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1. Full Text Capability of Artificial Neural Network for Forward Conversion of Geodetic Coordinates $$(\phi ,\lambda ,h)$$ ( ϕ , λ , h ) to Cartesian Coordinates (X, Y, Z)
by Ziggah, Yao Yevenyo and Youjian, Hu and Yu, Xianyu and Basommi, Laari Prosper
Mathematical Geosciences, ISSN 1874-8961, 8/2016, Volume 48, Issue 6, pp. 687 - 721
The standard forward transformation equation plays a major role in coordinate transformation between global and local datums. Thus, it is a prerequisite step... 
Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences | Coordinate conversion | Earth Sciences | Hydrogeology | Standard forward transformation equation | Geotechnical Engineering & Applied Earth Sciences | Backpropagation artificial neural network | Earth Sciences, general | Multiple linear regression | Radial basis function neural network | TRANSFORMATION | VELOCITY | HOLE | ALGORITHM | EARTH ORIENTATION PARAMETERS | MODEL | LEAST-SQUARES | PREDICTION | GEOSCIENCES, MULTIDISCIPLINARY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Neural networks | Algorithms | Coordinate transformations | Approximation | Mathematical analysis | Artificial neural networks | Mathematical models | Geodetic coordinates | Conversion | Cartesian coordinates
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2. Full Text Transforming geocentric cartesian coordinates to geodetic coordinates by using differential search algorithm
by Civicioglu, Pinar
Computers and Geosciences, ISSN 0098-3004, 09/2012, Volume 46, pp. 229 - 247
In order to solve numerous practical navigational, geodetic and astro-geodetic problems, it is necessary to transform geocentric cartesian coordinates into... 
Coordinate transformation | Geodetic coordinates | Differential search algorithm | Geocentric cartesian coordinates | PARTICLE SWARM | DESIGN | CONVERSION | PERFORMANCE | MUTATION OPERATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | GEOSCIENCES, MULTIDISCIPLINARY | COLONY ABC ALGORITHM | EVOLUTION ALGORITHM | GLOBAL OPTIMIZATION | ADAPTATION | CONVERGENCE | Analysis | Algorithms | Aeronautics
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3. Full Text Non-commutativity in polar coordinates
by Edwards, James P
European Physical Journal C, ISSN 1434-6044, 05/2017, Volume 77, Issue 5, pp. 1 - 7
We reconsider the fundamental commutation relations for non-commutative R-2 described in polar coordinates with non-commutativity parameter theta. Previous... 
SPACE-TIME | PHYSICS, PARTICLES & FIELDS | Commutation | Mathematical analysis | Polar coordinates | Cartesian coordinates | Astrophysics | Black Hole | Mathematical Physics | Weyl Symbol | Nuclear and particle physics. Atomic energy. Radioactivity | Minimal Length Scale | Fuzzy Sphere | Undetermined Constant | High Energy Physics - Theory
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4. Full Text Efficient transformation from Cartesian to geodetic coordinates
by Claessens, S.J
Computers & Geosciences, ISSN 0098-3004, 12/2019, Volume 133, p. 104307
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5. One-dimensional vs. two-dimensional proton transport processes at solid–liquid zinc-oxide–water interfaces (Electronic supplementary information (ESI) available: Snapshots (Cartesian coordinates of the atoms including periodic lattice parameters) of the ZnO(1010) and ZnO(1120) surfaces in contact with liquid water. Details for the automated PT coordinate assignment. Calculated PTFELs for all proton transfer coordinates, and two-dimensional PTFELs for the PT coordinates in Fig. 4. Validation of the neural network by comparison to ab initio molecular dynamics simulations. See DOI: 10.1039/c8sc03033b)
by Matti Hellström and Vanessa Quaranta and Jörg Behler
Chemical Science, ISSN 2041-6520, 01/2019, Volume 10, Issue 4, pp. 1232 - 1243
Long-range charge transport is important for many applications like batteries, fuel cells, sensors, and catalysis. Obtaining microscopic insights into the... 
