A remark on totally smooth renormings

[EN] E. Oja, T. Viil, andD. Werner showed, in Totally smooth renormings, Archiv der Mathematik, 112, 3, (2019), 269-281, that a weakly compactly generated Banach space ( X, center dot) with the property that every linear functional on X has a unique Hahn-Banach extension to the bidual X ** (the so-called Phelps' property U in X **, also known as the Hahn-Banach smoothness property) can be renormed to have the stronger property that for every subspace Y of X, every linear functional on Y has a unique Hahn-Banach extension to X ** (the so-called total smoothness property of the space). We mention here that this result holds in full generality -without any restriction on the space- and in a stronger form, thanks to a result ofM. Raja, On dual locally uniformly rotund norms, Israel Journal of Mathematics 129 (2002), 77-91.Supported by AEI/FEDER (project MTM2017-83262-C2-2-P of Ministerio de Economia y Competitividad), by Fundacion Seneca, Region de Murcia (Grant 19368/PI/14), and Universitat Politecnica de Valencia (A. J. Guirao). Supported by AEI/FEDER (project MTM2017-83262-C2-1-P of Ministerio de Economia y Competitividad) and Universitat Politecnica de Valencia (V. Montesinos). We thank the referees for their work, that neatly improved the original version of this note to its final form.Cobollo, C.; Guirao Sánchez, AJ.; Montesinos Santalucia, V. (2020). A remark on totally smooth renormings. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 114(2):1-4. https://doi.org/10.1007/s13398-020-00831-5S141142Fabian, M., Habala, P., Hájek, P., Montesinos, V., Zizler, V.: Banach space theory: the basis of linear and nonlinear analysis. Springer, New York (2011)Fabian, M., Montesinos, V., Zizler, V.: Smoothness in Banach spaces. Selected problems. Rev. R. Acad. Cien. Ser. A. Mat. RACSAM. 100(1–2), 101–125 (2006)Ferrari, S., Orihuela, J., Raja, M.: Generalized metric properties of spheres and renorming of Banach spaces. Rev. R. Acad. Cienc. Exactas Fis. Natl. Ser. A Math. RACSAM. 113, 2655–2663 (2019)Foguel, S.R.: On a theorem by A. E. Taylor. Proc. Amer. Math. Soc. 9, 325 (1958)Godefroy, G.: Points de Namioka, espaces normants, applications à la théorie isométrique de la dualité. Israel J. Math. 38, 209–220 (1981)Guirao, A.J., Montesinos, V., Zizler, V.: Open Problems in the geometry and analysis of Banach spaces. Springer International Pub, Switzerland (2016)Harmand, P., Werner, D., Werner, W.: M-ideals in Banach spaces and Banach algebras. Lecture notes in math, vol. 1547. Springer, Berlin (1993)Haydon, R.: Locally uniformly rotund norms in Banach spaces and their duals. J. Funct. Anal. 254, 2023–2039 (2008)Oja, E., Viil, T., Werner, D.: Totally smooth renormings. Archiv. der. Mathematik. 112(3), 269–281 (2019)Phelps, R.R.: Uniqueness of Hahn–Banach extensions and unique best approximation. Trans. Amer. Math. Soc. 95, 238–255 (1960)Raja, M.: On dual locally uniformly rotund norms. Israel J. Math. 129, 77–91 (2002)Smith, R.J., Troyanski, S.L.: Renormings of $$C(K)$$ spaces. Rev. R. Acad. Cienc. Exactas Fís. Natl. Ser. A Math. RACSAM 104(2), 375–412 (2010)Sullivan, F.: Geometrical properties determined by the higher duals of a Banach space. Illinois J. Math. 21, 315–331 (1977)Taylor, A.E.: The extension of linear functionals. Duke Math. J. 5, 538–547 (1939

Schistosomiasis and Urinary Bladder Cancer in North Western Tanzania: A Retrospective Review of 185 Patients.

