2010, ISBN 981430493X, xiv, 344

Book

2.
Geometry of Möbius transformations

: elliptic, parabolic and hyperbolic actions of SL₂[real number]

2012, ISBN 1848168586, xiv, 192

Book

2017, Mathematical surveys and monographs, ISBN 9781470441463, Volume no. 227., xvi, 193 pages

Book

Fuzzy Sets and Systems, ISSN 0165-0114, 01/2016, Volume 283, pp. 83 - 107

In this study, we attempt to construct fuzzy circles in a fuzzy geometrical plane. We provide a comprehensive study where we find a fuzzy number with a...

Fuzzy distance | Fuzzy number | Fuzzy point | Same and inverse points | Fuzzy circle | Fuzzy number along a line | MATHEMATICS, APPLIED | SET | VORONOI DIAGRAM | STATISTICS & PROBABILITY | PROBABILITY | COMPUTER SCIENCE, THEORY & METHODS | POINTS

Fuzzy distance | Fuzzy number | Fuzzy point | Same and inverse points | Fuzzy circle | Fuzzy number along a line | MATHEMATICS, APPLIED | SET | VORONOI DIAGRAM | STATISTICS & PROBABILITY | PROBABILITY | COMPUTER SCIENCE, THEORY & METHODS | POINTS

Journal Article

2014

Circles | Euclidean geometry | Lines (Geometry) | Parallels (Geometry) | Proof (Mathematics) | Area measurement | Triangles (Geometry) | Angles | Pythagorean theorem | Points (Geometry) | Volume (Geometry) | Geometry | Planes (Geometry) | Right angle | Axioms | Quadrilaterals | Geometric constructions

Reference

Astrophysical Journal, ISSN 0004-637X, 03/2017, Volume 837, Issue 2, p. 105

We present modeling of line polarization to study the multidimensional geometry of stripped-envelope core-collapse supernovae (SNe). We demonstrate that a...

techniques: polarimetric | supernovae: general | RAYLEIGH-TAYLOR INSTABILITIES | NEUTRINO-DRIVEN SUPERNOVA | IA SUPERNOVA | NEBULAR SPECTRA | ACCRETION-SHOCK INSTABILITY | CIRCLE-DOT STAR | CARLO RADIATIVE-TRANSFER | LATE-TIME SPECTRA | ASTRONOMY & ASTROPHYSICS | HYDRODYNAMICS SIMULATIONS | SN 1987A | Collapse | Angles (geometry) | Polarization | Cassiopeia A | Accretion | Supernovae | Convection | Geometry | Photosphere | Ejecta | Absorption | Mathematical analysis | Clumps | Modelling | Three dimensional models | Deposition

techniques: polarimetric | supernovae: general | RAYLEIGH-TAYLOR INSTABILITIES | NEUTRINO-DRIVEN SUPERNOVA | IA SUPERNOVA | NEBULAR SPECTRA | ACCRETION-SHOCK INSTABILITY | CIRCLE-DOT STAR | CARLO RADIATIVE-TRANSFER | LATE-TIME SPECTRA | ASTRONOMY & ASTROPHYSICS | HYDRODYNAMICS SIMULATIONS | SN 1987A | Collapse | Angles (geometry) | Polarization | Cassiopeia A | Accretion | Supernovae | Convection | Geometry | Photosphere | Ejecta | Absorption | Mathematical analysis | Clumps | Modelling | Three dimensional models | Deposition

Journal Article

Chemometrics and Intelligent Laboratory Systems, ISSN 0169-7439, 2009, Volume 96, Issue 1, pp. 22 - 26

The spectral pre-treatments known as standard normal variate (SNV) and multiplicative scatter correction (MSC) often give very similar results, and are widely...

