Results 301 to 310 of about 193,577 (332)
Physics-informed neural network with weighted loss and hard constraints for hyperbolic conservation laws. [PDF]
Sci RepGhoreishi MS, Naderan H.
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Designing nonlinearity in a current-starved ring oscillator for reservoir computing hardware. [PDF]
Sci RepTun NN, Sun S, Iizuka T, Yajima T.
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Immersive experience in virtual reality gamification teaching: analysis of the mediating effect on educational learning outcomes. [PDF]
Sci RepLin J.
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2017
This chapter deals with hyperbolic groups. It begins with an overview of curvature, a fundamental way of understanding the intrinsic geometry of manifolds, and its three regimes—positive, zero, and negative. In terms of surfaces, each regime corresponds to the sphere, the plane, and the saddle, respectively.
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This chapter deals with hyperbolic groups. It begins with an overview of curvature, a fundamental way of understanding the intrinsic geometry of manifolds, and its three regimes—positive, zero, and negative. In terms of surfaces, each regime corresponds to the sphere, the plane, and the saddle, respectively.
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PERIODIC FACTOR GROUPS OF HYPERBOLIC GROUPS
Mathematics of the USSR-Sbornik, 1992Summary: It is proved that for any noncyclic hyperbolic torsion-free group \(G\) there exists an integer \(n(G)\) such that the factor group \(G/G^ n\) is infinite for any odd \(n \geq n(G)\). In addition, \(\bigcap^ \infty_{i = 1} G^ i = \{1\}\). (Here \(G^ i\) is the subgroup generated by the \(i\)th powers of all elements of the groups \(G\).).
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Examples of Relatively Hyperbolic Groups
Geometriae Dedicata, 2002The author uses ideas on weak hyperbolicity and relative hyperbolicity which originate in work of Gromov. He uses the following definition of weak hyperbolicity that has been formulated by \textit{B. Farb} [in Geom. Funct. Anal. 8, No. 5, 810-840 (1998; Zbl 0985.20027)].
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Discriminating Completions of Hyperbolic Groups
Geometriae Dedicata, 2002Let \(A\) be an additively written Abelian group. The authors of the paper under review call a group \(G\) an \(A\)-group if it comes equipped with an action of \(A\) on \(G\) which mimics the way in which \(\mathbb{Z}\) acts on any group. More precisely, they call \(A\) unitary if it comes equipped with a distinguished nonzero element, which denoted ...
Baumslag, Gilbert +2 more
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Journal of Group Theory, 2006
We prove that a δ-hyperbolic group for δ < 1 2 is a free product F ∗ G1 ∗ . . . ∗Gn where F is a free group of finite rank and each Gi is a finite group.
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We prove that a δ-hyperbolic group for δ < 1 2 is a free product F ∗ G1 ∗ . . . ∗Gn where F is a free group of finite rank and each Gi is a finite group.
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Russian Mathematical Surveys, 1985
An abstract group \(\Gamma\) with a finite set of generators \(R_i\) is called the Coxeter group if \(R^2_i=1\), \((R_i\cdot R_j)^{n_{ij}}=1\), where \(n_{ij}\geq 2\). \textit{J. Tits} [Symp. Math. 1, 175--185 (1969; Zbl 0206.03002)] proved that every Coxeter group with the finite set of generators is represented by the reflexive group discrete in some
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An abstract group \(\Gamma\) with a finite set of generators \(R_i\) is called the Coxeter group if \(R^2_i=1\), \((R_i\cdot R_j)^{n_{ij}}=1\), where \(n_{ij}\geq 2\). \textit{J. Tits} [Symp. Math. 1, 175--185 (1969; Zbl 0206.03002)] proved that every Coxeter group with the finite set of generators is represented by the reflexive group discrete in some
openaire +2 more sources