Worldwide, cancers of the urinary bladder are well known to be associated with environmental chemical carcinogens such as smoking and occupational exposure to polycyclic aromatic hydrocarbons. These cancers are typically transitional cell carcinoma (urothelial carcinoma). In areas where schistosomiasis is endemic there is a high incidence of squamous cell carcinoma of the urinary bladder. Schistosomiasis causes chronic granulomatous cystitis leading to squamous metaplasia of transitional epithelium, and subsequently development of squamous cell carcinoma. The western part of Tanzania on the shores of Lake Victoria is such an endemic area. This study was done to document the burden of urinary bladder cancer associated with schistosomiasis in this region. This was a descriptive retrospective study of histologically confirmed cases of urinary bladder cancer seen at the Department of Pathology Bugando Medical Centre (BMC) over a period of 10 years. Data were retrieved from the records of the Departments of Pathology, Medical Records and Surgery. Data were analyzed by the use of contingency tables. A total of 185 patients were diagnosed with cancer of the urinary bladder during the study period, where as 90 (48.6%) were males and 95 (51.4) were females. The mean age at diagnosis was 54.3 years. Squamous cell carcinoma was the most frequent histological type (55.1%), followed by conventional transitional cell carcinoma (40.5%). Eighty three of all cancer cases (44.9%) were found to have schistosomal eggs. Schistosomiasis was commonly associated with squamous cancers compared to non squamous cancers. Most of the cancers associated with schistosomiasis had invaded the muscularis propria of the urinary bladder at the time of diagnosis (p<0.001) and such cancers were frequent below 50 years of age with a significant statistical difference (p<0.001). Poorly differentiated tumors were more frequent in females than males with a significant statistical difference (p=0.006). The majority of urinary bladder cancers seen in the Lake Region were squamous cell carcinoma associated with schistosomiasis. These cancers showed an aggressive behavior and were commonly seen in the younger age groups. Effective control of schistosomiasis in this region should significantly reduce the burden of urinary bladder cancer

Dust-free quasars in the early Universe

The most distant quasars known, at redshifts z=6, generally have properties indistinguishable from those of lower-redshift quasars in the rest-frame ultraviolet/optical and X-ray bands. This puzzling result suggests that these distant quasars are evolved objects even though the Universe was only seven per cent of its current age at these redshifts. Recently one z=6 quasar was shown not to have any detectable emission from hot dust, but it was unclear whether that indicated different hot-dust properties at high redshift or if it is simply an outlier. Here we report the discovery of a second quasar without hot-dust emission in a sample of 21 z=6 quasars. Such apparently hot-dust-free quasars have no counterparts at low redshift. Moreover, we demonstrate that the hot-dust abundance in the 21 quasars builds up in tandem with the growth of the central black hole, whereas at low redshift it is almost independent of the black hole mass. Thus z=6 quasars are indeed at an early evolutionary stage, with rapid mass accretion and dust formation. The two hot-dust-free quasars are likely to be first-generation quasars born in dust-free environments and are too young to have formed a detectable amount of hot dust around them.Comment: To be published in Nature on the 18 March 2010

