Reduced pre-Lie algebraic structures, the weak and weakly deformed Balinsky-Novikov type symmetry algebras and related Hamiltonian operators

The Lie algebraic scheme for constructing Hamiltonian operators is differential-algebraically recast and an effective approach is devised for classifying the underlying algebraic structures of integrable Hamiltonian systems. Lie–Poisson analysis on the adjoint space to toroidal loop Lie algebras is employed to construct new reduced pre-Lie algebraic structures in which the corresponding Hamiltonian operators exist and generate integrable dynamical systems. It is also shown that the Balinsky–Novikov type algebraic structures, obtained as a Hamiltonicity condition, are derivations on the Lie algebras naturally associated with differential toroidal loop algebras. We study nonassociative and noncommutive algebras and the related Lie-algebraic symmetry structures on the multidimensional torus, generating via the Adler–Kostant–Symes scheme multi-component and multi-dimensional Hamiltonian operators. In the case of multidimensional torus, we have constructed a new weak Balinsky–Novikov type algebra, which is instrumental for describing integrable multidimensional and multicomponent heavenly type equations. We have also studied the current algebra symmetry structures, related with a new weakly deformed Balinsky–Novikov type algebra on the axis, which is instrumental for describing integrable multicomponent dynamical systems on functional manifolds. Moreover, using the non-associative and associative left-symmetric pre-Lie algebra theory of Zelmanov, we also explicate Balinsky–Novikov algebras, including their fermionic version and related multiplicative and Lie structures

Integrability analysis of regular and fractional Blackmore-Samulyak-Rosato fields

Blackmore-Samulyak-Rosato (BSR) fields, originally developed as a means of obtaining reliable continuum approximations for granular flow dynamics in terms of relatively simple integro-differential equations, can be used to model a wide range of physical phenomena. Owing to results obtained for one-dimensional granular flow configurations, it has been conjectured that BSR models of fields with perfectly elastic interactions are completely integrable infinite-dimensional Hamiltonian systems. This conjecture is proved for BSR models in one space dimension, and analogues of BSR fields involving fractional time derivatives are briefly investigated.Установлено, що BSR поля, початково розвинені як засіб одержання надійних континуумних апроксимацій для динаміки гранулярних потоків на мові відносно простих інтегро-диференціальних рівнянь, можна використовувати для моделювання широкого спектра фізичних явищ. Завдяки результатам, одержаним для конфігурацій одновимірного гранулярного потоку, зроблено припущення, що BSR моделі полів із ідеально пружними взаємодіями є повністю інтегровними нескінченновимірними гамільтоновими системами. Це припущення доведено для BSR моделей в одновимірному просторі, і аналоги BSR полів, що включають часткові похідні за часом, досліджені стисло

Mediating boundaries between knowledge and knowing: ICT and R4D praxis

Research for development (R4D) praxis (theory-informed practical action) can be underpinned by the use of Information and Communication Technologies (ICTs) which, it is claimed, provide opportunities for knowledge working and sharing. Such a framing implicitly or explicitly constructs a boundary around knowledge as reified, or commodified – or at least able to be stabilized for a period of time (first order knowledge). In contrast ‘third-generation knowledge’ emphasizes the social nature of learning and knowledge-making; this reframes knowledge as a negotiated social practice, thus constructing a different system boundary. This paper offers critical reflections on the use of a wiki as a data repository and mediating technical platform as part of innovating in R4D praxis. A sustainable social learning process was sought that fostered an emergent community of practice among biophysical and social researchers acting for the first time as R4D co-researchers. Over time the technologically mediated element of the learning system was judged to have failed. This inquiry asks: How can learning system design cultivate learning opportunities and respond to learning challenges in an online environment to support R4D practice? Confining critical reflection to the online learning experience alone ignores the wider context in which knowledge work took place; therefore the institutional setting is also considered

The differential-algebraic and bi-Hamiltonian integrability analysis of the Riemann type hierarchy revisited

A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic hierarchy is revisited, its new Lax type representation and Poisson structures constructed in exact form. The related bi-Hamiltonian integrability and compatible Poissonian structures of the generalized Riemann type hierarchy are also discussed.Comment: 18 page

A Tentative Modeling Study of the Effect of Wall Reactions on Oxidation Phenomena

This paper gives details of a tentative modeling study that investigates the inhibiting effect of internal reactor walls treated with acid..

Further Evidence for the Decay K+ to pi+ neutrino-antineutrino

Additional evidence for the rare kaon decay K+ to pi+ neutrino-antineutrino has been found in a new data set with comparable sensitivity to the previously reported result. One new event was observed in the pion momentum region examined, 211<P<229 MeV/c, bringing the total for the combined data set to two. Including all data taken, the backgrounds were estimated to contribute 0.15 pm 0.05 events. The branching ratio is B=1.57^{+1.75}_{-0.82} 10^{-10}.Comment: 10 pages, 2 figure

Policy, Performativity and Partnership: an Ethical Leadership Perspective

This article identifies the need to think differently about educational partnerships in a changing and turbulent post compulsory policy environment in England. The policy and institutional contexts in which universities and colleges currently operate seem to be fuelling performativity at the expense of educational values. There appears to be a sharp interruption in the steady increase in educational partnerships as a vehicle for increasing and widening participation in higher education. We are witnessing a marked change in university / college relationships that appears to be a consequence of government calling a halt to increased participation in higher education, creating an increasingly competitive market for a more limited pool of student places. The implication that educational policy at the national level determines a particular pattern or mode of leadership decision making throughout an institution should however be resisted. Policy developments that challenge the moral precepts of education should not be allowed to determine how a leader acts, rather they should prompt actions that are truly educational, rooted in morality, and atached to identifiable educational values. Educational leaders have agency to resist restricted discourses in favour of ethical and principled change strategies that are a precondition for sustainable transformative partnerships in post compulsory education. University leaders in particular are called upon to use their considerable influence to resist narrow policy or managerial instrumentalism or performativity and embrace alternatives that are both educationally worthwhile and can enhance institutional resilience