Abstract In this article we introduce the p -adic cellular neural networks which are mathematical generalizations of classical (CNNs) introduced by Chua and Yang. The new have infinitely many cells organized hierarchically in rooted trees, also they hidden layers. Intuitively, CNNs occur as limits large hierarchical discrete CNNs. More precisely, can be very well approximated Mathematically spe...

We give a brief overview of the theory of complex dimensions of real (archimedean) fractal strings via an illustrative example, the ordinary Cantor string, and a detailed survey of the theory of p-adic (nonarchimedean) fractal strings and their complex dimensions. Moreover, we present an explicit volume formula for the tubular neighborhood of a p-adic fractal string Lp, expressed in terms of th...

We define complexes analogous to Goncharov’s complexes for the K–theory of discrete valuation rings of characteristic zero. Under suitable assumptions in K–theory, there is a map from the cohomology of those complexes to the K–theory of the ring. In case the ring is the localization of the ring of integers in a number field, there are no assumptions necessary. We compute the composition of our ...

It has been known since the last century that a single quadratic form in at least five variables has a nontrivial zero in any p-adic field, but the analogous question for systems of quadratic forms remains unanswered. It is plausible that the number of variables required for solubility of a system of quadratic forms simply is proportional to the number of forms; however, the best result to date...

In this paper we generalize work of Amice and Lazard from the early sixties. Amice determined the dual of the space of locally Qp-analytic functions on Zp and showed that it is isomorphic to the ring of rigid functions on the open unit disk over Cp. Lazard showed that this ring has a divisor theory and that the classes of closed, finitely generated, and principal ideals in this ring coincide. W...

This paper presents a novel remote sensing image fusion algorithm, which implements panchromatic sharpening of multispectral data through application of the principal component analysis (PCA) transform and the dual-tree compactly supported shearlet transform (DT CSST). Shearlet transforms provide near optimal representation of the anisotropic features of an image. The compactly supported shearl...