Related papers: On the Smoothness of Functors
Given a smooth curve $\gamma$ in some $m$-dimensional surface $M$ in $\mathbb{R}^{m+1}$, we study existence and uniqueness of a flat surface $H$ having the same field of normal vectors as $M$ along $\gamma$, which we call a flat…
We investigate commutator operations on compatible uniformities of an algebra. We present a commutator operation for compatible uniformities of an algebra in a congruence-modular variety which extends the commutator on congruences, and…
Several notions of "analytic" functor introduced recently in the literature fit into the graphic fourier transform context presented in [D].
In this paper we define a functor-- leveled sub-cohomology. (It bears no relation with the level of elliptic curves). It is based on leveled cycles on a smooth projective variety, and will be expected to reveal a structure in the level.
Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…
Let $X$ be a compact subset of the complex plane and let $R^p(X)$, $2< p < \infty$, denote the closure of the rational functions with poles off $X$ in the $L^p$ norm. In this paper we consider three conditions that show how the functions in…
Recently, a new definition of $\mathbb P$-functors was proposed by Anno and Logvinenko. In their article, the authors wonder whether this notion is symmetric in the sense that the adjoints of $\mathbb P$-functors are again $\mathbb…
In this short article we present some properties regarding the order and the type of an entire function.
This paper defines symplectic scale manifolds based on Hofer-Wysocki-Zehnder's scale calculus. We introduce Hamiltonian vector fields and flows on these by narrowing down sc-smoothness to what we denote by strong sc-smoothness, a concept…
In this survey, I suggest to approach the problem of functorial properties of quantum cohomology by drawing lessons from several versions of Mirror duality involving deformation spaces.
In this work we provide detailed estimates of maximal principal angles between subspaces and we analyze their smoothness for smoothly varying subspaces. This leads to a new definition of angular values for linear dynamical systems in…
We compare various different definitions of "the category of smooth objects". The definitions compared are due to Chen, Fr\"olicher, Sikorski, Smith, and Souriau. The method of comparison is to construct functors between the categories that…
The note is about some nonlinear curvature conditions which arise naturally in conformal geometry.
In this paper we will prove that there exists a covariant functor from the category of schemes to the category of graphs. This functor provides a combination between algebraic varieties and combinatorial graphs so that the invariants…
This is a review of the basic concepts of the theory of real and complex smooth vector bundles with finite rank. Besides, the concept of a tensor field is studied within the general framework of a smooth vector bundle rather than a smooth…
This paper consists in discussing some issues on generic local classification of typical singularities of $2D$ piecewise smooth vector fields when the switching set is an algebraic variety. The main focus is to obtain classification results…
We prove two-sided inequalities between the integral moduli of smoothness of a function on $\mathbb{R}^d/\mathbb{T}^d$ and the weighted tail-type integrals of its Fourier transform/series. Sharpness of obtained results in particular is…
We use gauge theoretic and algebraic methods to examine sufficient conditions for smooth points on the moduli space of flat connections on a compact manifold and on the character variety of a finitely generated and presented group. We give…
We introduce and study in a general setting the concept of homogeneity of an operator and, in particular, the notion of homogeneity of an integral operator. In the latter case, homogeneous kernels of such operators are also studied. The…
In this paper, a $k$-th generalized modulus of smoothness is defined based on an asymmetric operator of generalized translation and a theorem is proved about the coincidence of class of functions defined by this modulus and a class of…