Results 21 to 30 of about 1,025,793 (179)
Ptolemy’s Theorem in the Relativistic Model of Analytic Hyperbolic Geometry
, 2023 Ptolemy’s Theorem in Euclidean geometry, named after the Greek astronomer and mathematician Ptolemy, is well-known. By means of the relativistic model of hyperbolic geometry, we translate Ptolemy’s Theorem from Euclidean geometry into the ...
Abraham A. Ungar
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Asymptotic Properties of Hilbert Geometry [PDF]
, 2008 It is shown that the spheres in Hilbert geometry have the same volume growth entropy as those in the Lobachevsky space. Asymptotic estimates for the ratio of the volume of metric ball to the area of the metric sphere in Hilbert geometry are given ...
Olin, E.A., Borisenko, A.A.
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UniverseThe origin and evolution of supermassive black holes (SMBHs) in our universe have sparked controversy. In this study, we explore the hypothesis that some of these black holes may have seeded from the direct collapse of dark energy domains with density ...
Arkady A. Popov +2 more
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Oscillating Cosmological Solutions in the Modified Theory of Induced Gravity
Advances in Astronomy, Volume 2019, Issue 1, 2019., 2019 This work is the extension of author’s research, where the modified theory of induced gravity (MTIG) is proposed. In the framework of the MTIG, the mechanism of phase transitions and the description of multiphase behavior of the cosmological scenario are proposed. The theory describes two systems (stages): Einstein (ES) and “restructuring” (RS).
Farkhat Zaripov, Roberto Turolla
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Inhomogeneous Extra Space as a Tool for the Top‐Down Approach
Advances in High Energy Physics, Volume 2018, Issue 1, 2018., 2018 The top‐down approach for the 6‐dimensional space has been elaborated. The connection between the cosmological constant and the extra space metric has been obtained. The metric can be found with the necessary accuracy. It is shown that descent from high energies to the low ones leads to the quantum corrections which influence weakly the metric of extra
Sergey G. Rubin, Elias C. Vagenas
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Journal of Function Spaces, Volume 2016, Issue 1, 2016., 2016 We introduce a C⁎‐algebra A(x,Q) attached to the cluster x and a quiver Q. If QT is the quiver coming from triangulation T of the Riemann surface S with a finite number of cusps, we prove that the primitive spectrum of A(x,QT) times R is homeomorphic to a generic subset of the Teichmüller space of surface S.
Igor V. Nikolaev, Gelu Popescu
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Dimer models and conformal structures
Communications on Pure and Applied Mathematics, Volume 79, Issue 2, Page 340-446, February 2026.Abstract Dimer models have been the focus of intense research efforts over the last years. Our paper grew out of an effort to develop new methods to study minimizers or the asymptotic height functions of general dimer models and the geometry of their frozen boundaries.
Kari Astala +3 more
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Variations in the Intragene Methylation Profiles Hallmark Induced Pluripotency
BioMed Research International, Volume 2015, Issue 1, 2015., 2015 We demonstrate the potential of differentiating embryonic and induced pluripotent stem cells by the regularized linear and decision tree machine learning classification algorithms, based on a number of intragene methylation measures. The resulting average accuracy of classification has been proven to be above 95%, which overcomes the earlier ...
Pavel Druzhkov +7 more
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Journal of Honai MathThe axiom of Lobachevsky's parallelism is one of the topics that students often find difficult. The purpose of this research is to design a learning trajectory about the Lobachevsky axiom of parallelism using the context of a valid, practical and ...
Abdurrobbil Falaq Dwi Anggoro +3 more
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Curvature‐dimension condition of sub‐Riemannian α$\alpha$‐Grushin half‐spaces
Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.Abstract We provide new examples of sub‐Riemannian manifolds with boundary equipped with a smooth measure that satisfy the RCD(K,N)$\mathsf {RCD}(K, N)$ condition. They are constructed by equipping the half‐plane, the hemisphere and the hyperbolic half‐plane with a two‐dimensional almost‐Riemannian structure and a measure that vanishes on their ...
Samuël Borza, Kenshiro Tashiro
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