scholarly journals Periodic Staircase Matrices and Generalized Cluster Structures

2020 ◽  
Author(s):  
Misha Gekhtman ◽  
Michael Shapiro ◽  
Alek Vainshtein
Keyword(s):  
Difference Operators ◽  
Drinfeld Double ◽  
Similar Role ◽  
Geometric Type ◽  
Plücker Relations ◽  
Lie Brackets

Abstract As is well known, cluster transformations in cluster structures of geometric type are often modeled on determinant identities, such as short Plücker relations, Desnanot–Jacobi identities, and their generalizations. We present a construction that plays a similar role in a description of generalized cluster transformations and discuss its applications to generalized cluster structures in $GL_n$ compatible with a certain subclass of Belavin–Drinfeld Poisson–Lie brackets, in the Drinfeld double of $GL_n$, and in spaces of periodic difference operators.

scholarly journals Focus and contrastive topic in questions and answers, with particular reference to Turkish

2020 ◽  
Vol 46 (1-2) ◽  
pp. 1-71 ◽  
Author(s):  
Beste Kamali ◽  
Manfred Krifka
Keyword(s):  
Algebraic Representation ◽  
Similar Role ◽  
Discourse Coherence ◽  
Dynamic Interpretation ◽  
Contrastive Topic ◽  
Questions And Answers ◽  
Alternative Questions

AbstractMuch recent research has recognized the importance of focus and contrastive topic in assertions for discourse coherence. However, with few exceptions, it has been neglected that focus and contrastive topic also occur in questions, and have a similar role in establishing coherence. We propose a framework of dynamic interpretation based on the notion of Commitment Spaces that show that a uniform interpretation of focus and contrastive topic is possible. The algebraic representation format is rich enough so that a separate introduction of discourse trees is not necessary. The paper discusses these phenomena for Turkish, a language with an explicit focus marker for polar and alternative questions, which distinguishes focus from contrastive topic.

scholarly journals Novel vocalizations are understood across cultures

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Aleksandra Ćwiek ◽  
Susanne Fuchs ◽  
Christoph Draxler ◽  
Eva Liina Asu ◽  
Dan Dediu ◽  
...  
Keyword(s):  
Cultural Study ◽  
Cross Cultural ◽  
English Speakers ◽  
Linguistic Communication ◽  
Similar Role ◽  
Iconic Representation ◽  
Cross Cultural Study ◽  
Linguistic Backgrounds

AbstractLinguistic communication requires speakers to mutually agree on the meanings of words, but how does such a system first get off the ground? One solution is to rely on iconic gestures: visual signs whose form directly resembles or otherwise cues their meaning without any previously established correspondence. However, it is debated whether vocalizations could have played a similar role. We report the first extensive cross-cultural study investigating whether people from diverse linguistic backgrounds can understand novel vocalizations for a range of meanings. In two comprehension experiments, we tested whether vocalizations produced by English speakers could be understood by listeners from 28 languages from 12 language families. Listeners from each language were more accurate than chance at guessing the intended referent of the vocalizations for each of the meanings tested. Our findings challenge the often-cited idea that vocalizations have limited potential for iconic representation, demonstrating that in the absence of words people can use vocalizations to communicate a variety of meanings.

New fractional order discrete Grüss type inequality

2021 ◽  
Vol 71 (1) ◽  
pp. 33-42
Author(s):  
Serkan Asliyüce ◽  
A. Feza Güvenilir
Keyword(s):  
Fractional Order ◽  
Type Inequality ◽  
Difference Operators

Abstract The aim of this study is to establish new discrete Grüss type inequality using fractional order h-sum and h-difference operators that generalize the fractional sum and difference operators.

scholarly journals NONRELATIVISTIC HOLOGRAPHY — A GROUP-THEORETICAL PERSPECTIVE

2014 ◽  
Vol 29 (03n04) ◽  
pp. 1430001 ◽  
Author(s):  
V. K. DOBREV
Keyword(s):  
Representation Theory ◽  
Theoretical Perspective ◽  
Explicit Construction ◽  
Intertwining Operators ◽  
Difference Operators ◽  
Semisimple Lie Groups ◽  
Boundary Operators ◽  
Boundary Fields ◽  
Theoretical Results ◽  
Schrödinger Algebra

We give a review of some group-theoretical results related to nonrelativistic holography. Our main playgrounds are the Schrödinger equation and the Schrödinger algebra. We first recall the interpretation of nonrelativistic holography as equivalence between representations of the Schrödinger algebra describing bulk fields and boundary fields. One important result is the explicit construction of the boundary-to-bulk operators in the framework of representation theory, and that these operators and the bulk-to-boundary operators are intertwining operators. Further, we recall the fact that there is a hierarchy of equations on the boundary, invariant with respect to Schrödinger algebra. We also review the explicit construction of an analogous hierarchy of invariant equations in the bulk, and that the two hierarchies are equivalent via the bulk-to-boundary intertwining operators. The derivation of these hierarchies uses a mechanism introduced first for semisimple Lie groups and adapted to the nonsemisimple Schrödinger algebra. These require development of the representation theory of the Schrödinger algebra which is reviewed in some detail. We also recall the q-deformation of the Schrödinger algebra. Finally, the realization of the Schrödinger algebra via difference operators is reviewed.

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