Related papers: Manifold-valued generalized functions in full Colo…

In this paper, we introduce the concept of nearly convex set-valued mappings and investigate fundamental properties of these mappings. Additionally, we establish a geometric approach for generalized differentiation of nearly convex…

We study the notion of duality in the context of graded manifolds. For graded bundles, somehow like in the case of Gelfand representation and the duality: points vs. functions, we obtain natural dual objects which belongs to a different…

An explicit counterexample shows that contrary to the situation in the special Colombeau algebra, positivity and invertibility cannot be characterized pointwise in algebras of tempered generalized functions. Further a point value…

In this paper we focus on functions of the form $A^n\rightarrow \mathcal{P}(B)$, for possibly different arbitrary non-empty sets $A$ and $B$, and where $\mathcal{P}(B)$ denotes the set of all subsets of $B$. These mappings are called…

The paper is devoted to quantization of polynomial momentum observables in the cotangent bundle of a smooth manifold. A quantization procedure is proposed allowing to quantize a wide class of functions which are polynomials of any order in…

It is shown that a smooth n dimensional manifold with a boundary in R^n admits a Boolean representation in terms of closed half spaces defined by the tangent hyperplanes at the points on its boundary. A similar result is established for…

Monge gauge in differential geometry is generalized. The original Monge gauge is based on a surface defined as a height function $h(x,y)$ above a flat reference plane. The total curvature and the Gaussian curvature are found in terms of the…

We give a general description of the construction of weighted spherically symmetric metrics on vector bundle manifolds, i.e. the total space of a vector bundle $E\rightarrow M$, over a Riemannian manifold $M$, when $E$ is endowed with a…

A tangent category is a category equipped with an endofunctor that satisfies certain axioms which capture the abstract properties of the tangent bundle functor from classical differential geometry. Cockett and Cruttwell introduced…

The paper addresses linear hyperbolic systems in one space dimension with random field coefficients. In many applications, a low degree of regularity of the paths of the coefficients is required, which is not covered by classical stochastic…

We study how the notion of tangent space can be extended from smooth manifolds to diffeological spaces, which are generalizations of smooth manifolds that include singular spaces and infinite-dimensional spaces. We focus on two definitions.…

Generic approximation of entire functions by their Pad\'{e} approximants has been achieved in the past (\cite{3}). In the present article we obtain generic approximation of holomorphic functions on arbitrary open sets by sequences of their…

Special generic maps are generalizations of Morse functions with exactly two singular points on spheres and canonical projections of unit spheres. They restrict the manifolds of the domains strongly in considerable cases and are important…

Based on the definition of generalized partially bent functions, using the theory of linear transformation, the relationship among generalized partially bent functions over ring Z N, generalized bent functions over ring Z N and affine…

An operator generalisation of the notion of geometric phase has been recently proposed purely based on physical grounds. Here we provide a mathematical foundation for its existence, while uncovering new geometrical structures in quantum…

Classes of branched surfaces extend the classes of surfaces or 2-dimensional manifolds satisfying suitable properties and defined in various manners. Reeb spaces of smooth maps of suitable classes into surfaces whose codimensions are…

Algebraists asked whether or not an operator on the module of smooth sections of the tangent bundle over the commutative ring of smooth functions of a smooth (orientable) manifold (can be any piece of a compact or a complete manifold) can…

A generalized matrix function is a generalization of determinant and permanent function. In this paper, we introduced the formula for the value of a generalized matrix function of a linear sum of permutation matrices. We show that a linear…

We adapt the framework of geometric quantization to the polysymplectic setting. Considering prequantization as the extension of symmetries from an underlying polysymplectic manifold to the space of sections of a Hermitian vector bundle, a…

We review the concept of a graded bundle, which is a generalisation of a vector bundle, its linearisation, and a double structure of this kind. We then present applications of these structures in geometric mechanics including systems with…