This survey article is concerned with two basic approximation concepts and their interrelation with the numerical solution of elliptic operator equations, namely nonlinear and adaptive approximation. On one hand, for nonlinear approximation based on wavelet expansions the best possible approximation rate, which a function can have for a given number of degrees of freedom, is characterized in te...

Cooperative games with transferable utilities belong to a branch of game theory where groups of players can enter into binding agreements and form coalitions in order to jointly achieve some objectives. In a cooperative setting, one of the most important questions to address is how to establish a payoff distribution among the players in such a way to ensure the stability of the game. Classical ...

Interpretation of outputs of fuzzy systems often involves the use of linguistic approximation that assigns a linguistic label to a fuzzy set based on the predefined primary terms, linguistic modifiers and linguistic connectives. More formally linguistic approximation can be considered in the terms of retranslation rules that correspond to the translation rules in explicitation in computing with...

Cooperative games with transferable utilities belong to a branch of game theory where groups of players can enter into binding agreements and form coalitions in order to jointly achieve some objectives. In a cooperative setting, one of the most important questions to address is how to establish a payoff distribution among the players in such a way to ensure the stability of the game. Classical ...

Bi ideals are the generalisation of quasi ideals. In this article, it is defined that notion bi-ideals in semirings on weak nearness approximation spaces. Afterwards, explained some concepts and definitions related to subject. Also, given definition m-bi (m,n)-quasi Thus, we examine relationship between .

This paper presents an expressive language for representing knowledge about vague concepts. It is based on the rough set formalism and it caters for implicit definition of rough relations by combining different regions (e.g. upper approximation, lower approximation, boundary) of other rough relations. The semantics of the proposed language is obtained by translating it to the language of extend...

Brain networks are increasingly understood as one of a large class of information processing systems that share important organizational principles in common, including the property of a modular community structure. A module is topologically defined as a subset of highly inter-connected nodes which are relatively sparsely connected to nodes in other modules. In brain networks, topological modul...

Several computational and mathematical features of the h-p cloud method are demonstrated in this paper. We show how h, p and h-p adaptivity can be implemented in the h-p cloud method without traditional grid concepts typical of finite element methods. The mathematical derivation of an a posteriori error estimate for the h-p cloud method is also presented. Severalnumerical examples illustrate th...

Research on mathematics education has shown that learners' actions can influence how they think and vice versa. Much of this work has been rooted in the use of manipulatives, gestures, and body movements. Our article dissects the mechanisms that underscore the impact of embodied activities and applies this lens to explore how to harness the affordances of new technology to enhance mathematical ...

Ricci scalar is the key ingredient of non-Newtonian theory of gravity, where space-time geometry has a crucial role. Normally, it is supposed to be a geometrical field, but interestingly it also behaves like a physical field. Thus it plays dual role in the arena of gravitation. This article is an overview of the work related to dual roles of the Ricci scalar. A scalar is a mathematical concept ...