On the continuous Cesàro operator in certain function spaces

“The final publication is available at Springer via http://dx.doi.org/10.1007/s11117-014-0321-5"Various properties of the (continuous) Cesàro operator C, acting on Banach and Fréchet spaces of continuous functions and L p-spaces, are investigated. For instance, the spectrum and point spectrum of C are completely determined and a study of certain dynamics of C is undertaken (eg. hyper- and supercyclicity, chaotic behaviour). In addition, the mean (and uniform mean) ergodic nature of C acting in the various spaces is identified.The research of the first two authors was partially supported by the projects MTM2010-15200 and GVA Prometeo II/2013/013 (Spain). The second author gratefully acknowledges the support of the Alexander von Humboldt Foundation.Albanese, AA.; Bonet Solves, JA.; Ricker, WJ. (2015). On the continuous Cesàro operator in certain function spaces. Positivity. 19:659-679. https://doi.org/10.1007/s11117-014-0321-5S65967919Albanese, A.A.: Primary products of Banach spaces. Arch. Math. 66, 397–405 (1996)Albanese, A.A.: On subspaces of the spaces $$L^p_{\rm loc}$$ L loc p and of their strong duals. Math. Nachr. 197, 5–18 (1999)Albanese, A.A., Moscatelli, V.B.: Complemented subspaces of sums and products of copies of $$L^1 [0,1]$$ L 1 [ 0 , 1 ] . Rev. Mat. Univ. Complut. Madr. 9, 275–287 (1996)Albanese, A.A., Bonet, J., Ricker, W.J.: Mean ergodic operators in Fréchet spaces. Ann. Acad. Sci. Fenn. Math. 34, 401–436 (2009)Albanese, A.A., Bonet, J., Ricker, W.J.: On mean ergodic operators. In: Curbera, G.P. (eds.) Vector Measures, Integration and Related Topics. Operator Theory: Advances and Applications, vol. 201, pp. 1–20. Birkhäuser, Basel (2010)Albanese, A.A., Bonet, J., Ricker, W.J.: $$C_0$$ C 0 -semigroups and mean ergodic operators in a class of Fréchet spaces. J. Math. Anal. Appl. 365, 142–157 (2010)Albanese, A.A., Bonet, J., Ricker, W.J.: Convergence of arithmetic means of operators in Fréchet spaces. J. Math. Anal. Appl. 401, 160–173 (2013)Bayart, F., Matheron, E.: Dynamics of linear operators. Cambridge Tracts in Mathematics, vol. 179. Cambridge University Press, Cambridge (2009)Bellenot, S.F., Dubinsky, E.: Fréchet spaces with nuclear Köthe quotients. Trans. Am. Math. Soc. 273, 579–594 (1982)Bonet, J., Frerick, L., Peris, A., Wengenroth, J.: Transitive and hypercyclic operators on locally convex spaces. Bull. Lond. Math. Soc. 37, 254–264 (2005)Boyd, D.W.: The spectrum of the Cesàro operator. Acta Sci. Math. (Szeged) 29, 31–34 (1968)Brown, A., Halmos, P.R., Shields, A.L.: Cesàro operators. Acta Sci. Math. (Szeged) 26, 125–137 (1965)Dierolf, S., Zarnadze, D.N.: A note on strictly regular Fréchet spaces. Arch. Math. 42, 549–556 (1984)Dunford, N., Schwartz, J.T.: Linear Operators I: General Theory (2nd Printing). Wiley-Interscience, New York (1964)Galaz Fontes, F., Solís, F.J.: Iterating the Cesàro operators. Proc. Am. Math. Soc. 136, 2147–2153 (2008)Galaz Fontes, F., Ruiz-Aguilar, R.W.: Grados de ciclicidad de los operadores de Cesàro–Hardy. Misc. Mat. 57, 103–117 (2013)González, M., León-Saavedra, F.: Cyclic behaviour of the Cesàro operator on $$L_2(0,+\infty )$$ L 2 ( 0 , + ∞ ) . Proc. Am. Math. Soc. 137, 2049–2055 (2009)Grosse-Erdmann, K.G., Peris Manguillot, A.: Linear chaos. In: Universitext. Springer, London (2011)Hardy, G.H., Littlewood, J.E., Pólya, G.: Inequalities. In: Reprint of the 1952 Edition. Cambridge Mathematical Library. Cambridge University Press, Cambridge (1988)Krengel, U.: Ergodic theorems. In: De Gruyter Studies in Mathematics, vol. 6. Walter de Gruyter Co., Berlin (1985)Leibowitz, G.M.: Spectra of finite range Cesàro operators. Acta Sci. Math. (Szeged) 35, 27–28 (1973)Leibowitz, G.M.: The Cesàro operators and their generalizations: examples in infinite-dimensional linear analysis. Am. Math. Mon. 80, 654–661 (1973)León-Saavedra, F., Piqueras-Lerena, A., Seoane-Sepúlveda, J.B.: Orbits of Cesàro type operators. Math. Nachr. 282, 764–773 (2009)Lin, M.: On the uniform ergodic theorem. Proc. Am. Math. Soc. 43, 337–340 (1974)Meise, R., Vogt, D.: Introduction to functional analysis. In: Oxford Graduate Texts in Mathematics, vol. 2. The Clarendon Press; Oxford University Press, New York (1997)Metafune, G., Moscatelli, V.B.: Quojections and prequojections. In: Terzioğlu, T. (ed.) Advances in the Theory of Fréchet spaces. NATO ASI Series, vol. 287, pp. 235–254. Kluwer Academic Publishers, Dordrecht (1989)Moscatelli, V.B.: Fréchet spaces without norms and without bases. Bull. Lond. Math. Soc. 12, 63–66 (1980)Piszczek, K.: Quasi-reflexive Fréchet spaces and mean ergodicity. J. Math. Anal. Appl. 361, 224–233 (2010)Piszczek, K.: Barrelled spaces and mean ergodicity. Rev R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 104, 5–11 (2010)Yosida, K.: Functional Analysis, 6th edn. Springer, Berlin (1980

