A new structure of an integral operator associated with trigonometric Dunkl settings

In this paper, we discuss a generalization to the Cherednik–Opdam integral operator to an abstract space of Boehmians. We introduce sets of Boehmians and establish delta sequences and certain class of convolution products. Then we prove that the extended Cherednik–Opdam integral operator is linear, bijective and continuous with respect to the convergence of the generalized spaces of Boehmians. Moreover, we derive embeddings and discuss properties of the generalized theory. Moreover, we obtain an inversion formula and provide several results.

Mapping conversations about land use: How modern farmers practice individuality

In this article, drawing on the discursive psychology of Rom Harré, we show how mapping the exchange of words among people might disclose a complex reality; not merely that which farmers explicitly talk ‘about’ but the reality implicitly at stake within the communication. More specifically, we show how discourses involving modern farmers reveal an underlying placing in an abstract space, having sub-spaces defined by the life-orientation, sense of self and according self-positioning of modern people. In this way, we construct a road map of a set of ‘individualities’ characterizing the life of modern farmers: an individuality of citizenship, an individuality of geographies and an individuality of experience. Consequently, farmers face the problem that this multiplicity of individuality prevents them from communicating, as we will call it, univocally in the public by contrast to the univocal voices of other established social groups. We will analyse the structure of that problem by viewing diverse relations between the authority and the authenticity of different partners in the conversation on land use.

An immersive first-person navigation task for abstract knowledge acquisition

Advances in virtual reality (VR) technology have greatly benefited spatial navigation research. By presenting space in a controlled manner, changing aspects of the environment one at a time or manipulating the gain from different sensory inputs, the mechanisms underlying spatial behaviour can be investigated. In parallel, a growing body of evidence suggests that the processes involved in spatial navigation extend to non-spatial domains. Here, we leverage VR technology advances to test whether participants can navigate abstract knowledge. We designed a two-dimensional quantity space—presented using a head-mounted display—to test if participants can navigate abstract knowledge using a first-person perspective navigation paradigm. To investigate the effect of physical movement, we divided participants into two groups: one walking and rotating on a motion platform, the other group using a gamepad to move through the abstract space. We found that both groups learned to navigate using a first-person perspective and formed accurate representations of the abstract space. Interestingly, navigation in the quantity space resembled behavioural patterns observed in navigation studies using environments with natural visuospatial cues. Notably, both groups demonstrated similar patterns of learning. Taken together, these results imply that both self-movement and remote exploration can be used to learn the relational mapping between abstract stimuli.

The Hilbert Space of Double Fourier Coefficients for an Abstract Wiener Space

Fourier series is a well-established subject and widely applied in various fields. However, there is much less work on double Fourier coefficients in relation to spaces of general double sequences. We understand the space of double Fourier coefficients as an abstract space of sequences and examine relationships to spaces of general double sequences: p-power summable sequences for p = 1, 2, and the Hilbert space of double sequences. Using uniform convergence in the sense of a Cesàro mean, we verify the inclusion relationships between the four spaces of double sequences; they are nested as proper subsets. The completions of two spaces of them are found to be identical and equal to the largest one. We prove that the two-parameter Wiener space is isomorphic to the space of Cesàro means associated with double Fourier coefficients. Furthermore, we establish that the Hilbert space of double sequence is an abstract Wiener space. We think that the relationships of sequence spaces verified at an intermediate stage in this paper will provide a basis for the structures of those spaces and expect to be developed further as in the spaces of single-indexed sequences.

Embedding cosmology and gravity

I start with a scenario where the universe is an abstract space $${\mathcal {M}}$$ M having d dimensions. There is a two dimensional surface embedded in it. Embedding is a map from the embedded surface to $${\mathcal {M}}$$ M that has a field theory described by Sigma model. I take d directions of $${\mathcal {M}}$$ M to be the generators of a symmetry group SU(n) of the Lagrangian of the embedding. This means embedding has n flavors. Then I introduce spontaneous symmetry breaking in the theory and define the direction along which the symmetry breaking occurs as time. Next I write down the modified Einstein’s equation including the embedding. Then I discuss embedding’s relation to the expansion of the universe. After that I construct an inflationary scenario with embedding as inflaton and discuss its connection to Starobinsky $$R^{2}$$ R 2 model. Finally, I discuss the effect of inflation on the non-commutativity of the spacetime.

Collective Imagining: The Early Genesis and Development of a sense of Collectiveness during Infancy

On entering formal education, infants face the demand of participating in collective educational rou¬tines and learning experiences. However, in this age period, the sense of collectiveness is still in an embry¬onic form. This study explored how infants enter into and experience the need for collectiveness and how teachers create the conditions for the development of a sense of collectiveness during infancy. Our educa¬tional experiment drew on a Conceptual PlayWorld, as a collective model of practice for the development of play and imagination. Thirteen infants (0,5—2 years old) participated in the study. Visual methods were used for digital data collection and analysis. It was found that, being in the imaginary situation as play part¬ners, teachers introduced to the infants’ environment the demand to align with the collective, consistently facilitated and sustained infants’ motive orientation to the collective. The use of props, the embodiment of the experience and the shift from physical objects and concrete spaces to a shared intellectual and abstract space appeared to be critical. The findings inform everyday practice and policy opening up a new area of understanding about the concept of collective imagining, as an important concept for the development of a collective orientation for infants.

