Results 131 to 140 of about 62,458 (328)
Generating Ideals in Rings of Integer-Valued Polynomials
Canadian Mathematical Bulletin, 1985 AbstractLetRbe a one-dimensional locally analytically irreducible Noetherian domain with finite residue fields. In this note it is shown that if I is a finitely generated ideal of the ring Int(R) of integer-valued polynomials such that for eachx∈ R the idealis stronglyn-generated,n≥ 2, thenIisn-generated, and some variations of this result.
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Advanced Science, EarlyView.Hyperfine coupling to 29Si$^{29}{\rm Si}$ and 73Ge$^{73}{\rm Ge}$ nuclear spins limits hole spin‐qubit coherence in Ge heterostructures. We demonstrate device‐grade, nuclear‐spin‐free 70Ge$^{70}{\rm Ge}$/28Si70Ge$^{28}{\rm Si}^{70}{\rm Ge}$ quantum wells grown on industrial SiGe buffers with minimal use of enriched precursors.
Patrick Daoust +11 more
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Concerning the Solutions of Some Lebesgue-Ramanujan-Nagell Equations
Communications in Advanced Mathematical SciencesIn this paper, we provide a complete classification of the integer solutions to the Diophantine equation $x^2 + 3^a 19^b 73^c = \lambda y^n,$ where \( \lambda = 2^{\delta} \), \( x, y \geq 1 \), \( a, b, c, \delta \geq 0 \), \( n \geq 3 \), \( \gcd(x, y)
Mustafa Aydın, Murat Alan
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Elimination theory for the ring of algebraic integers.
Journal für die reine und angewandte Mathematik (Crelles Journal), 1988 Let \(\mathcal R\) be the ring of all algebraic integers, \(\mathcal R\subset\mathbb C\). The author proves the following elimination theorem: Each elementary problem about \(\mathcal R\) can be effectively reduced to a finite number of ideal membership questions about the algebraic integers constructed by a simple algorithm from the parameters of the ...
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Unit Fractions in Norm-Euclidean Rings of Integers
, 2014 In this paper we make a Gaussian integer version of the Erd s-Straus conjecture and we solve the Erd s-Straus diophantine equation over the rings of integers of norm-Euclidean quadratic fields.
Bradford, K., Ionascu, E. J.
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ML Workflows for Screening Degradation‐Relevant Properties of Forever Chemicals
Advanced Science, EarlyView.The environmental persistence of per‐ and polyfluoroalkyl substances (PFAS) necessitates efficient remediation strategies. This study presents physics‐informed machine learning workflows that accurately predict critical degradation properties, including bond dissociation energies and polarizability.
Pranoy Ray +3 more
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Unit, Irreducible, and Prime Elements of The Integral Domain Z[sqrt (5)]
Jurnal MatematikaIn abstract algebra at the undergraduate level, the ring Z[sqrt(5)] is often used as a simple example of an integral domain that does not satisfy the unique factorization domain (UFD) but Z[sqrt(5)] is Halfway Factorial Domain (HFD).
Daisyah Alifian Fatahillaj
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The associated orders of rings of integers in Lubin-Tate division fields over the $p$-adic number field [PDF]
, 1995 Chong-Hai Lim
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Advanced Science, EarlyView.A meta‐YAG crystal with artificially order/disorder structures was fabricated to realize the efficient third‐harmonic generation at 343 nm with a conversion efficiency of 4.5×10−3, surpassing six orders of magnitude compared to bulk YAG crystal. Moreover, a wide spectral tunability from 331 to 356 nm was also achieved in the meta‐YAG, indicating its ...
Xiaotian Guo +6 more
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Graph of Orthogonal Idempotent Elements in Rings of Integers Modulo n With Spectral Clustering
Journal of MathematicsThe zero-divisor graph provides a relationship between abstract algebra and graph theory. Based on this concept, a new graph is defined using the orthogonal idempotent elements in a ring.
Shaimaa H. Ahmad +3 more
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