Mean ergodic composition operators on generalized Fock spaces

[EN] Every bounded composition operator C psi defined by an analytic symbol psi on the complex plane when acting on generalized Fock spaces F phi p,1 <= p <=infinity and p=0, is power bounded. Mean ergodic and uniformly mean ergodic bounded composition operators on these spaces are characterized in terms of the symbol. The behaviour for p=0 and p=infinity differs. The set of periodic points of these operators is also determined.The research of the first author is supported by ISP project, Addis Ababa University, Ethiopia. The research of the third author was partially supported by the research projects MTM2016-76647-P and GV Prometeo 2017/102 (Spain).Seyoum, W.; Mengestie, T.; Bonet Solves, JA. (2019). Mean ergodic composition operators on generalized Fock spaces. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 114(1):1-11. https://doi.org/10.1007/s13398-019-00738-wS1111141Albanese, A.A., Bonet, J., Ricker, W.J.: Mean ergodic operators in Fréchet spaces. Anal. Acad. Sci. Fenn. Math. 34, 401–436 (2009)Beltrán-Meneu, M.J., Gómez-Collado, M.C., Jordá, E., Jornet, D.: Mean ergodic composition operators on Banach spaces of holomorphic functions. J. Funct. Anal. 270, 4369–4385 (2016)Bierstedt, K.D., Summers, W.H.: Biduals of weighted Banach spaces of analytic functions. J. Austr. Math. Soc. Ser. A 54, 70–79 (1993)Blasco, O.: Boundedness of Volterra operators on spaces of entire functions. Ann. Acad. Sci. Fenn. Math. 43, 89–107 (2018)Bonet, J., Domański, P.: A note on mean ergodic composition operators on spaces of holomorphic functions. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 105, 389–396 (2011)Bonet, J., Mangino, E.: Associated weights for spaces of $$p$$-integrable entire functions. Quaestiones Math. (2019). https://doi.org/10.2989/16073606.2019.1605420Bonet, J., Ricker, W.J.: Mean ergodicity of multiplication operators in weighted spaces of holomorphic functions. Arch. Math. 92, 428–437 (2009)Carswell, B.J., MacCluer, B.D., Schuster, A.: Composition operators on the Fock space. Acta Sci. Math. (Szeged) 69, 871–887 (2003)Constantin, O., Peláez, J.Á.: Integral operators, embedding theorems and a Littlewood-Paley formula on weighted Fock spaces. J. Geom. Anal. 26, 1109–1154 (2015)Cowen, C., MacCluer, B.: Composition Operators on Spaces of Analytic Functions. CRC Press, Boca Raton (1995)Dunford, N.: Spectral theory I convergence to projections. Trans. Am. Math. Soc. 54, 185–217 (1943)Guo, K., Izuchi, K.: Composition operators on Fock type space. Acta Sci. Math. (Szeged) 74, 807–828 (2008)Krengel, U.: Ergodic Theorems. Walter de Gruyter, Berlin (1985)Lotz, H.P.: Tauberian theorems for operators on $$L^1$$ and similar spaces. In: Bierstedt, K.D., Fuchssteiner, B. (eds.) Functional Analysis: Surveys and Recent Results III, pp. 117–133. North Holland, Amsterdam (1984)Lotz, H.P.: Uniform convergence of operators on $$L^{\infty }$$ and similar spaces. Math. Z. 190, 207–220 (1985)Lusky, W.: On the isomophism classes of weighted spaces of harmonic and holomorphic functions. Studia Math. 175, 19–45 (2006)Mengestie, T., Ueki, S.: Integral, differential and multiplication operators on weighted Fock spaces. Complex Anal. Oper. Theory. 13, 935–958 (2019)Mengestie, T., Seyoum, W.: Topological and dynamical properties of composition operators. Complex Anal. Oper. Theory (2018) (to appear)Mengestie, T., Seyoum, W.: Spectral properties of composition operators on Fock-Type spaces. Quaest. Math. (2019). https://doi.org/10.2989/16073606.2019.1692092Shapiro, J.H.: Composition Operators and Classical Function Theory. Springer, New York (1993)Wolf, E.: Power bounded composition operator. Comp. Method Funct. Theory 12, 105–117 (2012)Yosida, K.: Functional Analysis. Springer, Berlin (1978)Yosida, K., Kakutani, S.: Operator-theoretical treatment of Markoff’s Process and Mean Ergodic Theorem. Ann. Math. 42, 188–228 (1941

Finite element analysis of the effect of cementing concepts on implant stability and cement fatigue failure

Background and purpose Two contradictory cementing techniques (using an undersized stem versus a canal-filling stem) can both lead to excellent survival rates, a phenomenon known as the “French paradox”. Furthermore, previous studies have indicated that the type of bone supporting the cement mantle may affect implant survival. To further evaluate the mechanical consequences of variations in cementing technique, we studied the effect of implant size and type of bone supporting the cement mantle on the mechanical performance of cemented total hip arthroplasty, using finite element analysis

