Dynamics of the Volterra-type integral and differentiation operators on generalized Fock spaces

[EN] Various dynamical properties of the differentiation and Volterra-type integral operators on generalized Fock spaces are studied. We show that the differentiation operator is always supercyclic on these spaces. We further characterize when it is hypercyclic, power bounded and uniformly mean ergodic. We prove that the operator satisfies the Ritt's resolvent condition if and only if it is power bounded and uniformly mean ergodic. Some similar results are obtained for the Volterra-type and Hardy integral operators.J. Bonet was partially supported by the research projects MTM2016-76647-P and GV Prometeo 2017/102 (Spain). M. Worku is supported by ISP project, Addis Ababa University, Ethiopia.Bonet Solves, JA.; Mengestie, T.; Worku, M. (2019). Dynamics of the Volterra-type integral and differentiation operators on generalized Fock spaces. Results in Mathematics. 74(4):1-15. https://doi.org/10.1007/s00025-019-1123-7S115744Abanin, A.V., Tien, P.T.: Differentiation and integration operators on weighted Banach spaces of holomorphic functions. Math. Nachr. 290(8–9), 1144–1162 (2017)Atzmon, A., Brive, B.: Surjectivity and invariant subspaces of differential operators on weighted Bergman spaces of entire functions, Bergman spaces and related topics in complex analysis, Contemp. Math., vol. 404, Amer. Math. Soc., Providence, RI, pp. 27–39 (2006)Bayart, F., Matheron, E.: Dynamics of Linear Operators, Cambridge Tracts in Math, vol. 179. Cambridge Univ. Press, Cambridge (2009)Bermúdez, T., Bonilla, A., Peris, A.: On hypercyclicity and supercyclicity criteria. Bull. Austral. Math. Soc. 70, 45–54 (2004)Beltrán, M.J.: Dynamics of differentiation and integration operators on weighted space of entire functions. Studia Math. 221, 35–60 (2014)Beltrán, M.J., Bonet, J., Fernández, C.: Classical operators on weighted Banach spaces of entire functions. Proc. Am. Math. Soc. 141, 4293–4303 (2013)Bès, J., Peris, A.: Hereditarily hypercyclic operators. J. Funct. Anal. 167, 94–112 (1999)Bonet, J.: Dynamics of the differentiation operator on weighted spaces of entire functions. Math. Z. 26, 649–657 (2009)Bonet, J.: The spectrum of Volterra operators on weighted Banach spaces of entire functions. Q. J. Math. 66, 799–807 (2015)Bonet, J., Bonilla, A.: Chaos of the differentiation operator on weighted Banach spaces of entire functions. Complex Anal. Oper. Theory 7, 33–42 (2013)Bonet, J., Taskinen, J.: A note about Volterra operators on weighted Banach spaces of entire functions. Math. Nachr. 288, 1216–1225 (2015)Constantin, O., Persson, A.-M.: The spectrum of Volterra-type integration operators on generalized Fock spaces. Bull. Lond. Math. Soc. 47, 958–963 (2015)Constantin, O., Peláez, J.-Á.: Integral operators, embedding theorems and a Littlewood–Paley formula on weighted Fock spaces. J. Geom. Anal. 26, 1109–1154 (2016)De La Rosa, M., Read, C.: A hypercyclic operator whose direct sum is not hypercyclic. J. Oper. Theory 61, 369–380 (2009)Dunford, N.: Spectral theory. I. Convergence to projections. Trans. Am. Math. Soc. 54, 185–217 (1943)Grosse-Erdmann, K.G., Peris Manguillot, A.: Linear Chaos. Springer, New York (2011)Harutyunyan, A., Lusky, W.: On the boundedness of the differentiation operator between weighted spaces of holomorphic functions. Studia Math. 184, 233–247 (2008)Krengel, U.: Ergodic Theorems. Walter de Gruyter, Berlin (1985)Lyubich, Yu.: Spectral localization, power boundedness and invariant subspaces under Ritt’s type condition. Studia Mathematica 143(2), 153–167 (1999)Mengestie, T.: A note on the differential operator on generalized Fock spaces. J. Math. Anal. Appl. 458(2), 937–948 (2018)Mengestie, T.: Spectral properties of Volterra-type integral operators on Fock–Sobolev spaces. J. Kor. Math. Soc. 54(6), 1801–1816 (2017)Mengestie, T.: On the spectrum of volterra-type integral operators on Fock–Sobolev spaces. Complex Anal. Oper. Theory 11(6), 1451–1461 (2017)Mengestie, T., Ueki, S.: Integral, differential and multiplication operators on weighted Fock spaces. Complex Anal. Oper. Theory 13, 935–95 (2019)Mengestie, T., Worku, M.: Isolated and essentially isolated Volterra-type integral operators on generalized Fock spaces. Integr. Transf. Spec. Funct. 30, 41–54 (2019)Nagy, B., Zemanek, J.A.: A resolvent condition implying power boundedness. Studia Math. 134, 143–151 (1999)Nevanlinna, O.: Convergence of iterations for linear equations. Lecture Notes in Mathematics. ETH Zürich, Birkhäuser, Basel (1993)Ritt, R.K.: A condition that $$\lim _{n\rightarrow \infty } n^{-1}T^n =0$$. Proc. Am. Math. Soc. 4, 898–899 (1953)Ueki, S.: Characterization for Fock-type space via higher order derivatives and its application. Complex Anal. Oper. Theory 8, 1475–1486 (2014)Yosida, K.: Functional Analysis. Springer, Berlin (1978)Yosida, K., Kakutani, S.: Operator-theoretical treatment of Marko’s process and mean ergodic theorem. Ann. Math. 42(1), 188–228 (1941

