Gravity Recovery and Climate Experiment (GRACE) mission data is widely used in various fields of science. GRACE explored changes of the gravity field regularly from April 2002 to June 2017. In the following research, we examine variance of signal contained in two different formats of GRACE data: standard spherical harmonics and mass concentration blocks (so-called “mascons”) solutions, both provided in the most recent releases. For spherical harmonics-based solution, we use monthly gravity field solutions provided up to degree and order (d/o) 96 by three different computing centers, i.e. the NASA’s Jet Propulsion Laboratory (JPL), the German Research Center for Geosciences (GFZ) and the Center for Space Research (CSR). For the mass concentration blocks, we use values of total water storage provided by the CSR, JPL and the Goddard Space Flight Center (GSFC) computing centers, which we convert to spherical harmonic coefficients up to d/o 96. We show that using the anisotropic DDK3 filter to smooth the north-south stripes present in total wate storage obtained from standard spherical harmonics solution leaves more information than common isotropic Gaussian filter. In the case of mascons, GSFC solution contains much more information than the CSR and JPL releases, relevant for corresponding d/o. Differences in variance of signal arise from different background models as well as various shape and size of mascons used during processing of GRACE observations.
The focus of the paper is the historical comparison of E fist and P pięść from the perspective of diachronic phonology. The paper specifically addresses the issue of the phonological development of this pair of cognates. The main aim is to explain the relatedness and differentiations of the modern reflexes of the original Proto-Indo-European roots and to account for their different phonological developments in both languages with a view to understanding the connection between the contemporary cognates. These aims are realised by means of searching for sound changes that explain the discrepancy in the phonological shapes of modern cognates and collecting other pairs of cognates that demonstrate the effect of theses sound changes. As the result of the historical and comparative analysis, it is argued that some of the Proto-Germanic reconstructions are more likely than others and in conclusion the most probable development of the two cognates is outlined in the chronological order. It is remarkable that the cognates of the compounds pięść / fist are to be found almost exclusively in Slavic and Germanic and the effect of their development resembles blending.
The formulation of a plate finite element with so called ‘physical’ shape functions is revisited. The derivation of the ‘physical’ shape functions is based on Hencky-Bollé theory of moderately thick plates. The considered finite element was assessed in the past, and the tests showed that the solution convergence was achieved in a wide range of thickness to in-plane dimensions ratios. In this paper a holistic correctness assessment is presented, which covers three criteria: the ellipticity, the consistency and the inf-sup conditions. Fulfilment of these criteria assures the existence of a unique solution, and a stable and optimal convergence to the correct solution. The algorithms of the numerical tests for each test case are presented and the tests are performed for the considered formulation. In result it is concluded that the finite element formulation passes every test and therefore is a good choice for modeling plate structural elements regardless of their thickness.