A note on boundedness of operators in Grand Grand Morrey spaces

In this note we introduce grand grand Morrey spaces, in the spirit of the grand Lebesgue spaces. We prove a kind of \textit{reduction lemma} which is applicable to a variety of operators to reduce their boundedness in grand grand Morrey spaces to the corresponding boundedness in Morrey spaces. As a result of this application, we obtain the boundedness of the Hardy-Littlewood maximal operator and Calder\'on-Zygmund operators in the framework of grand grand Morrey spaces.Comment: 8 page

Quantum Degenerate Systems

Degenerate dynamical systems are characterized by symplectic structures whose rank is not constant throughout phase space. Their phase spaces are divided into causally disconnected, nonoverlapping regions such that there are no classical orbits connecting two different regions. Here the question of whether this classical disconnectedness survives quantization is addressed. Our conclusion is that in irreducible degenerate systems --in which the degeneracy cannot be eliminated by redefining variables in the action--, the disconnectedness is maintained in the quantum theory: there is no quantum tunnelling across degeneracy surfaces. This shows that the degeneracy surfaces are boundaries separating distinct physical systems, not only classically, but in the quantum realm as well. The relevance of this feature for gravitation and Chern-Simons theories in higher dimensions cannot be overstated.Comment: 18 pages, no figure

What went wrong? Predictors of contact tracing adoption in Italy during COVID-19 pandemic

Together with vaccines, contact tracing systems (CTS) have proved to be one of the best strategies to deal with the current COVID-19 pandemic. However, the adoption of such systems has been quite limited in EU countries, and Italy was no exception. The present research aimed to investigate the factors drawn from the most relevant psychological models in the literature, most associated with the adoption of CTS. The data analysis of the 501 surveyed answers (329 from CTS adopters) showed that knowing important others who have downloaded the CTS, CTS attitudes, CTS perceived efficacy, COVID-19 risk perception, and trust in the government and its actions influenced the adoption of the Italian CTS (52% of explained variance). These factors defined a new specific model that can be used to more effectively promote CTS adoption and thus increase the protective potential of these technologies, whose effectiveness is inevitably linked to adoption

T Cell Leukemia/Lymphoma 1A is essential for mouse epidermal keratinocytes proliferation promoted by insulin-like growth factor 1

T Cell Leukemia/Lymphoma 1A is expressed during B-cell differentiation and, when overexpressed, acts as an oncogene in mouse (Tcl1a) and human (TCL1A) B-cell chronic lymphocytic leukemia (B-CLL) and T-cell prolymphocytic leukemia (T-PLL). Furthermore, in the murine system Tcl1a is expressed in the ovary, testis and in pre-implantation embryos, where it plays an important role in blastomere proliferation and in embryonic stem cell (ESC) proliferation and self-renewal. We have also observed that Tcl1-/-adult mice exhibit alopecia and deep ulcerations. This finding has led us to investigate the role of TCL1 in mouse skin and hair follicles. We have found that TCL1 is expressed in the proliferative structure (i.e.The secondary hair germ) and in the stem cell niche (i.e.The bulge) of the hair follicle during regeneration phase and it is constitutively expressed in the basal layer of epidermis where it is required for the correct proliferative-differentiation program of the keratinocytes (KCs). Taking advantage of the murine models we have generated, including the Tcl1-/-and the K14-TCL1 transgenic mouse, we have analysed the function of TCL1 in mouse KCs and the molecular pathways involved. We provide evidence that in the epidermal compartment TCL1 has a role in the regulation of KC proliferation, differentiation, and apoptosis. In particular, the colony-forming efficiency (CFE) and the insulin-like growth factor 1 (IGF1)-induced proliferation are dramatically impaired, while apoptosis is increased, in KCs from Tcl1-/-mice when compared to WT. Moreover, the expression of differentiation markers such as cytokeratin 6 (KRT6), filaggrin (FLG) and involucrin (IVL) are profoundly altered in mutant mice (Tcl1-/-). Importantly, by over-expressing TCL1A in basal KCs of the K14-TCL1 transgenic mouse model, we observed a significant rescue of cell proliferation, differentiation and apoptosis of the mutant phenotype. Finally, we found TCL1 to act, at least in part, via increasing phospho-ERK1/2 and decreasing phospho-P38 MAPK. Hence, our data demonstrate that regulated levels of Tcl1a are necessary for the correct proliferation and differentiation of the interfollicular KC

Sums over Graphs and Integration over Discrete Groupoids

We show that sums over graphs such as appear in the theory of Feynman diagrams can be seen as integrals over discrete groupoids. From this point of view, basic combinatorial formulas of the theory of Feynman diagrams can be interpreted as pull-back or push-forward formulas for integrals over suitable groupoids.Comment: 27 pages, 4 eps figures; LaTeX2e; uses Xy-Pic. Some ambiguities fixed, and several proofs simplifie