Protons | Water | Computer simulation | Proton conduction | Migration | Molecular dynamics | Charge transport | Batteries | Lattice parameters | Current carriers | Nanoparticles | Zinc oxides | Liquid-solid interfaces | Mathematical analysis | Neural networks | Morphology | Fuel cells | Zinc oxide | Catalysis | Nanowires | Cartesian coordinates
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6. Full Text General formulation of vibronic spectroscopy in internal coordinates
by Baiardi, Alberto and Bloino, Julien and Barone, Vincenzo
The Journal of Chemical Physics, ISSN 0021-9606, 02/2016, Volume 144, Issue 8, pp. 084114 - 084114
Our general platform integrating time-independent and time-dependent evaluations of vibronic effects at the harmonic level for different kinds of absorption... 
EFFICIENT OPTIMIZATION | ELECTRONIC-ABSORPTION | VIRTUAL SPECTROMETER | TEMPERATURE-DEPENDENCE | FEASIBLE COMPUTATIONS | RESONANCE-RAMAN-SPECTRA | AB-INITIO | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | GEOMETRY OPTIMIZATION | FRANCK-CONDON FACTORS | MOLECULAR GEOMETRIES | Chemical bonds | Time dependence | Electron states | Mathematical analysis | System effectiveness | Cartesian coordinates
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7. Full Text Transport Phenomena in Eccentric Cylindrical Coordinates
by Gilbert, P. H and Saengow, C and Giacomin, A. J
AIChE Journal, ISSN 0001-1541, 08/2017, Volume 63, Issue 8, pp. 3563 - 3581
Studies in transport phenomena have been limited to a select few coordinate systems. Specifically, Cartesian, cylindrical, spherical, Dijksman toroidal, and... 
equations of change | coordinate systems | eccentric cylinders | transport phenomena | ENGINEERING, CHEMICAL | DIES | CYLINDERS | AXIAL-FLOW | Viscosity | Energy use | Eccentricity | Exact solutions | Mass transport | Velocity | Mass transfer | Heat | Energy | Mathematical analysis | Flow control | Mathematical models | Continuity | Transport | Cylindrical coordinates | Cartesian coordinates
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8. Full Text Pedal coordinates, dark Kepler, and other force problems
by Blaschke, Petr
Journal of Mathematical Physics, ISSN 0022-2488, 06/2017, Volume 58, Issue 6, p. 63505
Pedal coordinates (instead of polar or Cartesian coordinates) are more natural settings in which to study force problems of classical mechanics in the plane.... 
ORBITS | PHYSICS, MATHEMATICAL | Dark energy | Dark matter | Classical mechanics | Differential equations | Cartesian coordinates
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9. Full Text The rotated Cartesian coordinate method to remove the axial singularity of cylindrical coordinates in finite‐difference schemes for elastic and viscoelastic waves
by Zhuang, Mingwei and Zhou, Jianyang and Wei, Songlin and Liu, Qing Huo
Geophysical Prospecting, ISSN 0016-8025, 03/2018, Volume 66, Issue S1, pp. 27 - 39
ABSTRACT When modelling the propagation of 3D non‐axisymmetric elastic and viscoelastic waves in cylindrical coordinates using the finite‐difference... 
The rotated Cartesian coordinate method | Elastic waves | Cylindrical coordinates | FDTD method | Numerical singularity | ACOUSTIC LOGS | PERFECTLY MATCHED LAYERS | ELEMENT-METHOD | EQUATIONS | GEOCHEMISTRY & GEOPHYSICS | INTEGRATION TECHNIQUE | TIME-DOMAIN ALGORITHM | BOREHOLE | ATTENUATION | SIMULATIONS | PROPAGATION
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10. Structures and properties of large supramolecular coordination complexes predicted with the generalized energy-based fragmentation method (Electronic supplementary information (ESI) available: (1). Relative energies for six conformers of M7(timb)2(tim)2; (2) the coordinate bond lengths in M7(timb)2(tim)2; (3) the coordinate bond lengths in Fe2Zn2(RuL2)2; (4) the superposition of the optimized structure and the crystal structure for Pd4L8(BF4−)3; (5) the coordinate bond lengths in Pd4L8(BF4−)3; (6) Cartesian coordinates of the studied supramolecular coordination complexes. See DOI: 10.1039/c8cp05548c)
by Dandan Yuan and Yunzhi Li and Wei Li and Shuhua Li
Physical Chemistry Chemical Physics : PCCP, ISSN 1463-9076, 01/2018, Volume 20, Issue 45, pp. 28894 - 28902
The generalized energy-based fragmentation (GEBF) method has been extended to facilitate ab initio calculations of large supramolecular coordination complexes.... 
