Related papers: Lipshitzian Vector Fields, Upper Gradients And Dis…

In this paper we introduce Lipschitz spaces with respect to the Gaussian measure, and study the boundedness of the fractional integral and fractional derivative operators on them.The methods are general enough to provide alternative proofs…

We prove that every local derivation on a finite-dimensional semisimple Lie algebra over an algebraically closed field of characteristic zero is a derivation. We also give examples of finite-dimensional nilpotent Lie algebras $\mathcal{L}$…

In this contribution, we build up an axiomatic local metric derivative that exhibits the Mittag-Leffler as an eigenfunction and is valid for low-level fractionality, whenever the order parameter is close to $1$. This version of deformed or…

Using a geometric argument, we show that under a reasonable continuity condition, the Clarke subdifferential of a semi-algebraic (or more generally stratifiable) directionally Lipschitzian function admits a simple form: the normal cone to…

We first introduce the arithmetic subderivative of a positive integer with respect to a non-empty set of primes. This notion generalizes the concepts of the arithmetic derivative and arithmetic partial derivative. More generally, we then…

We prove a local gradient estimate for positive eigenfunctions of $ \mathcal{L} $-operator on conformal solitons given by a general conformal vector field. As an application, we obtain a Liouville type theorem for $ \mathcal{L} u = 0 $,…

Level proximal subdifferential was introduced by Rockafellar recently for studying proximal mappings of possibly nonconvex functions. In this paper a systematic study of level proximal subdifferential is given. We characterize variational…

We consider in this paper an area functional defined on submanifolds of fixed degree immersed into a graded manifold equipped with a Riemannian metric. Since the expression of this area depends on the degree, not all variations are…

We prove maximum and comparison principles for fractional discrete derivatives in the integers. Regularity results when the space is a mesh of length $h$, and approximation theorems to the continuous fractional derivatives are shown. When…

The main contribution of this paper is that every convex function with non-empty relative algebraic interior of its domain is Lipschitz and subdifferentiable in some algebraic sense without any additional topological constraints. The…

In probabilistic coherence spaces, a denotational model of probabilistic functional languages, mor-phisms are analytic and therefore smooth. We explore two related applications of the corresponding derivatives. First we show how derivatives…

Given a two-variable function $f$ without critical points and a compact region $R$ bounded by two level curves of $f$, this note proves that the integral over $R$ of the second-order directional derivative of $f$ in the tangential…

We reprove the results of Jordan [18] and Siebert [31] and show that the Lie algebra of polynomial vector fields on an irreducible affine variety X is simple if and only if X is a smooth variety. Given proof is self-contained and does not…

We investigate the connection between maximal directional derivatives and differentiability for Lipschitz functions defined on Laakso space. We show that maximality of a directional derivative for a Lipschitz function implies…

We present a local and constructive differential geometric description of finite-dimensional solvable and transitive Lie algebras of vector fields. We show that it implies a Lie's conjecture for such Lie algebras. Also infinite-dimensional…

In this paper, we discuss the validity of the Liouville property for $X$-harmonic functions, i.e. positive solution to $\Delta_{X}u=0$, where $X$ is a vector field on a complete, non-compact Riemannian manifold and $\Delta_{X}$ is the…

Let $K$ be a global field and $n > 1$ an integer. We show $n$ is composite if and only if there is an irreducible polynomial $f(x) \in K[x]$ of degree $n$ which is reducible $q$-adically for all the primes $q$ of $K$.

We consider planar vector field without zeroes X and study the image of the associated Lie derivative operator LX acting on the space of smooth functions. We show that the cokernel of LX is infinite-dimensional as soon as X is not…

Let $M$ be a complex manifold of complex dimension $n+k$. We say that the functions $u_1,...s,u_k$ and the vector fields $\xi_1,...,\xi_k$ on $M$ form a \emph{complex gradient system} if $\xi_1,...,\xi_k,J\xi_1,...,J\xi_k$ are linearly…

A computably presented algebraic field $F$ has a \emph{splitting algorithm} if it is decidable which polynomials in $F[X]$ are irreducible there. We prove that such a field is computably categorical iff it is decidable which pairs of…