Related papers: The oriented derivative

Let ${\mathcal A}$ be a Banach algebra with the properties that $\mathrm{rad}({\mathcal A})={\rm rann}({\mathcal A})$ and the algebra ${\mathcal A}/\mathrm{rad}({\mathcal A})$ is commutative. We show that a derivation of ${\mathcal A}$ maps…

We establish differentiability properties of the value function of problems of Static Optimization in an abstract infinite dimensional setting and we apply that to problems of Calculus of Variations. We lighten the assumptions of existing…

In this paper we consider convex subsets of locally-convex topological vector spaces. Given a fixed point in such a convex subset, we show that there exists a curve completely contained in the convex subset and leaving the point in a given…

We use techniques of proof mining to extract a uniform rate of metastability (in the sense of Tao) for the strong convergence of approximants to fixed points of uniformly continuous pseudocontractive mappings in Banach spaces which are…

We study three types of generalized partial fractional operators. An extension of Green's theorem, by considering partial fractional derivatives with more general kernels, is proved. New results are obtained, even in the particular case…

Let B be a translation invariant Banach function space (BF-space). In this paper we prove that every temperate distribution f can be associated with a function F analytic in the convex tube Omega={z in C^d; |Im z|<1} such that the…

We prove a result on the convex dependence of solutions of ordinary differential equations on an ordered finite-dimensional real vector space with respect to the initial data.

Suppose $\mathcal{Z}$ is the space of all tuples of operators on a finite-dimensional Banach space endowed with the joint numerical radius norm. We obtain the structure of the extreme points of the dual unit ball of $\mathcal{Z}.$ Using…

We extend to higher order a recently published method for calculating the deflection angle of light in a general static and spherically symmetric metric. Since the method is convergent we obtain very accurate analytical expressions that we…

Opial's inequality and its ramifications play an important role in the theory of differential and difference equations. A sharp unifying generalization of Opial's inequality is presented that contains both its continuous and discrete…

We consider fractional directional derivatives and establish some connection with stable densities. Solutions to advection equations involving fractional directional derivatives are presented and some properties investigated. In particular…

We study an infinite system of ordinary differential equations that models the evolution of coagulating and fragmenting clusters, which we assume to be composed of identical units. Under very mild assumptions on the coefficients we prove…

We generalize Bourgain's discretized projection theorem to higher rank situations. Like Bourgain's theorem, our result yields an estimate for the Hausdorff dimension of the exceptional sets in projection theorems formulated in terms of…

In this paper, we investigate direct and inverse source problems for the diffusion equation with two-term generalized fractional derivative (Hilfer derivative) in a rectangular domain. Using spectral expansion method, we derive two-term…

Let $n$ and $k$ be nonnegative integers such that $1\le k\le n+1$. The convex cone $\mathcal{F}_+^{k:n}$ of all functions $f$ on an arbitrary interval $I\subseteq\mathbb{R}$ whose derivatives $f^{(j)}$ of orders $j=k-1,\dots,n$ are…

Derivatives with respect to the parameters of the integral Mittag-Leffler function and the integral Wright function, recently introduced by us, are calculated. These derivatives can be expressed in the form of infinite sums of quotients of…

We derive global analytic representations of fundamental solutions for a class of linear parabolic systems with full coupling of first order derivative terms where coefficient may depend on space and time. Pointwise convergence of the…

This paper presents an approach for the development of a number theoretic discrete Hilbert transform. The forward transformation has been applied by taking the odd reciprocals that occur in the DHT matrix with respect to a power of 2.…

In this paper, we extend the classical arithmetic defined over the set of natural numbers N, to the set of all finite directed connected multigraphs having a pair of distinct distinguished vertices. Specifically, we introduce a model F on…

In recent works, [20],[21], descendent integrals on the moduli space of Riemann surfaces with boundary were defined. It was conjectured in [20] that the generating function of these integrals satisfies the open KdV equations. In this paper…