Relevant bibliographies by topics / Tangent sphere coordinates

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Academic literature on the topic 'Tangent sphere coordinates'

Author: Grafiati
Published: 5 June 2025
Last updated: 1 August 2025

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Journal articles on the topic "Tangent sphere coordinates"

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Maurya, Deepak Kumar, and Vikas Kumar Sharma. "BRINKMAN EQUATION IN TANGENT SPHERE AND CARDIOID COORDINATE SYSTEMS: STREAM FUNCTION SOLUTION." jnanabha 54, no. 01 (2024): 329–37. http://dx.doi.org/10.58250/jnanabha.2024.54140.

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In the present investigation, analytical stream function solutions of the Brinkman equation in cardioid coordinates (λ, σ, ζ) and tangent sphere coordinates (τ, η, ζ) are investigated. Trigonometric functions, special functions such as modified Bessel functions and Bessel functions, are contained in the analytical expressions of the stream function and velocity components. Authors also discuss about how permeability depends on the estimated stream function solution for the Brinkman equation in the cardioid and tangent sphere coordinate systems, which can be deduced as a particular scenario tha
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Medvedev, P. A., and M. V. Novgorodskaya. "Development of mathematical model Gauss – Kruger coordinate system for calculating planimetric rectangular coordinates using geodesic coordinates." Geodesy and Cartography 926, no. 8 (2017): 10–19. http://dx.doi.org/10.22389/0016-7126-2017-926-8-10-19.

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Algorithms with improved convergence for the calculation of rectangular coordinates in the Gauss – Kruger coordinate system according to the parameters of any ellipsoid were designed. The approach of definition the spherical components in the classic series defined variables x, y, represented by the difference between the degrees of longitude l, followed by the replacement of their sums by formulas of spherical trigonometry. For definition of the amounts of spherical components of the relevant decompositions patterns of transverse-cylindrical sphere plane projection in the condition of the ini
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Bektaş, Sebahattin. "Rigorous spherical bearing with Soldner coordinates and azimuth angles on sphere." Earth Sciences Research Journal 26, no. 3 (2022): 205–10. http://dx.doi.org/10.15446/esrj.v26n3.100754.

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Meridian systems, called Soldner coordinates (parallel coordinate) systems, have found wide application in geodesy. In particular, the meridian system constitutes a suitable base for the Gauss-Kruger projection of the ellipsoid and the sphere. Soldner coordinates can be used in Cassini-Soldner projection without any processing. As it is known, the directions of the edges are shown with azimuth angles in the geographic coordinate system and the bearing angles in the Soldner coordinate system. Bearing or azimuth angles are frequently used in geodetic calculations. These angles give the direction
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Fransaer, J., M. De Graef, and J. Roos. "The Temperature Distribution Around a Spherical Particle on a Planar Surface." Journal of Heat Transfer 112, no. 3 (1990): 561–66. http://dx.doi.org/10.1115/1.2910423.

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The solutions for three related boundary value problems in tangent sphere coordinates are presented; two of these problems involve a conducting and a nonconducting sphere on a conducting flat surface when the field at infinity is linear. The third problem describes the potential field around a conducting sphere on an insulating surface where the field at infinity vanishes. Depending on the nature of the problem, either the Laplace equation or the Stokes stream function formalism is used. The integral solutions are rewritten as series expansions, which are numerically easier to evaluate.
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Parker, Gregory A., Mark Keil, Michael A. Morrison, and Stefano Crocchianti. "Quantum reactive scattering in three dimensions: Using tangent-sphere coordinates to smoothly transform from hyperspherical to Jacobi regions." Journal of Chemical Physics 113, no. 3 (2000): 957–70. http://dx.doi.org/10.1063/1.481876.

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SAYGILI, K. "TOPOLOGICALLY MASSIVE ABELIAN GAUGE THEORY." International Journal of Modern Physics A 23, no. 13 (2008): 2015–35. http://dx.doi.org/10.1142/s0217751x08039840.

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We discuss three mathematical structures which arise in topologically massive Abelian gauge theory. First, the Euclidean topologically massive Abelian gauge theory defines a contact structure on a manifold. We briefly discuss three solutions and the related contact structures on the flat 3-torus, the AdS space, the 3-sphere which respectively correspond to Bianchi type I, VIII, IX spaces. We also present solutions on Bianchi type II, VI and VII spaces. Secondly, we discuss a family of complex (anti-)self-dual solutions of the Euclidean theory in Cartesian coordinates on [Formula: see text] whi
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7

Constantin, A., and R. S. Johnson. "An Exact, Steady, Purely Azimuthal Equatorial Flow with a Free Surface." Journal of Physical Oceanography 46, no. 6 (2016): 1935–45. http://dx.doi.org/10.1175/jpo-d-15-0205.1.

