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Cognitive processes of the brain: An ultrametric model of information dynamics in unconsciousness
Pleiades Publishing Ltd - Tập 6 - Trang 293-302 - 2014
We discuss differences in mathematical representations of the physical and mental worlds. Following Aristotle, we present the mental space as discrete, hierarchic, and totally disconnected topological space. One of the basic models of such spaces is given by ultrametric spaces and more specially by m-adic trees. We use dynamical systems in such spaces to model flows of unconscious information at d......
On Quasisymmetric Mappings Between Ultrametric Spaces
Pleiades Publishing Ltd - Tập 13 - Trang 231-238 - 2021
In 1980 P. Tukia and J. Väisälä in seminal paper [23] extended a concept of quasisymmetric mapping known from the theory of quasiconformal mappings to the case of general metric spaces. They also found an estimation for the ratio of diameters of two subsets which are images of two bounded subsets of a metric space under a quasisymmetric mapping. We improve this estimation for the case of ultramet......
A theorem on weighted means in non-archimedean fields
Pleiades Publishing Ltd - Tập 2 - Trang 363-367 - 2010
K denotes a complete, non-trivially valued, non-archimedean field. Infinite matrices, sequences and series have entries in K. In this paper, we prove an interesting result, which gives an equivalent formulation of summability by weighted mean methods. Incidentally this result includes the non-archimedean analogue of a theorem proved by Móricz and Rhoades (see [2], Theorem MR, p.188).
Hörmander Classes of Pseudo-Differential Operators over the Compact Group of p-Adic Integers
Pleiades Publishing Ltd - Tập 12 - Trang 134-162 - 2020
The purpose of this paper is to introduce new definitions of Hörmander classes for pseudo-differential operators over the compact group of p-adic integers. Our definitions possesses a symbolic calculus, asymptotic expansions and parametrices, together with an interesting relation with the infinite matrices algebras studied by K. Gröchenig and S. Jaffard. Also, we show how our definition of Hörmand......
On $$p$$ -Adic Description of Glutathione Synthesis
Pleiades Publishing Ltd - Tập 13 - Trang 250-254 - 2021
In this paper, we use a mathematical approach to glutathione synthesis. We establish a downward tree to describe the glutathione syntheses based on three amino acids. We assign
$$C=1$$
,
$$A=2$$
,
......
On the functional equation Af 2 + Bg 2 = 1 on the field of complex p-adic numbers
Pleiades Publishing Ltd - Tập 2 - Trang 68-76 - 2010
For a fixed prime p, let C
p
denote the complex p-adic numbers. For polynomials A, B ε C p [x] we consider decompositions A (x) f
2 (x) + B (x) g
2 (x) = 1 of entire functions f, g on C p and try to improve an impossibility result due to A. Boutabaa concerning transcendental f, g. We also provide a new proof of a p-......
p-adic valuation of exponential sums associated to trinomials and some consequences
Pleiades Publishing Ltd - Tập 9 - Trang 257-266 - 2017
In this paper, we compute the p-adic valuation of exponential sums associated to trinomials
$$F\left( X \right) = a{X^{{d_1}}} + b{X^{{d_2}}} + c{X^{{d_3}}}$$
over Fp. As a byproduct of our results, we obtain restrictions for permutation polynomi......
A Beilinson-Bernstein Theorem for Analytic Quantum Groups. I
Pleiades Publishing Ltd - Tập 13 - Trang 44-82 - 2021
In this two-part paper, we introduce a
$$p$$
-adic analytic analogue of Backelin and Kremnizer’s construction of the quantum flag variety of a semisimple algebraic group, when
$$q$$
is not a root of unity and
......
Self-similar p-adic fractal strings and their complex dimensions
Pleiades Publishing Ltd - Tập 1 - Trang 167-180 - 2009
We develop a geometric theory of self-similar p-adic fractal strings and their complex dimensions. We obtain a closed-form formula for the geometric zeta functions and show that these zeta functions are rational functions in an appropriate variable. We also prove that every self-similar p-adic fractal string is lattice. Finally, we define the notion of a nonarchimedean self-similar set and discuss......
On some 2-adic properties of a recurrence involving stirling numbers
Pleiades Publishing Ltd - Tập 4 Số 3 - Trang 179-186 - 2012
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