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Том 9, № 3 (2017)
- Год: 2017
- Статей: 7
- URL: https://journals.rcsi.science/2070-0466/issue/view/12514
Research Articles
A heat equation on some adic completions of ℚ and ultrametric analysis
Аннотация
For each finite set S of prime numbers there exists a unique completion ℚS of ℚ, which is a second countable, locally compact and totally disconnected topological ring. This topological ring has a natural ultrametric that allows to define a pseudodifferential operator Dα and to study an abstract heat equation on the Hilbert space L2(ℚS). The fundamental solution of this equation is a normal transition function of a Markov process on ℚS. The techniques developed provides a general framework for these kind of problems on different ultrametric groups.
165-182
Blow-up phenomena for p-adic semilinear heat equations
Аннотация
The problem of existence of solutions to p-adic semilinear heat equations with particular nonlinear terms has already been studied in the literature but the occurrence of blow-up phenomena has not been considered yet. We initiate the study of finite time blow-up for solutions of this kind of p-adic semilinear equations, proving that this phenomenon always arises under appropriate assumptions in the case when the exponent of nonlinearity times the dimension is strictly less than the order of the operator.
183-196
G-ultrametric dynamics and some fixed point theorems for single valued mappings in G-ultrametric spaces
Аннотация
This paper is concerned with dynamics in general G-ultrametric spaces, hence we discuss the introduced concepts of such spaces. Also, we obtain some fixed point existing results of strongly contractive and non-expansive mappings defined on these spaces by inspiring from the theorems proved by Mustafa and Sims.
197-203
q-Deformations of statistical mechanical systems and motives over finite fields
Аннотация
We consider q-deformations of Witt rings, based on geometric operations on zeta functions of motives over finite fields, and we use these deformations to construct q-analogs of the Bost-Connes quantum statistical mechanical system. We show that the q-deformations obtained in this way can be related to Habiro ring constructions of analytic functions over F1 and to categorifications of Bost-Connes systems.
204-227
The p-adic order of some fibonomial coefficients whose entries are powers of p
Аннотация
Let (Fn)n≥0 be the Fibonacci sequence. For 1 ≤ k ≤ m, the Fibonomial coefficient is defined as
228-235
Weak and strong estimates for rough Hausdorff type operator defined on p-adic linear space
Аннотация
For rough Hausdorff type operator defined on p-adic linear space Qpn and its commutator with symbol from Lipschitz space, we give sufficient conditions of their boundedness from one Lorentz space into another.
236-241
Short Communications
Spectral analysis for infinite rank perturbations of unbounded diagonal operators
Аннотация
In this paper we study the spectral theory for the class of linear operators A∞ defined on the so-called non-archimedean Hilbert space Eω by, A∞:= D + F∞ where D is an unbounded diagonal linear operator and F∞:= Σk=1∞uk ⊗ vk is an operator of infinite rank on Eω.
242-246