Graph complexes in deformation quantization

Kontsevich's formality theorem and the consequent star-product formula rely on the construction of an $L_\infty$-morphism between the DGLA of polyvector fields and the DGLA of polydifferential operators. This construction uses a version of graphical calculus. In this article we present the details of this graphical calculus with emphasis on its algebraic features. It is a morphism of differential graded Lie algebras between the Kontsevich DGLA of admissible graphs and the Chevalley-Eilenberg DGLA of linear homomorphisms between polyvector fields and polydifferential operators. Kontsevich's proof of the formality morphism is reexamined in this light and an algebraic framework for discussing the tree-level reduction of Kontsevich's star-product is described.Comment: 39 pages; 3 eps figures; uses Xy-pic. Final version. Details added, mainly concerning the tree-level approximation. Typos corrected. An abridged version will appear in Lett. Math. Phy

A solar photothermocatalytic approach for the CO2 conversion: Investigation of different synergisms on CoO-CuO/brookite TiO2-CeO2 catalysts

The photoactive features of the least common polymorph of TiO2, i.e. brookite, were combined with the thermocatalytic redox ones of cerium oxide, focusing on the effects of the addition of small amounts of Co-Cu oxides for the solar CO2 conversion. By considering the characterization data, a surface segregation of the hosted metal oxides on the TiO2-CeO2 composite was evidenced, and their presence increased the amount of oxygen vacancies and improved the charge carriers separation. The bimetallic oxides-based sample was the most performing one in the photocatalytic carbon dioxide reduction at room temperature. The formation of carbon monoxide and methane was 5 and 0.5 μmol g−1h−1, respectively, i.e. about 10 times higher than that found with bare brookite. A further enhancement was obtained with the same CoO-CuO/TiO2-CeO2 catalyst applying the photothermal approach. The CO2-TPD and the FTIR measurements highlighted the high interaction between CO2 and the surface sites

Exploring the photothermo-catalytic performance of brookite tio2-ceo2 composites

The thermocatalytic, photocatalytic and photothermo-catalytic oxidation of some volatile organic compounds (VOCs), 2-propanol, ethanol and toluene, was investigated over brookite TiO2-CeO2 composites. The multi-catalytic approach based on the synergistic effect between solar photocatalysis and thermocatalysis led to the considerable decrease in the conversion temperatures of the organic compounds. In particular, in the photothermo-catalytic runs, for the most active samples (TiO2-3 wt% CeO2 and TiO2-5 wt% CeO2). the temperature at which 90% of VOC conversion occurred was about 60◦ C, 40◦ C and 20◦ C lower than in the thermocatalytic tests for 2-propanol, ethanol and toluene, respectively. Furthermore. the addition of cerium oxide to brookite TiO2 favored the total oxidation to CO2 already in the photocatalytic tests at room temperature. The presence of small amounts of cerium oxide allowed to obtain efficient brookite-based composites facilitating the space charge separation and increasing the lifetime of the photogenerated holes and electrons as confirmed by the characterization measurements. The possibility to concurrently utilize the photocatalytic properties of brookite and the redox properties of CeO2, both activated in the photothermal tests, is an attractive approach easily applicable to purify air from VOCs

Nanoaperture fabrication via colloidal lithography for single molecule fluorescence analysis

In single molecule fluorescence studies, background emission from labeled substrates often restricts their concentrations to non-physiological nanomolar values. One approach to address this challenge is the use of zero-mode waveguides (ZMWs), nanoscale holes in a thin metal film that physically and optically confine the observation volume allowing much higher concentrations of fluorescent substrates. Standard fabrication of ZMWs utilizes slow and costly E-beam nano-lithography. Herein, ZMWs are made using a self-assembled mask of polystyrene microspheres, enabling fabrication of thousands of ZMWs in parallel without sophisticated equipment. Polystyrene 1 mu m dia. microbeads self-assemble on a glass slide into a hexagonal array, forming a mask for the deposition of metallic posts in the inter-bead interstices. The width of those interstices (and subsequent posts) is adjusted within 100-300 nm by partially fusing the beads at the polystyrene glass transition temperature. The beads are dissolved in toluene, aluminum or gold cladding is deposited around the posts, and those are dissolved, leaving behind an array ZMWs. Parameter optimization and the performance of the ZMWs are presented. By using colloidal self-assembly, typical laboratories can make use of sub-wavelength ZMW technology avoiding the availability and expense of sophisticated clean-room environments and equipment