487 research outputs found
On permutable meromorphic functions
We study the class of functions meromorphic outside a countable closed set of essential singularities. We show that if a function in , with at least one essential singularity, permutes with a non-constant rational map , then is a Möbius map that is not conjugate to an irrational rotation. For a given function which is not a Möbius map, we show that the set of functions in that permute with Æ is countably infinite. Finally, we show that there exist transcendental meromorphic functions such that, among functions meromorphic in the plane, Æ permutes only with itself and with the identity map
Abel's Functional Equation and Eigenvalues of Composition Operators on Spaces of Real Analytic Functions
We obtain full description of eigenvalues and eigenvectors
of composition operators CÏ : A (R) â A (R) for a real analytic self
map Ï : R â R as well as an isomorphic description of corresponding
eigenspaces. We completely characterize those Ï for which Abelâs equation
f âŠ Ï = f + 1 has a real analytic solution on the real line. We find
cases when the operator CÏ has roots using a constructed embedding of
Ï into the so-called real analytic iteration semigroups.(1) The research of the authors was partially supported by MEC and FEDER Project MTM2010-15200 and MTM2013-43540-P and the work of Bonet also by GV Project Prometeo II/2013/013. The research of Domanski was supported by National Center of Science, Poland, Grant No. NN201 605340. (2) The authors are very indebted to K. Pawalowski (Poznan) for providing us with references [26,27,47] and also explaining some topological arguments of [10]. The authors are also thankful to M. Langenbruch (Oldenburg) for providing a copy of [29].Bonet Solves, JA.; Domanski, P. (2015). Abel's Functional Equation and Eigenvalues of Composition Operators on Spaces of Real Analytic Functions. Integral Equations and Operator Theory. 81(4):455-482. https://doi.org/10.1007/s00020-014-2175-4S455482814Abel, N.H.: Determination dâune function au moyen dâune equation qui ne contient quâune seule variable. In: Oeuvres ComplĂštes, vol. II, pp. 246-248. Christiania (1881)Baker I.N.: Zusammensetzung ganzer Funktionen. Math. Z. 69, 121â163 (1958)Baker I.N.: Permutable power series and regular iteration. J. Aust. Math. Soc. 2, 265â294 (1961)Baker I.N.: Permutable entire functions. Math. Z. 79, 243â249 (1962)Baker I.N.: Fractional iteration near a fixpoint of multiplier 1. J. Aust. Math. Soc. 4, 143â148 (1964)Baker I.N.: Non-embeddable functions with a fixpoint of multiplier 1. Math. Z. 99, 337â384 (1967)Baker I.N.: On a class of nonembeddable entire functions. J. Ramanujan Math. Soc. 3, 131â159 (1988)Baron K., Jarczyk W.: Recent results on functional equations in a single variable, perspectives and open problems. Aequ. Math. 61, 1â48 (2001)Belitskii G., Lyubich Y.: The Abel equation and total solvability of linear functional equations. Studia Math. 127, 81â97 (1998)Belitskii G., Lyubich Yu.: The real analytic solutions of the Abel functional equation. Studia Math. 134, 135â141 (1999)Belitskii G., Tkachenko V.: One-Dimensional Functional Equations. Springer, Basel (2003)Belitskii G., Tkachenko V.: Functional equations in real analytic functions. Studia Math. 143, 153â174 (2000)Bonet J., DomaĆski P.: Power bounded composition operators on spaces of analytic functions. Collect. Math. 62, 69â83 (2011)Bonet J., DomaĆski P.: Hypercyclic composition operators on spaces of real analytic functions. Math. Proc. Camb. Philos. Soc. 153, 489â503 (2012)Bracci, F., Poggi-Corradini, P.: On Valironâs theorem. In: Proceedings of Future Trends in Geometric Function Theory. RNC Workshop JyvĂ€skylĂ€ 2003, Rep. Univ. JyvĂ€skylĂ€ Dept. Math. Stat., vol. 92, pp. 39â55 (2003)Contreras, M.D.: IteraciĂłn de funciones analĂticas en el disco unidad. Universidad de Sevilla (2009). (Preprint)Contreras M.D., DĂaz-Madrigal S., Pommerenke Ch.: Some remarks on the Abel equation in the unit disk. J. Lond. Math. Soc. 75(2), 623â634 (2007)Cowen C.: Iteration and the solution of functional equations for functions analytic in the unit disc. Trans. Am. Math. Soc. 265, 69â95 (1981)Cowen C.C., MacCluer B.D.: Composition operators on spaces of analytic functions. In: Studies in Advanced Mathematics. CRC Press, Boca Raton (1995)DomaĆski, P.: Notes on real analytic functions and classical operators. In: Topics in Complex Analysis and Operator Theory (Winter School in Complex Analysis and Operator Theory, Valencia, February 2010). Contemporary Math., vol. 561, pp. 3â47. Am. Math. Soc., Providence (2012)DomaĆski P., GoliĆski M., Langenbruch M.: A note on composition operators on spaces of real analytic functions. Ann. Polon. Math. 103, 209â216 (2012)P. DomaĆski M. Langenbruch 2003 Language="En"Composition operators on spaces of real analytic functions Math. Nachr. 