Thermostatistics of deformed bosons and fermions

Based on the q-deformed oscillator algebra, we study the behavior of the mean occupation number and its analogies with intermediate statistics and we obtain an expression in terms of an infinite continued fraction, thus clarifying successive approximations. In this framework, we study the thermostatistics of q-deformed bosons and fermions and show that thermodynamics can be built on the formalism of q-calculus. The entire structure of thermodynamics is preserved if ordinary derivatives are replaced by the use of an appropriate Jackson derivative and q-integral. Moreover, we derive the most important thermodynamic functions and we study the q-boson and q-fermion ideal gas in the thermodynamic limit.Comment: 14 pages, 2 figure

Narrow genetic base in forest restoration with holm oak (Quercus ilex L.) in Sicily

In order to empirically assess the effect of actual seed sampling strategy on genetic diversity of holm oak (Quercus ilex) forestations in Sicily, we have analysed the genetic composition of two seedling lots (nursery stock and plantation) and their known natural seed origin stand by means of six nuclear microsatellite loci. Significant reduction in genetic diversity and significant difference in genetic composition of the seedling lots compared to the seed origin stand were detected. The female and the total effective number of parents were quantified by means of maternity assignment of seedlings and temporal changes in allele frequencies. Extremely low effective maternity numbers were estimated (Nfe $\approx$ 2-4) and estimates accounting for both seed and pollen donors gave also low values (Ne $\approx$ 35-50). These values can be explained by an inappropriate forestry seed harvest strategy limited to a small number of spatially close trees

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 Cϕ : A (R) → A (R) for a real analytic self map ϕ : R → R as well as an isomorphic description of corresponding eigenspaces. We completely characterize those ϕ for which Abel’s equation f ◦ ϕ = f + 1 has a real analytic solution on the real line. We find cases when the operator Cϕ has roots using a constructed embedding of ϕ 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 d’une function au moyen d’une equation qui ne contient qu’une seule variable. In: Oeuvres Complètes, vol. II, pp. 246-248. Christiania (1881)Baker I.N.: Zusammensetzung ganzer Funktionen. Math. Z. 69, 121–163 (1958)Baker I.N.: Permutable power series and regular iteration. J. Aust. Math. Soc. 2, 265–294 (1961)Baker I.N.: Permutable entire functions. Math. Z. 79, 243–249 (1962)Baker I.N.: Fractional iteration near a fixpoint of multiplier 1. J. Aust. Math. Soc. 4, 143–148 (1964)Baker I.N.: Non-embeddable functions with a fixpoint of multiplier 1. Math. Z. 99, 337–384 (1967)Baker I.N.: On a class of nonembeddable entire functions. J. Ramanujan Math. Soc. 3, 131–159 (1988)Baron K., Jarczyk W.: Recent results on functional equations in a single variable, perspectives and open problems. Aequ. Math. 61, 1–48 (2001)Belitskii G., Lyubich Y.: The Abel equation and total solvability of linear functional equations. Studia Math. 127, 81–97 (1998)Belitskii G., Lyubich Yu.: The real analytic solutions of the Abel functional equation. Studia Math. 134, 135–141 (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, 153–174 (2000)Bonet J., Domański P.: Power bounded composition operators on spaces of analytic functions. Collect. Math. 62, 69–83 (2011)Bonet J., Domański P.: Hypercyclic composition operators on spaces of real analytic functions. Math. Proc. Camb. Philos. Soc. 153, 489–503 (2012)Bracci, F., Poggi-Corradini, P.: On Valiron’s theorem. In: Proceedings of Future Trends in Geometric Function Theory. RNC Workshop Jyväskylä 2003, Rep. Univ. Jyväskylä Dept. Math. Stat., vol. 92, pp. 39–55 (2003)Contreras, M.D.: Iteración de funciones analíticas en el disco unidad. Universidad de Sevilla (2009). (Preprint)Contreras M.D., Díaz-Madrigal S., Pommerenke Ch.: Some remarks on the Abel equation in the unit disk. J. Lond. Math. Soc. 75(2), 623–634 (2007)Cowen C.: Iteration and the solution of functional equations for functions analytic in the unit disc. Trans. Am. Math. Soc. 265, 69–95 (1981)Cowen C.C., MacCluer B.D.: Composition operators on spaces of analytic functions. In: Studies in Advanced Mathematics. CRC Press, Boca Raton (1995)Domański, 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. 3–47. Am. Math. Soc., Providence (2012)Domański P., Goliński M., Langenbruch M.: A note on composition operators on spaces of real analytic functions. Ann. Polon. Math. 103, 209–216 (2012)P. Domański M. Langenbruch 2003 Language="En"Composition operators on spaces of real analytic functions Math. Nachr. 254–255, 68–86 (2003)Domański P., Langenbruch M.: Coherent analytic sets and composition of real analytic functions. J. Reine Angew. Math. 582, 41–59 (2005)Domański P., Langenbruch M.: Composition operators with closed image on spaces of real analytic functions. Bull. Lond. Math. Soc. 38, 636–646 (2006)Domański P., Vogt D.: The space of real analytic functions has no basis. Studia Math. 142, 187–200 (2000)Fuks D.B., Rokhlin V.A.: Beginner’s 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. für Neuvorpommernund Rügen, Greifswald 57, 18–25 (1930)Heinrich T., Meise R.: A support theorem for quasianalytic functionals. Math. Nachr. 280(4), 364–387 (2007)Karlin S., McGregor J.: Embedding iterates of analytic functions with two fixed points into continuous group. Trans.Am. Math. Soc. 132, 137–145 (1968)Kneser H.: Reelle analytische Lösungen der Gleichung $${\varphi(\varphi(x))=e^x}$$ φ ( φ ( x ) ) = e x und verwandter Funktionalgleichungen. J. Reine Angew. Math. 187, 56–67 (1949)Königs, G.: Recherches sur les intégrales de certaines équations fonctionnelles. Ann. Sci. Ecole Norm. Sup. (3) 1, Supplément, 3–41 (1884)Kuczma M.: Functional Equations in a Single Variable. PWN-Polish Scientific Publishers, Warszawa (1968)Kuczma M., Choczewski B., Ger R.: Iterative Functional Equations. Cambridge University Press, Cambridge (1990)Meise R., Vogt D.: Introduction to Functional Analysis. Clarendon Press, Oxford (1997)Milnor, J.: Dynamics in One Complex Variable. Vieweg, Braunschweig (2006)Schröder E.: über iterierte Funktionen. Math. Ann. 3, 296–322 (1871)Shapiro J.H.: Composition Operators and Classical Function Theory, Universitext: Tracts in Mathematics. Springer, New York (1993)Shapiro, J.H.: Notes on the dynamics of linear operators. 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. 213–228. Am. Math. Soc., Providence (1998)Szekeres G.: Regular iteration of real and complex functions. Acta Math. 100, 203–258 (1958)Szekeres G.: Fractional iteration of exponentially growing functions. J. Aust. Math. Soc. 2, 301–320 (1961)Szekeres G.: Fractional iteration of entire and rational functions. J. Aust. Math. Soc. 4, 129–142 (1964)Szekeres G.: Abel’s equations and regular growth: variations on a theme by Abel. Exp. Math. 7, 85–100 (1998)Trappmann H., Kouznetsov D.: Uniqueness of holomorphic Abel function at a complex fixed point pair. Aequ. Math. 81, 65–76 (2011)Viro, O.: 1-manifolds. Bull. Manifold Atlas. http://www.boma.mpim-bonn.mpg.de/articles/48 (a prolonged version also http://www.map.mpim-bonn.mpg.de/1-manifolds#Differential_structures )Walker P.L.: A class of functional equations which have entire solutions. Bull. Aust. Math. Soc. 39, 351–356 (1988)Walker P.L.: The exponential of iteration of e x −1. Proc. Am. Math. Soc. 110, 611–620 (1990)Walker P.L.: On the solution of an Abelian functional equation. J. Math. Anal. Appl. 155, 93–110 (1991)Walker P.L.: Infinitely differentiable generalized logarithmic and exponential functions. Math. Comp. 57, 723–733 (1991

