The slope filtration theorem gives a partial analogue of the eigenspace decomposition of a linear transformation, for a Frobenius-semilinear endomorphism of a finite free module over the Robba ring (the ring of germs of rigid analytic functions on an unspecified open annulus of outer radius 1) over a discretely valued field. In this paper, we give a third-generation proof of this theorem, which...

In smooth manifold theory, the notion of a tangent space makes it possible for differentiation to take place on an abstract manifold. In this paper, the notion of a distribution will be presented which makes it possible for integration to take place on an abstract manifold. The first section introduces terminology and builds intuition via an analogy to the concept of integral curves. The second...

Let k be an algebraically closed field of characteristic p > 0. A theorem of de Jong shows that morphisms of modules over W (k)[[t]] with Frobenius and connection structure descend from the completion of W (k)((t)). A careful reading of de Jong’s proof suggests the possibility that an analogous theorem holds for modules with only a Frobenius structure. We show that this analogue holds in one na...

We study Galois extensions M (co-)H ⊂ M for H-(co)module algebras M if H is a Frobenius Hopf algebroid. The relation between the action and coaction pictures is analogous to that found in Hopf-Galois theory for finite dimensional Hopf algebras over fields. So we obtain generalizations of various classical theorems of Kreimer-Takeuchi, Doi-Takeuchi and Cohen-FischmanMontgomery. We find that the ...

structures on a model based on available prior informaAlgorithms are presented for least-squares approximation. Earlier work on these problems has primarily contion of Toeplitz and Hankel matrices from noise corsisted of using Singular Value Decomposition [4, 5, 81, rupted or ill-composed matrices, which may not have where only the rank information of the underlying sigcorrect structural or ran...

We consider a topological dynamical system T : Y ! Y on a metric space Y which forms a bre bundle over another dynamical system. If T is brewise expanding and exact along bres and if ' is a HH older continuous function we prove the existence of a system of conditional measures (called a family of Gibbs measures) where the Jacobian is determined by '. This theorem reduces to Ruelle's Perron-Frob...

in this paper, by using of frobenius theorem a relation between lie subalgebras of the lie algebra of a top space t and lie subgroups of t(as a lie group) is determined. as a result we can consider these spaces by their lie algebras. we show that a top space with the finite number of identity elements is a c^{∞} principal fiber bundle, by this method we can characterize top spaces.

The starting point of this paper is given by Priestley’s papers, where a theory of representation of distributive lattices is presented. The purpose of this paper is to develop a representation theory of fuzzy distributive lattices in the finite case. In this way, some results of Priestley’s papers are extended. In the main theorem, we show that the category of finite fuzzy Priestley space...

Frobenius is generally considered the creator of character theory finite groups. This achievement came from study group determinant, which determinant a matrix coming regular representation. We generalize several Frobenius’ results about and use them to find new formulation supercharacter in terms factorizations determinant.