$\mathcal {T}$-semiring pairs

Jaiung Jun; Kalina Mincheva; Louis Rowen

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Displaying similar documents to “ $𝒯$ -semiring pairs”

Cycles on algebraic models of smooth manifolds

Wojciech Kucharz (2009)

Journal of the European Mathematical Society

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Every compact smooth manifold $M$ is diffeomorphic to a nonsingular real algebraic set, called an algebraic model of $M$ . We study modulo 2 homology classes represented by algebraic subsets of $X$ , as $X$ runs through the class of all algebraic models of $M$ . Our main result concerns the case where $M$ is a spin manifold.

Algebraic Superconnections, $S U (2 ∣ 1)$ and Electroweak Interactions

R. Coquereaux (1992)

Recherche Coopérative sur Programme n°25

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The R₂ measure for totally positive algebraic integers

V. Flammang (2016)

Colloquium Mathematicae

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Let α be a totally positive algebraic integer of degree d, i.e., all of its conjugates $α ₁ = α, . . ., α_{d}$ are positive real numbers. We study the set ₂ of the quantities ${(\prod_{i = 1}^{d} {(1 + α ²_{i})}^{1 / 2})}^{1 / d}$ . We first show that √2 is the smallest point of ₂. Then, we prove that there exists a number l such that ₂ is dense in (l,∞). Finally, using the method of auxiliary functions, we find the six smallest points of ₂ in (√2,l). The polynomials involved in the auxiliary function are found by a recursive algorithm.

Algebraic independence of the values at algebraic points of a class of functions considered by Mahler

N. Ch. Wass

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This thesis is concerned with the problem of determining a measure of algebraic independence for a particular m-tuple θ₁,..., $θ_{m}$ of complex numbers. Specifically, let K be a number field and let f₁(z),..., $f_{m} (z)$ be elements of K[[z]] algebraically independent over K(z) satisfying equations of the form(*) $f_{j} (z^{b}) = \sum_{i = 1}^{m} f_{i} (z) a_{i j} (z) + b_{j} (z)$ (j = i,...,m)for b ≥ 2, $a_{i j} (z)$ , $b_{j} (z)$ in K(z). Suppose finally that α ∈ K is such that 0 < |α| < 1, the $f_{j} (z$ ) converge at z = α and the $a_{i j} (z)$ , $b_{j} (z)$ are analytic at $z = α, α^{b}, α^{b ²}, . . .$ Then the $θ_{i} = f_{i} (α)$ are algebraically independent...

On the principle of real moduli flexibility: perfect parametrizations

Edoardo Ballico, Riccardo Ghiloni (2014)

Annales Polonici Mathematici

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Let V be a real algebraic manifold of positive dimension. The aim of this paper is to show that, for every integer b (arbitrarily large), there exists a trivial Nash family $= {V_{y}}_{y \in R^{b}}$ of real algebraic manifolds such that V₀ = V, is an algebraic family of real algebraic manifolds over $y \in R^{b} ∖ 0$ (possibly singular over y = 0) and is perfectly parametrized by $R^{b}$ in the sense that $V_{y}$ is birationally nonisomorphic to $V_{z}$ for every $y, z \in R^{b}$ with y ≠ z. A similar result continues to hold if V is a singular real algebraic...

Diagonalization and rationalization of algebraic Laurent series

Boris Adamczewski, Jason P. Bell (2013)

Annales scientifiques de l'École Normale Supérieure

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We prove a quantitative version of a result of Furstenberg [20] and Deligne [14] stating that the diagonal of a multivariate algebraic power series with coefficients in a field of positive characteristic is algebraic. As a consequence, we obtain that for every prime $p$ the reduction modulo $p$ of the diagonal of a multivariate algebraic power series $f$ with integer coefficients is an algebraic power series of degree at most $p^{A}$ and height at most $A p^{A}$ , where $A$ is an effective constant that only...