254â255, 68â86 (2003)DomaĆski P., Langenbruch M.: Coherent analytic sets and composition of real analytic functions. J. Reine Angew. Math. 582, 41â59 (2005)DomaĆski P., Langenbruch M.: Composition operators with closed image on spaces of real analytic functions. Bull. Lond. Math. Soc. 38, 636â646 (2006)DomaĆski P., Vogt D.: The space of real analytic functions has no basis. Studia Math. 142, 187â200 (2000)Fuks D.B., Rokhlin V.A.: Beginnerâs Course in Topology. Springer, Berlin (1984)Greenberg M.J.: Lectures on Algebraic Topology. W. A. Benjamin Inc., Reading (1967)Hammond, C.: On the norm of a composition operator, PhD. dissertation, Graduate Faculty of the University of Virginia (2003). http://oak.conncoll.edu/cnham/Thesis.pdfHandt T., Kneser H.: Beispiele zur Iteration analytischer Funktionen. Mitt. Naturwiss. Ver. fĂŒr Neuvorpommernund RĂŒgen, Greifswald 57, 18â25 (1930)Heinrich T., Meise R.: A support theorem for quasianalytic functionals. Math. Nachr. 280(4), 364â387 (2007)Karlin S., McGregor J.: Embedding iterates of analytic functions with two fixed points into continuous group. Trans.Am. Math. 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Lecture Notes. http://www.mth.msu.edu/~hapiro/Pubvit/Downloads/LinDynamics/LynDynamics.htmlShapiro, J.H.: Composition operators and Schröder functional equation. In: Studies on Composition Operators (Laramie, WY, 1996), Contemp. Math., vol. 213, pp. 213â228. Am. Math. Soc., Providence (1998)Szekeres G.: Regular iteration of real and complex functions. Acta Math. 100, 203â258 (1958)Szekeres G.: Fractional iteration of exponentially growing functions. J. Aust. Math. Soc. 2, 301â320 (1961)Szekeres G.: Fractional iteration of entire and rational functions. J. Aust. Math. Soc. 4, 129â142 (1964)Szekeres G.: Abelâs equations and regular growth: variations on a theme by Abel. Exp. Math. 7, 85â100 (1998)Trappmann H., Kouznetsov D.: Uniqueness of holomorphic Abel function at a complex fixed point pair. Aequ. Math. 81, 65â76 (2011)Viro, O.: 1-manifolds. Bull. 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The relationship between duodenal ulcer depth and gastric acid output
In the course of 750 routine duodenoscopies. 119 patients with duodenal ulcers who also had gastric acid tests, were assessed. A relationship was found between the depth of duodenal ulcers and the height of the gastric acid output. In both Black and Indian patients, maximal acid output was significantly higher in patients with deep duodenal ulcers compared with flat duodenal ulcers. There were more Blacks with deep ulcers, and more Indians with flat ulcers.S. Afr. Med. J., 48, 1405 (1974)
On quantum deformation of conformal symmetry: Gauge dependence via field redefinitions
The effective action in gauge theories is known to depend on a choice of
gauge fixing conditions. This dependence is such that any change of gauge
conditions is equivalent to a field redefinition in the effective action. In
this sense, the quantum deformation of conformal symmetry in the N = 4 super
Yang-Mills theory, which was computed in 't Hooft gauge in hep-th/9808039 and
hep-th/0203236, is gauge dependent. The deformation is an intrinsic property of
the theory in that it cannot be eliminated by a local choice of gauge (although
we sketch a field redefinition induced by a nonlocal gauge which, on the
Coulomb branch of the theory, converts the one-loop quantum-corrected conformal
transformations to the classical ones). We explicitly compute the deformed
conformal symmetry in R_\xi gauge. The conformal transformation law of the
gauge field turns out to be \xi-independent. We construct the scalar field
redefinition which relates the 't Hooft and R_\xi gauge results. A unique
feature of 't Hooft gauge is that it makes it possible to consistently truncate
the one-loop conformal deformation to the terms of first order in derivatives
of the fields such that the corresponding transformations form a field
realization of the conformal algebra.Comment: 14 pages, latex, no figures; references and comments added, the final
version to appear in PL
Bifurcations in the Space of Exponential Maps
This article investigates the parameter space of the exponential family
. We prove that the boundary (in \C) of every
hyperbolic component is a Jordan arc, as conjectured by Eremenko and Lyubich as
well as Baker and Rippon. In fact, we prove the stronger statement that the
exponential bifurcation locus is connected in \C, which is an analog of
Douady and Hubbard's celebrated theorem that the Mandelbrot set is connected.
We show furthermore that is not accessible through any nonhyperbolic
("queer") stable component.
