Duals of variable exponent Hörmander spaces (0<p−≤p+≤10< p^- \le p^+ \le 1) and some applications

In this paper we characterize the dual \bigl(\B^c_{p(\cdot)} (\Omega) \bigr)' of the variable exponent H\"or\-man\-der space \B^c_{p(\cdot)} (\Omega) when the exponent $p(\cdot)$ satisfies the conditions $0 < p^- \le p^+ \le 1$, the Hardy-Littlewood maximal operator $M$ is bounded on $L_{p(\cdot)/p_0}$ for some $0 < p_0 < p^-$ and $\Omega$ is an open set in $\R^n$. It is shown that the dual \bigl(\B^c_{p(\cdot)} (\Omega) \bigr)' is isomorphic to the H\"ormander space \B^{\mathrm{loc}}_\infty (\Omega) (this is the $p^+ \le 1$ counterpart of the isomorphism \bigl(\B^c_{p(\cdot)} (\Omega) \bigr)' \simeq \B^{\mathrm{loc}}_{\widetilde{p'(\cdot)}} (\Omega), $1 < p^- \le p^+ < \infty$, recently proved by the authors) and hence the representation theorem \bigl( \B^c_{p(\cdot)} (\Omega) \bigr)' \simeq l^{\N}_\infty is obtained. Our proof relies heavily on the properties of the Banach envelopes of the steps of \B^c_{p(\cdot)} (\Omega) and on the extrapolation theorems in the variable Lebesgue spaces of entire analytic functions obtained in a precedent paper. Other results for $p(\cdot) \equiv p$, $0 < p < 1$, are also given (e.g. \B^c_p (\Omega) does not contain any infinite-dimensional $q$-Banach subspace with $p < q \le 1$ or the quasi-Banach space \B_p \cap \E'(Q) contains a copy of $l_p$ when $Q$ is a cube in $\R^n$). Finally, a question on complex interpolation (in the sense of Kalton) of variable exponent H\"ormander spaces is proposed.J. Motos is partially supported by grant MTM2011-23164 from the Spanish Ministry of Science and Innovation. The authors wish to thank the referees for the careful reading of the manuscript and for many helpful suggestions and remarks that improved the exposition. In particular, the remark immediately following Theorem 2.1 and the Question 2 were motivated by the comments of one of them.Motos Izquierdo, J.; Planells Gilabert, MJ.; Talavera Usano, CF. (2015). Duals of variable exponent Hörmander spaces ($0< p^- \le p^+ \le 1$) and some applications. Revista- Real Academia de Ciencias Exactas Fisicas Y Naturales Serie a Matematicas. 109(2):657-668. https://doi.org/10.1007/s13398-014-0209-zS6576681092Aboulaich, R., Meskine, D., Souissi, A.: New diffussion models in image processing. Comput. Math. Appl. 56(4), 874–882 (2008)Acerbi, E., Mingione, G.: Regularity results for stationary electro-rheological fluids. Arch. Ration. Mech. Anal. 164(3), 213–259 (2002)Bastero, J.: $$l^q$$ l q -subspaces of stable $$p$$ p -Banach spaces, $$0 < p \le 1$$ 0 < p ≤ 1 . Arch. Math. (Basel) 40, 538–544 (1983)Boas, R.P.: Entire functions. Academic Press, London (1954)Boza, S.: Espacios de Hardy discretos y acotación de operadores. Dissertation, Universitat de Barcelona (1998)Cruz-Uribe, D., Fiorenza, A.: Variable Lebesgue spaces, foundations and harmonic analysis. Birkhäuser, Basel (2013)Cruz-Uribe, D.: SFO, A. Fiorenza, J. M. Martell, C. Pérez: The boundedness of classical operators on variable $$L^p$$ L p spaces. Ann. Acad. Sci. Fenn. Math. 31, 239–264 (2006)Diening, L., Harjulehto, P., Hästö, P., Růžička, M.: Lebesgue and sobolev spaces with variable exponents. lecture notes in mathematics, vol. 2007. Springer, Berlin, Heidelberg (2011)Hörmander, L.: The analysis of linear partial operators II, Grundlehren 257. Springer, Berlin, Heidelberg (1983)Hörmander, L.: The analysis of linear partial operators I, Grundlehren 256. Springer, Berlin, Heidelberg (1983)Kalton, N.J., Peck, N.T., Roberts, J.W.: An $$F$$ F -space sampler, London Mathematical Society Lecture Notes, vol. 89. Cambridge University Press, Cambridge (1985)Kalton, N.J.: Banach envelopes of non-locally convex spaces. Canad. J. Math. 38(1), 65–86 (1986)Kalton, N.J., Mitrea, M.: Stability results on interpolation scales of quasi-Banach spaces and applications. Trans. Am. Math. Soc. 350(10), 3903–3922 (1998)Kalton, N.J.: Quasi-Banach spaces, Handbook of the Geometry of Banach Spaces, vol. 2. In: Johnson, W.B., Lindenstrauss, J. (eds.), pp. 1099–1130. Elsevier, Amsterdam (2003)Köthe, G.: Topological vector spaces I. Springer, Berlin, Heidelberg (1969)Motos, J., Planells, M.J., Talavera, C.F.: On variable exponent Lebesgue spaces of entire analytic functions. J. Math. Anal. Appl. 388, 775–787 (2012)Motos, J., Planells, M.J., Talavera, C.F.: A note on variable exponent Hörmander spaces. Mediterr. J. Math. 10, 1419–1434 (2013)Stiles, W.J.: Some properties of $$l_p$$ l p , $$0 < p < 1$$ 0 < p < 1 . Studia Math. 42, 109–119 (1972)Triebel, H.: Theory of function spaces. Birkhäuser, Basel (1983)Vogt, D.: Sequence space representations of spaces of test functions and distributions. In: Zapata, G.I. (ed.) Functional analysis, holomorphy and approximation theory, Lecture Notes in Pure and Applied Mathematics, vol. 83, pp. 405–443 (1983

