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Unramified Quadratic Extensions of a Quadratic Field
Rocky Mountain Journal of Mathematics, 1995 The authors determine all quartic number fields \(L/\mathbb{Q}\) possessing a quadratic subfield \(\mathbb{Q}\subset K\subset L\) such that \(L/K\) is unramified at all finite primes. They do this by an explicit calculation of the generators and make no use of Hilbert's theory.
Blair K Spearman
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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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Extensions of dissipative operators with closable imaginary part [PDF]
Opuscula Mathematica, 2021 Given a dissipative operator \(A\) on a complex Hilbert space \(\mathcal{H}\) such that the quadratic form \(f \mapsto \text{Im}\langle f, Af \rangle\) is closable, we give a necessary and sufficient condition for an extension of \(A\) to still be ...
Christoph Fischbacher
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Explicitly solvable systems of two autonomous first-order Ordinary Differential Equations with homogeneous quadratic right-hand sides [PDF]
Open Communications in Nonlinear Mathematical Physics, 2021 After tersely reviewing the various meanings that can be given to the property of a system of nonlinear ODEs to be solvable, we identify a special case of the system of two first-order ODEs with homogeneous quadratic right-hand sides which is explicitly ...
Francesco Calogero, Farrin Payandeh
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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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Existence of Split Property in Quaternion Algebra Over Composite of Quadratic Fields
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2023 Quaternions are extensions of complex numbers that are four-dimensional objects. Quaternion consists of one real number and three complex numbers, commonly denoted by the standard vectors and .
Muhammad Faldiyan +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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Coordination of Home Appliances for Demand Response: An Improved Optimization Model and Approach
IEEE Access, 2021 Home appliances constitute an interesting source of flexibility for demand response programs. However, their control and coordination are challenging, since typically a high number of such appliances has to be aggregated in order to provide a sufficient ...
Steffen Limmer +3 more
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Parallel machine arithmetic for recurrent number systems in non-quadratic fields [PDF]
Компьютерная оптика, 2020 The paper proposes a new method of synthesis of computer arithmetic systems for "error-free" parallel calculations. The difference between the proposed approach and calculations in traditional systems of Residue Number Systems for the direct sum of ...
Vladimir Chernov
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