Related papers: Some maximal isotropic distributions and their rel…

A new cohomology, induced by a vector field, is defined on pairs of differential forms ($1$--differentiable forms) in a manifold. It is proved a link with the classical de Rham cohomology and an $1$-differentable cohomology of Lichnerowicz…

We investigate diagonal forms of degree $d$ over the function field $F$ of a smooth projective $p$-adic curve: if a form is isotropic over the completion of $F$ with respect to each discrete valuation of $F$, then it is isotropic over…

For a vector random field that is isotropic and mean square continuous on a sphere and stationary on a temporal domain, this paper derives a general form of its covariance matrix function and provides a series representation for the random…

We review properties of closed meromorphic $1$-forms and of the foliations defined by them. We present and explain classical results from foliation theory, like index theorems, the existence of separatrices, and resolution of singularities…

In order to meet the requirements of practical applications, a model of deforming manifold in the embedded space is proposed. The deforming vector and deforming field are presented to precisely describe the deforming process, which have…

We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…

Using the structural theorems developed in [Hua13], we study the deformation theory of coisotropic submanifolds in contact manifolds, under the assumption that the characteristic foliation is nonsingular. In the "middle" dimensions, we find…

We show that the de Rham theorem, interpreted as the isomorphism between distributional de Rham cohomology and simplicial homology in the dual dimension for a simplicial decomposition of a compact oriented manifold, is a straightforward…

A stationary random sequence admits under some assumptions a representation as the sum of two others: one of them is a martingale difference sequence, and another is a so-called coboundary. Such a representation can be used for proving some…

This paper develops a geometrical model of dislocations and disclinations in single crystals at the mesoscopic scale. In the continuation of previous work the distribution theory is used to represent concentrated effects in the defect lines…

We show that every sheaf on the site of smooth manifolds with values in a stable (infinity,1)-category (like spectra or chain complexes) gives rise to a differential cohomology diagram and a homotopy formula, which are common features of…

We describe arbitrary multiplicative differential forms on Lie groupoids infinitesimally, i.e., in terms of Lie algebroid data. This description is based on the study of linear differential forms on Lie algebroids and encompasses many known…

We outline an approach to the inverse problem of Calder\'on that highlights the role of microlocal normal forms and propagation of singularities and extends a number of earlier results also in the anisotropic case. The main result states…

We develop a theory to represent dislocated single crystals at the mesoscopic scale by considering concentrated effects, governed by the distribution theory combined with multiple-valued kinematic fields. Our approach gives a new…

We study the classification of singularities of holomorphic foliations and non-integrable one-forms under the hypothesis of transversality with real hypersurfaces.

The restriction of a supercuspidal representation of SL_2(k), for k a local nonarchimedean field, to a maximal compact subgroup decomposes as a multiplicity-free direct sum of irreducible representations. We explicitly describe this…

Inspired by superstring field theory, we study differential, integral, and inverse forms and their mutual relations on a supermanifold from a sheaf-theoretical point of view. In particular, the formal distributional properties of integral…

The maximally-decoupled method has been considered as a theory to apply an basic idea of an integrability condition to certain multiple parametrized symmetries. The method is regarded as a mathematical tool to describe a symmetry of a…

Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…

We study anisotropic universal quadratic forms over semi-global fields; i.e., over one-variable function fields over complete discretely valued fields. In particular, given a semi-global field $F$, we compute both the $m$-invariant of $F$…