Multiplicatively dependent triples of Tribonacci numbers

Carlos Alexis Ruiz Gómez, Florian Luca (2015)

Acta Arithmetica

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We consider the Tribonacci sequence $T : = {T_{n}}_{n \geq 0}$ given by T₀ = 0, T₁ = T₂ = 1 and $T_{n + 3} = T_{n + 2} + T_{n + 1} + T_{n}$ for all n ≥ 0, and we find all triples of Tribonacci numbers which are multiplicatively dependent.

Quasi-algebraic representability of sets in $R^{n}$ .

W. Waliszewski (1984)

Banach Center Publications

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Computation of linear algebraic equations with solvability verification over multi-agent networks

Xianlin Zeng, Kai Cao (2017)

Kybernetika

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In this paper, we consider the problem of solving a linear algebraic equation $A x = b$ in a distributed way by a multi-agent system with a solvability verification requirement. In the problem formulation, each agent knows a few columns of $A$ , different from the previous results with assuming that each agent knows a few rows of $A$ and $b$ . Then, a distributed continuous-time algorithm is proposed for solving the linear algebraic equation from a distributed constrained optimization viewpoint. The...

On a linear homogeneous congruence

A. Schinzel, M. Zakarczemny (2006)

Colloquium Mathematicae

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The number of solutions of the congruence $a ₁ x ₁ + \dots + a_{k} x_{k} \equiv 0 (m o d n)$ in the box $0 \leq x_{i} \leq b_{i}$ is estimated from below in the best possible way, provided for all i,j either $(a_{i}, n) | (a_{j}, n)$ or $(a_{j}, n) | (a_{i}, n)$ or $n | [a_{i}, a_{j}]$ .

Polynomial relations amongst algebraic units of low measure

John Garza (2014)

Acta Arithmetica

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For an algebraic number field and a subset $α_{1}, . . ., α_{r} \subseteq_{}$ , we establish a lower bound for the average of the logarithmic heights that depends on the ideal of polynomials in $ℚ [x_{1}, . . ., x_{r}]$ vanishing at the point $(α_{1}, . . ., α_{r})$ .

Rational fixed points for linear group actions

Pietro Corvaja (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We prove a version of the Hilbert Irreducibility Theorem for linear algebraic groups. Given a connected linear algebraic group $G$ , an affine variety $V$ and a finite map $π : V \to G$ , all defined over a finitely generated field $κ$ of characteristic zero, Theorem 1.6 provides the natural necessary and sufficient condition under which the set $π (V (κ))$ contains a Zariski dense sub-semigroup $Γ \subset G (κ)$ ; namely, there must exist an unramified covering $p : \tilde{G} \to G$ and a map $θ : \tilde{G} \to V$ such that $π \circ θ = p$ . In the case $κ = ℚ$ , $G = 𝔾_{a}$ is the additive group, we...

Automatic continued fractions are transcendental or quadratic

Yann Bugeaud (2013)

Annales scientifiques de l'École Normale Supérieure

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We establish new combinatorial transcendence criteria for continued fraction expansions. Let $α = [0; a_{1}, a_{2}, ...]$ be an algebraic number of degree at least three. One of our criteria implies that the sequence of partial quotients ${(a_{ℓ})}_{ℓ \geq 1}$ of $α$ is not ‘too simple’ (in a suitable sense) and cannot be generated by a finite automaton.

Harmonic functions in four variables with rational and algebraic $p_{4}$ -associates

R. P. Gilbert (1964)

Annales Polonici Mathematici

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Algebraic continued fractions in $_{q} ((T^{- 1}))$ and recurrent sequences in $_{q}$

Alain Lasjaunias (2008)

Acta Arithmetica

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Congruence preserving operations on the ring $ℤ_{p^{3}}$

Cyril Gavala, Miroslav Ploščica, Ivana Varga (2023)

Mathematica Bohemica

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We investigate the interval $I (p^{3})$ in the lattice of clones on the ring $ℤ_{p^{3}}$ between the clone of polynomial operations and the clone of congruence preserving operations. All clones in this interval are known and described by means of generators. In this paper, we characterize each of these clones by the property of preserving a small set of relations. These relations turn out to be in a close connection to commutators.

Displaying similar documents to “ 𝒯 -semiring pairs”

Displaying similar documents to “ $𝒯$ -semiring pairs”