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Multifractality of light in photonic arrays based on algebraic number theory [PDF]
Communications Physics, 2020 Many natural patterns and shapes, such as meandering coastlines, clouds, or turbulent flows, exhibit a characteristic complexity that is mathematically described by fractal geometry.
F. Sgrignuoli +5 more
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N\'eron models of Jacobians over bases of arbitrary dimension [PDF]
Épijournal de Géométrie Algébrique, 2022 We work with a smooth relative curve $X_U/U$ with nodal reduction over an excellent and locally factorial scheme $S$. We show that blowing up a nodal model of $X_U$ in the ideal sheaf of a section yields a new nodal model, and describe how these models ...
Thibault Poiret
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On the Prym variety of genus 3 covers of genus 1 curves [PDF]
Épijournal de Géométrie Algébrique, 2018 Given a generic degree-2 cover of a genus 1 curve D by a non hyperelliptic genus 3 curve C over a field k of characteristic different from 2, we produce an explicit genus 2 curve X such that Jac(C) is isogenous to the product of Jac(D) and Jac(X).
Christophe Ritzenthaler +1 more
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Formal proofs in real algebraic geometry: from ordered fields to quantifier elimination [PDF]
Logical Methods in Computer Science, 2012 This paper describes a formalization of discrete real closed fields in the Coq proof assistant. This abstract structure captures for instance the theory of real algebraic numbers, a decidable subset of real numbers with good algorithmic properties.
Assia Mahboubi, Cyril Cohen
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Finite-time average consensus for multi-agent systems under impulsive disturbances
Nantong Daxue xuebao. Ziran kexue ban, 2023 This study explores finite-time average consensus in multi-agent systems with switching topologies under impulsive disturbances. Utilizing algebraic graph theory, finite-time stability theorems, and impulsive control theory,criteria for finite-time ...
GENG Xiaopeng; Lü Xiaoxiao
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Q_l-cohomology projective planes and singular Enriques surfaces in characteristic two [PDF]
Épijournal de Géométrie Algébrique, 2019 We classify singular Enriques surfaces in characteristic two supporting a rank nine configuration of smooth rational curves. They come in one-dimensional families defined over the prime field, paralleling the situation in other characteristics, but ...
Matthias Schütt
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Square Integer Matrix with a Single Non-Integer Entry in Its Inverse
Mathematics, 2021 Matrix inversion is one of the most significant operations on a matrix. For any non-singular matrix A∈Zn×n, the inverse of this matrix may contain countless numbers of non-integer entries. These entries could be endless floating-point numbers.
Arif Mandangan +2 more
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, 2022 First published in 1975, this classic book gives a systematic account of transcendental number theory, that is, the theory of those numbers that cannot be expressed as the roots of algebraic equations having rational coefficients.
Alan Baker, D. Masser
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Prime Spectrum of the Ring of Adeles of a Number Field
Mathematics, 2022 Much is known about the adele ring of an algebraic number field from the perspective of harmonic analysis and class field theory. However, its ring-theoretical aspects are often ignored.
Álvaro Serrano Holgado
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An Introduction to Probabilistic Number Theory, 2020 : Let K be a number field. Then we completely classify the preperiodic portraits of the maps f ( x ) = x d + c where c ∈ K is an algebraic integer and d ≫ K 0 . More precisely, we prove that, up to accounting for the natural action of d th roots of unity
Don Redmond
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