Quasi-linear Cycle Sets and the Retraction Problem for Set-theoretic Solutions of the Quantum Yang-Baxter Equation

2016 ◽  
Vol 23 (01) ◽  
pp. 149-166 ◽  
Author(s):  
Wolfgang Rump

Cycle sets were introduced to reduce non-degenerate unitary Yang-Baxter maps to an algebraic system with a single binary operation. Every finite cycle set extends uniquely to a finite cycle set with a compatible abelian group structure. Etingof et al. introduced affine Yang-Baxter maps. These are equivalent to cycle sets with a specific abelian group structure. Abelian group structures have also been essential to get partial results for the still unsolved retraction problem. We introduce two new classes of cycle sets with an underlying abelian group structure and show that they can be transformed into each other while keeping the group structure fixed. This leads to a proper extension of the retractibility conjecture and new evidence for its truth.

Fishes ◽  
2019 ◽  
Vol 4 (1) ◽  
pp. 21 ◽  
Author(s):  
Aurore Cortay ◽  
Tatiana Colchen ◽  
Pascal Fontaine ◽  
Alain Pasquet

Cannibalism occurs in many cultured fish species, especially at the larval and juvenile stages of piscivorous taxa. In farmed percid species, such as pikeperch (Sander lucioperca), intra-cohort cannibalism is a major issue inducing significant losses of the initial stocking density during the first weeks of rearing. Therefore, the present study was designed to investigate the effects of perch larvae (Perca fluviatilis) as live prey on growth, survival and cannibalism in pikeperch larvae under experimental conditions. Additionally, zootechnical and behavioural variables linked to aggressiveness (S postures, attacks, bites and ingestion), and group structures were considered. The survival rate was not different between the two groups (72% with prey vs. 69% without prey), but the cannibalism rate was higher in the group with the prey (28% vs. 10%). The means of final weight and length of pikeperch larvae were higher in the group fed with perch larvae, but size heterogeneity measured by the coefficients of variation for these two parameters did not differ. The specific growth rate was higher in the group fed with perch larvae, but there was no difference between the two groups concerning Fulton’s condition factor. Among all the behavioural variables (aggressiveness, group structure), none differed between the two groups.


2014 ◽  
Vol 48 (1) ◽  
Author(s):  
Roger Grainger

The dominant form of group work in the Church of England is educational and directive. An investigation was carried out to determine whether other forms of group work could be valuable for the Church in addition to this approach. The same group of nine members, members of two Church of England parishes in the North of England, were involved in 12 sessions of group work, four sessions of each of the three types of group structure, in order for them to report their individual reactions to each type. An Interpretive Phenomenological Analysis (IPA) showed that all three kinds of groups drew attention to four principle areas of comment. In all these kinds of groups, belonging, safety, enrichment and personalvalidation, with each one of the three groups scoring more highly than the other two on one or other of these dimensions. No group showed itself as more directly educational than the others, showing that, for church educational purposes, a range of group structures maybe used as actual learning comes from the experience of group membership itself. Using the qualitative research model of IPA, an investigation was carried out into the principal themes emerging from members’ self-reports concerning their experiences of the three different group structures, revealing four value constructs – belonging or alienation, safety or danger, enrichment or impoverishment and validation or rejection – which played a dominant role in all three kinds of groups. Taken together, each of the three group structures gave a different degree of prominence to each of the four evaluative constructs so that each of the three was shown to be particularly relevant for, and associated with, a particular area of experiential learning.Die onderrig van Anglikane – ’n ondersoek na groepwerk in die Kerk van Engeland: ’n gevallestudie. Die belangrikste vorm van groepwerk in die Kerk van Engeland is opvoedkundig en rigtinggewend van aard. ’n Ondersoek is gedoen na die waarde van bykomende metodes van groepwerk. Dieselfde groep van nege lede uit twee gemeentes in die Noorde van Engeland, was by die 12 groepwerksessies betrokke – vier sessies vir elk van die drie tipes groepstrukture – om hulle in staat te stel om hulle onderskeie reaksies op elkeen van die tipes groepstrukture te rapporteer. ’n Interpretiewe fenomenologiese analise het aangetoon dat al drie tipes groepstrukture die soeklig op vier hoofkenmerke laat val het, naamlik om te behoort, veiligheid, verryking en bevestigingvan eiewaarde. By elke groep het een of meer van hierdie kenmerke swaarder geweeg as by die ander twee groepe. Geeneen van die groepe het opvoedkundig meer as die ander uitgestaan nie, wat bewys dat ’n reeks groepstrukture vir kerklike opvoedkundige doeleindes gebruik kan word, aangesien leer in wese uit die ervaring van die groeplede self kom. Met behulp van die kwalitatiewe navorsingsmodel van die interpretiewe fenomenologiese analise is ondersoek ingestel na die hooftemas soos blyk uit die lede se individuele verslae ten opsigte van hulle ervaring van die drie verskillende groepstrukture. Die verslae het vier waardekonsepte openbaar wat ’n dominante rol in al drie tipes groepe gespeel het, naamlik om te behoort of te vervreem, veiligheid of gevaar, verryking of verarming, en bevestiging van eiewaarde of verwerping. Samevattend blyk dat die drie groepstrukture elkeen ’n ander graad van prominensie aan die vier verskillende waardekonsepte toeken sodat elke groep spesifiek relevant is vir en geassosieer word met ’n spesifieke area van ervaringsleer.


