scenario. Instead all mathematically applicable, i.e., theoretically and/or computationally significant facets and obligations of the Earth’s system are welcome for scientific distribution by means of GEM. In 2017, GEM essentially dealt with the following scientific topics and research areas (cf. Fig. A.1) associated with selected editors: 1. modeling and simulation problems of the system Earth (geosphere, cryosphere, hydrosphere, atmosphere, biosphere, anthroposphere), 2. fluid dynamics problems (e.g., ocean currents, atmospheric circulation, etc.), 3. inverse problems (e.g., in satellite technology, geoexploration, etc.), 4. geoscientifically relevant differential and integral equations (concerning systems of potential fields, diffusion fields, wave fields or combinations of them), 5. constructive approximation, 6. numerical methods, efficient and economical computational algorithms and procedures. 96 A GEM International Journal on Geomathematics In addition, the role of GEM as a scientic bridge between geomathematics and other geoscientic disciplines plays a particular, whose articulation is found in survey papers by distinguished geoscientists. Accordingly, in adaptation to the aforementioned list, future editorial work within the GEM-reviewing process will provide a more specific and specialized basis for collecting publishable contributions in certain areas of geomathematics. All in all, the essential goal of the Editor-in-Chief as well as the publisher is that GEM more and more emerges as an active and dynamic journal for the dissemination of creative and innovative ideas and concepts with the motivation to help the mathematically interested readership to understand the Earth as our living environment. As in the last ten years, high mathematical quality in combination with georelevance will be canonically expected from the contributions to the journal. Survey-like articles bridging between mathematical theory and geophysical as well as geotechnical practice constitute complementing research-oriented GEM areas for publication. A.4 Previous Publications in GEM International Journal on Geomathematics Since its launch the journal has published every year between 300 and 400 pages and has established itself as one of the leading journals in its field. Vol. 1, Issue 1 GEM: International Journal on Geomathematics Author: Willi Freeden The ‘Regiments’ of sun and pole star: on declination tables in early modern England Author: Thomas Sonar Randomized anisotropic transform for nonlinear dimensionality reduction Authors: Charles K. Chui, Jianzhong Wang Limit formulae and jump relations of potential theory in Sobolev spaces Authors: Martin Grothaus, Thomas Raskop Regularisation of the Helmholtz decomposition and its application to geomagnetic field modelling Authors: M. Akram, V. Michel Estimation of linear functionals from indirect noisy data without knowledge of the noise level Authors: Sergei V. Pereverzev, Bernd Hofmann A.4 Previous Publications in GEM International Journal on Geomathematics 97 Vol. 1, Issue 2 Delayed progress in navigation: the introduction of line of position navigation in Germany and Austria Author: Günther Oestmann Space gradiometry: tensor-valued ellipsoidal harmonics, the datum problem and application of the Lusternik–Schnirelmann category to construct a minimum atlas Author: Erik W. Grafarend Spline multiresolution and numerical results for joint gravitation and normal-mode inversion with an outlook on sparse regularisation Authors: Paula Berkel, Doreen Fischer, Volker Michel Spherical decompositions in a global and local framework: theory and an application to geomagnetic modeling Author: C. Gerhards Modeling anomalous heat transport in geothermal reservoirs via fractional diffusion equations Authors: Yury Luchko, Alessandro Punzi Vol. 2, Issue 1 Hybrid regularization methods for seismic reflectivity inversion Authors: Yanfei Wang, Yan Cui, Changchun Yang Spatiospectral concentration in the Cartesian plane Authors: Frederik J. Simons, Dong V. Wang Three-dimensional modeling of heat transport in deep hydrothermal reservoirs Author: Isabel Ostermann Spherical fast multiscale approximation by locally compact orthogonal wavelets Authors: Frank Bauer, Martin Gutting A minimal atlas for the rotation group SO(3) Authors: Erik W. Grafarend, Wolfgang Kühnel Vol. 2, Issue 2 Natural convection in horizontal annuli: evaluation of the error for two approxima- tions Authors: Agnes Lamacz, Arianna Passerini, Gudrun Thäter On homogenization of stokes flow in slowly varying media with
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