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Logarithmic kinetics and bundling in random packings of elongated 3D physical links. [PDF]
Proc Natl Acad Sci U S ABonamassa I +8 more
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Algorithmic Breakthroughs in Factoring Sparse Polynomials over Algebraic Number Fields
SÉRGIO DE ANDRADE, PAULO
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The Physical Spectrum of a Driven Jaynes-Cummings Model. [PDF]
Entropy (Basel)Medina-Dozal L +6 more
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Unraveling the Link Between n-Back Working Memory and Algebraic Ability in Adolescents: Correlations and Training Effects. [PDF]
Psych JLi J +6 more
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Critical points and syzygies for Feynman integrals. [PDF]
J High Energy PhysPage B, Song Q.
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Realizing Algebraic Number Fields
1983In the paper [13], the authors studied the problem of realizing rational division algebras in a special way. Let D be a division algebra that is finite dimensional over the rational field Q. If p is a prime, we say that D is p-realizable when there is a p-local torsion free abelian group A whose rank is the dimension of D over Q, such that D is ...
R. S. Pierce, C. I. Vinsonhaler
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ON NONMONOGENIC ALGEBRAIC NUMBER FIELDS
Rocky Mountain Journal of Mathematics, 2023Let \(p\) be a prime number and \(f (x) = x^{p^ s}- ax^m- b\) belonging to \(\mathbb Z[x]\) be an irreducible polynomial. Let \( K = \mathbb Q(\theta )\) be an algebraic number field with \(\theta\) a root of \( f (x)\). Let \(r_1\) stand for the highest power of \(p\) dividing \(b^{p^s}- b -ab^m.\) This paper gives some explicit conditions involving ...
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2016
Arithmetical algorithms considered in Chap. 5 are based on the arithmetical operations with matrices of the number systems. If the entries of these matrices are not integers or rationals, we need arithmetical algorithms which work with them. Such algorithms exist for algebraic numbers.
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Arithmetical algorithms considered in Chap. 5 are based on the arithmetical operations with matrices of the number systems. If the entries of these matrices are not integers or rationals, we need arithmetical algorithms which work with them. Such algorithms exist for algebraic numbers.
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2019
A complex number \(\xi \) is called an algebraic integer if \(\mathbf {Z}[ \xi ]\) is a finitely generated \(\mathbf {Z}\)-module; this condition is equivalent to the fact that \(f( \xi )=0\) for some polynomial \(f(X)=X^m+a_1X^{m-1}+ \cdots +a_m\), \(a_i \in \mathbf {Z}\). Let \(\mathbf {A}\) be the set of all algebraic integers.
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A complex number \(\xi \) is called an algebraic integer if \(\mathbf {Z}[ \xi ]\) is a finitely generated \(\mathbf {Z}\)-module; this condition is equivalent to the fact that \(f( \xi )=0\) for some polynomial \(f(X)=X^m+a_1X^{m-1}+ \cdots +a_m\), \(a_i \in \mathbf {Z}\). Let \(\mathbf {A}\) be the set of all algebraic integers.
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Journal of Soviet Mathematics, 1987
Translation from Itogi Nauki Tekh., Ser. Algebra Topol. Geom. 22, 117--204 (Russian) (1984; Zbl 0563.12002).
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Translation from Itogi Nauki Tekh., Ser. Algebra Topol. Geom. 22, 117--204 (Russian) (1984; Zbl 0563.12002).
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