Hyperbolic Geometry
Applications of hyperbolic geometry in physics
... We remember from hyperbolic geometry in three dimensions that the set of all timelike unit vectors creates the unit hyperbolic plane, analogous to. the unit sphere in spherical geometry[r] ...
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A Scrutiny on Hyperboloid Model and Hypothesis of Hyperbolic Geometry
... Euclidean Geometry is the Hyperbolic Geometry. In Hyperbolic Geometry all the three angles in a triangle will sum to a number less than 180 ...In Hyperbolic Geometry if ...
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Braid Forcing, Hyperbolic Geometry, and Pseudo-Anosov Sequences of Low Entropy
... compute hyperbolic volume and perform Dehn ...The hyperbolic volume function was critical initially in searching for and figuring out the correct manifolds/surgery ...
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An Extension of Poincare Model of Hyperbolic Geometry with Gyrovector Space Approach
... bolic geometry, and the gyrovector space ( C , ⊕, ⊗) is an extension of it to C , so ( C , ⊕, ⊗) provides the algebraic settings for a new model of hyperbolic geometry just as vector spaces provide ...
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Using hyperbolic geometry for visualisation of concept spaces for adaptive e learning
... 1. Anderson, J.W. (2005) Hyperbolic Geometry. 2nd Edition. Springer-Verlag, London. 2. Dagger, D., Conlan, O., Wade, V. (2005) Fundamental Requirements of Person- alised eLearning Development Environments ...
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Clustering and the hyperbolic geometry of complex networks
... Abstract. Clustering is a fundamental property of complex networks and it is the mathematical expression of a ubiquitous phenomenon that arises in various types of self-organized networks such as biological net- works, ...
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Clustering and the hyperbolic geometry of complex networks
... Clustering is a fundamental property of complex networks and it is the mathemati- cal expression of a ubiquitous phenomenon that arises in various types of self-organized networks such as biological networks, computer ...
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Geometric group theory and hyperbolic geometry: Recent contributions from Indian mathematicians
... relatively hyperbolic subgroup of relatively hyperbolic group under natural ...closed hyperbolic surface group on the curve complex of a surface with one puncture and use it to show that the boundary ...
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Conics in the hyperbolic plane
... Non-Euclidean geometry was one of the most momentous mathematical discov eries of the 19th ...century. Hyperbolic geometry is a non-Euclidean geometry which obeys all the Euclidean postulates ...
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Hyperbolic monotonicity in the Hilbert ball
... [4] H. H. Bauschke, E. Matouˇskov´a, and S. Reich, Projection and proximal point methods: convergence results and counterexamples, Nonlinear Analysis. Theory, Methods & Applications. An Interna- tional ...
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Spherical and hyperbolic embeddings of data
... Most embedding methods produce an embedding that is Euclidean. However, dissimilarity data cannot always be em- bedded exactly into a Euclidean space. This is the case when the symmetric similarity matrix (the equivalent ...
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Hyperbolic Ordinal Embedding
... Recently, hyperbolic space has been extensively studied in many research areas (Alanis- Lobato et ...in hyperbolic space, since Internet structure has a highly connected core and long stretched tendrils, ...
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Quantum Dark Energy from the Hyperbolic Transfinite Cantorian Geometry of the Cosmos
... The quintessence of hyperbolic geometry is transferred to a transfinite Cantorian-fractal setting in the present work. Starting from the building block of E-infinity Cantorian spacetime theory, namely a ...
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Geometry and dynamics in Gromov hyperbolic metric spaces : With an emphasis on non-proper settings
... the geometry and represen- tation theory of infinite-dimensional hyperbolic space H ∞ and its isometry group have been studied in the last decade by a handful of mathematicians, see ...infinite-dimensional ...
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Hyperbolic metamaterials: fundamentals and applications
... with hyperbolic dispersion and present the various applications where such media offer potential for transformative ...achieve hyperbolic dispersion using thin film and nanowire ...of hyperbolic ...
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Geometry without topology as a new conception of geometry
... But the curve L appears to be not an attribute of geometry. It is some additional object external with respect to geometry. A corollary of this is an appearance of a new geometry property, which is ...
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Applications of Riemannian Geometry Comparing with Symplectic Geometry
... According to Einstein, matter is the cause of the gravitational field and the causative matter is described in his theory by a mathematical object called the energy-momentum tensor, which is coupled to geometry ...
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New inequalities involving circular, inverse circular, hyperbolic, inverse hyperbolic and exponential functions
... Abstract. In this article, inequalities involving circular, inverse circular, hyperbolic, inverse hyperbolic and expo- nential functions are established. Obtained results provide new low[r] ...
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DERIVATION OF FORMULAS FOR EVALUATING INTEGRALS OF POWERS AND PRODUCTS OF HYPERBOLIC SINE AND HYPERBOLIC COSINE
... reduce the powers of each function and the integrand is transformed into an expression where appropriate integration formulas can be easily applied. However, this method of finding the integrals of powers and products of ...
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FRACTAL GEOMETRY. Introduction to Fractal Geometry
... recursive formula zz^2+c, where c is some real number and z is a complex number such as “a+bi.” Depending on the number put in, Mandelbrot discovered that some get larger and go off to infinity, while some get smaller ...
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