相关论文: Concerning problems about cardinal invariants on B…
We deal with some of problems posed by Monk and related to cardinal invariant of ultraproducts of Boolean algebras. We also introduce and investigate some new cardinal invariants.
We construct Boolean Algebras answering questions of Monk on cardinal invariants. The results are proved in ZFC (rather than giving consistency results). We deal with the existence of superatomic Boolean Algebras with ``few automorphisms'',…
This book aims to provide a brief overview of recent advancements in the theory of inverse problems for stochastic partial differential equations. In order to keep the content concise, we will only discuss the inverse problems of two…
We answer three problems by J. D. Monk on cardinal invariants of Boolean algebras. Two of these are whether taking the algebraic density pi(A), resp. the topological density d(A), of a Boolean algebra A commutes with formation of…
We discuss new problems in universal algebraic geometry and explain them by boolean equations.
We report on results about a study of algebraic graph invariants, based on computer exploration, and motivated by graph-isomorphism and reconstruction problems.
Classification theorems for linear differential equations in two real variables, possessing eigenfunctions in the form of the polynomials (the generalized Bochner problem) are given. The main result is based on the consideration of the…
A survey of recent results concerning cardinal invariants of measure and category. Submitted as a chapter of the upcoming Handbook of Set Theory.
We survey various classical results on invariants of polynomials, or equivalently, of binary forms, focussing on explicit calculations for invariants of polynomials of degrees 2, 3, 4.
We discuss invariants in equivariant birational geometry.
In this note we present a brief overview of variational methods to solve homogenization problems. The purpose is to give a first insight on the subject by presenting some fundamental theoretical tools, both classical and modern. We conclude…
This text proposes geometrical descriptions of all variational problems invariant by conformal transformations in two variables. First a characterisation in terms of C-Finsler manifolds, a suitable generalization of Finsler manifolds, is…
This book introduces the concept of neutrosophic bilinear algebras and their generalizations to n-linear algebras, n>2. This book has five chapters. The first chapter is introductory in nature and gives a few essential definitions and…
We discuss the Borel Tukey ordering on cardinal invariants of the continuum. We observe that this ordering makes sense for a larger class of cardinals than has previously been considered. We then provide a Borel version of a large portion…
Let inv denote the cardinal invariants Depth^+ and Length^+ on Boolean algebras. For many singular cardinals we create a strict inequality between the product of the inv values and the inv of the product algebra. The proof holds in ZFC.
A classification of ordinary differential equations and finite-difference equations in one variable having polynomial solutions (the generalized Bochner problem) is given. The method used is based on the spectral problem for a polynomial…
The structure of quotient Boolean algebras in terms of cardinal invariants is investigated. Some results of Gitik and Shelah regarding atomless ideals are reproved and proofs are significantly simplified.
This paper surveys some results by the author and collaborators on the existence of invariant Lagrangian graphs for Tonelli Hamiltonian systems. The presentation is based on an invited talk by the author at XIX Congresso Unione Matematica…
This contribution presents a comprehensive analysis of Colombeau (-type) algebras in the range between the diffeomorphism invariant algebra introduced in Part I and Colombeau's original algebra. Along the way, it provides several…
This paper presents an overview of the current state of knowledge in the field of equivariant map algebras and discusses some open problems in this area.