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Splines in geometry and topology [PDF]
Computer Aided Geometric Design, 2016 This survey paper describes the role of splines in geometry and topology, emphasizing both similarities and differences from the classical treatment of splines. The exposition is non-technical and contains many examples, with references to more thorough treatments of the subject.
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An Application of Total-Colored Graphs to Describe Mutations in Non-Mendelian Genetics
Mathematics, 2019 Any gene mutation during the mitotic cell cycle of a eukaryotic cell can be algebraically represented by an isotopism of the evolution algebra describing the genetic pattern of the inheritance process.
Raúl M. Falcón +2 more
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On the initial singularity and extendibility of flat quasi-de Sitter spacetimes
Journal of High Energy Physics, 2023 Inflationary spacetimes have been argued to be past geodesically incomplete in many situations. However, whether the geodesic incompleteness implies the existence of an initial spacetime curvature singularity or whether the spacetime may be extended ...
Ghazal Geshnizjani +2 more
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Geometry and topological photonics
Journal of Optics, 2023 Abstract Topological photonics provides a powerful framework to describe and understand many nontrivial wave phenomena in complex electromagnetic platforms. The topological index of a physical system is an abstract global property that depends on the family of operators that describes the propagation of Bloch waves.
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On the monopole Lefschetz number of finite-order diffeomorphisms [PDF]
, 2021 Let K be a knot in an integral homology 3-sphere Y and Sigma the corresponding n-fold cyclic branched cover. Assuming that Sigma is a rational homology sphere (which is always the case when n is a prime power), we give a formula for the Lefschetz number ...
Saveliev, Nikolai +2 more
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Advances in Difference Equations, 2021 The constant elasticity of substitution (CES for short) is a basic property widely used in some areas of economics that involves a system of second-order nonlinear partial differential equations.
Haila Alodan +3 more
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Differential Geometry of Submanifolds in Complex Space Forms Involving δ-Invariants
Mathematics, 2022 One of the fundamental problems in the theory of submanifolds is to establish optimal relationships between intrinsic and extrinsic invariants for submanifolds.
Bang-Yen Chen +2 more
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Varieties of Topological Geometries [PDF]
Transactions of the American Mathematical Society, 1993 A variety of topological geometries is either A. a projective variety L ( F ) \mathcal {L}(F) over some topological field F F , or B. a matchstick variety M ( X ) \mathcal {M}(X) over some topological space
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Geometry of CMC surfaces of finite index
Advanced Nonlinear Studies, 2023 Given r0>0{r}_{0}\gt 0, I∈N∪{0}I\in {\mathbb{N}}\cup \left\{0\right\}, and K0,H0≥0{K}_{0},{H}_{0}\ge 0, let XX be a complete Riemannian 3-manifold with injectivity radius Inj(X)≥r0\hspace{0.1em}\text{Inj}\hspace{0.1em}\left(X)\ge {r}_{0} and with the ...
Meeks William H., Pérez Joaquín
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On Canonical Almost Geodesic Mappings of Type π2(e)
Mathematics, 2020 In the paper, we consider canonical almost geodesic mappings of type π 2 ( e ) . We have found the conditions that must be satisfied for the mappings to preserve the Riemann tensor.
Volodymyr Berezovski +3 more
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