Related papers: Logic and operator algebras
This survey provides an elementary introduction to operads and to their applications in homotopical algebra. The aim is to explain how the notion of an operad was prompted by the necessity to have an algebraic object which encodes higher…
We formalise the modal operators from the concurrent dynamic logics of Peleg, Nerode and Wijesekera in a multirelational algebraic language based on relation algebra and power allegories, using relational approximation operators on…
We seize the opportunity of the publication of selected papers from the \emph{Logic, categories, semantics} workshop in the \emph{Journal of Applied Logic} to survey some current trends in logic, namely intuitionistic and linear type…
In this article we investigate the notion and basic properties of Boolean algebras and prove the Stone's representation theorem. The relations of Boolean algebras to logic and to set theory will be studied and, in particular, a neat proof…
The aim of this paper is to present remarkable classes of Lie-admissible algebras containing in particular the associative algebras, the Vinberg algebras and pre-Lie algebras. We determine the associated quadratic operads and their dual…
Operator learning refers to the application of ideas from machine learning to approximate (typically nonlinear) operators mapping between Banach spaces of functions. Such operators often arise from physical models expressed in terms of…
In this paper, we investigate the properties of sequences and series under the action of the log-concave operator \(\mathcal{L}\). We explore the relationship between the convergence of a sequence \((a_k)\) and the convergence of sequences…
In this article, we describe how coalgebraic structures on operads induce algebraic structures on their categories of algebras and coalgebras.
We discuss and develop some connections between analysis on singular spaces and operator algebras, as presented in my sequence of four lectures at the conference "Noncommutative geometry and applications," Frascati, Italy, June 16-21, 2014.…
This paper is the second part of an introduction to linear logic and ludics, both due to Girard. It is devoted to proof nets, in the limited, yet central, framework of multiplicative linear logic and to ludics, which has been recently…
Research in operations management has traditionally focused on models for understanding, mostly at a strategic level, how firms should operate. Spurred by the growing availability of data and recent advances in machine learning and…
Differentiations of operator algebras over non-archimedean spherically complete fields are investigated. Theorems about a differentiation being internal are demonstrated.
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…
We showcase applications of nonlinear algebra in the sciences and engineering. Our review is organized into eight themes: polynomial optimization, partial differential equations, algebraic statistics, integrable systems, configuration…
In this paper, we investigate the power of nearly purely operational techniques in the study of umbral calculus. We present a concise reconstruction of the theory based on a systematic use of linear operators, with particular attention to…
Complexity and decidability of logics is a major research area involving a huge range of different logical systems. This calls for a unified and systematic approach for the field. We introduce a research program based on an algebraic…
In this survey I should like to introduce some concepts of algebraic geometry and try to demonstrate the fruitful interaction between algebraic geometry and computer algebra and, more generally, between mathematics and computer science. One…
The four authors present their speculations about the future developments of mathematical logic in the twenty-first century. The areas of recursion theory, proof theory and logic for computer science, model theory, and set theory are…
Logic not only helps to solve complicated and safety-critical problems, but also disciplines the mind and helps to develop abstract thinking, which is very important for any area of Engineering. In this technical report, we present an…
Quantum Physics and Logic is an annual conference that brings together researchers working on mathematical foundations of quantum physics, quantum computing, and related areas, with a focus on structural perspectives and the use of logical…