HQET at order 1/m1/m: II. Spectroscopy in the quenched approximation

Using Heavy Quark Effective Theory with non-perturbatively determined parameters in a quenched lattice calculation, we evaluate the splittings between the ground state and the first two radially excited states of the $B_s$ system at static order. We also determine the splitting between first excited and ground state, and between the $B_s^*$ and $B_s$ ground states to order $1/m_b$. The Generalized Eigenvalue Problem and the use of all-to-all propagators are important ingredients of our approach.Comment: (1+18) pages, 3 figures (4 pdf files); pdflatex; v2: corrections to table 1, results unaffecte

The nation and the family: the impact of national identification and perceived importance of family values on homophobic attitudes in Lithuania and Scotland

The meanings attached to the nation can be consequential for group members’ attitudes and beliefs. We examined how national identity definition can influence the extent of individuals’ homophobia with 159 Lithuanian and 176 Scottish university students who completed a questionnaire which measured their national identification, homophobia, and the extent to which they felt traditional family values were central to their nation’s identity. Consistent with nation-wide differences in the significance given to the family, Lithuanian participants perceived family values to be more important for their national identity and expressed higher levels of homophobia than did Scottish participants. Moreover, the relationship between level of national identification and homophobia was stronger in Lithuania than in Scotland. Analyses revealed that the perceived importance of family values helped explain the difference between homophobia levels in Lithuania and Scotland. In both sites we found an indirect effect of national identification on homophobia via the perceived importance of family values, but this effect was significantly stronger for Lithuanian participants. These findings illustrate the ways in which identification with the nation is relevant to attitudes concerning sexuality, and how this varies according to national context. Our work indicates that LGBT rights campaigns should be informed by the knowledge that homophobia may be perpetuated by national valorisation of the family

Biomass in the manufacture of industrial products—the use of proteins and amino acids

The depletion in fossil feedstocks, increasing oil prices, and the ecological problems associated with CO2 emissions are forcing the development of alternative resources for energy, transport fuels, and chemicals: the replacement of fossil resources with CO2 neutral biomass. Allied with this, the conversion of crude oil products utilizes primary products (ethylene, etc.) and their conversion to either materials or (functional) chemicals with the aid of co-reagents such as ammonia and various process steps to introduce functionalities such as -NH2 into the simple structures of the primary products. Conversely, many products found in biomass often contain functionalities. Therefore, it is attractive to exploit this to bypass the use, and preparation of, co-reagents as well as eliminating various process steps by utilizing suitable biomass-based precursors for the production of chemicals. It is the aim of this mini-review to describe the scope of the possibilities to generate current functionalized chemical materials using amino acids from biomass instead of fossil resources, thereby taking advantage of the biomass structure in a more efficient way than solely utilizing biomass for the production of fuels or electricity

