A classification of dihedral folding tessellations of the sphere whose prototiles are a kite and an equilateral or isosceles triangle was obtained in recent four papers by Avelino and Santos (2012, 2013, 2014 and 2015). In this paper we extend this classification, presenting all dihedral folding tessellations of the sphere by kites and scalene triangles in which the shorter side of the kite is equal to the longest side of the triangle. Within two possible cases of adjacency, only one will be addressed. The combinatorial structure of each tiling is also analysed., Catarina P. Avelino, Altino F. Santos., and Obsahuje bibliografii
The deformation measurements are performed for the purpose of obtaining information concerning ground movement and objects on the ground within given time intervals. For the purpose of improving conventional models of deformation analysis (CDA) it is desirable to use several different methods and also implement alternative proce dures as a further improvement, such as the concept of robust geodetic networks and strain analysis, aimed at obtaining objective information about the movements. In the present paper, in addition to the CDA methods, we also analyze the robust methods in deformation detecting and the method of the strain analysis based on elasticity theory as a supplement to the conventional geometric deformation methods (CDA). The mentioned methods are applied and analysed for the case of a test example of Fruška Gora in Serbia, for which there exist geological and geophysical studies of recent tectonic movements. The measuring results for two measuring epochs concern the GNSS vectors measured by applying the fast static method within closed polygons over a ten-year interval, where only the horizontal movement component is analysed. The efficiency of the applied CDA and robust methods is measured by applying a mean success rate (MSR) by applying Monte Carlo simulations in order to investigate the efficiency of a given methods for a given control network., Zoran Sušić, Mehmed Batilović, Toša Ninkov, Vladimir Bulatović, Ivan Aleksić and Gojko Nikolić., and Obsahuje bibliografické odkazy
We study some geometric properties associated with the t-geometric means A ♯_{t} B:= A^{1/2}(A^{-1/2}BA^{-1/2})^{t} A^{1/2}of two n × n positive definite matrices A and B. Some geodesical convexity results with respect to the Riemannian structure of the n × n positive definite matrices are obtained. Several norm inequalities with geometric mean are obtained. In particular, we generalize a recent result of Audenaert (2015). Numerical counterexamples are given for some inequality questions. A conjecture on the geometric mean inequality regarding m pairs of positive definite matrices is posted., Trung Hoa Dinh, Sima Ahsani, Tin-Yau Tam., and Obsahuje seznam literatury