On Besov spaces modelled on Zygmund spaces

Working on the d-torus, we show that Besov spaces Bps(Lp(logL)a) modelled on Zygmund spaces can be described in terms of classical Besov spaces. Several other properties of spaces Bps(Lp(logL)a) are also established. In particular, in the critical case s=d/p, we characterize the embedding of Bpd/p(Lp(logL)a) into the space of continuous functions.

Mackey topology on locally convex spaces and on locally quasi-convex groups. Similarities and historical remarks

A counterpart of the Mackey–Arens Theorem for the class of locally quasi-convex topological Abelian groups (LQC-groups) was initiated in Chasco et al. (Stud Math 132(3):257–284, 1999). Several authors have been interested in the problems posed there and have done clarifying contributions, although the main question of that source remains open. Some differences between the Mackey Theory for locally convex spaces and for locally quasi-convex groups, stem from the following fact: The supremum of all compatible locally quasi-convex topologies for a topological abelian group G may not coincide with the topology of uniform convergence on the weak quasi-convex compact subsets of the dual groupG∧. Thus, a substantial part of the classical Mackey–Arens Theorem cannot be generalized to LQC-groups. Furthermore, the mentioned fact gives rise to a grading in the property of “being a Mackey group”, as defined and thoroughly studied in Díaz Nieto and Martín-Peinador (Proceedings in Mathematics and Statistics 80:119–144, 2014). At present it is not known—and this is the main open question—if the supremum of all the compatible locally quasi-convex topologies on a topological group is in fact a compatible topology. In the present paper we do a sort of historical review on the Mackey Theory, and we compare it in the two settings of locally convex spaces and of locally quasi-convex groups. We point out some general questions which are still open, under the name of Problems.

Sharing through Collaborative Spaces: Enhancing Collaborative Networks Interoperability

Part 14: Interoperability and Integration

Truncated projective spaces, Brown–Gitler spectra and indecomposable A(1)-modules

MSC 19L41; 55S10.

Convolution of Orbital Measures on Symmetric Spaces of type Cp and Dp

International audience

Smallest disentangling state spaces for general entangled bipartite quantum states

Entangled quantum states can be given a separable decomposition if we relax the restriction that the local operators be quantum states. Motivated by the construction of classical simulations and local hidden variable models, we construct `smallest' local sets of operators that achieve this. In other words, given an arbitrary bipartite quantum state we construct convex sets of local operators that allow for a separable decomposition, but that cannot be made smaller while continuing to do so. We then consider two further variants of the problem where the local state spaces are required to contain the local quantum states, and obtain solutions for a variety of cases including a region of pure states around the maximally entangled state. The methods involve calculating certain forms of cross norm. Two of the variants of the problem have a strong relationship to theorems on ensemble decompositions of positive operators, and our results thereby give those theorems an added interpretation. The results generalise those obtained in our previous work on this topic [New J. Phys. 17, 093047 (2015)].

On Gruenhage spaces, separating σ-isolated families, and their relatives

We prove that, given a topological space X, the following conditions are equivalent. (α) X is a Gruenhage space. (β) X has a countable cover by sets of small local diameter (property SLD) by F∩G sets. (γ) X has a separating σ-isolated family M⊂F∩G. (δ) X has a one-to-one continuous map into a metric space which has a σ-isolated base of F∩G sets. Besides, we provide an example which shows Fragmentability ⇏ property SLD ⇏ the space to be Gruenhage.

WEAK ISOMETRIES OF HAMMING SPACES

In this thesis we study weak isometries of Hamming spaces. These are permutations of a Hamming space that preserve some but not necessarily all distances. We wish to find conditions under which a weak isometry is in fact an isometry. This type of problem was first posed by Beckman and Quarles for Rn. In chapter 2 we give definitions pertinent to our research. The 3rd chapter focuses on some known results in this area with special emphasis on papers by V. Krasin as well as S. De Winter and M. Korb who solved this problem for the Boolean cube, that is, the binary Hamming space. We attempted to generalize some of their methods to the non-boolean case. The 4th chapter has our new results and is split into two major contributions. Our first contribution shows if n=p or p < n2, then every weak isometry of Hnq that preserves distance p is an isometry. Our second contribution gives a possible method to check if a weak isometry is an isometry using linear algebra and graph theory.

Resistance performances: (Re)constructing spaces of resistance and contention in the 2010-2011 University of Puerto Rico student movement

On the night of April 20, 2010, a group of students from the University of Puerto Rico (UPR), Río Piedras campus, met to organize an indefinite strike that quickly broadened into a defense of accessible public higher education of excellence as a fundamental right and not a privilege. Although the history of student activism in the UPR can be traced back to the early 1900s, the 2010-2011 strike will be remembered for the student activists’ use of new media technologies as resources that rapidly prompted and aided the numerous protests. ^ This activist research entailed a critical ethnography and a critical discourse analysis (CDA) of traditional and alternative media coverage and treatment during the 2010 -2011 UPR student strike. I examined the use of the 2010-2011 UPR student activists’ resistance performances in constructing local, corporeal, and virtual spaces of resistance and contention during their movement. In particular, I analyzed the different tactics and strategies of resistance or repertoire of collective actions that student activists used (e.g. new media technologies) to frame their collective identities via alternative news media’s (re)presentation of the strike, while juxtaposing the university administration’s counter-resistance performances in counter-framing the student activists’ collective identity via traditional news media representations of the strike. I illustrated how both traditional and alternative media (re)presentations of student activism developed, maintained, and/or modified students activists’ collective identities. ^ As such, the UPR student activism’s success should not be measured by the sum of demands granted, but by the sense of community achieved and the establishment of networks that continue to create resistance and change. These networks add to the debate surrounding Internet activism and its impact on student activism. Ultimately, the results of this study highlight the important role student movements have had in challenging different types of government policies and raising awareness of the importance of an accessible public higher education of excellence.^