1993 ◽  
Vol 114 (1) ◽  
pp. 163-189 ◽  
Author(s):  
M. Bullejos ◽  
P. Carrasco ◽  
A. M. Cegarra

AbstractIn this paper we use Takeuchy–Ulbrich's cohomology of complexes of categories with abelian group structure to introduce a cohomology theory for simplicial sets, or topological spaces, with coefficients in symmetric cat-groups . This cohomology is the usual one when abelian groups are taken as coefficients, and the main topological significance of this cohomology is the fact that it is equivalent to the reduced cohomology theory defined by a Ω-spectrum, {}, canonically associated to . We use the spaces to prove that symmetric cat-groups model all homotopy type of spaces X with Πi(X) = 0 for all i ╪ n, n + 1 and n ≥ 3, and then we extend Eilenberg–MacLane's classification theorem to those spaces: .


Author(s):  
Marco Di Filippo ◽  
Jiri Krepel ◽  
Konstantin Mikityuk ◽  
Horst-Michael Prasser

Nuclear reactor simulation is often based on multi-group cross-section libraries. The structure and resolution of these libraries have a strong influence on the accuracy and computational time; hence, number of groups and energy structure must be carefully considered. The relationship between group structures and how they impact generated cross-sections can be a critical parameter. Common energy boundaries shared among major group structures were identified and the relative kinship among those was reconstructed in an effort to build a family tree of major group structures. Stochastic code Serpent2 [1] was employed to generate cross-sections of selected isotopes at different reactor compositions and conditions, using the investigated energy group structures. The impact on their generation was quantified by spectral weighted deviation. The 35 major energy structures were divided into three basic families. The key parameters distinguishing them were their applicability to thermal or fast reactors and their applicability in neutronic or multiphysics investigations. A sensitivity threshold of the generated cross-sections over the group structure resolution was investigated. The aim was to identify a group structure with very low dependency on the actual reactor spectrum.


2019 ◽  
Vol 62 (4) ◽  
pp. 1089-1113 ◽  
Author(s):  
K. De Commer

AbstractA skew brace, as introduced by L. Guarnieri and L. Vendramin, is a set with two group structures interacting in a particular way. When one of the group structures is abelian, one gets back the notion of brace as introduced by W. Rump. Skew braces can be used to construct solutions of the quantum Yang–Baxter equation. In this article, we introduce a notion of action of a skew brace, and show how it leads to solutions of the closely associated reflection equation.


Author(s):  
Michael Thomas

By using a systems biological perspective and available literature on human social interaction, grouping, and cohesiveness, a new coherent model is proposed that integrates existing social integration and neurobiological research into a theoretical neurobiological framework of personality and social interaction. This model allows for the coherent analysis of complex social systems and interactions within them, and proposes a framework for estimating group cohesiveness and evaluating group structures in order to build and organize optimized social groups. This „Neurobiological-Associative“ model proposes two primary feedback loops, with environmental conditioning (learning) being sorted into an associative model that modulates interaction with the social environment, and which impacts the second feedback loop involving the individuals' neurobiological capacity. In this paper, the concept of neurobiological capacity is developed and based upon contemporary research on intelligence, personality, and social behavior with a focus on the oxytocin, serotonin, and dopamine systems. The basis of social exclusion and group structure is thus, expressed in the very most simple terms, neurobiological compatibility and risk assessment modulated by an internal associative model.


2016 ◽  
Vol 15 (07) ◽  
pp. 1650135 ◽  
Author(s):  
Wolfgang Rump

Set-theoretic solutions of the quantum dynamical Yang–Baxter equation are analyzed by means of dynamical analogues of braces (=bijective 1-cocycles). It is shown that every abelian group [Formula: see text] acts on a universal parameter set [Formula: see text] such that the orbits correspond to the faithful irreducible dynamical braces with underlying abelian group [Formula: see text]. Braces correspond to the fixed points of this action. Relations between linear extendability of solutions, non-degeneracy, and existence of a double, are established for the dynamical case.


2009 ◽  
Vol 13 (04) ◽  
pp. 521-535 ◽  
Author(s):  
ROBERT DEW ◽  
GREG HEARN

This paper examines how to structure resource-constrained innovation teams in order to maximise learning and creativity within organisations. Past research suggest that nominal groups (based on independent operations by individuals) outperform interactive groups. The results of this study suggest hybrid group structures based on independent operating pairs can be as effective as nominal groups. The study segmented 672 business managers and university post-graduate students into nominal, hybrid and interactive groups of six members. Three groups (one of each structural type) were pitted against each other to solve 4 related puzzles as quickly as possible. The results of these 28 problem-solving task races were aggregated to determine which group structure was most productive. Overall, the results confirmed that nominal groups of six significantly outperform interactive groups of the same size. More importantly, however, the results showed no significant difference between the productivity of nominal groups of six and hybrid groups comprised of three interactive pairs, where each pair operated separately to complete the same puzzle in parallel with the rest of the group. This suggests that structuring innovation teams into networked, nominal pairs may be just as productive as purely nominal group structures. This significantly extends the existing research on nominal groups versus interactive groups as it suggests that completely eliminating interactivity is not the optimal management approach.


2007 ◽  
Vol 82 (3) ◽  
pp. 297-314 ◽  
Author(s):  
Lynn M. Batten ◽  
Robert S. Coulter ◽  
Marie Henderson

AbstractFor any abelian group G and any function f: G → G we define a commutative binary operation or ‘multiplication’ on G in terms of f. We give necessary and sufficient conditions on f for G to extend to a commutative ring with the new multiplication. In the case where G is an elementary abelian p–group of odd order, we classify those functions which extend G to a ring and show, under an equivalence relation we call weak isomorphism, that there are precisely six distinct classes of rings constructed using this method with additive group the elementary abelian p–group of odd order p2.


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