Related papers: Reconstruction of weak bialgebra maps and its appl…

In this paper we consider disjoint decomposition of algebraic and non-linear partial differential systems of equations and inequations into so-called simple subsystems. We exploit Thomas decomposition ideas and develop them into a new…

Weak (Hopf) bialgebras are described as (Hopf) bimonoids in appropriate duoidal (also known as 2-monoidal) categories. This interpretation is used to define a category wba of weak bialgebras over a given field. As an application, the "free…

This short note modifies a reconstruction method by the author (Comm. PDE, 45(9):1118-1133, 2020), for reconstructing piecewise constant conductivities in the Calder\'on problem (electrical impedance tomography). In the former paper, a…

The present paper deals with the discrete inverse problem of reconstructing binary matrices from their row and column sums under additional constraints on the number and pattern of entries in specified minors. While the classical…

Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…

The space of weak expectations for a given representation of a (unital) separable C*-algebra is a compact convex set of (unital) completely positive maps in the BW topology, when it is non-empty. An application of the classical Choquet…

Two cochain complexes are constructed for an algebra A and a coalgebra C entwined with each other via the map $\psi:C\otimes A\to A\otimes C$. One complex is associated to an A-bimodule, the other to a C-bicomodule. In the former case the…

A constructive method for decomposing finite dimensional representations of semisimple real Lie algebras is developed. The method is illustrated by an example. We also discuss an implementation of the algorithm in the language of the…

Idempotent analogues of convexity are introduced. It is proved that the category of algebras for the capacity monad in the category of compacta is isomorphic to the category of $(\max,\min)$-idempotent biconvex compacta and their biaffine…

For a cellular algebra $\A$ with a cellular basis $\ZC$, we consider a decomposition of the unit element $1_\A$ into orthogonal idempotents (not necessary primitive) satisfying some conditions. By using this decomposition, the cellular…

The results of this thesis allows one to replace calculations in tricategories with equivalent calculations in Gray categories (aka semistrict tricategories). In particular the rewriting calculus for Gray categories as used for example by…

We shall develop a notion of amenability for dual Banach algebras, namely weak Connes amenability, which will play the role that weak amenability does for usual Banach algebras

This is a survey article on real algebra and geometry, and in particular on its recent applications in optimization and convexity. We first introduce basic notions and results from the classical theory. We then explain how these relate to…

We provide a criterion for a vertex operator superalgebra homomorphism from an affine vertex algebra to another vertex superalgebra to be conformal, and an additional criterion that guarantees that this homomorphism is surjective. This…

Based on a generalization of Lebesgue decomposition we obtain a characterization of weak compactness in the space $ba$, a representation of its dual space and some results on the structure of finitely additive measures.

After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…

In this article, we define and study a geometry and an order on the set of partitions of an even number of objects. One of the definitions involves the partition algebra, a structure of algebra on the set of such partitions depending on an…

Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…

The area of inverse problems in mathematics is highly interdisciplinary. In various fields of science, engineering, medicine, and industry, there arises a need to reconstruct information about unknown entities that cannot be directly…

We investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups. We first describe computational methods for the construction of irreducible representations of these algebras,…