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Mathematische Zeitschrift, ISSN 0025-5874, 6/2013, Volume 274, Issue 1, pp. 647 - 665
We discuss the Funk function $$F(x,y)$$ on a Teichmüller space with its Weil–Petersson metric $$(\mathcal{T },d)$$ introduced in Yamada (Convex bodies in... 
Weil–Petersson metric | Hilbert metric | 51K05 | Funk metric | Mathematics, general | Teichmüller space | Non-symmetric distance | Mathematics | Mapping class groups | 53C60 | Weil-Petersson metric | MATHEMATICS | Teichmuller space | ISOMETRIES
Journal Article
Nonlinear Analysis, Theory, Methods and Applications, ISSN 0362-546X, 06/2015, Volume 119, pp. 199 - 208
We study Sobolev spaces on the n-dimensional unit ball Bn (1) endowed with a parameter-depending Finsler metric Fa , a∈[0,1], which interpolates between the... 
Funk metric Klein metric Finsler-Laplace operator Sobolev space Variational methods | MATHEMATICS | MATHEMATICS, APPLIED | Variational methods | Sobolev space | Klein metric | Funk metric | FINSLER MANIFOLDS | Finsler-Laplace operator | Manifolds | Nonlinearity | Operators | Vector spaces | Standards
Journal Article
Journal of Convex Analysis, ISSN 0944-6532, 2017, Volume 24, Issue 1, pp. 67 - 73
Given a convex set C in a real vector space E and two points x, y is an element of C, we investigate which are the possible values for the variation f(y)... 
Funk metric | Variations | Convex functions | Hilbert metric | Thompson metric | MATHEMATICS | variations
Journal Article
Monatshefte für Mathematik, ISSN 0026-9255, 10/2013, Volume 172, Issue 1, pp. 97 - 120
The goal of this paper is to introduce and to study analogues of the Euclidean Funk and Hilbert metrics on open convex subsets of the hyperbolic space... 
Hilbert metric | 53A35 | Funk metric | Minkowski space | 51A05 | Mathematics | Constant curvature | Non-Euclidean geometry | Generalized Beltrami–Klein model | Cross ratio | Mathematics, general | Primary 58B20 | Secondary 53C60 | Non-Euclidean trigonometry | Projective geometry | Generalized Beltrami-Klein model | MATHEMATICS | Geometric Topology
Journal Article
Popular Music, ISSN 0261-1430, 1/2008, Volume 27, Issue 1, pp. 53 - 76
In this essay, I examine how aspects of rhythm and metre play a fundamental role in shaping and defining Led Zeppelin's musical style. At the same time, I will... 
Musical meter | Musical bands | Guitars | Music practice | Music instrumentation | Funk | Musical rhythm | Drums | Music genres | Popular music | MUSIC | rock and roll song | Led Zeppelin | meter | folk poetry | England | folk song | rock and roll music | rhythm | folk literature | Rhythm | Style, Musical | Criticism and interpretation | Analysis | Bands (Music) | Bands | Rock music | Musical criticism | Musical styles
Journal Article
by Li, Y and Mo, XH
PUBLICATIONES MATHEMATICAE-DEBRECEN, ISSN 0033-3883, 2019, Volume 94, Issue 3-4, pp. 493 - 505
Dually flat Finsler metrics arise from alpha-flat information structures on Riemann-Finsler manifolds. Inspired by the theory of Funk functions and Hamel... 
Hamel function | MATHEMATICS | dually flat | Funk function | Finsler metric | spherically symmetric
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 06/2015, Volume 92, pp. 194 - 209
In Minkowski geometry the metric features are based on a compact convex body containing the origin in its interior. This body works as a unit ball and its... 
Minkowski functionals | Finsler spaces | Funk metrics | RIEMANNIAN METRICS | MATHEMATICS, APPLIED | SPACES | BERWALD MANIFOLDS | QUASI-TANGENT STRUCTURE | CONNECTIONS | PHYSICS, MATHEMATICAL
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2015, Volume 421, Issue 2, pp. 1274 - 1294
A version of Young's inequality for convolution is introduced and employed to some topics in convex- and set-valued analysis. The following problems are... 
Isoperimetric inequality | Multifunction | Funk–Radon transform | Young's inequality | Metrics for convex sets | Uniform equivalence | Funk-Radon transform | SPACE | MATHEMATICS | COMPACT | MATHEMATICS, APPLIED | METRICS | BODIES | Equality
Journal Article
Houston Journal of Mathematics, ISSN 0362-1588, 2018, Volume 44, Issue 2, pp. 495 - 520
The classical version of the problem we are going to discuss here is to minimize the so-called volume product [21]. The Blaschke-Santalo point as the solution... 
