Zobrazeno 1 - 10
of 316
pro vyhledávání: '"KATZ, MIKHAIL G."'
Autor:
Hebda, James J., Katz, Mikhail G.
We study the maximum ratio of the Euclidean norm to the comass norm of p-covectors in Euclidean n-space and improve the known upper bound found in the standard references by Whitney and Federer. We go on to prove stable systolic inequalities when the
Externí odkaz:
http://arxiv.org/abs/2411.13966
Publikováno v:
London Mathematical Society Newsletter (2024), no. 512, 33-37
We present some similarities between Leibnizian and Robinsonian calculi, and address some objections raised by historians. The comparison with NSA facilitates our appreciation of some Leibnizian procedures that may otherwise seem obscure. We argue th
Externí odkaz:
http://arxiv.org/abs/2409.17154
Publikováno v:
Journal of Geometry 114 (2023), article 23
The existence of nontrivial cup products or Massey products in the cohomology of a manifold leads to inequalities of systolic type, but in general such inequalities are not optimal (tight). Gromov proved an {optimal} systolic inequality for complex p
Externí odkaz:
http://arxiv.org/abs/2407.03803
Autor:
Katz, Mikhail G., Sabourau, Stephane
More than thirty years ago, Brooks and Buser-Sarnak constructed sequences of closed hyperbolic surfaces with logarithmic systolic growth in the genus. Recently, Liu and Petri showed that such logarithmic systolic lower bound holds for every genus (no
Externí odkaz:
http://arxiv.org/abs/2407.02041
Autor:
Katz, Mikhail G.
We give a synthetic construction of a complete system of mutually unbiased bases in $\mathbb{C}^3$.
Comment: 6 pages, to appear in Open Mathematics
Comment: 6 pages, to appear in Open Mathematics
Externí odkaz:
http://arxiv.org/abs/2405.20873
Autor:
Katz, Mikhail G., Sabourau, Stephane
We show that every closed nonpositively curved surface satisfies Loewner's systolic inequality. The proof relies on a combination of the Gauss-Bonnet formula with an averaging argument using the invariance of the Liouville measure under the geodesic
Externí odkaz:
http://arxiv.org/abs/2404.00757
Publikováno v:
Antiquitates Mathematicae 17 (2023), 29-65
An alleged opposition between David Hilbert and Felix Klein as modern vs countermodern has been pursued by marxist historian Herbert Mehrtens and others. Scholars such as Epple, Grattan-Guinness, Gray, Quinn, Rowe, and recently Siegmund-Schultze and
Externí odkaz:
http://arxiv.org/abs/2402.00122
Publikováno v:
REVISTA LATINOAMERICANA de FILOSOF\'\IA 49 (2023), no. 2, 241-258
In his 1676 text De Quadratura Arithmetica, Leibniz distinguished infinita terminata from infinita interminata. The text also deals with the notion, originating with Desargues, of the perspective point of intersection at infinite distance for paralle
Externí odkaz:
http://arxiv.org/abs/2311.06023
Autor:
Hrbacek, Karel, Katz, Mikhail G.
Publikováno v:
Journal of Logic and Analysis 15:6 (2023), 1-19
We provide choiceless proofs using infinitesimals of the global versions of Peano's existence theorem and Osgood's theorem on maximal solutions. We characterize all solutions in terms of infinitesimal perturbations. Our proofs are more effective than
Externí odkaz:
http://arxiv.org/abs/2311.01374
Autor:
Ugaglia, Monica, Katz, Mikhail G.
Publikováno v:
B. Sriraman (ed.), Handbook of the History and Philosophy of Mathematical Practice, Springer, 2023
In this paper we offer a reconstruction of the evolution of Leibniz's thought concerning the problem of the infinite divisibility of bodies, the tension between actuality, unassignability and syncategorematicity, and the closely related question of t
Externí odkaz:
http://arxiv.org/abs/2310.14249