Rota's universal operators and invariant subspaces in Hilbert spaces

A Hilbert space operator is called universal (in the sense of Rota) if every operator on the Hilbert space is similar to a multiple of the restriction of the universal operator to one of its invariant subspaces. We exhibit an analytic Toeplitz operator whose adjoint is universal in the sense of Rota and commutes with a quasi-nilpotent injective compact operator with dense range. In particular, this new universal operator invites an approach to the Invariant Subspace Problem that uses properties of operators that commute with the universal operator.

Equivalent norms in polynomial spaces and applications.

In this paper, equivalence constants between various polynomial norms are calculated. As an application, we also obtain sharp values of the Hardy Littlewood constants for 2-homogeneous polynomials on l(p)(2) spaces, 2 < p <= infinity. We also provide lower estimates for the Hardy-Littlewood constants for polynomials of higher degrees.

Lighting ambiances and materialities of wood in architecture: a comparative evaluation of the quality of spaces in relation to interior finishes

Le bois est un matériau souvent utilisé par les architectes pour améliorer l’ambiance générale d’un espace, mais peu de recherches en présentent l’impact réel du matériau sur les impressions visuelles et les effets lumineux. Cette recherche étudie l’influence de la matérialité du bois par rapport à la création d’ambiances d’éclairage spécifiques dans l’architecture. Plus particulièrement, elle se concentre sur l’impact des panneaux décoratifs en bois à générer de la diversité lumineuse dans les espaces intérieurs et son potentiel à améliorer la satisfaction environnementale et l’efficacité énergétique. La recherche utilise des maquettes à l’échelle pour leur précision dans la représentation des ambiances lumineuses d’espaces éclairés naturellement ainsi que les technologies récentes d’imagerie digitale pour capturer et analyser les résultats. La méthodologie permet la comparaison entre les différents réglages des espaces intérieurs créés par une sélection des types de matérialités du bois: la réflectance (valeur), la couleur et la réflectivité. Les modalités spatiales sont comparées en présence d’ensoleillement direct et sous des conditions de ciel couvert puisque les modèles d’éclairage et les ambiances diffèrent considérablement. Les résultats permettent d’établir une discussion sur les ambiances en termes de brillance et de contraste, sur la couleur ainsi que la répartition des zones lumineuses dans l’espace. La recherche souligne le rôle des matérialités que peuvent prendre le bois pour optimiser la diversité lumineuse et la création d’ambiances visuellement confortables, ainsi que ses possibilités d’améliorer les ambiances architecturales par rapport à la lumière.

Influence of the natural environment on health: evaluation of different environmental contexts (urban, green spaces) and intervention proposals

Urbanization has grown during the last decades, with an increase in population concentrated in cities. Cities are usually relatively nature-poor, and the loss of green urban space likely leads to less contact with the natural world for urban dwellers. It is known that the natural environment could provide important advantages, and the loss of contact with this type of environment has potential negative impacts on the quality of life. The use of green urban space demonstrated stronger benefits for mental health and stress reduction. In general, exposure to green urban space is linked to a reduction in mortality rates, due to the promotion of a healthy lifestyle. Green urban space could be an optimal environment in which to perform physical activity. Undertaking regular physical activity is one of the major determinants of health. The benefits of exercise have been widely demonstrated through a wide range of studies. Benefits are linked to the treatment and prevention of most chronic and non-communicable diseases, that are not contagious, but they are usually long-lasting. Regular physical activity could reduce mental health problems, such as anxiety. The World Health Organization proposed to improve physical activity programs through the implementation of interventions in green urban spaces. Green urban space provides a safe, accessible, and attractive place to perform physical activity. All the interventions aimed to promote the practice of physical activity and to reduce sedentary behavior are important. It is well known that physical activity has several positive effects, a great amount of the population remains inactive. A good strategy could be to show people how integrated physical activity into their all-day life, for example through the use of green urban space or active commuting. The results in the present thesis showed the effectiveness of performing physical activity in a natural environment and of active commuting.

Coworking spaces: thriving and organizing in the new world of work

The present Ph.D. thesis proposes three studies on coworking spaces to understand how they foster thriving and organizing in the new world of work. The first study maps and analyzes the thematic structure and evolution of the academic debate that has emerged around coworking spaces in recent years. In doing so, it conducts a science mapping analysis of 351 publications on coworking spaces to detect and visualize key themes in the literature and their co-occurrence with subthemes. The second study proposes an interpretive review of 98 publications from multiple disciplines to shed light on how coworking spaces emerge as sites of organizing for professionals who are not formally connected to one another. It suggests five dimensions that articulate coworking spaces as sites of organizing – ‘materiality,’ ‘temporality,’ ‘affect,’ ‘identity,’ and ‘formalization.’ This study aims to go beyond the community-related understanding of coworking that has characterized most scholarly attention, instead focusing on coworking spaces’ organizational character. The third study investigates what drives thriving at work for remote workers in coworking spaces. In doing so, it acknowledges the potential complex set of interrelationships underpinning thriving at work and mobilizes complexity theory and qualitative comparative analysis to uncover six different, yet equifinal, configurations of antecedents driving remote workers’ thriving in coworking spaces.