相关论文: Some research perspectives in nonlinear functional…

The purpose of this article is to survey certain aspects of multilinear harmonic analysis related to notions of transversality. Particular emphasis will be placed on the multilinear restriction theory for the euclidean Fourier transform,…

The aim of this short lecture series is to expose the students to the beautiful theory of lattices by, on one hand, demonstrating various basic ideas that appear in this theory and, on the other hand, formulating some of the celebrated…

In this presentation, we will develop a short overview of main trends of optimization in systems and control, and from there outline some new perspectives emerging today. More specifically, we will focus on the current situation, where it…

We review the status of (scalar) quantum field theory on curved spacetimes using a novel formulation in terms of non linear functionals over the smooth configuration fields. In particular, this entails also a new foundation of locally…

The variant of calculation of functions of set and their application is offered. In particular: the new measure of system of sets generalizing classical concept of a measure is entered; the variation of set that has allowed to construct a…

Fractal functions that produce smooth and non-smooth approximants constitute an advancement to classical nonrecursive methods of approximation. In both classical and fractal approximation methods emphasis is given for investigation of…

We formulate symmetric versions of classical variational principles. Within the framework of non-smooth critical point theory, we detect Palais-Smale sequences with additional second order and symmetry information. We discuss applications…

Many different and complementary strategies for translating the basic principle of multiple topological imaging into observational analysis are now available, both for three-dimensional and two-dimensional catalogues.

In recent years, manifold methods have moved into focus as tools for dimension reduction. Assuming that the high-dimensional data actually lie on or close to a low-dimensional nonlinear manifold, these methods have shown convincing results…

We survey the field of nonparametric inference under shape constraints, providing a historical overview and a perspective on its current state. An outlook and some open problems offer thoughts on future directions.

We describe the new field of mathematical analysis of deep learning. This field emerged around a list of research questions that were not answered within the classical framework of learning theory. These questions concern: the outstanding…

Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to…

This note has two principal aims: to portray an essence of Non-Standard Analysis as a particular structure (which we call lim-rim), noting its interplay with the notion of ultrapower, and to present a construction of Non-Standard Analysis,…

Causal inference is a central goal across many scientific disciplines. Over the past several decades, three major frameworks have emerged to formalize causal questions and guide their analysis: the potential outcomes framework, structural…

Accretive and monotone operator theory are central branches of nonlinear functional analysis and constitute the abstract study of set-valued mappings between function spaces. This paper deals with the computational properties of certain…

This article belongs to a subject, Directed Algebraic Topology, whose general aim is including non-reversible processes in the range of topology and algebraic topology. Here, as a further step, we also want to cover "critical processes",…

This article has one single purpose: introduce a new and simple, yet highly insightful approach to capture, fully and quantitatively, the dynamics of the circular flow of income in economies. The proposed approach relies mostly on basic…

Many contemporary applications in signal processing and machine learning give rise to structured non-convex non-smooth optimization problems that can often be tackled by simple iterative methods quite effectively. One of the keys to…

There is an overwhelmingly large literature and algorithms already available on `large scale inference problems' based on different modeling techniques and cultures. Our primary goal in this paper is \emph{not to add one more new…

The first purpose of this work is to provide a friendly introduction to the theory of nonautonomous linear systems of ordinary differential equations, the property of exponential dichotomy and its corresponding spectral theory. The second…