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AbstractThe general problem of an ocean on a rotating sphere is considered. The governing equations for an inviscid, incompressible fluid, written in spherical coordinates that are fixed at a point on the rotating Earth, together with the free surface and rigid bottom boundary conditions, are introduced. An exact solution of this system is presented; this describes a steady flow that is moving only in the azimuthal direction, with no variation in this direction. However, this azimuthal velocity component has an arbitrary variation with depth (i.e., radius), and so, for example, an Equatorial U
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AKUESON, P., and D. GUREVICH. "COTANGENT AND TANGENT MODULES ON QUANTUM ORBITS." International Journal of Modern Physics B 14, no. 22n23 (2000): 2335–47. http://dx.doi.org/10.1142/s0217979200001850.

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Let [Formula: see text] be the "coordinate ring" of a quantum sphere. We introduce the cotangent module on the quantum sphere as a one-sided [Formula: see text]-module and show that there is no Yang–Baxter type operator converting it into a [Formula: see text]-bimodule which would be a flatly deformed object w.r.t. its classical counterpart. This implies non-flatness of any covariant differential calculus on the quantum sphere making use of the Leibniz rule. Also, we introduce the cotangent and tangent modules on generic quantum orbits and discuss some related problems of "braided geometry".
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A., M. Abdel-Wahab. "Field Assessment to Determine The KIBLAH Direction of Mosques in MAKKAH." International Journal of Engineering and Advanced Technology (IJEAT) 9, no. 2 (2019): 388–94. https://doi.org/10.5281/zenodo.5602226.

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Every Muslim must pray to ALLAH five times every day and they must direct their faces toward the KABAH (KIBLAH direction) in each prayer. Muslims Scientifics and Astronomers since the eighth century (A.D) have been concerned with the determination of the KIBLAH direction. The KIBLAH direction at any point on the earth's surface; assuming the earth to be a perfect sphere; is given by the great circle passing through that point and holy city MAKKAH. Furthermore, the KIBLAH direction from the geographic north at this point is the angle between the tangent of the meridian passing through this
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Waters, Thomas, and Matthew Cherrie. "The conjugate locus in convex 3-manifolds." New Zealand Journal of Mathematics 54 (July 1, 2023): 17–30. http://dx.doi.org/10.53733/139.

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In this paper we study the conjugate locus in convex manifolds. Our main tool is Jacobi fields, which we use to define a special coordinate system on the unit sphere of the tangent space; this provides a natural coordinate system to study and classify the singularities of the conjugate locus. We pay particular attention to 3-dimensional manifolds, and describe a novel method for determining conjugate points. We then make a study of a special case: the 3-dimensional (quadraxial) ellipsoid. We emphasise the similarities with the focal sets of 2-dimensional ellipsoids.
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Books on the topic "Tangent sphere coordinates"

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Zeitlin, Vladimir. Simplifying Primitive Equations: Rotating Shallow-Water Models and their Properties. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198804338.003.0003.

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In this chapter, one- and two-layer versions of the rotating shallow-water model on the tangent plane to the rotating, and on the whole rotating sphere, are derived from primitive equations by vertical averaging and columnar motion (mean-field) hypothesis. Main properties of the models including conservation laws and wave-vortex dichotomy are established. Potential vorticity conservation is derived, and the properties of inertia–gravity waves are exhibited. The model is then reformulated in Lagrangian coordinates, variational principles for its one- and two-layer version are established, and c
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Zeitlin, Vladimir. Primitive Equations Model. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198804338.003.0002.

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The chapter gives the foundations of modelling of large-scale atmospheric and oceanic motions and presents the ‘primitive equations’ (PE) model. After a concise reminder on general fluid mechanics, the main hypotheses leading to the PE model are explained, together with the tangent-plane (so-called f and beta plane) approximations, and ‘traditional’ approximation to the hydrodynamical equations on the rotating sphere. PE are derived in parallel for the ocean and for the atmosphere. It is then shown that, with a judicious choice of the vertical coordinate, the ‘pseudo-height’, in the atmosphere
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Conference papers on the topic "Tangent sphere coordinates"

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Vasilca, Doina, and Oana-Mihaela Biscoveanu. "ALGORITHM FOR THE TRANSFORMATION OF THE COORDINATES NEEDED TO SET OBJECTIVES EXTENDING OVER LARGE AREAS." In 24th SGEM International Multidisciplinary Scientific GeoConference 2024. STEF92 Technology, 2024. https://doi.org/10.5593/sgem2024/2.1/s09.21.

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Constructions extending over large areas or distances raise problems regarding their setting out, because these elements are determined in the official projection of Romania, namely the 1970 Stereographic map projection. For the territory of our country, this produces distortions from -25 cm/km to approximately +64 cm/km in terms of distances and between -5 sq. m/ha and +12.76 sq. m/ha in terms of areas, depending on the distance from the projection pole and, implicitly, from the circle of zero distortions. For them to be applied on the ground, the coordinates should be calculated in a local p
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Journal articles
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