Droplet activation behaviour of atmospheric black carbon particles in fog as a function of their size and mixing state

Among the variety of particle types present in the atmosphere, black carbon (BC), emitted by combustion processes, is uniquely associated with harmful effects to the human body and substantial radiative forcing of the Earth. Pure BC is known to be non-hygroscopic, but its ability to acquire a coating of hygroscopic organic and inorganic material leads to increased diameter and hygroscopicity, facilitating droplet activation. This affects BC radiative forcing through aerosol–cloud interactions (ACIs) and BC life cycle. To gain insights into these processes, we performed a field campaign in winter 2015–2016 in a residential area of Zurich which aimed at establishing relations between the size and mixing state of BC particles and their activation to form droplets in fog. This was achieved by operating a CCN counter (CCNC), a scanning mobility particle sizer (SMPS), a single-particle soot photometer (SP2) and an aerosol chemical speciation monitor (ACSM) behind a combination of a total- and an interstitial-aerosol inlet. Our results indicate that in the morning hours of weekdays, the enhanced traffic emissions caused peaks in the number fraction of externally mixed BC particles, which do not act as CCN within the CCNC. The very low effective peak supersaturations (SSpeak) occurring in fog (between approximately 0.03&thinsp;% and 0.06&thinsp;% during this campaign) restrict droplet activation to a minor fraction of the aerosol burden (around 0.5&thinsp;% to 1&thinsp;% of total particle number concentration between 20 and 593&thinsp;nm) leading to very selective criteria on diameter and chemical composition. We show that bare BC cores are unable to activate to fog droplets at such low SSpeak, while BC particles surrounded by thick coating have very similar activation behaviour to BC-free particles. Using simplified κ-Köhler theory combined with the ZSR mixing rule assuming spherical core–shell particle geometry constrained with single-particle measurements of respective volumes, we found good agreement between the predicted and the directly observed size- and mixing-state-resolved droplet activation behaviour of BC-containing particles in fog. This successful closure demonstrates the predictability of their droplet activation in fog with a simplified theoretical model only requiring size and mixing state information, which can also be applied in a consistent manner in model simulations.</p