Nuclear magnetic resonance--NMR | Quantum chemistry | Palladium | Superposition (mathematics) | Covalent bonds | Fragmentation | Organic chemistry | Electronic structure | Mathematical analysis | Infrared radiation | Ligands | Coordination compounds | Crystal structure | Magnetic properties | Metal ions | Cartesian coordinates
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11. Full Text Explicitly computing geodetic coordinates from Cartesian coordinates
by Zeng, Huaien
Earth, Planets and Space, ISSN 1343-8832, 4/2013, Volume 65, Issue 4, pp. 291 - 298
This paper presents a new form of quartic equation based on Lagrange’s extremum law and a Groebner basis under the constraint that the geodetic height is the... 
Earth Sciences | Geology | Groebner basis | convergence region | Earth Sciences, general | Geophysics/Geodesy | Geodetic coordinates | Ferrari’s solution | Cartesian coordinates | Convergence region | Ferrari's solution | TRANSFORMATION | GEOSCIENCES, MULTIDISCIPLINARY | Earth | Quartic equations | Algorithms | Law | Ellipsoids | Convergence
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12. Full Text Principal component analysis of molecular dynamics: On the use of Cartesian vs. internal coordinates
by Sittel, Florian and Jain, Abhinav and Stock, Gerhard
Journal of Chemical Physics, ISSN 0021-9606, 07/2014, Volume 141, Issue 1, p. 014111
Principal component analysis of molecular dynamics simulations is a popular method to account for the essential dynamics of the system on a low-dimensional... 
PATHWAYS | ROTATION | FREE-ENERGY LANDSCAPES | HIDDEN COMPLEXITY | EQUILIBRIUM | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | RELAXATION | PROTEIN MOTIONS | PANCREATIC TRYPSIN-INHIBITOR | SIMULATIONS | FORCE-FIELDS | Thermodynamics | Protein Conformation | Principal Component Analysis | Molecular Dynamics Simulation | Protein Folding | Dynamic structural analysis | Proteins | Moments of inertia | Molecular structure | Molecular dynamics | Principal components analysis | Rotation | Free energy | Cartesian coordinates
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13. Full Text Computational Methods for Configurational Entropy Using Internal and Cartesian Coordinates
by Hikiri, Simon and Yoshidome, Takashi and Ikeguchi, Mitsunori
Journal of Chemical Theory and Computation, ISSN 1549-9618, 12/2016, Volume 12, Issue 12, pp. 5990 - 6000
The configurational entropy of solute molecules is a crucially important quantity to study various biophysical processes. Consequently, it is necessary to... 
CONFORMATIONAL ENTROPY | MOLECULAR-DYNAMICS | PROTEIN | RECOGNITION | MACROMOLECULES | INTEGRATION | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | FORCE-FIELD | SIMULATIONS | MODEL | FREE-ENERGY | Quantum Theory | Protein Unfolding | Entropy | Kinetics | Oligopeptides - metabolism | Oligopeptides - chemistry | Molecular Dynamics Simulation | Protein Folding | Computation | Identification methods | Mathematical analysis | Mathematical models | Approximation methods | Folding | Cartesian coordinates
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14. Full Text Global structure search for molecules on surfaces: Efficient sampling with curvilinear coordinates
by Krautgasser, Konstantin and Panosetti, Chiara and Palagin, Dennis and Reuter, Karsten and Maurer, Reinhard J and Yale Univ., New Haven, CT (United States)
The Journal of Chemical Physics, ISSN 0021-9606, 08/2016, Volume 145, Issue 8, p. 084117
Efficient structure search is a major challenge in computational materials science. We present a modification of the basin hopping global geometry optimization... 
