Related papers: On the Smoothness of Functors

In this paper, we investigate the differential smoothness of graded skew Clifford algebras.

Real valued homomorphisms on the algebra of smooth functions on a differential space are described. The concept of generators of this algebra is emphasized in this description.

This text surveys cohomological properties of pairs $(U,f)$ consisting of a smooth complex quasi-projective variety $U$ together with a regular function on~it. On the one hand, one tries to mimic the case of a germ of holomorphic function…

Models for fluid deformable surfaces provide valid theories to describe the dynamics of thin fluidic sheets of soft materials. To use such models in morphogenesis and development requires to incorporate active forces. We consider active…

Algebras of generalized functions offer possibilities beyond the purely distributional approach in modelling singular quantities in non-smooth differential geometry. This article presents an introductory survey of recent developments in…

We introduce vectorial and topological continuities for functions defined on vector metric spaces and illustrate spaces of such functions. Also, we describe some fundamental classes of vector valued functions and extension theorems.

A new object, called the velocity tensor, is introduced. It allows to formulate a generally covariant mechanics. Some properties of the velocity tensor are derived.

Smoothness of a function $f:{\mathbb R}^n\to {\mathbb R}$ can be measured in terms of the rate of convergence of $f\ast\rho_\varepsilon$ to $f$, where $\rho$ is an appropriate mollifier. In the framework of fractional Sobolev spaces, we…

We prove smoothness in the dg sense of the bounded derived category of finitely generated modules over any finite-dimensional algebra over a perfect field, hereby answering a question of Iyama. More generally, we prove this statement for…

In this article we construct a smooth Euler flow supported in a neighborhood of a helix. It may be considered a generalization of a similar solution found by the author for a circle.

In this note we obtain a formula for the sectional curvature on an arbitrary two-dimensional smooth manifold $M$ equipped with a Lorentzian metric $g$.

We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…

In this study, after given the definition of soft sets and their basic operations we define convex soft sets which is an important concept for operation research, optimization and related problems. Then, we define concave soft sets and give…

This paper presents necessary, sufficient, and equivalent conditions for the spherical convexity of non-homogeneous quadratic functions. In addition to motivating this study and identifying useful criteria for determining whether such…

In this paper a functional definition of geodesics is introduced which allows to generalize the notion of a geodesic from smooth to topological manifolds. It is shown that in the smooth case the new definition coincides with the classical…

A result is given to find points where a real valued function on the plane is not smooth. Provided this function is induced by a smooth mapping from three dimensions to the plane, from a function on surfaces in three dimensions. This has…

Let X be a smooth irreducible projective surface. The aim of this paper is to establish a version of Clifford's theorem for coherent systems on X.

We study the smoothness of the stationary measure with respect to smooth perturbations of the iterated function scheme and the weight functions that define it. Our main theorems relate the smoothness of the perturbation of: the iterated…

Let $\mathfrak{a}$ be an ideal in a commutative ring $R$. For an $R$-module $M$, we consider the small $\mathfrak{a}$-torsion $\Gamma_{\mathfrak{a}}(M)=\{x\in M\mid\exists n\in\mathbb{N}:\mathfrak{a}^n\subseteq(0:_Rx)\}$ and the large…

We introduce a derived smooth duality functor on the unbounded derived category of smooth mod p representations of a p-adic Lie group. Using this functor we relate various subcategories of admissible complexes.