New characterizations for differences of composition operators between weighted-type spaces in the unit ball

In this paper, we present some asymptotically equivalent expressions to the essential norm of differences of composition operators acting on weighted-type spaces of holomorphic functions in the unit ball of . Especially, the descriptions in terms of are described. From which the sufficient and necessary conditions of compactness follows immediately. Also, we characterize the boundedness of these operators.

Teasing and claims to non-serious intent in Chinese talk shows

While teasing can sometimes cause offence, the limits of what counts as acceptable teasing is a function of the localised sequential environment and broader socio cultural context in which it occurs. In this article, we examine the sequential and moral implications of claims to non-serious intent in teasing sequences arising in television talk shows. Drawing from an analysis of over 28 hours of variety shows broadcast in Mainland China and Taiwan, we examined 25 sequences involving claims by participants to be ‘kidding’ (kaiwanxiao). From this analysis it emerged that claims to be ‘kidding’ are used in these contexts to: (1) disclaim any (potential) offence caused through teasing, (2) signal a return to serious talk following teasing, (3) reproach the other for teasing that is construed as going too far, (4) and boost the humorous impact of self-boasting in response to teasing. While the first two are consistent with the usage of equivalent expressions in other languages, the latter two have not been identified in studies to date, thereby underscoring the importance of studying jocular forms of teasing in different linguistic and sociocultural contexts.

Compact Fuzzy Systems Based on Boolean Relations

This document presents some considerations and procedures to design a compact fuzzy system based on Boolean relations. In the design process, a Boolean codification of two elements is extended to a Kleene’s of three elements to perform simplifications for obtaining a compact fuzzy system. The design methodology employed a set of considerations producing equivalent expressions when using Boole and Kleene algebras establishing cases where simplification can be carried out, thus obtaining compact forms. In addition, the development of two compact fuzzy systems based on Boolean relations is shown, presenting its application for the identification of a nonlinear plant and the control of a hydraulic system where it can be seen that compact structures describes satisfactory performance for both identification and control when using algorithms for optimizing the parameters of the compact fuzzy systems. Finally, the applications where compact fuzzy systems are based on Boolean relationships are discussed allowing the observation of other scenarios where these structures can be used.

Revisiting the Melvin-Morton-Rozansky expansion, or there and back again

Alexander polynomial arises in the leading term of a semi-classical Melvin-Morton-Rozansky expansion of colored knot polynomials. In this work, following the opposite direction, we propose how to reconstruct colored HOMFLY-PT polynomials, superpolynomials, and newly introduced $$ \hat{Z} $$ Z ̂ invariants for some knot complements, from an appropriate rewriting, quantization and deformation of Alexander polynomial. Along this route we rederive conjectural expressions for the above mentioned invariants for various knots obtained recently, thereby proving their consistency with the Melvin-Morton-Rozansky theorem, and derive new formulae for colored superpolynomials unknown before. For a given knot, depending on certain choices, our reconstruction leads to equivalent expressions, which are either cyclotomic, or encode certain features of HOMFLY-PT homology and the knots-quivers correspondence.

О новых точных теоремах разложения для многофункциональных пространств типа ВМОА в ограниченных псевдовыпуклых областях

We provide new equivalent expressions in the unit ball and pseudoconvex domains for multifunctional analytic BMOA type space. We extend in various directions a known theorem of atomic decomposition of BMOA type spaces in the unit ball. Мы приводим новые эквивалентные выражения в единичных шаровых и псевдовыпуклых областях для многофункционального аналитического пространства типа BMOA. Мы расширяем в различных направлениях известную теорему атомарного разложения пространств типа BMOA в единичном шаре.

GPS: Equivalent Expressions

Equality is one of the main concepts in K–12 mathematics. Students should develop the understanding that equality is a relationship between two mathematical expressions. In this month's GPS, we share tasks asking students one main question: how do they know whether or not two mathematical expressions are equivalent?

The Rectifications of the Cassinian Ovals: Third Round

Here we derive a bunch of explicit formulas for the circumferences of all types of Cassinian ovals in terms of the complete elliptic integrals of the first kind and their equivalent expressions in terms of the hypergeometric functions.

Learning algebraic procedures through problem solving

In this paper, I attempt to present several examples of tasks and some relevant findings that investigate the possibility of basing a part of the practice-oriented tasks on higher-level thinking skills, that are usually associated with processes of problem solving. The tasks presented and analysed here integrate problem solving-components – namely, reversed thinking, expressing and analysing patterns, and employing multiple solution methods, into the learning and practicing of algebraic procedures – such as creating equivalent expressions and solving equations.