And phrases. Minkowski functionals | Finsler spaces | Area function | Funk metrics | RIEMANNIAN METRICS | MATHEMATICS | area function | Minkowski functionals | FINSLER | QUASI-TANGENT STRUCTURE
Journal Article
Differential Geometry and its Applications, ISSN 0926-2245, 12/2019, Volume 67, p. 101554
A timelike space is a Hausdorff topological space equipped with a partial order relation < and a distance function ρ satisfying a collection of axioms... 
Busemann geometry | Time inequality | Timelike Funk geometry | Exterior convex geometry | Timelike space | Timelike Hilbert geometry | MATHEMATICS | MATHEMATICS, APPLIED | Geometric Topology | Mathematics | Differential Geometry | Metric Geometry
Journal Article
中国科学:数学英文版, ISSN 1674-7283, 2017, Volume 60, Issue 12, pp. 2447 - 2464
Funk metrics are a kind of important Finsler metrics with constant negative flag curvature. In this paper, it is proved that any isoparametric hypersurface in... 
34D23 | principal curvature | Funk metric | Mathematics | Applications of Mathematics | Finsler-Laplacian | isoparametric hypersurfaces | 53C60 | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS, ISSN 1223-7027, 2010, Volume 72, Issue 2, pp. 3 - 12
The present paper deals with the Gaussian curvature K of a particular indicatrix in a general Finsler manifold. A formula for K similar to the one obtained by... 
MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | Gauss curvature | Funk metric | Finsler connection | hypersurface (alpha, beta)-metric | indicatrix | Randers metric | Finsler spaces | Hypersurface | Metric | Indicatrix
Journal Article
Journal of Geometric Analysis, ISSN 1050-6926, 10/2016, Volume 26, Issue 4, pp. 3056 - 3065
In 2001, Zhongmin Shen asked if it is possible for two projectively related Finsler metrics to have the same Riemann curvature (Shen in Differential Geometry... 
Jacobi endomorphism | Finsler metrizability | Riemann curvature | Funk function | Projective deformation | MATHEMATICS | HILBERTS 4TH PROBLEM | GEOMETRY | Mathematics - Differential Geometry
Journal Article
Pacific Journal of Mathematics, ISSN 0030-8730, 2013, Volume 265, Issue 1, pp. 185 - 197
We consider Hilbert and Funk geometries on a strongly convex domain in Euclidean space. We show that, with respect to the Lebesgue measure on the domain, the... 
Ricci curvature | Curvature-dimension condition | Hilbert geometry | Funk geometry | METRIC-MEASURE-SPACES | MATHEMATICS | curvature-dimension condition | MANIFOLDS
Journal Article
IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE, ISSN 1028-6276, 2005, Volume 29, Issue A3, pp. 357 - 366
In this paper the general relatively isotropic L-curvature Finsler metrics are studied. It is shown that on constant relatively Landsberg spaces, the concepts... 
Douglas tensor | MULTIDISCIPLINARY SCIENCES | (generalized) Landsberg metric | (mean) Cartan tensor | Funk metric | Finsler metric | Randers metric | (mean) Landsberg curavture
Journal Article
SUT Journal of Mathematics, ISSN 0916-5746, 2004, Volume 40, Issue 2, pp. 133 - 156
Journal Article
Mathematical Proceedings, ISSN 0305-0041, 2009, Volume 147, Issue 2
We discuss general notions of metrics and of Finsler structures which we call weak metrics and weak Finsler structures. Any convex domain carries a canonical... 
Geometric Topology | Mathematics
Journal Article
RIMS Kokyuroku Bessatsu, ISSN 1881-6193, 06/2014, Volume 48, pp. 57 - 72
Journal Article
Expositiones Mathematicae, ISSN 0723-0869, 2009, Volume 27, Issue 2, pp. 109 - 124
David Hilbert discovered in 1895 an important metric that is canonically associated to an arbitrary convex domain Ω in the Euclidean (or projective) space.... 
Weak Finsler structure | Tautological Finsler structure | Funk weak metric | Hilbert metric | Harmonic symmetrization | MATHEMATICS | Geometric Topology | Mathematics | Differential Geometry | Metric Geometry
Journal Article
Pattern Recognition, ISSN 0031-3203, 10/2019, Volume 94, pp. 96 - 109
•The proposed model can effectively transfer knowledge from auxiliary domains, and evaluate the importance of auxiliary domains.•The proposed model can well... 
Cross-domain collaborative filtering | Feature expansion | Funk-SVD decomposition | Classification | Latent factor space | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Information science | Control engineering | Usage | Algorithms | Analysis
Journal Article
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