The main part of the argument consists of demonstrating a general "Squeezing
Lemma", which controls the structure of parameter space near infinity. We also
prove a second conjecture of Eremenko and Lyubich concerning bifurcation trees
of hyperbolic components.Comment: 29 pages, 3 figures. The main change in the new version is the
introduction of Theorem 1.1 on the connectivity of the bifurcation locus,
which follows from the results of the original version but was not explicitly
stated. Also, some small revisions have been made and references update
Search for narrow resonances in e+ e- annihilation between 1.85 and 3.1 GeV with the KEDR Detector
We report results of a search for narrow resonances in e+ e- annihilation at
center-of-mass energies between 1.85 and 3.1 GeV performed with the KEDR
detector at the VEPP-4M e+ e- collider. The upper limit on the leptonic width
of a narrow resonance Gamma(R -> ee) Br(R -> hadr) < 120 eV has been obtained
(at 90 % C.L.)
Search for direct production of charginos and neutralinos in events with three leptons and missing transverse momentum in âs = 7 TeV pp collisions with the ATLAS detector
A search for the direct production of charginos and neutralinos in final states with three electrons or muons and missing transverse momentum is presented. The analysis is based on 4.7 fbâ1 of protonâproton collision data delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with Standard Model expectations in three signal regions that are either depleted or enriched in Z-boson decays. Upper limits at 95% confidence level are set in R-parity conserving phenomenological minimal supersymmetric models and in simplified models, significantly extending previous results
Jet size dependence of single jet suppression in lead-lead collisions at sqrt(s(NN)) = 2.76 TeV with the ATLAS detector at the LHC
Measurements of inclusive jet suppression in heavy ion collisions at the LHC
provide direct sensitivity to the physics of jet quenching. In a sample of
lead-lead collisions at sqrt(s) = 2.76 TeV corresponding to an integrated
luminosity of approximately 7 inverse microbarns, ATLAS has measured jets with
a calorimeter over the pseudorapidity interval |eta| < 2.1 and over the
transverse momentum range 38 < pT < 210 GeV. Jets were reconstructed using the
anti-kt algorithm with values for the distance parameter that determines the
nominal jet radius of R = 0.2, 0.3, 0.4 and 0.5. The centrality dependence of
the jet yield is characterized by the jet "central-to-peripheral ratio," Rcp.
Jet production is found to be suppressed by approximately a factor of two in
the 10% most central collisions relative to peripheral collisions. Rcp varies
smoothly with centrality as characterized by the number of participating
nucleons. The observed suppression is only weakly dependent on jet radius and
transverse momentum. These results provide the first direct measurement of
inclusive jet suppression in heavy ion collisions and complement previous
measurements of dijet transverse energy imbalance at the LHC.Comment: 15 pages plus author list (30 pages total), 8 figures, 2 tables,
submitted to Physics Letters B. All figures including auxiliary figures are
available at
http://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/HION-2011-02
Search for displaced vertices arising from decays of new heavy particles in 7 TeV pp collisions at ATLAS
We present the results of a search for new, heavy particles that decay at a
significant distance from their production point into a final state containing
charged hadrons in association with a high-momentum muon. The search is
conducted in a pp-collision data sample with a center-of-mass energy of 7 TeV
and an integrated luminosity of 33 pb^-1 collected in 2010 by the ATLAS
detector operating at the Large Hadron Collider. Production of such particles
is expected in various scenarios of physics beyond the standard model. We
observe no signal and place limits on the production cross-section of
supersymmetric particles in an R-parity-violating scenario as a function of the
neutralino lifetime. Limits are presented for different squark and neutralino
masses, enabling extension of the limits to a variety of other models.Comment: 8 pages plus author list (20 pages total), 8 figures, 1 table, final
version to appear in Physics Letters
Measurement of the polarisation of W bosons produced with large transverse momentum in pp collisions at sqrt(s) = 7 TeV with the ATLAS experiment
This paper describes an analysis of the angular distribution of W->enu and
W->munu decays, using data from pp collisions at sqrt(s) = 7 TeV recorded with
the ATLAS detector at the LHC in 2010, corresponding to an integrated
luminosity of about 35 pb^-1. Using the decay lepton transverse momentum and
the missing transverse energy, the W decay angular distribution projected onto
the transverse plane is obtained and analysed in terms of helicity fractions
f0, fL and fR over two ranges of W transverse momentum (ptw): 35 < ptw < 50 GeV
and ptw > 50 GeV. Good agreement is found with theoretical predictions. For ptw
> 50 GeV, the values of f0 and fL-fR, averaged over charge and lepton flavour,
are measured to be : f0 = 0.127 +/- 0.030 +/- 0.108 and fL-fR = 0.252 +/- 0.017
+/- 0.030, where the first uncertainties are statistical, and the second
include all systematic effects.Comment: 19 pages plus author list (34 pages total), 9 figures, 11 tables,
revised author list, matches European Journal of Physics C versio
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