Sunlight-Exposed Biofilm Microbial Communities Are Naturally Resistant to Chernobyl Ionizing-Radiation Levels

BACKGROUND: The Chernobyl accident represents a long-term experiment on the effects of exposure to ionizing radiation at the ecosystem level. Though studies of these effects on plants and animals are abundant, the study of how Chernobyl radiation levels affect prokaryotic and eukaryotic microbial communities is practically non-existent, except for a few reports on human pathogens or soil microorganisms. Environments enduring extreme desiccation and UV radiation, such as sunlight exposed biofilms could in principle select for organisms highly resistant to ionizing radiation as well. METHODOLOGY/PRINCIPAL FINDINGS: To test this hypothesis, we explored the diversity of microorganisms belonging to the three domains of life by cultivation-independent approaches in biofilms developing on concrete walls or pillars in the Chernobyl area exposed to different levels of radiation, and we compared them with a similar biofilm from a non-irradiated site in Northern Ireland. Actinobacteria, Alphaproteobacteria, Bacteroidetes, Acidobacteria and Deinococcales were the most consistently detected bacterial groups, whereas green algae (Chlorophyta) and ascomycete fungi (Ascomycota) dominated within the eukaryotes. Close relatives to the most radio-resistant organisms known, including Rubrobacter species, Deinococcales and melanized ascomycete fungi were always detected. The diversity of bacteria and eukaryotes found in the most highly irradiated samples was comparable to that of less irradiated Chernobyl sites and Northern Ireland. However, the study of mutation frequencies in non-coding ITS regions versus SSU rRNA genes in members of a same actinobacterial operational taxonomic unit (OTU) present in Chernobyl samples and Northern Ireland showed a positive correlation between increased radiation and mutation rates. CONCLUSIONS/SIGNIFICANCE: Our results show that biofilm microbial communities in the most irradiated samples are comparable to non-irradiated samples in terms of general diversity patterns, despite increased mutation levels at the single-OTU level. Therefore, biofilm communities growing in sunlight exposed substrates are capable of coping with increased mutation rates and appear pre-adapted to levels of ionizing radiation in Chernobyl due to their natural adaptation to periodical desiccation and ambient UV radiation

Alignment of the ALICE Inner Tracking System with cosmic-ray tracks

37 pages, 15 figures, revised version, accepted by JINSTALICE (A Large Ion Collider Experiment) is the LHC (Large Hadron Collider) experiment devoted to investigating the strongly interacting matter created in nucleus-nucleus collisions at the LHC energies. The ALICE ITS, Inner Tracking System, consists of six cylindrical layers of silicon detectors with three different technologies; in the outward direction: two layers of pixel detectors, two layers each of drift, and strip detectors. The number of parameters to be determined in the spatial alignment of the 2198 sensor modules of the ITS is about 13,000. The target alignment precision is well below 10 micron in some cases (pixels). The sources of alignment information include survey measurements, and the reconstructed tracks from cosmic rays and from proton-proton collisions. The main track-based alignment method uses the Millepede global approach. An iterative local method was developed and used as well. We present the results obtained for the ITS alignment using about 10^5 charged tracks from cosmic rays that have been collected during summer 2008, with the ALICE solenoidal magnet switched off.Peer reviewe

