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A closed-form analytical method needing no approximation and deduced from a single quartic equation is offered to transform geocentric into geodetic coordinates. It is valid at any point inside and outside the Earth including the ...
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A closed-form analytical method needing no approximation and deduced from a single quartic equation is offered to transform geocentric into geodetic coordinates. It is valid at any point inside and outside the Earth including the polar axis, the equatorial plane and the Earth's center. Comparison with the method of extrema with constraints to obtain this quartic equation is made.
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Manifolds endowed with an affine geometry of general type with nontrivial metric, torsion, and nonmetricity tensor are considered. Such manifolds have recently attracted much attention due to the construction of generalized gravit...
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Manifolds endowed with an affine geometry of general type with nontrivial metric, torsion, and nonmetricity tensor are considered. Such manifolds have recently attracted much attention due to the construction of generalized gravity models. Under the assumption that all geometric objects are real analytic functions, normal coordinates in a neighborhood of an arbitrary point are constructed by expanding the connection and the metric in Taylor series. It is shown that the normal coordinates are a generalization of a Cartesian coordinate system in Euclidean space to the case of manifolds with any affine geometry. Moreover, the components of any real analytic tensor field in a neighborhood of any given point are represented in the form of a power series whose coefficients are constructed from the covariant derivatives and the curvature and torsion tensors evaluated at this point. For constant curvature spaces, these series are explicitly summed, and an expression for the metric in normal coordinates is found. It is shown that normal coordinates determine a smooth surjective mapping of Euclidean space to a constant curvature manifold. The equations for extremals are explicitly integrated in normal coordinates for constant curvature spaces. A relationship between normal coordinates and the exponential mapping is analyzed.
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The derivation of algorithms for the computation of geodetic coordinates from 3D Cartesian coordinates has been a very active field of research among geodesists for more than forty years. Many authors have sought the most efficien...
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The derivation of algorithms for the computation of geodetic coordinates from 3D Cartesian coordinates has been a very active field of research among geodesists for more than forty years. Many authors have sought the most efficient method, i.e. the method that provides the fastest computational speed, which nevertheless yields sufficient accuracy for practical applications. The problem is a special case of a more general mathematical problem that has also been studied by researchers in other fields. This paper investigates the applicability of methods by Sampson (1982, Computer graphics and image processing, 18: 97-108) and Uteshev and Goncharova (2018, Journal of Computational and Applied Mathematics, 328: 232-251) to the computation of geodetic coordinates. Both methods have been modified to make them more suitable for this particular problem. The methods are compared to several commonly used geodetic methods in terms of accuracy and computational efficiency. It is found that a simple modification improves the accuracy of the methods by similar to 3 orders of magnitude, and the modified method of Uteshev and Goncharova (2018) achieves an accuracy of <0.1 mm anywhere on the surface of the Earth. The methods are especially efficient in the computation of ellipsoidal height. As an additional result of this study, a new formulation of the well-known method by Bowring (1976, Survey Review, 23: 323-327) is derived, and it is shown to improve the computation speed of Bowring's method by similar to 12%similar to 27% compared to the conventional formulation.
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? 2022 Elsevier B.V.We report the synthesis and structure of coordination compounds in which betaine acts as a ligand towards Pearson-hard cations. The overall neutral zwitterion was reacted with the corresponding nitrate salts in...
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? 2022 Elsevier B.V.We report the synthesis and structure of coordination compounds in which betaine acts as a ligand towards Pearson-hard cations. The overall neutral zwitterion was reacted with the corresponding nitrate salts in polar protic solvents such as water or methanol or mechanochemically by grinding the reaction partners. Reaction of MgII, CaII, SrII and BaII resulted in the first alkaline earth derivatives of betaine. The products comprise mono- and oligonuclear cations for the light, and cationic chain polymers for the heavy group 2 metals. In the case of CaII, the betaine stoichiometry was decisive for the outcome of the reaction; solids with 1:4 and the less intuitive 3:16 cation to ligand ratio have been structurally characterized. Coordination numbers increase from six for MgII and CaII over seven and eight for the two independent SrII to eight for BaII cations. Coordination of betaine to trivalent Y, La and Pr results in the formation of structurally related dinuclear cations, with coordination numbers eight for Y and nine for the larger lanthanides. Water and betaine compete for coordination; aqua ligands prevail for the smaller, betaine for the larger cations. Betaine coordination to all these hard cations occurs in various modes, similar to those of other carboxylates. Bridging betaine subtends cation?cation distances between 4.5 and 6.1 ?. Nitrate coordination was only observed in the BaII chain polymer.
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Cells rely on the coordinated regulation of lipid phosphoinositides and Rab GTPases to define membrane compartment fates along distinct trafficking routes. The family of disease-related myotubularin (MTM) phosphoinositide phosphat...