Detecting dysphagia in inclusion body myositis

Dysphagia is an important yet inconsistently recognized symptom of inclusion body myositis (IBM). It can be disabling and potentially life-threatening. We studied the prevalence and symptom-sign correlation of dysphagia. Fifty-seven IBM patients were interviewed using a standard questionnaire for dysphagia and 43 of these underwent swallowing videofluoroscopy (VFS). Symptoms of dysphagia were present in 37 of 57 patients (65%). Nevertheless, only 17 of these patients (46%) had previously and spontaneously complained about swallowing to their physicians. Both symptoms of impaired propulsion (IP) (59%) and aspiration-related symptoms (52%) were frequently mentioned. Swallowing abnormalities on VFS were present in 34 of 43 patients (79%) with IP of the bolus in 77% of this group. The reported feeling of IP was confirmed by VFS in 92% of these patients. Dysphagia in IBM is common but underreported by the vast majority of patients if not specifically asked for. In practice, two questions reliably predict the presence of IP on VFS: ‘Does food get stuck in your throat’ and ‘Do you have to swallow repeatedly in order to get rid of food’. These questions are an appropriate means in selecting IBM patients for further investigation through VFS and eventual treatment

The spectrum of thyroid dysfunction in an Australian hepatitis C population treated with combination Interferon-α2β and Ribavirin

BACKGROUND: The study aims to assess the pattern of thyroid response to combination Interferon-α2β (IFN-α) and Ribavirin (RBV) anti-viral therapy in an Australian hepatitis C cohort. These include the prevalence of thyroid dysfunction (TD) including hyperthyroidism and hypothyroidism and their possible predictors, the common overall pattern of thyroid function tests whilst receiving therapy and TD outcomes, and the correlation with HCV status outcome. METHODS: A retrospective analysis of all medical records was performed to assess thyroid function in Hepatitis C Virus (HCV) patients who were treated at the Hunter Area hepatitis C treatment center between 1995 and March 2004. The centre is part of the John Hunter hospital, a major tertiary referral centre in New South Wales, Australia. RESULTS: There were 272 cases available for review. The prevalence of TD is 6.7 percent and is made up predominantly of females (80 percent). There were 3 (1.1 percent) cases of hyperthyroidism with 2 (67 percent) females. Thirteen out of fifteen (80 percent) cases of hypothyroidism were females with the overall prevalence of 5.5 percent. The majority of hypothyroid patients still required Thyroxine supplement at the end of follow up. CONCLUSION: Ninety three percent of HCV treated patients have intact thyroid function at the end of treatment. The predominant TD is hypothyroidism. The predominant pattern of thyrotoxicosis (TTX) is that of thyroiditis although the number is small. Graves' like disease was not observed. People with pre-existing thyroid auto-antibodies should be closely monitored for thyroid dysfunction, particularly hypothyroidism

An 84 microGauss Magnetic Field in a Galaxy at Redshift z=0.692

The magnetic field pervading our Galaxy is a crucial constituent of the interstellar medium: it mediates the dynamics of interstellar clouds, the energy density of cosmic rays, and the formation of stars. The field associated with ionized interstellar gas has been determined through observations of pulsars in our Galaxy. Radio-frequency measurements of pulse dispersion and the rotation of the plane of linear polarization, i.e., Faraday rotation, yield an average value B ~ 3 microGauss. The possible detection of Faraday rotation of linearly polarized photons emitted by high-redshift quasars suggests similar magnetic fields are present in foreground galaxies with redshifts z > 1. As Faraday rotation alone, however, determines neither the magnitude nor the redshift of the magnetic field, the strength of galactic magnetic fields at redshifts z > 0 remains uncertain. Here we report a measurement of a magnetic field of B ~ 84 microGauss in a galaxy at z =0.692, using the same Zeeman-splitting technique that revealed an average value of B = 6 microGauss in the neutral interstellar gas of our Galaxy. This is unexpected, as the leading theory of magnetic field generation, the mean-field dynamo model, predicts large-scale magnetic fields to be weaker in the past rather than stronger

Effect of discriminative plant-sugar feeding on the survival and fecundity of Anopheles gambiae

