Results 11 to 20 of about 7,643 (261)
On the Content Bound for Real Quadratic Field Extensions
Axioms, 2012 Let K be a finite extension of Q and let S = {ν} denote the collection of K normalized absolute values on K. Let V+K denote the additive group of adeles over K and let K ≥0 c : V + → R denote the content map defined as c({aν }) = Q K ν ∈S ν (aν ) for
Robert G. Underwood
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Formalized Mathematics, 2021 Summary In this article we further develop field theory [6], [7], [12] in Mizar [1], [2], [3]: we deal with quadratic polynomials and quadratic extensions [5], [4]. First we introduce quadratic polynomials, their discriminants and prove the midnight formula. Then we show that - in case the discriminant of
Schwarzweller, Christoph +1 more
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Quadratic Extensions in ACL2 [PDF]
Electronic Proceedings in Theoretical Computer Science, 2020 Given a field K, a quadratic extension field L is an extension of K that can be generated from K by adding a root of a quadratic polynomial with coefficients in K. This paper shows how ACL2(r) can be used to reason about chains of quadratic extension fields Q = K_0, K_1, K_2, ..., where each K_i+1 is a quadratic extension field of K_i.
Ruben Gamboa +2 more
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Trims and extensions of quadratic APN functions [PDF]
Designs, Codes and Cryptography, 2022 AbstractIn this work, we study functions that can be obtained by restricting a vectorial Boolean function$$F :\mathbb {F}_{2}^n \rightarrow \mathbb {F}_{2}^n$$F:F2n→F2nto an affine hyperplane of dimension$$n-1$$n-1and then projecting the output to an$$n-1$$n-1-dimensional space.
Christof Beierle +2 more
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Supersimplicity and quadratic extensions [PDF]
Archive for Mathematical Logic, 2008 The paper deals with the algebraic characterization of supersimple fields. Pillay conjectured that such a field \(K\) is perfect, bounded and pseudo algebraically closed, and with Poizat proved both perfection and boundedness. Thus it remains to prove or disprove pseudo algebraic closedness, in other words that every absolutely irreducible plane curve ...
Amador Martin-Pizarro, Frank O. Wagner
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The quadratic Graver cone, quadratic integer minimization, and extensions [PDF]
Mathematical Programming, 2012 We consider the nonlinear integer programming problem of minimizing a quadratic function over the integer points in variable dimension satisfying a system of linear inequalities. We show that when the Graver basis of the matrix defining the system is given, and the quadratic function lies in a suitable {\em dual Graver cone}, the problem can be solved ...
Jon Lee 0001 +3 more
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The size function for quadratic extensions of complex quadratic fields [PDF]
Journal de théorie des nombres de Bordeaux, 2017 The function h 0 for a number field is an analogue of the dimension of the Riemann–Roch spaces of divisors on an algebraic curve.
Tran Nguyen Thanh, Ha
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Quadratic Zonotopes:An extension of Zonotopes to Quadratic Arithmetics
CoRR, 2014 Affine forms are a common way to represent convex sets of $\mathbb{R}$ using a base of error terms $ε\in [-1, 1]^m$. Quadratic forms are an extension of affine forms enabling the use of quadratic error terms $ε_i ε_j$. In static analysis, the zonotope domain, a relational abstract domain based on affine forms has been used in a wide set of settings, e ...
Assalé, Adjé +2 more
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On quadratic Ostrowski extensions of imaginary quadratic fields
The Ramanujan Journal, 2022 Abstract In this paper we discuss an analogue of Hilbert’s theorems 105 and106, i.e. a re-interpretation of Gauss’ “genus theory”, for imaginary quadratic fields of class number one. We explicitly compute all biquadratic fields whose ambiguous ideal classes over an imaginary quadratic field of class number one are principal.
Naroui, Razieh, Rajaei, Ali
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Nonlinear evolution of water waves and their dispersion relation in coastal waters [PDF]
Theoretical and Applied Mechanics, 2023 Preliminary results of the derivation of a new phase-resolving (deterministic) spatio-temporal nonlinear model of water wave evolution in nondeep waters with constant bathymetry are presented in this paper. The model is the first of its kind to include a
Vrećica Teodor, Toledo Yaron
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