Outlier | Circle | Standard normal variate | Ellipse | Multiplicative scatter correction | Scores | SNV | Imaging spectroscopy | MSC | CHEMISTRY, ANALYTICAL | STATISTICS & PROBABILITY | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | INSTRUMENTS & INSTRUMENTATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | AUTOMATION & CONTROL SYSTEMS

Outlier | Circle | Standard normal variate | Ellipse | Multiplicative scatter correction | Scores | SNV | Imaging spectroscopy | MSC | CHEMISTRY, ANALYTICAL | STATISTICS & PROBABILITY | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | INSTRUMENTS & INSTRUMENTATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | AUTOMATION & CONTROL SYSTEMS

Journal Article

AIChE Journal, ISSN 0001-1541, 08/2019, Volume 65, Issue 8, p. n/a

Different pore shapes correspond to different interaction strengths between pore surface and molecules, which will result in discrepancy of nanoconfined water...

various pore shapes | water viscosity | water slip phenomenon | nanoconfined water flow | MOLECULAR-DYNAMICS | CARBON | GRAPHENE | VISCOSITY | MODEL | GAS-TRANSPORT | DIFFUSIVE LEAKAGE | SHEAR DISPERSION | ENGINEERING, CHEMICAL | FRACTURED VERTICAL WELL | NEWTONIAN FLUID-FLOWS | Viscosity | Transport phenomena | Hydrophilicity | Slip | Water transport | Contact angle | Hydrophobicity | Porosity | Aspect ratio | Ellipses | Circles (geometry)

various pore shapes | water viscosity | water slip phenomenon | nanoconfined water flow | MOLECULAR-DYNAMICS | CARBON | GRAPHENE | VISCOSITY | MODEL | GAS-TRANSPORT | DIFFUSIVE LEAKAGE | SHEAR DISPERSION | ENGINEERING, CHEMICAL | FRACTURED VERTICAL WELL | NEWTONIAN FLUID-FLOWS | Viscosity | Transport phenomena | Hydrophilicity | Slip | Water transport | Contact angle | Hydrophobicity | Porosity | Aspect ratio | Ellipses | Circles (geometry)

Journal Article

2016, ISBN 9781633881679, 349 pages

Book

The American Mathematical Monthly, ISSN 0002-9890, 02/2015, Volume 122, Issue 2, pp. 144 - 150

In this article, we discuss the cardiod. We give purely geometric proofs of its wellknown properties.

Circles | Geometry | Tangents | Cardioids | Triangles | Geometric centers | Perpendicular lines | Parabolas | ARTICLES | Mathematical cusps | Vertices | MATHEMATICS | Usage | Design and construction | Proof theory | Geometric constructions | Closed curves | Methods | Curves

Circles | Geometry | Tangents | Cardioids | Triangles | Geometric centers | Perpendicular lines | Parabolas | ARTICLES | Mathematical cusps | Vertices | MATHEMATICS | Usage | Design and construction | Proof theory | Geometric constructions | Closed curves | Methods | Curves

Journal Article

Magnetic Resonance in Medicine, ISSN 0740-3194, 01/2018, Volume 79, Issue 1, pp. 489 - 500

Purpose To investigate the effect of realistic microstructural geometry on the susceptibility‐weighted MR signal in white matter (WM), with application to...

myelin | GRE phase signal | magnetic susceptibility modeling | white matter microstructure | MYELIN WATER | NMR LINE | BRAIN-TISSUE | PHASE | MULTIPLE-SCLEROSIS | MAGNETIC-SUSCEPTIBILITY | IN-VIVO | CENTRAL-NERVOUS-SYSTEM | GRADIENT-ECHO MRI | FIELD INHOMOGENEITY | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | Demyelinating Diseases - diagnostic imaging | Mice, Inbred C57BL | Axons - physiology | Biophysics | Diffusion Tensor Imaging | Magnetic Resonance Imaging | White Matter - diagnostic imaging | Algorithms | Animals | Fourier Analysis | Anisotropy | Computer Simulation | Mice | Myelin Sheath - chemistry | Cuprizone - chemistry | Disease Models, Animal | Animal models | Computer simulation | Myelin | Magnetic resonance | Electron micrographs | Substantia alba | Circles (geometry) | Geometry | Axons | Properties (attributes) | Cuprizone | Magnetic permeability | Demyelination | Mathematical models | Physics - Biological Physics | Full Paper | Full Papers—Biophysics and Basic Biomedical Research

