相关论文: Generalized Differentiation and Characterizations …

This work provides a systematic study of the variational properties of decomposable functions which are compositions of an outer support function and an inner smooth mapping under certain constraint qualifications. A particular focus is put…

A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher…

Non-closedness of subexponentiality by the convolution operation is well-known. We go a step further and show that subexponentiality and non-subexponentiality are generally changeable by the convolution. We also give several conditions, by…

We study the approximation of functions which are invariant with respect to certain permutations of the input indices using flow maps of dynamical systems. Such invariant functions includes the much studied translation-invariant ones…

Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…

A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…

We collect here some known results on the subdifferential of one-homogeneous functionals, which are anisotropic and nonhomogeneous variants of the total variation and establish a new relationship between Lebesgue points of the calibrating…

Understanding the role that subgradients play in various second-order variational analysis constructions can help us uncover new properties of important classes of functions in variational analysis. Focusing mainly on the behavior of the…

We introduce a proximal subdifferential and develop a calculus for nonsmooth functions defined on any Riemannian manifold $M$. We give several applications of this theory, concerning: 1) differentiability and geometrical properties of the…

The purpose of this paper is to discuss a generalization of the bubble transform to differential forms. The bubble transform was discussed in a previous paper by the authors for scalar valued functions, or zero-forms, and represents a new…

The goal of this paper is to construct a multivariate generalisation of the Grunwald-Letnikov derivative, a classical fractional derivative operator. To do so, we first produce a formalism of fractional derivatives in terms of infinitesimal…

We extend the well-known Shannon decomposition of Boolean functions to more general classes of functions. Such decompositions, which we call pivotal decompositions, express the fact that every unary section of a function only depends upon…

Vanilla convolutional neural networks are known to provide superior performance not only in image recognition tasks but also in natural language processing and time series analysis. One of the strengths of convolutional layers is the…

From physical perspective, derivatives can be viewed as mathematical idealizations of the linear growth. The linear growth condition has special properties, which make it preferred. The manuscript investigates the general properties of the…

This paper is devoted to the proof Gauss' divergence theorem in the framework of "ultrafunctions". They are a new kind of generalized functions, which have been introduced recently [2] and developed in [4], [5] and [6]. Their peculiarity is…

We define the tangential derivative, a notion of directional derivative which is invariant under diffeomorphisms. In particular this derivative is invariant under changes of chart and is thus well-defined for functions defined on a…

We introduce two kinds of generalized $s$-convex functions on real linear fractal sets $\mathbb{R}^{\alpha}(0<\alpha<1)$. And similar to the class situation, we also study the properties of these two kinds of generalized $s$-convex…

Some sorts of generalized morphisms are defined from very basic mathematical objects such as sets, functions, and partial functions. A wide range of mathematical notions such as continuous functions between topological spaces, ring…

This paper considers convolution equations that arise from problems such as measurement error and non-parametric regression with errors in variables with independence conditions. The equations are examined in spaces of generalized functions…

Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…