The Ny-Ålesund Aerosol Cloud Experiment (NASCENT): Overview and First Results

The Arctic is warming at more than twice the rate of the global average. This warming is influenced by clouds, which modulate the solar and terrestrial radiative fluxes and, thus, determine the surface energy budget. However, the interactions among clouds, aerosols, and radiative fluxes in the Arctic are still poorly understood. To address these uncertainties, the Ny-Ålesund Aerosol Cloud Experiment (NASCENT) study was conducted from September 2019 to August 2020 in Ny-Ålesund, Svalbard. The campaign’s primary goal was to elucidate the life cycle of aerosols in the Arctic and to determine how they modulate cloud properties throughout the year. In situ and remote sensing observations were taken on the ground at sea level, at a mountaintop station, and with a tethered balloon system. An overview of the meteorological and the main aerosol seasonality encountered during the NASCENT year is introduced, followed by a presentation of first scientific highlights. In particular, we present new findings on aerosol physicochemical and molecular properties. Further, the role of cloud droplet activation and ice crystal nucleation in the formation and persistence of mixed-phase clouds, and the occurrence of secondary ice processes, are discussed and compared to the representation of cloud processes within the regional Weather Research and Forecasting Model. The paper concludes with research questions that are to be addressed in upcoming NASCENT publications

Physicochemical characterization and source apportionment of Arctic ice-nucleating particles observed in Ny-Ålesund in autumn 2019

Ice-nucleating particles (INPs) initiate primary ice formation in Arctic mixed-phase clouds (MPCs), altering cloud radiative properties and modulating precipitation. For atmospheric INPs, the complexity of their spatiotemporal variations, heterogeneous sources, and evolution via intricate atmospheric interactions challenge the understanding of their impact on microphysical processes in Arctic MPCs and induce an uncertain representation in climate models. In this work, we performed a comprehensive analysis of atmospheric aerosols at the Arctic coastal site in Ny-Ålesund (Svalbard, Norway) from October to November 2019, including their ice nucleation ability, physicochemical properties, and potential sources. Overall, INP concentrations (NINP) during the observation season were approximately up to 3 orders of magnitude lower compared to the global average, with several samples showing degradation of NINP after heat treatment, implying the presence of proteinaceous INPs. Particle fluorescence was substantially associated with INP concentrations at warmer ice nucleation temperatures, indicating that in the far-reaching Arctic, aerosols of biogenic origin throughout the snow- and ice-free season may serve as important INP sources. In addition, case studies revealed the links between elevated NINP and heat lability, fluorescence, high wind speeds originating from the ocean, augmented concentration of coarse-mode particles, and abundant organics. Backward trajectory analysis demonstrated a potential connection between high-latitude dust sources and high INP concentrations, while prolonged air mass history over the ice pack was identified for most scant INP cases. The combination of the above analyses demonstrates that the abundance, physicochemical properties, and potential sources of INPs in the Arctic are highly variable despite its remote location.</p

Varicella zoster virus glycoprotein C increases chemokine-mediated leukocyte migration.

Varicella zoster virus (VZV) is a highly prevalent human pathogen that establishes latency in neurons of the peripheral nervous system. Primary infection causes varicella whereas reactivation results in zoster, which is often followed by chronic pain in adults. Following infection of epithelial cells in the respiratory tract, VZV spreads within the host by hijacking leukocytes, including T cells, in the tonsils and other regional lymph nodes, and modifying their activity. In spite of its importance in pathogenesis, the mechanism of dissemination remains poorly understood. Here we addressed the influence of VZV on leukocyte migration and found that the purified recombinant soluble ectodomain of VZV glycoprotein C (rSgC) binds chemokines with high affinity. Functional experiments show that VZV rSgC potentiates chemokine activity, enhancing the migration of monocyte and T cell lines and, most importantly, human tonsillar leukocytes at low chemokine concentrations. Binding and potentiation of chemokine activity occurs through the C-terminal part of gC ectodomain, containing predicted immunoglobulin-like domains. The mechanism of action of VZV rSgC requires interaction with the chemokine and signalling through the chemokine receptor. Finally, we show that VZV viral particles enhance chemokine-dependent T cell migration and that gC is partially required for this activity. We propose that VZV gC activity facilitates the recruitment and subsequent infection of leukocytes and thereby enhances VZV systemic dissemination in humans

Measurement of Upper Limb Range of Motion Using Wearable Sensors: A Systematic Review.