The elements of human cyclin D1 promoter and regulation involved

Cyclin D1 is a cell cycle machine, a sensor of extracellular signals and plays an important role in G1-S phase progression. The human cyclin D1 promoter contains multiple transcription factor binding sites such as AP-1, NF-қB, E2F, Oct-1, and so on. The extracellular signals functions through the signal transduction pathways converging at the binding sites to active or inhibit the promoter activity and regulate the cell cycle progression. Different signal transduction pathways regulate the promoter at different time to get the correct cell cycle switch. Disorder regulation or special extracellular stimuli can result in cell cycle out of control through the promoter activity regulation. Epigenetic modifications such as DNA methylation and histone acetylation may involved in cyclin D1 transcriptional regulation

Measurement of the muon flux at the SND@LHC experiment

The Scattering and Neutrino Detector at the LHC (SND@LHC) started taking data at the beginning of Run 3 of the LHC. The experiment is designed to perform measurements with neutrinos produced in proton-proton collisions at the LHC in an energy range between 100 GeV and 1 TeV. It covers a previously unexplored pseudo-rapidity range of 7.2 < η< 8.4 . The detector is located 480 m downstream of the ATLAS interaction point in the TI18 tunnel. It comprises a veto system, a target consisting of tungsten plates interleaved with nuclear emulsion and scintillating fiber (SciFi) trackers, followed by a muon detector (UpStream, US and DownStream, DS). In this article we report the measurement of the muon flux in three subdetectors: the emulsion, the SciFi trackers and the DownStream Muon detector. The muon flux per integrated luminosity through an 18 × 18 cm 2 area in the emulsion is: 1.5±0.1(stat)×104fb/cm2. The muon flux per integrated luminosity through a 31 × 31 cm 2 area in the centre of the SciFi is: 2.06±0.01(stat)±0.12(sys)×104fb/cm2 The muon flux per integrated luminosity through a 52 × 52 cm 2 area in the centre of the downstream muon system is: 2.35±0.01(stat)±0.10(sys)×104fb/cm2 The total relative uncertainty of the measurements by the electronic detectors is 6 % for the SciFi and 4 % for the DS measurement. The Monte Carlo simulation prediction of these fluxes is 20–25 % lower than the measured values

Comorbid mental disorders in substance users from a single catchment area - a clinical study

<p>Abstract</p> <p>Background</p> <p>The optimal treatment of patients with substance use disorders (SUDs) requires an awareness of their comorbid mental disorders and vice versa. The prevalence of comorbidity in first-time-admitted SUD patients has been insufficiently studied. Diagnosing comorbidity in substance users is complicated by symptom overlap, symptom fluctuations, and the limitations of the assessment methods. The aim of this study was to diagnose all mental disorders in substance users living in a single catchment area, without any history of treatment for addiction or psychiatric disorders, admitted consecutively to the specialist health services. The prevalence of substance-induced versus substance-independent disorders according to the Diagnostic and Statistical Manual of Mental Disorders, Fourth Edition (DSM-IV), in SUD patients will be described.</p> <p>Methods</p> <p>First-time consecutively admitted patients from a single catchment area, aged 16 years or older, admitted to addiction clinics or departments of psychiatry as outpatients or inpatients will be screened for substance-related problems using the Alcohol Use Disorder Identification Test and the Drug Use Disorder Identification Test. All patients with scores above the cutoff value will be asked to participate in the study. The patients included will be diagnosed for SUD and other axis I disorders by a psychiatrist using the Psychiatric Research Interview for Substance and Mental Disorders. This interview was designed for the diagnosis of primary and substance-induced disorders in substance users. Personality disorders will be assessed according to the Structured Clinical Interview for DSM-IV axis II disorders. The Symptom Checklist-90-Revised, the Inventory of Depressive Symptoms, the Montgomery Asberg Depression Rating Scale, the Young Mania Rating Scale, and the Angst Hypomania Check List will be used for additional diagnostic assessments. The sociodemographic data will be recorded with the Stanley Foundation's Network Entry Questionnaire. Biochemical assessments will reveal somatic diseases that may contribute to the patient's symptoms.</p> <p>Discussion</p> <p>This study is unique because the material represents a complete sample of first-time-admitted treatment seekers with SUD from a single catchment area. Earlier studies have not focused on first-time-admitted patients, so chronically ill patients, may have been overrepresented in those samples. This study will contribute new knowledge about mental disorders in first-time-admitted SUD patients.</p

