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Том 8, № 3 (2016)
- Год: 2016
- Статей: 5
- URL: https://journals.rcsi.science/2070-0466/issue/view/12499
Review Articles
p-Adic probability logics
Аннотация
This paper represents an comprehensive overview of the results from three papers where we developed several propositional logics for reasoning about p-adic valued probability.Each of these logics is a sound, complete and decidable extension of classical propositional logic.
177-203
Research Articles
The p-adic weighted Hardy-Cesàro operators on weighted Morrey-Herz space
Аннотация
In this article we give necessary and sufficient conditions for the boundedness of the weighted Hardy-Cesà ro operators which is associated to the parameter curve γ(t, x) = γ(t)x defined by \({U_{\psi ,\gamma }}f\left( x \right) = \int {\left( {\gamma \left( t \right)x} \right)} \psi \left( t \right)dt\) on the weighted Morrey-Herz space over the p-adic field. Especially, the corresponding operator norms are established in each case. These results actually extend those of K. S. Rim and J. Lee [27] and of the authors [9]. Moreover, the sufficient conditions of boundedness of commutators of p-adic weighted Hardy-Cesàro operator with symbols in the Lipschitz space on the weighted Morrey-Herz space are also established.
204-216
Painlevé VI equations in p-adic time
Аннотация
Using the description of Painlevé VI family of differential equations in terms of a universal elliptic curve, going back to R. Fuchs, we translate it into the realm of Buium’s p-adic Arithmetic Differential Equations, where the role of derivative is played by a version of Fermat quotient.
217-224
On periodic Gibbs measures of p-adic Potts model on a Cayley tree
Аннотация
In the present paper, we study the existence of periodic p-adic quasi Gibbs measures of p-adic Potts model over the Cayley tree of order two. We first prove that the renormalized dynamical system associated with the model is conjugate to the symbolic shift. As a consequence of this result we obtain the existence of countably many periodic p-adic Gibbs measures for the model.
225-235
Sparse p-adic data coding for computationally efficient and effective big data analytics
Аннотация
We develop the theory and practical implementation of p-adic sparse coding of data. Rather than the standard, sparsifying criterion that uses the L0 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 computational processing operations are direct reading of the data, or are bounded by a constant number of direct readings of the data, implying linear computational time. Through p-adic sparse data coding, efficient storage results, and for bounded p-adic norm stored data, search and retrieval are constant time operations. Examples show the effectiveness of this new approach to content-driven encoding and displaying of data.
236-247