Related papers: Nonlinear generalised functions on manifolds

We study the application of generalized symmetry for reducing nonlinear partial differential equations. We construct the ansatzes for dependent variable $u$ which reduce the scalar partial differential equation with two independent…

We trace derivations through Demazure's correspondence between a finitely generated positively graded normal $k$-algebras $A$ and normal projective $k$-varieties $X$ equipped with an ample $\mathbb{Q}$-Cartier $\mathbb{Q}$-divisor $D$. We…

In this paper, we establish and employ a local framework to the first order of Riemann's curvature tensor in order to develop the corresponding coordinate non commutativity into general manifolds. We also exploit a new translation of…

The commutative algebra of functions on a manifold is extended to a noncommutative algebra by considering its tensor product with the algebra of nxn complex matrices. Noncommutative geometry is used to formulate an extension of the…

We investigate homogeneity in the special Colombeau algebra. It is shown that strongly scaling invariant functions on the d-dimensional space are simply the constants. On the pierced space, strongly homogeneous functions admit tempered…

The main aim of the present work is to arrive at a mathematical theory close to the historically original conception of generalized functions, i.e. set theoretical functions defined on, and with values in, a suitable ring of scalars and…

We generalize Kuznetsov's theory of homological projective duality to the setting of noncommutative algebraic geometry. Simultaneously, we develop the theory over general base schemes, and remove the usual smoothness, properness, and…

Colombeau's generalized functions are used to adapt the distributional approach to singular hypersurfaces in general relativity with signature change. Equations governing the dynamics of singular hypersurface is obtained and it is shown…

In this paper we show how connections and their generalizations on transitive Lie algebroids are related to the notion of connections in the framework of the derivation-based noncommutative geometry. In order to compare the two…

We define and characterize spaces of manifold-valued generalized functions and generalized vector bundle homomorphisms in the setting of the full diffeomorphism-invariant vector-valued Colombeau algebra. Furthermore, we establish point…

For a smooth (locally trivial) principal bundle in Ehresmann's sense, the relation between the commuting vertical and horizontal actions of the structural Lie group and the structural Lie groupoid (isomorphisms between vertical fibers) is…

This paper gives a survey of the index theory of tangentially elliptic and transversally elliptic operators on foliated manifolds as well as of related notions and results in non-commutative geometry.

We expose some simple facts at the interplay between mathematics and the real world, putting in evidence mathematical objects " nonlinear generalized functions" that are needed to model the real world, which appear to have been generally…

We develop a generalised gauge theory in which the role of gauge group is played by a coalgebra and the role of principal bundle by an algebra. The theory provides a unifying point of view which includes quantum group gauge theory,…

We introduce Hopf algebroid covariance on Woronowicz's differential calculus. Using it, we develop quite a general framework of noncommutative complex geometry that subsumes the one in [2]. We present transverse complex and K\"ahler…

Generalized linear models (GLM) are link function based statistical models. Many supervised learning algorithms are extensions of GLMs and have link functions built into the algorithm to model different outcome distributions. There are two…

We consider a generalisation of vector fields on a vector space, where the vector space is generalised to a highest-weight module over a Kac-Moody algebra. The generalised vector field is an element in a non-associative superalgebra defined…

This article explores the structure theory of compatible generalized derivations of finite-dimensional $\omega$-Lie algebras over a field $\mathbb{K}$. We prove that any compatible quasiderivation of an $\omega$-Lie algebra can be embedded…

The space of differential operators acting on skewsymmetric tensor fields or on smooth forms of a smooth manifold are representations of its Lie algebra of vector fields. We compute the first cohomology spaces of these representations and…

Let $E_1,\dots ,E_k$ and $E$ be natural vector bundles defined over the category $\Cal Mf_m^+$ of smooth oriented $m$--dimensional manifolds and orientation preserving local diffeomorphisms, with $m\geq 2$. Let $M$ be an object of $\Cal…