myelin | GRE phase signal | magnetic susceptibility modeling | white matter microstructure | MYELIN WATER | NMR LINE | BRAIN-TISSUE | PHASE | MULTIPLE-SCLEROSIS | MAGNETIC-SUSCEPTIBILITY | IN-VIVO | CENTRAL-NERVOUS-SYSTEM | GRADIENT-ECHO MRI | FIELD INHOMOGENEITY | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | Demyelinating Diseases - diagnostic imaging | Mice, Inbred C57BL | Axons - physiology | Biophysics | Diffusion Tensor Imaging | Magnetic Resonance Imaging | White Matter - diagnostic imaging | Algorithms | Animals | Fourier Analysis | Anisotropy | Computer Simulation | Mice | Myelin Sheath - chemistry | Cuprizone - chemistry | Disease Models, Animal | Animal models | Computer simulation | Myelin | Magnetic resonance | Electron micrographs | Substantia alba | Circles (geometry) | Geometry | Axons | Properties (attributes) | Cuprizone | Magnetic permeability | Demyelination | Mathematical models | Physics - Biological Physics | Full Paper | Full Papers—Biophysics and Basic Biomedical Research

Journal Article

Results in Mathematics, ISSN 1422-6383, 12/2019, Volume 74, Issue 4, pp. 1 - 25

A geodesic circle in Finsler geometry is a natural extension of that in a Euclidean space. In this paper, we study geodesic circles and (infinitesimal)...

Einstein metric | 53B40 | Geodesic circle | lie derivative | Cartan Y -connection | Mathematics, general | Mathematics | 53C60 | conformal/concircular transformation | flag curvature | MATHEMATICS | MATHEMATICS, APPLIED | Cartan Y-connection | conformal | concircular transformation

Einstein metric | 53B40 | Geodesic circle | lie derivative | Cartan Y -connection | Mathematics, general | Mathematics | 53C60 | conformal/concircular transformation | flag curvature | MATHEMATICS | MATHEMATICS, APPLIED | Cartan Y-connection | conformal | concircular transformation

Journal Article

ACM Transactions on Graphics (TOG), ISSN 0730-0301, 11/2015, Volume 34, Issue 6, pp. 1 - 10

Structures and objects are often supposed to have idealized geometries such as straight lines or circles. Although not always visible to the naked eye, in...

deviation | geometry | magnification | Geometry | Deviation | Magnification | Eyes | Quantitative evaluation | Circles (geometry) | Images | Straight lines

deviation | geometry | magnification | Geometry | Deviation | Magnification | Eyes | Quantitative evaluation | Circles (geometry) | Images | Straight lines

Journal Article

Aequationes mathematicae, ISSN 0001-9054, 8/2018, Volume 92, Issue 4, pp. 763 - 800

The n-dimensional integer lattice, denoted by $${{\mathbb {Z}}}^n$$ Zn , is the subset of $${{\mathbb {R}}}^n$$ Rn consisting of those points whose coordinates...

52B20 | Geometry of numbers | Lattice polygon | 11P21 | 11H06 | 52C05 | Mathematics | 52C07 | Pick’s theorem | Steinhaus’ lattice point problem | Analysis | Integer lattice | Combinatorics | SIMPLICES | MATHEMATICS, APPLIED | POINT PROBLEM | NUMBER | SPACES | PICKS THEOREM | PROOF | POLYTOPES | CIRCLE | MATHEMATICS | Pick's theorem | Steinhaus' lattice point problem | EMBEDDINGS | POLYGONS | Integers | Set theory

52B20 | Geometry of numbers | Lattice polygon | 11P21 | 11H06 | 52C05 | Mathematics | 52C07 | Pick’s theorem | Steinhaus’ lattice point problem | Analysis | Integer lattice | Combinatorics | SIMPLICES | MATHEMATICS, APPLIED | POINT PROBLEM | NUMBER | SPACES | PICKS THEOREM | PROOF | POLYTOPES | CIRCLE | MATHEMATICS | Pick's theorem | Steinhaus' lattice point problem | EMBEDDINGS | POLYGONS | Integers | Set theory

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2017, Volume 445, Issue 1, pp. 746 - 761

For a general symmetric ordinary differential expression M and a positive weight function w, the authors characterized the dissipative and strictly dissipative...

