Sparse p-adic data coding for computationally efficient and effective big data analyticsPleiades Publishing Ltd - Tập 8 Số 3 - Trang 236-247 - 2016
Murtagh, F.
We develop the theory and practical implementation of p-adic sparse coding of data. Rather than the standard, sparsifying criterion that uses the L 0 pseudo-norm, we use the p-adic norm.We require that the hierarchy or tree be node-ranked, as is standard practice in agglomerative and other hierarchical clustering, but not necessarily with decision trees. In order to structure the data, all computa...... hiện toàn bộ
On countable unions of nonmeager sets in hereditarily Lindelöf spacesPleiades Publishing Ltd - Tập 3 - Trang 1-6 - 2011
Vitalij A. Chatyrko
It is well known that any Vitali set on the real line ℝ does not possess the Baire property. The same is valid for finite unions of Vitali sets. What can be said about infinite unions of Vitali sets? Let S be a Vitali set, S
r
be the image of S under the translation of ℝ by a rational number r and F = {S
...... hiện toàn bộ
Representation Theorems for Operators on Free Banach Spaces of Countable TypePleiades Publishing Ltd - Tập 11 - Trang 21-36 - 2019
J. Aguayo, M. Nova, J. Ojeda
This work will be centered in commutative Banach subalgebras of the algebra of bounded linear operators defined on free Banach spaces of countable type. The main goal of this work will be to formulate a representation theorem for these operators through integrals defined by spectral measures type. In order to get this objective, we will show that, under special conditions, each one of these algebr...... hiện toàn bộ
Zeros of p-adic differential polynomialsPleiades Publishing Ltd - Tập 6 - Trang 166-170 - 2014
A. Escassut, W. Lü, C. C. Yang
Let
$$\mathbb{K}$$
be a complete algebraically closed p-adic field of characteristic zero. We consider a differential polynomial of the form F = a
n
f
n
f
...... hiện toàn bộ
Cognitive processes of the brain: An ultrametric model of information dynamics in unconsciousnessPleiades Publishing Ltd - Tập 6 - Trang 293-302 - 2014
A. Yu. Khrennikov
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...... hiện toàn bộ
On Quasisymmetric Mappings Between Ultrametric SpacesPleiades Publishing Ltd - Tập 13 - Trang 231-238 - 2021
Evgeniy Petrov, Ruslan Salimov
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...... hiện toàn bộ
Factorizations of relative extremal projectorsPleiades Publishing Ltd - Tập 7 - Trang 276-290 - 2015
C. H. Conley, M. R. Sepanski
We survey earlier results on factorizations of extremal projectors and relative extremal projectors and present preliminary results on non-commutative factorizations of relative extremal projectors: we deduce the existence of such factorizations for sl4 and sl5.
A theorem on weighted means in non-archimedean fieldsPleiades Publishing Ltd - Tập 2 - Trang 363-367 - 2010
P. N. Natarajan
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 IntegersPleiades Publishing Ltd - Tập 12 - Trang 134-162 - 2020
J. P. Velasquez-Rodriguez
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...... hiện toàn bộ