Observation of Collider Muon Neutrinos with the SND@LHC Experiment

We report the direct observation of muon neutrino interactions with the SND@LHC detector at the Large Hadron Collider. A dataset of proton-proton collisions at √ s = 13.6 TeV collected by SND@LHC in 2022 is used, corresponding to an integrated luminosity of 36.8 fb − 1 . The search is based on information from the active electronic components of the SND@LHC detector, which covers the pseudorapidity region of 7.2 < η < 8.4 , inaccessible to the other experiments at the collider. Muon neutrino candidates are identified through their charged-current interaction topology, with a track propagating through the entire length of the muon detector. After selection cuts, 8 ν μ interaction candidate events remain with an estimated background of 0.086 events, yielding a significance of about 7 standard deviations for the observed ν μ signal

The SHiP experiment at the proposed CERN SPS Beam Dump Facility

The Search for Hidden Particles (SHiP) Collaboration has proposed a general-purpose experimental facility operating in beam-dump mode at the CERN SPS accelerator to search for light, feebly interacting particles. In the baseline configuration, the SHiP experiment incorporates two complementary detectors. The upstream detector is designed for recoil signatures of light dark matter (LDM) scattering and for neutrino physics, in particular with tau neutrinos. It consists of a spectrometer magnet housing a layered detector system with high-density LDM/neutrino target plates, emulsion-film technology and electronic high-precision tracking. The total detector target mass amounts to about eight tonnes. The downstream detector system aims at measuring visible decays of feebly interacting particles to both fully reconstructed final states and to partially reconstructed final states with neutrinos, in a nearly background-free environment. The detector consists of a 50 m long decay volume under vacuum followed by a spectrometer and particle identification system with a rectangular acceptance of 5 m in width and 10 m in height. Using the high-intensity beam of 400 GeV protons, the experiment aims at profiting from the 4 x 10(19) protons per year that are currently unexploited at the SPS, over a period of 5-10 years. This allows probing dark photons, dark scalars and pseudo-scalars, and heavy neutral leptons with GeV-scale masses in the direct searches at sensitivities that largely exceed those of existing and projected experiments. The sensitivity to light dark matter through scattering reaches well below the dark matter relic density limits in the range from a few MeV/c(2) up to 100 MeV-scale masses, and it will be possible to study tau neutrino interactions with unprecedented statistics. This paper describes the SHiP experiment baseline setup and the detector systems, together with performance results from prototypes in test beams, as it was prepared for the 2020 Update of the European Strategy for Particle Physics. The expected detector performance from simulation is summarised at the end

Preparation of HCPT-Loaded Nanoneedles with Pointed Ends for Highly Efficient Cancer Chemotherapy

The high-aspect-ratio nanoparticles were proved to be internalized much more rapidly and efficiently by cancer cells than the nanoparticles with an equal aspect ratio. Herein, a kind of high-aspect ratio, pointed-end nanoneedles (NDs) with a high drug loading (15.04 %) and the prolonged drug release profile were fabricated with an anti-tumor drug—10-hydroxycamptothecin (HCPT)—via an ultrasound-assisted emulsion crystallization technique. It is surprising to see that the cellular internalization of NDs with an average length of 5 μm and an aspect ratio of about 12:1 was even much faster and higher than that of nanorods with the same size and the nanospheres with a much smaller size of 150 nm. The results further validated that cellular internalization of the nanoparticles exhibited a strong shape-dependent effect, and cellular uptake may favor the particles with sharp ends as well as a high-aspect ratio instead of particle size. The NDs with enhanced cytotoxicity would lead to a promising sustained local drug delivery system for highly efficient anticancer therapy. More importantly, the fabrication of NDs opens a door to design new formulations of nanoneedle drug delivery systems for highly efficient cancer. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s11671-016-1491-9) contains supplementary material, which is available to authorized users