A global experiment on motivating social distancing during the COVID-19 pandemic

Finding communication strategies that effectively motivate social distancing continues to be a global public health priority during the COVID-19 pandemic. This cross-country, preregistered experiment (n = 25,718 from 89 countries) tested hypotheses concerning generalizable positive and negative outcomes of social distancing messages that promoted personal agency and reflective choices (i.e., an autonomy-supportive message) or were restrictive and shaming (i.e., a controlling message) compared with no message at all. Results partially supported experimental hypotheses in that the controlling message increased controlled motivation (a poorly internalized form of motivation relying on shame, guilt, and fear of social consequences) relative to no message. On the other hand, the autonomy-supportive message lowered feelings of defiance compared with the controlling message, but the controlling message did not differ from receiving no message at all. Unexpectedly, messages did not influence autonomous motivation (a highly internalized form of motivation relying on one’s core values) or behavioral intentions. Results supported hypothesized associations between people’s existing autonomous and controlled motivations and self-reported behavioral intentions to engage in social distancing. Controlled motivation was associated with more defiance and less long-term behavioral intention to engage in social distancing, whereas autonomous motivation was associated with less defiance and more short- and long-term intentions to social distance. Overall, this work highlights the potential harm of using shaming and pressuring language in public health communication, with implications for the current and future global health challenges

Laser Interactions for the Synthesis and In Situ Diagnostics of Nanomaterials

Laser interactions have traditionall been at thec center of nanomaterials science, providing highly nonequilibrium growth conditions to enable the syn- thesis of novel new nanoparticles, nanotubes, and nanowires with metastable phases. Simultaneously, lasers provide unique opportunities for the remote char- acterization of nanomaterial size, structure, and composition through tunable laser spectroscopy, scattering, and imaging. Pulsed lasers offer the opportunity, there- fore, to supply the required energy and excitation to both control and understand the growth processes of nanomaterials, providing valuable views of the typically nonequilibrium growth kinetics and intermediates involved. Here we illustrate the key challenges and progress in laser interactions for the synthesis and in situ diagnostics of nanomaterials through recent examples involving primarily carbon nanomaterials, including the pulsed growth of carbon nanotubes and graphene

A global experiment on motivating social distancing during the COVID-19 pandemic

Significance Communicating in ways that motivate engagement in social distancing remains a critical global public health priority during the COVID-19 pandemic. This study tested motivational qualities of messages about social distancing (those that promoted choice and agency vs. those that were forceful and shaming) in 25,718 people in 89 countries. The autonomy-supportive message decreased feelings of defying social distancing recommendations relative to the controlling message, and the controlling message increased controlled motivation, a less effective form of motivation, relative to no message. Message type did not impact intentions to socially distance, but people’s existing motivations were related to intentions. Findings were generalizable across a geographically diverse sample and may inform public health communication strategies in this and future global health emergencies. Abstract Finding communication strategies that effectively motivate social distancing continues to be a global public health priority during the COVID-19 pandemic. This cross-country, preregistered experiment (n = 25,718 from 89 countries) tested hypotheses concerning generalizable positive and negative outcomes of social distancing messages that promoted personal agency and reflective choices (i.e., an autonomy-supportive message) or were restrictive and shaming (i.e., a controlling message) compared with no message at all. Results partially supported experimental hypotheses in that the controlling message increased controlled motivation (a poorly internalized form of motivation relying on shame, guilt, and fear of social consequences) relative to no message. On the other hand, the autonomy-supportive message lowered feelings of defiance compared with the controlling message, but the controlling message did not differ from receiving no message at all. Unexpectedly, messages did not influence autonomous motivation (a highly internalized form of motivation relying on one’s core values) or behavioral intentions. Results supported hypothesized associations between people’s existing autonomous and controlled motivations and self-reported behavioral intentions to engage in social distancing. Controlled motivation was associated with more defiance and less long-term behavioral intention to engage in social distancing, whereas autonomous motivation was associated with less defiance and more short- and long-term intentions to social distance. Overall, this work highlights the potential harm of using shaming and pressuring language in public health communication, with implications for the current and future global health challenges