Strong congruence spaces and dimension in $\mathbb{F}_1$-geometry [PDF]
, 2023 We introduce strong congruence spaces, which are topological spaces that provide a useful concept of dimension for monoid schemes. We study their properties and show that, given a toric monoid scheme over an algebraically closed basis, its strong congruence space and the complex toric variety associated to its fan have the same dimension.
Manoel Jarra
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The Geometry of Modular Congruence Spaces
This paper delves into the intricate geometric structures arising from modular congruence spaces, which are quotients of the upper half-plane by congruence subgroups of the modular group SL(2,Z). These spaces serve as fundamental objects in number theory, algebraic geometry, and the theory of automorphic forms, encoding deep arithmetic information.
SÉRGIO DE ANDRADE, PAULO
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Mirror symmetry and projective geometry of Reye congruences I [PDF]
Journal of Algebraic Geometry, 2011 Studying the mirror symmetry of a Calabi-Yau threefold X X of the Reye congruence in P 4 \mathbb {P}^4 , we conjecture that X X has a non-trivial Fourier-Mukai partner Y Y .
Shinobu Hosono, Hiromichi Takagi
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A comparison between a patient-specific bone regenerative implant and the osteochondral allograft procedure in a Hill-Sachs lesion, a cadaveric study [PDF]
JSES Reviews, Reports, and TechniquesBackground: Anterior shoulder instability with >30% humeral bone loss is typically treated with an osteochondral allograft (OCA), though complications and reoperation rates remain high (20%-30%).
Michał S. Gałek-Aldridge, MD +6 more
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The topological shadow of $${{{\mathbb {F}}}_1}$$-geometry: congruence spaces
Mathematische ZeitschriftThis paper is based on monoid schemes, which are related to and are termed the minimalist approach to algebraic geometry over $\mathbb{F}_1$ or $\mathbb{F}_1$-geometry in short. Monoid schemes connect with various other geometry fields, such as those with toric geometry, which the reviewer was familiar with. One can refer to [\textit{A. Deitmar}, Beitr.
Oliver Lorscheid, Samarpita Ray
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Evolution of inhomogeneous LTB geometry with tilted congruence and modified gravity [PDF]
Canadian Journal of Physics, 2017 The goal of this paper is to shed some light on the significance of congruence of observers, which seems to affect the dynamics of the universe under Palatini f(R) formalism. Starting by setting up the formalism needed, we have explored the field equations using Lemaitre–Tolman–Bondi geometry as an interior metric.
Z. Yousaf, M. Z. Bhatti, Aamna Rafaqat
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Projective geometries of congruence and finite projective geometries [PDF]
Transactions of the American Mathematical Society, 1907 Beppo Levi
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Strong congruence spaces and dimension in
Journal of pure and applied algebraWe introduce strong congruence spaces, which are topological spaces that provide a useful concept of dimension for monoid schemes. We study their properties and show that, given a toric monoid scheme over an algebraically closed basis, its strong congruence space and the complex toric variety associated to its fan have the same dimension.
Manoel Jarra
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Student Teachers' Knowledge of Congruence before a University Course on Geometry
, 2022 Student Teachers' Knowledge of Congruence before a University Course on ...
Max Hoffmann, Rolf Biehler
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A new property of congruence lattices of slim, planar, semimodular lattices [PDF]
Categories and General Algebraic Structures with Applications, 2022 The systematic study of planar semimodular lattices started in2007 with a series of papers by G. Grätzer and E. Knapp. These lattices haveconnections with group theory and geometry. A planar semimodular latticeL is slim if M3 it is not a sublattice of L.
Gábor Cz´edli, George Gr¨atzer
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