Background: Wearable sensors are portable measurement tools that are becoming increasingly popular for the measurement of joint angle in the upper limb. With many brands emerging on the market, each with variations in hardware and protocols, evidence to inform selection and application is needed. Therefore, the objectives of this review were related to the use of wearable sensors to calculate upper limb joint angle. We aimed to describe (i) the characteristics of commercial and custom wearable sensors, (ii) the populations for whom researchers have adopted wearable sensors, and (iii) their established psychometric properties. Methods: A systematic review of literature was undertaken using the following data bases: MEDLINE, EMBASE, CINAHL, Web of Science, SPORTDiscus, IEEE, and Scopus. Studies were eligible if they met the following criteria: (i) involved humans and/or robotic devices, (ii) involved the application or simulation of wearable sensors on the upper limb, and (iii) calculated a joint angle. Results: Of 2191 records identified, 66 met the inclusion criteria. Eight studies compared wearable sensors to a robotic device and 22 studies compared to a motion analysis system. Commercial (n = 13) and custom (n = 7) wearable sensors were identified, each with variations in placement, calibration methods, and fusion algorithms, which were demonstrated to influence accuracy. Conclusion: Wearable sensors have potential as viable instruments for measurement of joint angle in the upper limb during active movement. Currently, customised application (i.e. calibration and angle calculation methods) is required to achieve sufficient accuracy (error < 5°). Additional research and standardisation is required to guide clinical application

Varicella zoster virus glycoprotein C increases chemokine-mediated leukocyte migration

Varicella zoster virus (VZV) is a highly prevalent human pathogen that establishes latency in neurons of the peripheral nervous system. Primary infection causes varicella whereas reactivation results in zoster, which is often followed by chronic pain in adults. Following infection of epithelial cells in the respiratory tract, VZV spreads within the host by hijacking leukocytes, including T cells, in the tonsils and other regional lymph nodes, and modifying their activity. In spite of its importance in pathogenesis, the mechanism of dissemination remains poorly understood. Here we addressed the influence of VZV on leukocyte migration and found that the purified recombinant soluble ectodomain of VZV glycoprotein C (rSgC) binds chemokines with high affinity. Functional experiments show that VZV rSgC potentiates chemokine activity, enhancing the migration of monocyte and T cell lines and, most importantly, human tonsillar leukocytes at low chemokine concentrations. Binding and potentiation of chemokine activity occurs through the C-terminal part of gC ectodomain, containing predicted immunoglobulin-like domains. The mechanism of action of VZV rSgC requires interaction with the chemokine and signalling through the chemokine receptor. Finally, we show that VZV viral particles enhance chemokine-dependent T cell migration and that gC is partially required for this activity. We propose that VZV gC activity facilitates the recruitment and subsequent infection of leukocytes and thereby enhances VZV systemic dissemination in humans

Anti-tumour necrosis factor discontinuation in inflammatory bowel disease patients in remission: study protocol of a prospective, multicentre, randomized clinical trial

Background: Patients with inflammatory bowel disease who achieve remission with anti-tumour necrosis factor (anti-TNF) drugs may have treatment withdrawn due to safety concerns and cost considerations, but there is a lack of prospective, controlled data investigating this strategy. The primary study aim is to compare the rates of clinical remission at 1?year in patients who discontinue anti-TNF treatment versus those who continue treatment. Methods: This is an ongoing, prospective, double-blind, multicentre, randomized, placebo-controlled study in patients with Crohn?s disease or ulcerative colitis who have achieved clinical remission for ?6?months with an anti-TNF treatment and an immunosuppressant. Patients are being randomized 1:1 to discontinue anti-TNF therapy or continue therapy. Randomization stratifies patients by the type of inflammatory bowel disease and drug (infliximab versus adalimumab) at study inclusion. The primary endpoint of the study is sustained clinical remission at 1?year. Other endpoints include endoscopic and radiological activity, patient-reported outcomes (quality of life, work productivity), safety and predictive factors for relapse. The required sample size is 194 patients. In addition to the main analysis (discontinuation versus continuation), subanalyses will include stratification by type of inflammatory bowel disease, phenotype and previous treatment. Biological samples will be obtained to identify factors predictive of relapse after treatment withdrawal. Results: Enrolment began in 2016, and the study is expected to end in 2020. Conclusions: This study will contribute prospective, controlled data on outcomes and predictors of relapse in patients with inflammatory bowel disease after withdrawal of anti-TNF agents following achievement of clinical remission. Clinical trial reference number: EudraCT 2015-001410-1

Erratum to: 36th International Symposium on Intensive Care and Emergency Medicine

[This corrects the article DOI: 10.1186/s13054-016-1208-6.]