相关论文: Some research perspectives in nonlinear functional…

This note aims to provide a systematic investigation of direct data-driven control, enriching the existing literature not by adding another isolated result, but rather by offering a unifying, versatile, and broad framework that enables the…

In these lecture notes, we give a brief introduction to some elements of category theory. The choice of topics is guided by applications to functional programming. Firstly, we study initial algebras, which provide a mathematical…

In this paper are briefly outlined the motivations, mathematical ideas in use, pre-formalization and assumptions, object-as-functor construction, `soft' types and concept constructions, case study for concepts based on variable domains,…

Perhaps, it is not too far from the truth to say that, among the great concepts (as compactness, completeness, order, convexity) on which functional analysis is based, connectedness is relatively less popular, though this does not mean that…

This book is not meant to be another compendium of select inequalities, nor does it claim to contain the latest or the slickest ways of proving them. This project is rather an attempt at describing how most functional inequalities are not…

The goal of this paper is to promote the use of fixed point strategies in data science by showing that they provide a simplifying and unifying framework to model, analyze, and solve a great variety of problems. They are seen to constitute a…

Several recent papers in digital topology have sought to obtain fixed point results by mimicking the use of tools from classical topology, such as complete metric spaces and homotopy invariant fixed point theory. We show that in many cases,…

Some notes and observations on analytic functions defined on an annulus

In this paper we review many interesting open problems in mathematical physics which may be attacked with the help of tools from constructive field theory. They could give work for future mathematical physicists trained with the…

This short review is an introduction to a great variety of methods, the collection of which is called the Painlev\'e analysis, intended at producing all kinds of exact (as opposed to perturbative) results on nonlinear equations, whether…

Our title challenges the reader to venture beyond linear algebra in designing models and in thinking about numerical algorithms for identifying solutions. This article accompanies the author's lecture at the International Congress of…

The aim of this paper is investigating the existence of solutions of some semilinear elliptic problems on open bounded domains when the nonlinearity is subcritical and asymptotically linear at infinity and there is a perturbation term which…

This opening editorial aims to interest researchers and encourage novel research in the closely related fields of sociophysics and computational social science. We briefly discuss challenges and possible research directions in the study of…

In this paper we present two different results in the context of nonlinear analysis. The first one is essentially a nonlinear technique that, in view of its strong generality, may be useful in different practical problems. The second…

This note points out a lemma on closures of monotonic increasing functions and shows how it is applicable to decomposition and modularity for semantics defined as the least fixedpoint of some monotonic function. In particular it applies to…

In this paper we study the existence and uniqueness of fixed points of a class of mappings defined on complete, (sequentially compact) cone metric spaces, without continuity conditions and depending on another function.

Plan of this report is given below: 1. Motivation from Physical and Mathematical Point of View; 2. Differential Calculi on Finite Groups; 3. Metrics; 4. Lagrangian Field Theory and Symplectic Structure; 5. Scalar Field Theory and Spectral…

The control function approach allows the researcher to identify various causal effects of interest. While powerful, it requires a strong invertibility assumption in the selection process, which limits its applicability. This paper expands…

We introduce a framework for online structure theory. Our approach generalises notions arising independently in several areas of computability theory and complexity theory. We suggest a unifying approach using operators where we allow the…

This paper presents a nonlinear approach to measurements a general framework for dealing with variations of environmental conditions. My method may prove promising to extensions beyond classical physics, economics, and other sciences. I…