Espaço abstrato e espaço diferencial: a compreensão do direito à cidade em Henri Lefebvre / Abstract and differential spaces: keys to understanding the right to the city in Henti Lefebvre

ResumoO presente trabalho possui o objetivo de fornecer uma visão panorâmica acerca das ancoragens teóricas da noção de direito à cidade, enquanto projeto orientador de uma hipótese virtual e possível, definida como sociedade urbana. Para tanto, através da revisão bibliográfica, recorre-se à reflexão acerca de alguns elementos, cuja análise se mostra fundamental para a delimitação do campo teórico em que o pensamento se constrói, na obra de Henri Lefebvre, especialmente no que concerne às categorias espaço abstrato e espaço diferencial. Conclui-se que a partir do estudo da obra de Lefebvre que o direito a cidade se constitui em um espaço de investigação onde é possível pensar os processos históricos assumidos em diferentes escalas até chegar a atualidade. Deste modo, o direito à cidade é adequado e objetiva fundir os conflitos e os processos urbanos com a produção do conhecimento socioespacial, permitindo a transformação do saber e da realidade da urbe.Palavras-chave: Henri Lefebvre; direito à cidade; sociedade urbana; espaço abstrato; espaço diferencial. AbstractThis article aims to provide a different angle of view about the theoretical anchors of the original notion of the right to the city, in Henri Lefebvre. Therefore, through literature review, of a qualitative-exploratory character, a dialectical reflection about the characteristics of the right to the city project is used, from the perspective of the spatial theory developed by the author at a later point in his work. Within this scope, and for the purposes of this study, the notions of “abstract space” and “differential space” were especially taken as analytical categories. In constant mobilization, these phenomena interact dialectically, and constitute the fundamental antithesis between domination and appropriation of the city, whose scan is promising for a particular understanding of the theoretical field in which the project of the right to the city is built on the work of Lefebvre. This analysis results in the understanding of the right to the city as a claim, which is established in the conflictive dialectic between two socio-spatial segments, present since the modern city: the abstract space, where the reason of State, the law and the capitalist ideology are allied in the project of homogenization of the society, and the differential space, founded on social relations rooted in the forms of using spaces that express ways of life that are resistant to the logic of capital.Keywords: Henri Lefebvre; right to the city; urban society; abstract space; differential space.

Urbanization as taxidermy: “Man”hattanization of Mannahatta

PurposeThis article unveils the similarities of today's space production systems with taxidermy. Giving examples from the transformation of natural environment during the history of Mannahatta (Manhattan), the article discusses the process of metamorphosis of habitats and ecosystems to anthropocentric artificial objects.Design/methodology/approachReferencing Lefebvre, urbanization is conceptualized as the production of abstract space that ultimately stifles life; by analogy, space taxidermy.FindingsUsing the analogy of taxidermy and abstract space production processes, the article introduces the necessity and the principles of restoring natural habitats.Originality/valueRe-writing the urban and architectural history of Manhattan by focusing on four different scenes from its life-span, the article introduces a novel; a new narrative of the history of the city from the perspective of human-nature relations and the various ways habitats were shaped on this island during history.

Sulla centralità di spazio e territorio nel progetto di rigenerazione delle montagne e delle aree interne

The crisis brought on by Covid-19 has dramatically highlighted how the territorial dimension has long been excluded from national policies to be reduced to a mere diagrammatic and abstract space to be reduced in a mere diagrammatic and abstract space. An unphysicality of things that also goes through philosophies of smart or replicable best practices, in the idea that it is enough to follow a procedure to solve the complexities of contemporary life. The crisis has also brought to light the theme of internal, mountain and marginal areas, which have already received strong and growing attention in recent years. All the researches of the last few years demonstrate how the frontier of innovation is placed along the margin lines, in territories such as the Alpine and Apennine ones: regeneration projects based on culture, community cooperatives, resettlement that arises on the recovery of legacy and on the new technologies. These are experiments as fragile as the places they insist on, but where the territorial and spatial dimension plays an active and new role, which should be carefully observed thanks to the new openings it can offer. The essay identifies some nodes that arise from a long process of analysis and field experiences, and which intertwine two strategic issues: on the one hand, the need for policies capable of actively addressing the issue of territories – overcoming the contrast between socio-economic and spatial disciplines –, and on the other hand the project of reactivation and regeneration of mountain and marginal spaces.