SPACE | TRANSITION | CLUSTER STRUCTURE OPTIMIZATION | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | GEOMETRY OPTIMIZATION | ENERGY LANDSCAPES | BIOMOLECULES | METAL-SURFACES | ADSORPTION | STRUCTURE PREDICTION | GENETIC ALGORITHM | Organic chemistry | Silver | Molecular structure | Coordinates | Adsorbates | Global geometry | Materials science | Coordination compounds | Optimization | Cartesian coordinates | Physics - Materials Science | chemical bonds | INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY | acids | integrated circuits | optimization | adsorbates | dissociation | methane | CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY | molecular conformation | MATERIALS SCIENCE | adsorbate structures
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15. Full Text Normal Coordinates in Affine Geometry
by Katanaev, M.O
Lobachevskii Journal of Mathematics, ISSN 1995-0802, 04/2018, Volume 39, Issue 3, pp. 464 - 476
To access, purchase, authenticate, or subscribe to the full-text of this article, please visit this link: http://dx.doi.org/10.1134/S199508021803006X Manifolds... 
Riemann coordinates | Normal coordinates | Gaussian coordinates
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16. Full Text Helmert transformation with mixed geodetic and Cartesian coordinates
by Lin, Peng and Chang, Guobin and Gao, Jingxiang and Wang, Qianxin and Bian, Hefang
Advances in Space Research, ISSN 0273-1177, 05/2019, Volume 63, Issue 9, pp. 2964 - 2971
It is common in geodetic practice that station geodetic coordinates in an old frame are measured/estimated by adjusting conventional leveling and vertical... 
Weighted least-squares | Helmert transformation | Geodetic coordinates | Cartesian coordinates | GEOSCIENCES, MULTIDISCIPLINARY | BIAS | ASTRONOMY & ASTROPHYSICS | MODEL | METEOROLOGY & ATMOSPHERIC SCIENCES | TOTAL LEAST-SQUARES | Mineral industry | Artificial satellites | Mining industry | Analysis
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17. Full Text A quartic force field coordinate substitution scheme using hyperbolic sine coordinates
by Alonso de Armiño, Diego J and Bustamante, Carlos M
International Journal of Quantum Chemistry, ISSN 0020-7608, 08/2017, Volume 117, Issue 15, p. n/a
Quartic force fields (QFF) are currently the most cost‐effective method for the approximation of potential energy surfaces for the calculation of anharmonic... 
vibrational structure | quantum chemistry | quartic force fields | FREQUENCIES | SCF CI | QUANTUM SCIENCE & TECHNOLOGY | SELF-CONSISTENT-FIELD | POLYATOMIC-MOLECULES | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | REPRESENTATION | CHEMISTRY, PHYSICAL | INTERPOLATION | WAVE-FUNCTIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | POTENTIAL-ENERGY SURFACES | VIBRATIONAL STRUCTURE-THEORY | FORMALDEHYDE | Formaldehyde | Force and energy
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18. Full Text Growing string method with interpolation and optimization in internal coordinates: Method and examples
by Zimmerman, Paul M
Journal of Chemical Physics, ISSN 0021-9606, 05/2013, Volume 138, Issue 18, p. 184102
The growing string method (GSM) has proven especially useful for locating chemical reaction paths at low computational cost. While many string methods use... 
NUDGED ELASTIC BAND | CHEMICAL-REACTIONS | FINDING TRANSITION-STATES | STATIONARY-POINTS | POTENTIAL-ENERGY SURFACES | EQUILIBRIUM GEOMETRIES | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | SADDLE-POINTS | CHEMISTRY, PHYSICAL | GEOMETRY OPTIMIZATION | DENSITY-FUNCTIONAL THEORY | REACTION PATHWAYS | Tangents | Interpolation | Mathematical models | Computational efficiency | Strings | Optimization | Convergence | Cartesian coordinates
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