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Том 11, № 4 (2019)
- Год: 2019
- Статей: 8
- URL: https://journals.rcsi.science/2070-0466/issue/view/12541
Research Articles
p-Adic Zeroes of the Kubota-Leopoldt Zeta-Function
Аннотация
In this paper we establish why the p-adic zeta function has a Dirichlet series expansion. We compute an improved expansion, which allows us to express it as a power-series modulo pn. Using this expansion, we compute all the zeros of Lp(s, χωj) for those quadratic characters χ of conductor < 200. For the calculation we use a PARI-GP Program.
255-269
Hysteresis, Unconscious and Economics
Аннотация
Considering the main aspects of a previous formal model of the relationships unconscious-conscious based on the representation of mental entities by m-adic numbers through hysteresis phenomenology, a pattern which has been then used to work out a possible psychoanalytic model of human consciousness as well as to argue on a simple derivations of p-adic Weber-Fechner laws of psychophysics, we now carry on along this formal analysis putting forward some remarks about the possible applications and consequences of this model of human psyche in regard to central themes of economics and sociology.
270-279
The Uniform Distribution of Sequences Generated by Iterated Polynomials
Аннотация
In the paper we show that given a polynomial f over ℤ = 0, ±1, ±2, ..., deg f ⩾ 2, the sequence x, f(x), f(f(x)) = f(2)(x), ..., where x is m-adic integer, produces a uniformly distributed set of points in every real unit hypercube under a natural map of the space ℤm of m-adic integers onto unit real interval. Namely, let m, s ∈ ℕ = {1, 2, 3, ...}, m > 1, let κn have a discrete uniform distribution on the set {0, 1, ..., mn - 1. We prove that with n tending to infinity random vectors
280-298
On the Nevanlinna-Cartan Second Main Theorem for non-Archimedean Holomorphic Curves
Аннотация
Recenty, J. M. Anderson and A. Hinkkanen ([2]) introduced the integrated reduced counting functions for holomorphic curves and proved an improved version of second main theorem for holomorphic curves with integrated reduced counting functions in the complex case. In this paper, we will prove a version of second main theorem for non-Archimedean holomorphic curves intersecting hyperplanes in general position with integrated reduced counting functions.
299-306
Fourier Transform of Dini-Lipschitz Functions on the Field of p-Adic Numbers
Аннотация
Let ℚp be the field of p-adic numbers, a function f(x) belongs to the the Lebesgue class Lρ(ℚp), 1 ρ ≤ 2, and let \(\hat{f}(\xi)\) be the Fourier transform of f. In this paper we give an answer to the next problem: if the function f belongs to the Dini-Lipschitz class DLip(α, β, ρ; ℚp), α > 0, β ∈ ℝ, then for which values of r we can guarantee that \(\hat{f} \in {L^r}(\mathbb{Q}_p)\)? The result is an analogue of one classical theorem of E. Titchmarsh about the Fourier transform of functions from the Lipschitz classes on ℝ.
307-318
Non Periodic p-Adic Generalized Gibbs Measure for Ising Model
Аннотация
In this paper we are aiming to study a new type of p-adic generalized Gibbs measures. We introduce two classes of p-adic generalized Gibbs measures for Ising model: p-adic (k0)-translational invariant and (k0)-periodic generalized Gibbs measures. It is proven that if k0 = 2,3 then the introduced classes are not empty.
319-327
Complete Integrability of Quantum and Classical Dynamical Systems
Аннотация
It is proved that the Schrödinger equation with any self-adjoint Hamiltonian is unitary equivalent to a set of non-interacting classical harmonic oscillators and in this sense any quantum dynamics is completely integrable. Integrals of motion are presented. A similar statement is proved for classical dynamical systems in terms of Koopman’s approach to dynamical systems. Examples of explicit reduction of quantum and classical dynamics to the family of harmonic oscillators by using direct methods of scattering theory and wave operators are given.
328-334
Short Communications
335-337