<p>Abstract</p> <p>Background</p> <p>A previous study showed for <it>Anopheles gambiae s.s</it>. a gradation of feeding preference on common plant species growing in a malaria holoendemic area in western Kenya. The present follow-up study determines whether there is a relationship between the mosquito's preferences and its survival and fecundity.</p> <p>Methods</p> <p>Groups of mosquitoes were separately given <it>ad libitum </it>opportunity to feed on five of the more preferred plant species (<it>Hamelia patens</it>, <it>Parthenium hysterophorus</it>, <it>Ricinus communis</it>, <it>Senna didymobotrya</it>, and <it>Tecoma stans</it>) and one of the less preferred species (<it>Lantana camara</it>). The mosquitoes were monitored daily for survival. Sugar solution (glucose 6%) and water were used as controls. In addition, the fecundity of mosquitoes on each plant after (i) only one blood meal (number of eggs oviposited), and (ii) after three consecutive blood meals (proportion of females ovipositing, number of eggs oviposited and hatchability of eggs), was determined. The composition and concentration of sugar in the fed-on parts of each plant species were determined using gas chromatography. Using SAS statistical package, tests for significant difference of the fitness values between mosquitoes exposed to different plant species were conducted.</p> <p>Results and Conclusion</p> <p><it>Anopheles gambiae </it>that had fed on four of the five more preferred plant species (<it>T. stans</it>, <it>S. didymobotrya</it>, <it>R. communis </it>and <it>H. patens</it>, but not <it>P. hysterophorus</it>) lived longer and laid more eggs after one blood meal, when compared with <it>An. gambiae </it>that had fed on the least preferred plant species <it>L. camara</it>. When given three consecutive blood-meals, the percentage of females that oviposited, but not the number of eggs laid, was significantly higher for mosquitoes that had previously fed on the four more preferred plant species. Total sugar concentration in the preferred plant parts was significantly correlated with survival and with the proportion of females that laid eggs. This effect was associated mainly with three sugar types, namely glucose, fructose, and gulose. Except for <it>P. hysterophorus</it>, the results suggest that feeding by mosquitoes on preferred plant species under natural conditions results in higher fitness-related benefits, and that the sugar content in preferred plant parts is largely responsible for these effects.</p

Autologous chondrocyte implantation-derived synovial fluids display distinct responder and non-responder proteomic profiles

Hulme, Charlotte H. & Wilson, Emma L. - Equal contributorsBackground Autologous chondrocyte implantation (ACI) can be used in the treatment of focal cartilage injuries to prevent the onset of osteoarthritis (OA). However, we are yet to understand fully why some individuals do not respond well to this intervention. Identification of a reliable and accurate biomarker panel that can predict which patients are likely to respond well to ACI is needed in order to assign the patient to the most appropriate therapy. This study aimed to compare the baseline and mid-treatment proteomic profiles of synovial fluids (SFs) obtained from responders and non-responders to ACI. Methods SFs were derived from 14 ACI responders (mean Lysholm improvement of 33 (17–54)) and 13 non-responders (mean Lysholm decrease of 14 (4–46)) at the two stages of surgery (cartilage harvest and chondrocyte implantation). Label-free proteome profiling of dynamically compressed SFs was used to identify predictive markers of ACI success or failure and to investigate the biological pathways involved in the clinical response to ACI. Results Only 1 protein displayed a ≥2.0-fold differential abundance in the preclinical SF of ACI responders versus non-responders. However, there is a marked difference between these two groups with regard to their proteome shift in response to cartilage harvest, with 24 and 92 proteins showing ≥2.0-fold differential abundance between Stages I and II in responders and non-responders, respectively. Proteomic data has been uploaded to ProteomeXchange (identifier: PXD005220). We have validated two biologically relevant protein changes associated with this response, demonstrating that matrix metalloproteinase 1 was prominently elevated and S100 calcium binding protein A13 was reduced in response to cartilage harvest in non-responders. Conclusions The differential proteomic response to cartilage harvest noted in responders versus non-responders is completely novel. Our analyses suggest several pathways which appear to be altered in non-responders that are worthy of further investigation to elucidate the mechanisms of ACI failure. These protein changes highlight many putative biomarkers that may have potential for prediction of ACI treatment success

The HST/ACS Coma Cluster Survey: I - Survey Objectives and Design

We describe the HST ACS Coma cluster Treasury survey, a deep two-passband imaging survey of one of the nearest rich clusters of galaxies, the Coma cluster (Abell 1656). The survey was designed to cover an area of 740 square arcmin in regions of different density of both galaxies and intergalactic medium within the cluster. The ACS failure of January 27th 2007 leaves the survey 28% complete, with 21 ACS pointings (230 square arcmin) complete, and partial data for a further 4 pointings (44 square arcmin). Predicted survey depth for 10 sigma detections for optimal photometry of point sources is g' = 27.6 in the F475W filter, and IC=26.8 mag in F814 (AB magnitudes). Initial simulations with artificially injected point sources show 90% recovered at magnitude limits of g' = 27.55 and IC = 26.65. For extended sources, the predicted 10 sigma limits for a 1 square arcsecond region are g' = 25.8 mag/sq. arcsec and IC = 25.0 mag/sq. arcsec. We highlight several motivating science goals of the survey, including study of the faint end of the cluster galaxy luminosity function, structural parameters of dwarf galaxies, stellar populations and their effect on colors and color gradients, evolution of morphological components in a dense environment, the nature of ultra compact dwarf galaxies, and globular cluster populations of cluster galaxies of a range of luminosities and types. This survey will also provide a local rich cluster benchmark for various well known global scaling relations and explore new relations pertaining to the nuclear properties of galaxies