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Related papers: Equations for formally real meadows

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In a recent paper, Freitas and Siksek proved an asypmtotic version of Fermat's Last Theorem for many totally real fields. We prove an extension of their result to generalized Fermat equations of the form $A x^p+B y^p+ C z^p=0$, where $A$,…

Number Theory · Mathematics 2015-05-25 Heline Deconinck

We provide a coherent picture of our efforts thus far in extending real algebra and its links to the theory of quadratic forms over ordered fields in the noncommutative direction, using hermitian forms and "ordered" algebras with…

Rings and Algebras · Mathematics 2018-04-19 Vincent Astier , Thomas Unger

We survey the 19th century development of the signature of a quadratic form, and the applications in the 20th and 21st century to the topology of manifolds and dynamical systems. Version 2 is an expanded and corrected version of Version 1,…

Algebraic Topology · Mathematics 2016-09-15 Etienne Ghys , Andrew Ranicki

We study the satisfiability problem of symbolic tree automata and decompose it into the satisfiability problem of the existential first-order theory of the input characters and the existential monadic second-order theory of the indices of…

Formal Languages and Automata Theory · Computer Science 2023-11-10 Rodrigo Raya

This paper proposes a new category theoretic account of equationally axiomatizable classes of algebras. Our approach is well-suited for the treatment of algebras equipped with additional computationally relevant structure, such as ordered…

Logic in Computer Science · Computer Science 2019-02-05 Stefan Milius , Henning Urbat

A biform theory is a combination of an axiomatic theory and an algorithmic theory that supports the integration of reasoning and computation. These are ideal for formalizing algorithms that manipulate mathematical expressions. A theory…

Logic in Computer Science · Computer Science 2017-07-27 Jacques Carette , William M. Farmer

Based on a new coinductive characterization of continuous functions we extract certified programs for exact real number computation from constructive proofs. The extracted programs construct and combine exact real number algorithms with…

Logic in Computer Science · Computer Science 2015-07-01 Ulrich Berger

We investigate the presence of twinlike models in theories described by several real scalar fields. We focus on the first-order formalism, and we show how to build distinct scalar field theories that support the same extended solution, with…

High Energy Physics - Theory · Physics 2014-03-17 D. Bazeia , A. S. Lobão , L. Losano , R. Menezes

We propose a geometric setting of the axiomatic mathematical formalism of quantum theory. Guided by the idea that understanding the mathematical structures of these axioms is of similar importance as was historically the process of…

Mathematical Physics · Physics 2017-11-27 Wolfgang Bertram

Axiomatic set theory is almost universally accepted as the basic theory which provides the foundations of mathematics, and in which the whole of present day mathematics can be developed. As such, it is the most natural framework for…

Logic in Computer Science · Computer Science 2012-03-29 Arnon Avron

This work is dedicated to the results were got in the model theory of the regular polygons. We give the characterization of the monoids with axiomatizable and model complete class of regular polygons. We describe the monoids with complete…

Logic · Mathematics 2018-05-09 A. V. Mikhalev , E. V. Ovchinnikova , E. A. Palyutin , A. A. Stepanova

We analyze the trade-off between model complexity and accuracy for random forests by breaking the trees up into individual classification rules and selecting a subset of them. We show experimentally that already a few rules are sufficient…

Machine Learning · Computer Science 2020-12-09 Michael Rapp , Eneldo Loza Mencía , Johannes Fürnkranz

A new scheme for proving pseudoidentities from a given set {\Sigma} of pseudoidentities, which is clearly sound, is also shown to be complete in many instances, such as when {\Sigma} defines a locally finite variety, a pseudovariety of…

Group Theory · Mathematics 2019-03-18 Jorge Almeida , Ondřej Klíma

A study of zero-dimensional theories, based on exact results, is presented. First, relying on a simple diagrammatic representation of the theory, equations involving the generating function of all connected Green's functions are…

High Energy Physics - Phenomenology · Physics 2009-01-07 E. N. Argyres , A. F. W. van Hameren , R. H. P. Kleiss , C. G. Papadopoulos

A realistic axiomatic formulation of Galilean Quantum Field Theories is presented, from which the most important theorems of the theory can be deduced. In comparison with others formulations, the formal aspect has been improved by the use…

Quantum Physics · Physics 2009-11-10 G. Puccini , H. Vucetich

We compute the continuous bounded cohomology of the full automorphism groups of regular trees in all positive degrees, with coefficients arising from any irreducible continuous unitary representations. To the author's knowledge, this seems…

Group Theory · Mathematics 2026-01-08 Cunyuan Zhao

One of the basic questions in number theory is to determine semi-simple l-adic representations of the absolute Galois group of a number field. In this paper, we discuss the question for two dimensional representations over a totally real…

Number Theory · Mathematics 2007-05-23 K. Fujiwara

Tree models are very widely used in practice of machine learning and data mining. In this paper, we study the problem of model integrity authentication in tree models. In general, the task of model integrity authentication is the design \&…

Cryptography and Security · Computer Science 2022-06-24 Weijie Zhao , Yingjie Lao , Ping Li

Meadows have been proposed as alternatives for fields with a purely equational axiomatization. At the basis of meadows lies the decision to make the multiplicative inverse operation total by imposing that the multiplicative inverse of zero…

Rings and Algebras · Mathematics 2014-11-04 J. A. Bergstra , C. A. Middelburg

The first-order formulation of the principal sigma model with a Lie group target space is performed. By using the dualisation of the algebra and the field content of the theory the field equations which are solely written in terms of the…

Mathematical Physics · Physics 2008-11-26 Nejat Tevfik Yilmaz