The original focus of this article was p-adic icosahedron. The discussion of attempt to define this notion however leads to the challenge of defining the concept of p-adic sphere, and more generally, that of p-adic manifold, and this problem soon became the main target of attention since it is one of the key challenges of also TGD. There exists two basic philosophies concerning the construction...

In this thesis, we set up the basic theory of p-adic modular forms over Shimura curves over Q, parallel to the classical case over modular curves. We define and study the structure of the spaces of p-adic modular forms with respect to certain quaternion algebras over Q. We study the relation of these modular forms with classical quaternionic modular forms. We prove a canonical subgroup theorem ...

In this paper we give an overview over the basic features of the continuous representation theory of p-adic Lie groups as it has emerged during the last five years. The main motivation for developing such a theory is a possible extension of the local Langlands program to p-adic Galois representations. This is still very much in its infancy. But in the last section we will describe a first appro...

In Dwork’s memoir [3] concerning the rationality of zeta functions, an essential role is played by the p-adic analytic function det(1− tu), where u is a certain infinite matrix. This analytic function is an entire function, exactly as in the classical Fredholm theory. It was natural to pursue this analogy and extend to u the spectral theory of F. Riesz; this is just what Dwork did ([4], §2). In...

ultrasound images suffer of multiplicative noise named speckle. different de-speckling algorithms run either in spatial domain or in transformed domain. in this paper, an adaptive filter in spatial domain according to assume the nakagami distribution as the statistic of log-compressed ultrasound images is used. for de-speckling in transformed domain, the non-sub sampled shearlet transform is us...

Recently, the research towards Brodatz database for texture classification done at considerable amount of study has been published, the effective classification are vulnerable towards for training and test sets. This study presents the novel texture classification method based on feature descriptor, called spatial cooccurrence with discrete shearlet transformation through the LPboosting classif...

The p-adic upper half plane X is a rigid analytic variety over a p-adic field K, on which the group GL2(K) acts, that Mumford introduced (as a formal scheme) as part of his efforts to generalize Tate’s p-adic uniformization of elliptic curves to curves of higher genus. The Cp–valued points of X are just P(Cp)−P(K), with GL2(K) acting by linear fractional transformations. Mumford showed that the...