Results 11 to 20 of about 282 (146)
Wave Transport and Localization in Prime Number Landscapes
Frontiers in Physics, 2021 In this paper, we study the wave transport and localization properties of novel aperiodic structures that manifest the intrinsic complexity of prime number distributions in imaginary quadratic fields.
Luca Dal Negro +4 more
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On the Galois Cohomology of the Ring of Integers in an Algebraic Number Field [PDF]
Proceedings of the American Mathematical Society, 1969 On the basis of these results he conjectured in [9] that the groups Hr(G, OF) have the same order also in the case when G is not cyclic. In the present note, we shall show that the conjecture is false. We shall also demonstrate how the problem of determining Hr(G, OF) can be localized.
Lee, M. P., Madan, M. L.
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Two-primary algebraic 𝐾-theory of rings of integers in number fields [PDF]
Journal of the American Mathematical Society, 1999 We relate the algebraic K K -theory of the ring of integers in a number field
J. Rognes +2 more
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Algorithmic search for integer Abelian roots of a polynomial with integer Abelian coefficients [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. ИнформатикаIn this work, we consider the operations over Abelian integers of rank $n$. By definition, such numbers are elements of the complex field and have the form of polynomials with integer coefficients from the $n$th degree primitive root of 1.
Tsybulya, Liliya Mikhailovna
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On the integer ring of the compositum of algebraic number fields [PDF]
Nagoya Mathematical Journal, 1980 Let k be an algebraic number field of finite degree. For a finite extension L/k we denote by L/k the different of L/k, and by L the integer ring of L. Let K1 and K2 be finite extensions of k.
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A Diophantine definition of rational integers over some rings of algebraic numbers. [PDF]
Notre Dame Journal of Formal Logic, 1992 After a negative answer was given to Hilbert's Tenth Problem (that is, is there an algorithm that identifies the diophantine equations which have rational integer solutions and those that don't?) it is natural to ask a similar question in various other domains, for example, in the ring of integers \({\mathcal O}_ K\) of a number field \(K\).
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On the Ring of Integers in an Algebraic Number Field as a representation Module of Galois Group [PDF]
Nagoya Mathematical Journal, 1960 1. Introduction. It is known that there are only three rationally inequivalent classes of indecomposable integral representations of a cyclic group of prime order l. The representations of these classes are: (I) identical representation,(II) rationally irreducible representation of degree l – 1,(III) indecomposable representation consisting of one ...
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An arithmetic site for the rings of integers of algebraic number fields
Inventiones mathematicae, 1996 Let \(K\) be an algebraic number field and \(S\) a finite set of primes of \(K\) containing the infinite primes and the primes dividing a given prime number \(p\). Let \(G_S (p)\) be the Galois group of the maximal \(p\)-extension of \(K\) unramified outside \(S\).
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Exact Discrete Stochastic Simulation With Deep‐Learning‐Scale Gradient Optimization
Advanced Science, EarlyView.A 203,796‐parameter gene regulatory network classifies handwritten digits with 98.4% accuracy using exact stochastic dynamics. The framework decouples forward simulation from backward differentiation, making continuous‐time Markov chain models compatible with deep‐learning optimization.
Jose M. G. Vilar, Leonor Saiz
wiley +1 more source
Hybrid structure of maximal ideals in near rings
Complex & Intelligent SystemsA hybrid structure is an arrangement that makes use of many hierarchical reporting structures and is applied to algebraic structures such as groups and rings.
B. Jebapresitha
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