Boundary conditions | Limit-circle solutions | Dissipative subspaces | Dissipative extensions | Symplectic geometry | MATHEMATICS | MATHEMATICS, APPLIED | ORDINARY DIFFERENTIAL-OPERATORS | SPECTRUM

Boundary conditions | Limit-circle solutions | Dissipative subspaces | Dissipative extensions | Symplectic geometry | MATHEMATICS | MATHEMATICS, APPLIED | ORDINARY DIFFERENTIAL-OPERATORS | SPECTRUM

Journal Article

Communications on Pure and Applied Analysis, ISSN 1534-0392, 07/2012, Volume 11, Issue 4, pp. 1407 - 1419

We show that the modified Constantin-Lax-Majda equation modeling vortex and quasi-geostrophic dynamics [27] can be recast as the geodesic flow on the subgroup...

Euler equation on diffeomorphisms group of the circle | CLM equation | DIFFEOMORPHISMS | MATHEMATICS | HUNTER-SAXTON EQUATION | MATHEMATICS, APPLIED | MOTION | ONE-DIMENSIONAL MODEL | GEODESIC-FLOW | Mathematics | Mathematical Physics | Analysis of PDEs | Physics

Euler equation on diffeomorphisms group of the circle | CLM equation | DIFFEOMORPHISMS | MATHEMATICS | HUNTER-SAXTON EQUATION | MATHEMATICS, APPLIED | MOTION | ONE-DIMENSIONAL MODEL | GEODESIC-FLOW | Mathematics | Mathematical Physics | Analysis of PDEs | Physics

Journal Article

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, ISSN 0138-4821, 6/2018, Volume 59, Issue 2, pp. 221 - 246

The principle of duality is well established in projective geometry but can hardly be found in the literature on Euclidean geometry where it is “more a...

03B30 | Euclidean geometry | Principle of duality | Mathematics | 51F15 | Geometry | Self-dual order structure | 51G05 | Algebra | 51M05 | Convex and Discrete Geometry | Algebraic Geometry | Circle geometry

03B30 | Euclidean geometry | Principle of duality | Mathematics | 51F15 | Geometry | Self-dual order structure | 51G05 | Algebra | 51M05 | Convex and Discrete Geometry | Algebraic Geometry | Circle geometry

Journal Article

Educational Studies in Mathematics, ISSN 0013-1954, 11/2013, Volume 84, Issue 3, pp. 439 - 460

In this paper, we discuss discernment of invariants in dynamic geometry environments (DGE) based on a combined perspective that puts together the lens of...

Geometry | Circles | Euclidean geometry | Axioms | Rectangles | Cognitive models | Simultaneity | Mathematics education | Sensory perception | Parallel lines | Dynamic geometry | Education | Mathematics Education | Mathematics, general | Perception | Discernment | Variation | Dragging control | EDUCATION & EDUCATIONAL RESEARCH | Models | Mathematics Instruction | Learning Processes | Geometric Concepts | Case Studies

Geometry | Circles | Euclidean geometry | Axioms | Rectangles | Cognitive models | Simultaneity | Mathematics education | Sensory perception | Parallel lines | Dynamic geometry | Education | Mathematics Education | Mathematics, general | Perception | Discernment | Variation | Dragging control | EDUCATION & EDUCATIONAL RESEARCH | Models | Mathematics Instruction | Learning Processes | Geometric Concepts | Case Studies

Journal Article

Discrete Mathematics, ISSN 0012-365X, 09/2014, Volume 330, pp. 61 - 75

Let F be a finite set of circles in the plane. The usual convex closure restricted to F yields a convex geometry, which is a combinatorial structure introduced...

Convex geometry | Anti-exchange property | Lower semimodular lattice | Geometry of circles | Planar lattice | MATHEMATICS | THEOREM | REPRESENTATION | LATTICES | COMPOSITION SERIES | Names | Planes | Mathematical analysis | Lattices | Proving | Closures | Circles (geometry) | Combinatorial analysis

Convex geometry | Anti-exchange property | Lower semimodular lattice | Geometry of circles | Planar lattice | MATHEMATICS | THEOREM | REPRESENTATION | LATTICES | COMPOSITION SERIES | Names | Planes | Mathematical analysis | Lattices | Proving | Closures | Circles (geometry) | Combinatorial analysis

Journal Article

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