On Symmetry Properties of Frobenius Manifolds and Related Lie-Algebraic Structures

The aim of this paper is to develop an algebraically feasible approach to solutions of the oriented associativity equations. Our approach was based on a modification of the Adler–Kostant–Symes integrability scheme and applied to the co-adjoint orbits of the diffeomorphism loop group of the circle. A new two-parametric hierarchy of commuting to each other Monge type Hamiltonian vector fields is constructed. This hierarchy, jointly with a specially constructed reciprocal transformation, produces a Frobenius manifold potential function in terms of solutions of these Monge type Hamiltonian systems.

Miura-Reciprocal Transformation and Symmetries for the Spectral Problems of KdV and mKdV

We present reciprocal transformations for the spectral problems of Korteveg de Vries (KdV) and modified Korteveg de Vries (mKdV) equations. The resulting equations, RKdV (reciprocal KdV) and RmKdV (reciprocal mKdV), are connected through a transformation that combines both Miura and reciprocal transformations. Lax pairs for RKdV and RmKdV are straightforwardly obtained by means of the aforementioned reciprocal transformations. We have also identified the classical Lie symmetries for the Lax pairs of RKdV and RmKdV. Non-trivial similarity reductions are computed and they yield non-autonomous ordinary differential equations (ODEs), whose Lax pairs are obtained as a consequence of the reductions.

A super Degasperis–Procesi equation and related integrable systems

Based on a 4 × 4 matrix spectral problem, a super Degasperis–Procesi (DP) equation is proposed. We show that under a reciprocal transformation, the super DP equation is related to the first negative flow of a super Kaup–Kupershmidt (KK) hierarchy, which turns out to be a particular reduction of a super Boussinesq hierarchy. The bi-Hamiltonian structure of the super Boussinesq hierarchy is established and subsequently produces a Hamiltonian structure, as well as a conjectured symplectic formulation of the super KK hierarchy via suitable reductions. With the help of the reciprocal transformation, the bi-Hamiltonian representation of the super DP equation is constructed from that of the super KK hierarchy. We also calculate a positive flow of the super DP hierarchy and explain its relations with the super KK equation. Infinitely many conservation laws are derived for the super DP equation, as well as its positive flow.

Rooftop as a reciprocal transformation per diem

This article focuses on rooftop architecture as an interface and confrontation between the inhabitants and the contemporary city of Ä°stanbul. The utilitised rooftop is suggested as an alternative habitable space in high-density urban environments and wherever there is a shortage of housing. The visibility on the rooftop displays signs of the effects of the limit to growth, such as economic factors, and is affected by the environment, and the utilisation of space depends on the needs of the inhabitants. In today's conditions, living in rooftop goes beyond the necessity actions such as dominating the landscape, looking, seeing and being seen, and bringing concepts such as social justice and chaos in the city.

ResearchingWITH: Narratives and Crafts in Research in Psychology

In this paper, we share research narratives based on our practice as researchers. We understand that narrating, researching, and weaving are intertwined processes that lead us into peculiar and unpredictable actions in the research field. Therefore, researching is a risky practice. It entails unforeseen transformations and is both a craft and an ontological policy: If there is no given reality, what realities are performed along with our research practices? For what and to whom do we produce knowledge? We aim to discuss research policies that are in tune with local, contextualized, and embodied knowledge, and ways of doing research that consider the other—or the “object”—not as a passive target from whom you get information, but as an expert. Consequently, researching is understood as sharing expertise and as a reciprocal transformation device that activates all of those involved. We intend to share what has been produced by our research groups in Brazil. Our studies are intertwined as a network of connections and affectations and are guided by ResearchWith, which is a way of undertaking research that weaves WITH others and not ABOUT them. We emphasize this experience as a way of doing science in the feminine and we understand this as a craft.

Are Reaction Time Transformations Really Beneficial?

We investigate whether or not the common practice of transforming response times prior to conventional analyses of central tendency yields any notable benefits. We generate data from a realistic single-bound drift diffusion model with parameters informed by several different typical experiments in cognition. We then examine the effects of log and reciprocal transformation on expected effect size, statistical power, and Type I error rates for conventional two-sample t-tests. One of the key elements of our setup is that RTs have a lower bound, called the shift, which is well above 0. We closely examine the effect that different shifts have for the analyses. We conclude that logarithm and reciprocal transformation offer no gain in power or Type I error control. In some typical cases, reciprocal transformations are detrimental as they lead to a lowering of power.

Text reinterpretation and the motif of transformation in a short form of Internet poetry

In this article, I analyse the vehicles of humour in two short forms of Internet poetry that developed in the 2000s: the pirozhok (literary, a ‘stuffed bun’) and the poroshok (‘powder’). Poems of these genres are quatrains written in iambic tetrameter. Pirozhoks have no rhyme scheme, whereas, in poroshoks, the fourth line truncated to two syllables rhymes with the second line. The poroshok as a genre is a descendant of the pirozhok. Just as in jokes and several other genres, a punchline plays an important role in pirozhoks and poroshoks. In Russian, the punchline is termed puant, which is a borrowing from French (la pointe). The truncation of the final line in a poroshok puts it in a special position. The truncated line, independently or together with the third line, comprises the punchline of a poroshok. The punchline is practically mandatory and may be presented in greater detail inasmuch as it does not simply violate the reader’s expectations but enters into conflict with the beginning of the verse and forces the reader to reinterpret it. Reinterpretation manes that readers change their perception of the situation or carry out a ‘transformation’, that is, substitute the character or the entire situation. I identify common transformations, namely: thing → person, person → thing, person → animal, etc. Most frequent is the reciprocal transformation of men and cats. The transformation motif binds objects in the manner of a metaphor.

Generalized cascade orthogonal filters based on symmetric bilinear transformation with application to modeling of dynamic systems

This paper presents generalized orthogonal cascade filters based on bilinear transformation for mapping poles to zeroes and zeroes to poles in transfer functions. The filters are orthogonal with respect to a new generalized inner product. Actually, they represent a generalization of several classes of existing traditional filters: the ones obtained by using linear transformation of poles to zeroes, and the ones obtained by reciprocal transformation of poles to zeroes. Generalized filters provide obtaining more precise models of dynamic systems. This is verified by comparison between models based on new filters and models based on classical filters. Practical realization of these filters with adjusting parameters of bilinear transformation and transfer function is performed. An application in modeling continuous-time systems as a complex industrial process is given, and it is shown that in that way we obtain more quality models than by using the classical filters.