Test of Lorentz and CPT violation with Short Baseline Neutrino Oscillation Excesses

The sidereal time dependence of MiniBooNE electron neutrino and anti-electron neutrino appearance data are analyzed to search for evidence of Lorentz and CPT violation. An unbinned Kolmogorov-Smirnov test shows both the electron neutrino and anti-electron neutrino appearance data are compatible with the null sidereal variation hypothesis to more than 5%. Using an unbinned likelihood fit with a Lorentz-violating oscillation model derived from the Standard Model Extension (SME) to describe any excess events over background, we find that the electron neutrino appearance data prefer a sidereal time-independent solution, and the anti-electron neutrino appearance data slightly prefer a sidereal time-dependent solution. Limits of order 10E-20 GeV are placed on combinations of SME coefficients. These limits give the best limits on certain SME coefficients for muon neutrino to electron neutrino and anti-muon neutrino to anti-electron neutrino oscillations. The fit values and limits of combinations of SME coefficients are provided.Comment: 14 pages, 3 figures, and 2 tables, submitted to Physics Letters

Observation of electroweak production of Wγ with two jets in proton-proton collisions at √s = 13 TeV

A first observation is presented for the electroweak production of a W boson, a photon, and two jets in proton-proton collisions. The W boson decays are selected by requiring one identified electron or muon and an imbalance in transverse momentum. The two jets are required to have a high dijet mass and a large separation in pseudorapidity. The measurement is based on data collected with the CMS detector at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. The observed (expected) significance for this process is 4.9 (4.6) standard deviations. After combining with previously reported CMS results at 8 TeV, the observed (expected) significance is 5.3 (4.8) standard deviations. The cross section for the electroweak W$_{γjj}$ production in a restricted fiducial region is measured as 20.4 +/- 4.5 fb and the total cross section for W$_{γ}$ production in association with 2 jets in the same fiducial region is 108 +/- 16 fb. All results are in good agreement with recent theoretical predictions. Constraints are placed on anomalous quartic gauge couplings in terms of dimension-8 effective field theory operators