Related papers: Topics on nonlinear generalized functions
The great advances of learning-based approaches in image processing and computer vision are largely based on deeply nested networks that compose linear transfer functions with suitable non-linearities. Interestingly, the most frequently…
I present a short review of models for transverse-momentum distributions and transversity, with a particular attention on general features common to many models. I compare some model results with experimental extractions. I discuss the…
The aim of this paper is to define a new operator by using the generalized Struve functions. By using this operator we define a subclass of analytic functions. We discuss some properties of this class such as inclusion problems, radius…
The purpose of this short note was to outline the current status, then in 2011, of some research programs aiming at a categorification of parts of A.Connes' non-commutative geometry and to provide an outlook on some possible subsequent…
We introduce sequences of functions orthogonal on a finite interval: proper orthogonal rational functions, orthogonal exponential functions, orthogonal logarithmic functions, and transmuted orthogonal polynomials
In the present paper, a generalized local Taylor formula with the local fractional derivatives (LFDs) is proposed based on the local fractional calculus (LFC). From the fractal geometry point of view, the theory of local fractional…
We consider an ordinary nonlinear differential equation with generalized coefficients as an equation in differentials in algebra of new generalized functions. Then the solution of such equation will be a new generalized function. In the…
The article contains an overview over locally stationary processes. At the beginning time varying autoregressive processes are discussed in detail - both as as a deep example and an important class of locally stationary processes. In the…
By discussing several examples, the theory of generalized functional models is shown to be very natural for modeling some situations of reasoning under uncertainty. A generalized functional model is a pair (f, P) where f is a function…
This paper presents a general study of one-dimensional differentiability for functionals defined on convex domains that are not necessarily open. The local approximation is carried out using affine functionals, as opposed to linear…
This paper introduces a new generalized superfactorial function (referable to as $n^{th}$- degree superfactorial: $sf^{(n)}(x)$) and a generalized hyperfactorial function (referable to as $n^{th}$- degree hyperfactorial: $H^{(n)}(x)$), and…
Ultrafunctions are a particular class of generalized functions defined on a hyperreal field $\mathbb{R}^{*}\supset\mathbb{R}$ that allow to solve variational problems with no classical solutions. We recall the construction of ultrafunctions…
Inspired by some new advances on normal factor graphs (NFGs), we introduce NFGs as a simple and intuitive diagrammatic approach towards encoding some concepts from linear algebra. We illustrate with examples the workings of such an approach…
In the last two decades, many algebras of generalized functions have been constructed, particularly the so-called generalized Sobolev algebras. Our goal is to study the latter and some of their main properties. In this framework, we pose…
This paper is intended as an introductory survey of a newly emerging field: a topological approach to the study of locally finite graphs that crucially incorporates their ends. Topological arcs and circles, which may pass through ends,…
In the paper we study nonlocal functionals whose kernels are homogeneous generalized functions. We also use such functionals to solve the Korteweg-de Vries , the nonlinear Schr\"odinger and the Davey-Stewartson equations.
We provide estimates for the convolution product of an arbitrary number of "resurgent functions", that is holomorphic germs at the origin of $C$ that admit analytic continuation outside a closed discrete subset of $C$ which is stable under…
This paper presents a new approach to distributed nonlinear control for formation acquisition and maintenance, inspired by recent results on cyclic topologies and based on tools from contraction theory. First, simple nonlinear control laws…
This paper introduces the fractal interpolation problem defined over domains with a nonlinear partition. This setting generalizes known methodologies regarding fractal functions and provides a new holistic approach to fractal interpolation.…
q-Gaussian distribution appear in many science areas where we can find systems that could be described within a nonextensive framework. Usually, a way to assert that these systems belongs to nonextensive framework is by means of numerical…