相关论文: The history of three wrong definitions

Certain notions of convergence of sequences functions such as pointwise convergence and (uniform) convergence on compact or bounded sets come from suitable topological function spaces; see [1]. Under certain conditions these topologies…

The concepts of the perfect system and degeneracy are introduced. A special symmetry is found which is related to the entropy invariant. The inversion relation of system is obtained which is used to give the oppsite direction of time to…

This paper improves two existing theorems of interest to neo-logicist philosophers of mathematics. The first is a classification theorem due to Fine for equivalence relations between concepts definable in a well-behaved second-order logic.…

We study computably enumerable equivalence relations (ceers) on N and unravel a rich structural theory for a strong notion of reducibility among ceers.

This essay traces the history of three interconnected strands. Firstly, changes in the concept of number, secondly, the study of the qualities of number, which evolved into number theory, and thirdly, the nature of mathematics itself, from…

Intuitively, the concept of similarity is the notion to measure an inexact matching between two entities of the same reference set. The notions of similarity and its close relative dissimilarity are widely used in many fields of Artificial…

The notion of an instruction sequence fault is considered from various perspectives. Four different viewpoints on what constitutes a fault, or how to use the notion of a fault, are formulated. An integration of these views is proposed.

We introduce a new definition of nonpositive curvature in metric spaces and study its relationship to the existing notions of nonpositive curvature in comparison geometry. The main feature of our definition is that it applies to all metric…

We survey some old and new results concerning the classification of complete metric spaces up to isometry, a theme initiated by Gromov, Vershik and others. All theorems concerning separable spaces appeared in various papers in the last…

This paper is a review of our recent work on three notorious problems of non-relativistic quantum mechanics: realist interpretation, quantum theory of classical properties and the problem of quantum measurement. A considerable progress has…

The temporal relations that hold between events described by successive utterances are often left implicit or underspecified. We address the role of two phenomena with respect to the recovery of these relations: (1) the referential…

This paper is concerned with analysis on metric spaces in a variety of settings and with several kinds of structure.

We focus on eventually non-linear abstract Cauchy problems with a generalized fractional derivative in time. First we prove a local existence and uniqueness result, then we focus on a generalized Gr\"onwall inequality. Before addressing the…

We introduce the class of synchronous subsequential relations, a subclass of the synchronous relations which embodies some properties of subsequential relations. If we take relations of this class as forming the possible transitions of an…

Linear topological spaces with partial ordering (linear kinematics) are studied. They are defined by a set of 8 axioms implying that topology, linear structure and ordering are compatible with each other. Most of the results are valid for…

This review describes the history of discovery of violation of spatial parity P, charge conjugation parity C, combined parity CP. The hypothesis of existence of mirror particles was called upon by its authors to restore the symmetry between…

Betweenness as a relation between three individual points has been widely studied in geometry and axiomatized by several authors in different contexts. The article proposes a more general notion of betweenness as a relation between three…

We derive strong variance-based uncertainty relations for arbitrary two and more unitary operators by re-examining the mathematical foundation of the uncertainty relation. This is achieved by strengthening the celebrated Cauchy-Schwarz…

We initiate the study of pseudofiniteness in continuous logic. We introduce a related concept, namely that of pseudocompactness, and investigate the relationship between the two concepts. We establish some basic properties of…

In this paper we survey wqo and bqo theory from the reverse mathematics perspective. We consider both elementary results (such as the equivalence of different definitions of the concepts, and basic closure properties) and more advanced…