Geometric properties and continuity of the pre-duality mapping in Banach space

We use the preduality mapping in proving characterizations of some geometric properties of Banach spaces. In particular, those include nearly strongly convexity, nearly uniform convexity-a property introduced by K. Goebel and T. Sekowski-, and nearly very convexity.We thank a referee for the careful reading of the manuscript. His/her observations substantially improved the overall aspect of the present work, detected several misprints and made some convenient changes. This work was supported by: (1) The National Natural Science Foundation of China (Grant no. 11271248). (2) Specific Academic Discipline Project of Shanghai Municipal Education Commission (Grant no. B-8932-13-0136). (3) Project MTM2011-22417, Ministerio de Ciencia e Innovacion, Spain (V. Montesinos).Zhang, ZH.; Montesinos Santalucia, V.; Liu, CY.; Gong, WZ. (2015). Geometric properties and continuity of the pre-duality mapping in Banach space. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas. 109(2):407-416. https://doi.org/10.1007/s13398-014-0190-6S4074161092Bandyopadhyay, P., Huang, D., Lin, B.L., Troyanski, S.L.: Some generalizations of local uniform rotundity. J. Math. Anal. Appl. 252, 906–916 (2000)Bandyopadhyay, P., Li, Y., Lin, B., Narayana, D.: Proximinality in Banach spaces. J. Math. Anal. Appl. 341, 309–317 (2008)Diestel, J.: Geometry of Banach Spaces. Selected Topics, LNM, vol. 485. Springer, Berlin (1975)Fabian, M., Habala, P., Hájek, P., Montesinos, V., Zizler, V.: Banach Space Theory. The Basis for Linear and Nonlinear Analysis, CMS Books in Mathematics. Springer, Berlin (2011)Giles, J.R., Gregory, D.A., Sims, B.: Geometrical implications of upper semi-continuity of the duality mapping on a Banach space. Pacific J. Math. 79(1), 99–109 (1978)Goebel, K., Sekowski, T.: The modulus of non-compact convexity. Ann. Univ. M. Curie-Sklodowska, Sect. A 38, 41–48 (1984)Guirao, A.J., Montesinos, V.: A note in approximative compactness and continuity of metric projections in Banach spaces. J. Convex Anal. 18, 397–401 (2011)Huff, R.: Banach spaces which are nearly uniformly convex. Rocky Mountain J. Math. 10(4), 743–749 (1980)Kutzarova, D., Rolewicz, S.: On nearly uniformly convex sets. Arch. Math. 57, 385–394 (1991)Kutzarova, D., Lin, B.L., Zhang, W.: Some geometrical properties of Banach spaces related to nearly uniform convexity. Contemp. Math. 144, 165–171 (1993)Kutzarova, D., Prus, S.: Operators which factor through nearly uniformly convex spaces. Boll. Un. Mat. Ital. B (7) 9, 2, 479–494 (1995)Montesinos, V.: Drop property equals reflexivity. Studia Math. 87, 93–100 (1987)Phelps, R.R.: Convex Functions, Monotone Operators and Differentiability, LNM, vol. 1364, 2nd edn. Springer, Berlin (1993)Rolewicz, S.: On drop property. Studia Math. 85, 27–37 (1986)Rolewicz, S.: On $$\Delta$$ Δ -uniform convexity and drop property. Studia Math. 87, 181–191 (1987)Wu, C.X., Li, Y.J.: Strong convexity in Banach spaces. J. Math. Wuhan Univ. 13(1), 105–108 (1993)Wang, J.H., Nan, C.X.: The continuity of subdifferential mapping. J. Math. Anal. Appl. 210, 206–214 (1997)Wang, J.H., Zhang, Z.H.: Characterization of the property (C-K). Acta Math. Sci. Ser. A Chin. Ed. 17(A)(3), 280–284 (1997)Zhang, Z.H., Liu, C.Y.: Some generalization of locally and weakly locally uniformly convex space. Nonlinear Anal. 74(12), 3896–3902 (2011)Zhang, Z.H., Liu, C.Y.: Convexity and proximinality in Banach spaces. J. Funct. Spaces Appl. 2012, 11 (2012). doi: 10.1155/2012/724120 . Article ID 724120Zhang, Z.H., Liu, C.Y.: Convexity and existence of the farthest point. Abstract Appl. Anal. 2011, 9 (2011). doi: 10.1155/2011/139597 . Article ID 139597Zhang, Z.H., Shi, Z.R.: Convexities and approximative compactness and continuity of the metric projection in Banach spaces. J. Approx. Theory 161(2), 802–812 (2009)Zhang, Z.H., Zhang, C.J.: On very rotund Banach spaces. Appl. Math. Mech. (English Ed.) 21(8), 965–970 (2000

Calculating the potential for within-flight transmission of influenza A (H1N1)

Abstract Background Clearly air travel, by transporting infectious individuals from one geographic location to another, significantly affects the rate of spread of influenza A (H1N1). However, the possibility of within-flight transmission of H1N1 has not been evaluated; although it is known that smallpox, measles, tuberculosis, SARS and seasonal influenza can be transmitted during commercial flights. Here we present the first quantitative risk assessment to assess the potential for within-flight transmission of H1N1. Methods We model airborne transmission of infectious viral particles of H1N1 within a Boeing 747 using methodology from the field of quantitative microbial risk assessment. Results The risk of catching H1N1 will essentially be confined to passengers travelling in the same cabin as the source case. Not surprisingly, we find that the longer the flight the greater the number of infections that can be expected. We calculate that H1N1, even during long flights, poses a low to moderate within-flight transmission risk if the source case travels First Class. Specifically, 0-1 infections could occur during a 5 hour flight, 1-3 during an 11 hour flight and 2-5 during a 17 hour flight. However, within-flight transmission could be significant, particularly during long flights, if the source case travels in Economy Class. Specifically, two to five infections could occur during a 5 hour flight, 5-10 during an 11 hour flight and 7-17 during a 17 hour flight. If the aircraft is only partially loaded, under certain conditions more infections could occur in First Class than in Economy Class. During a 17 hour flight, a greater number of infections would occur in First Class than in Economy if the First Class Cabin is fully occupied, but Economy class is less than 30% full. Conclusions Our results provide insights into the potential utility of air travel restrictions on controlling influenza pandemics in the winter of 2009/2010. They show travel by one infectious individual, rather than causing a single outbreak of H1N1, could cause several simultaneous outbreaks. These results imply that, during a pandemic, quarantining passengers who travel in Economy on long-haul flights could potentially be an important control strategy. Notably, our results show that quarantining passengers who travel First Class would be unlikely to be an effective control strategy