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Cells rely on the coordinated regulation of lipid phosphoinositides and Rab GTPases to define membrane compartment fates along distinct trafficking routes. The family of disease-related myotubularin (MTM) phosphoinositide phosphatases includes catalytically inactive members, or pseudophosphatases, with poorly understood functions. We found that Drosophila MTM pseudophosphatase Sbf coordinates both phosphatidylinositol 3-phosphate (PI(3)P) turnover and Rab21 GTPase activation in an endosomal pathway that controls macrophage remodeling. Sbf dynamically interacts with class II phosphatidylinositol 3-kinase and stably recruits Mtm to promote turnover of a PI(3)P subpool essential for endosomal trafficking. Sbf also functions as a guanine nucleotide exchange factor that promotes Rab21 GTPase activation associated with PI(3)P endosomes. Of importance, Sbf, Mtm, and Rab21 function together, along with Rab11-mediated endosomal trafficking, to control macrophage protrusion formation. This identifies Sbf as a critical coordinator of PI(3)P and Rab21 regulation, which specifies an endosomal pathway and cortical control.
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A closed-form algebraic method to transform geocentric coordinates to geodetic coordinates has previously been proposed. The validity domain of latitude and height formulae in the vicinity of the Earth's core is specified. A new e...
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A closed-form algebraic method to transform geocentric coordinates to geodetic coordinates has previously been proposed. The validity domain of latitude and height formulae in the vicinity of the Earth's core is specified. A new expression of longitude is proposed, excluding indetermination and sensitivity to round-off error around the ±180 degrees longitude discontinuity.
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При обработке результатов спутниковых измерений возникает необходимость преобразования координат из одной декартовой сист...
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При обработке результатов спутниковых измерений возникает необходимость преобразования координат из одной декартовой системы в другую и пересчета их в эллипсоидальные координаты. Показано, что процесс преобразования координат может быть существенно упрощен и при этом не потребуется знание аномалий высот пунктов. Окончательный результат таких вычислений — разности в проекции Гаусса, которые характеризуются точностью фазовых измерений при отсутствии дополнительных искажений.
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Thermal properties of a static horizon (like the entropy S, heat content T S, etc.) can be obtained either from the surface term of the Einstein–Hilbert action or by evaluating the Noether charge, corresponding to the diffeomorph...
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Thermal properties of a static horizon (like the entropy S, heat content T S, etc.) can be obtained either from the surface term of the Einstein–Hilbert action or by evaluating the Noether charge, corresponding to the diffeomorphisms generated by the timelike Killing vector field. We show that, for a wide class of geometries, the same results can be obtained using the vector field which produces an infinitesimal coordinate transformation between two physically relevant reference frames, viz. the freely falling frame near the horizon and the static, accelerated, frame. In particular, the infinitesimal coordinate transformation from inertial coordinates to a uniformly accelerated frame can be used to obtain the heat content and entropy of the Rindler horizon. This result offers insight into the observer-dependent degrees of freedom which contribute to the entropy of null surfaces.
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Cell migration is essential for various physiological and pathological processes. Polarization in motile cells requires the coordination of several key signaling molecules, including RhoA small GTPases and phosphoinositides. Altho...
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Cell migration is essential for various physiological and pathological processes. Polarization in motile cells requires the coordination of several key signaling molecules, including RhoA small GTPases and phosphoinositides. Although RhoA participates in a front-rear polarization in migrating cells, little is known about the functional interaction between RhoA and lipid turnover. We find here that src-homology 2-containing inositol-5-phosphatase 2 (SHIP2) interacts with RhoA in a GTP-dependent manner. The association between SHIP2 and RhoA is observed in spreading and migrating U251 glioma cells. The depletion of SHIP2 attenuates cell polarization and migration, which is rescued by wild-type SHIP2 but not by a mutant defective in RhoA binding. In addition, the depletion of SHIP2 impairs the proper localization of phosphatidylinositol 3,4,5-trisphosphate, which is not restored by a mutant defective in RhoA binding. These results suggest that RhoA associates with SHIP2 to regulate cell polarization and migration.
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Spatial Eulerian coordinates rather than freezed-in Lagrangian coordinates are proposed to be used in numerical modeling of problems of strong nonlinear deformation leveraging the method of parametric continuation of the solution....
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Spatial Eulerian coordinates rather than freezed-in Lagrangian coordinates are proposed to be used in numerical modeling of problems of strong nonlinear deformation leveraging the method of parametric continuation of the solution. The proposed technique helps avoid re-constructing the original coordinate grid. The numerical results obtained demonstrate the approach's efficiency.
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