Compton Thick AGN: the dark side of the X-ray background

The spectrum of the hard X-ray background records the history of accretion processes integrated over the cosmic time. Several pieces of observational and theoretical evidence indicate that a significant fraction of the energy density is obscured by large columns of gas and dust. The absorbing matter is often very thick, with column densities exceeding N_H > 1.5 10^24 cm-2, the value corresponding to unity optical depth for Compton scattering. These sources are called ``Compton thick'' and appear to be very numerous, at least in the nearby universe. Although Compton thick Active Galactic Nuclei (AGN) are thought to provide an important contribution to the overall cosmic energy budget, their space density and cosmological evolution are poorly known. The properties of Compton thick AGN are reviewed here, with particular emphasis on their contributions to the extragalactic background light in the hard X-ray and infrared bands.Comment: 28 pages, 10 figures. Review for "Supermassive Black Holes in the Distant Universe", Ed. A. J. Barger, Kluwer Academi

X-ray Absorption and Reflection in Active Galactic Nuclei

X-ray spectroscopy offers an opportunity to study the complex mixture of emitting and absorbing components in the circumnuclear regions of active galactic nuclei, and to learn about the accretion process that fuels AGN and the feedback of material to their host galaxies. We describe the spectral signatures that may be studied and review the X-ray spectra and spectral variability of active galaxies, concentrating on progress from recent Chandra, XMM-Newton and Suzaku data for local type 1 AGN. We describe the evidence for absorption covering a wide range of column densities, ionization and dynamics, and discuss the growing evidence for partial-covering absorption from data at energies > 10 keV. Such absorption can also explain the observed X-ray spectral curvature and variability in AGN at lower energies and is likely an important factor in shaping the observed properties of this class of source. Consideration of self-consistent models for local AGN indicates that X-ray spectra likely comprise a combination of absorption and reflection effects from material originating within a few light days of the black hole as well as on larger scales. It is likely that AGN X-ray spectra may be strongly affected by the presence of disk-wind outflows that are expected in systems with high accretion rates, and we describe models that attempt to predict the effects of radiative transfer through such winds, and discuss the prospects for new data to test and address these ideas.Comment: Accepted for publication in the Astronomy and Astrophysics Review. 58 pages, 9 figures. V2 has fixed an error in footnote

Persistent anthrax as a major driver of wildlife mortality in a tropical rainforest

Anthrax is a globally important animal disease and zoonosis. Despite this, our current knowledge of anthrax ecology is largely limited to arid ecosystems, where outbreaks are most commonly reported. Here we show that the dynamics of an anthrax-causing agent, Bacillus cereus biovar anthracis, in a tropical rainforest have severe consequences for local wildlife communities. Using data and samples collected over three decades, we show that rainforest anthrax is a persistent and widespread cause of death for a broad range of mammalian hosts. We predict that this pathogen will accelerate the decline and possibly result in the extirpation of local chimpanzee (Pan troglodytes verus) populations. We present the epidemiology of a cryptic pathogen and show that its presence has important implications for conservation

Seroprevalence of arthropod-borne bacterial infections in homeless individuals in Hamburg in 2020

PURPOSE: The number of homeless people in Germany is steadily increasing. Due to their often precarious living conditions, this specific population may be increasingly exposed to ectoparasites that can transmit various pathogens. To assess the prevalence and thus the risk of such infections, we analyzed the seropositivity of rickettsiosis, Q fever, tularemia and bartonellosis in homeless individuals. METHODS: A total of 147 homeless adults from nine shelters in Hamburg, Germany, were included. The individuals underwent questionnaire-based interviewing, physical examination, and venous blood was drawn between May and June 2020. Blood samples were analyzed for antibodies against rickettsiae (Rickettsia typhi and R. conorii), Coxiella burnetii, Francisella tularensis and bartonellae. RESULTS AND CONCLUSION: A very low seroprevalence of R. typhi and F. tularensis infection was found (0-1%), while antibodies against R. conorii and C. burnetii were more common (7% each), followed by a relatively high seroprevalence of 14% for bartonellosis. Q fever seroprevalence was associated with the country of origin, whereas bartonellosis seroprevalence was associated with the duration of homelessness. Preventive measures targeting ectoparasites, especially body lice, should be put in place continuously

IFNAR1-Signalling Obstructs ICOS-mediated Humoral Immunity during Non-lethal Blood-Stage Plasmodium Infection

Funding: This work was funded by a Career Development Fellowship (1028634) and a project grant (GRNT1028641) awarded to AHa by the Australian National Health & Medical Research Council (NHMRC). IS was supported by The University of Queensland Centennial and IPRS Scholarships. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Peer reviewedPublisher PD