325 research outputs found
Nuclear Effects on Heavy Boson Production at RHIC and LHC
We predict W and Z transverse momentum distributions from proton-proton and
nuclear collisions at RHIC and LHC. A resummation formalism with power
corrections to the renormalization group equations is used. The dependence of
the resummed QCD results on the non-perturbative input is very weak for the
systems considered. Shadowing effects are discussed and found to be unimportant
at RHIC, but important for LHC. We study the enhancement of power corrections
due to multiple scattering in nuclear collisions and numerically illustrate the
weak effects of the dependence on the nuclear mass.Comment: 21 pages, 11 figure
Superposition operators between weighted Banach spaces of analytic functions of controlled growth
The final publication is available at Springer via: http://dx.doi.org/10.1007/s00605-012-0441-6[EN] We characterize the entire functions which transform a weighted Banach space of holomorphic functions on the disc of type Hâ into another such space by superposition. We also show that all the superposition operators induced by such entire functions map bounded sets into bounded sets and are continuous. Superposition operators that map bounded sets into relatively compact sets are also considered. © 2012 Springer-Verlag Wien.The research of Bonet was partially supported by MICINN and FEDER Project MTM2010-15200, by GV project Prometeo/2008/101, and by ACOMP/2012/090. The research of Vukotic was partially supported by MICINN grant MTM2009-14694-C02-01, Spain and by the European ESF Network HCAA ("Harmonic and Complex Analysis and Its Applications").Bonet Solves, JA.; VukotiÄ, D. (2013). Superposition operators between weighted Banach spaces of analytic functions of controlled growth. Monatshefte fĂŒr Mathematik. 170(3-4):311-323. https://doi.org/10.1007/s00605-012-0441-6S3113231703-4Ălvarez, V., MĂĄrquez, M.A., VukotiÄ, D.: Superposition operators between the Bloch space and Bergman spaces. Ark. Mat. 42, 205â216 (2004)Appell, J., Zabrejko, P.P.: Nonlinear Superposition Operators, Cambridge Tracts in Mathematics 95. Cambridge University Press, London (1990)Appell, J., Zabrejko, P.P.: Remarks on the superposition operator problem in various function spaces. Complex Var. Elliptic Equ. 55(8â10), 727â737 (2010)Bierstedt, K.D., Bonet, J., Galbis, A.: Weighted spaces of holomorphic functions on bounded domains. Michigan Math. J. 40, 271â297 (1993)Bierstedt, K.D., Bonet, J., Taskinen, J.: Associated weights and spaces of holomorphic functions. Studia Math. 127, 137â168 (1998)Bonet, J., DomaĆski, P., Lindström, M.: Essential norm and weak compactness of composition operators on weighted Banach spaces of analytic functions. Can. Math. Bull. 42(2), 139â148 (1999)Bonet, J., DomaĆski, P., Lindström, M., Taskinen, J.: Composition operators between weighted Banach spaces of analytic functions. J. Aust. Math. Soc. (Ser. A) 64, 101â118 (1998)Boyd, C., Rueda, P.: Holomorphic superposition operators between Banach function spaces. Preprint (2011)Boyd, C., Rueda, P.: Superposition operators between weighted spaces of analytic functions. Preprint (2011)Buckley, S.M., FernĂĄndez, J.L., VukotiÄ, D.: Superposition operators on Dirichlet type spaces. In: Papers on Analysis: A Volume dedicaed to Olli Martio on the occasion of his 60th birthday. Rep. Univ. JyvĂ€skyla Dept. Math. Stat, vol. 83, pp. 41â61. Univ. JyvĂ€skyla, JyvĂ€skyla (2001)Buckley, S.M., VukotiÄ, D.: Univalent interpolation in Besov spaces and superposition into Bergman spaces. Potential Anal. 29(1), 1â16 (2008)CĂĄmera, G.A.: Nonlinear superposition on spaces of analytic functions. In: Harmonic Analysis and Operator Theory (CarĂĄcas, 1994), Contemp. Math, vol. 189, pp. 103â116. Am. Math. Soc, Providence (1995)CĂĄmera, G.A., GimĂ©nez, J.: The nonlinear superposition operators acting on Bergman spaces. Compositio Math. 93, 23â35 (1994)Castillo, R.E., Ramos FernĂĄndez, J.C., Salazar, M.: Bounded superposition operators between Bloch-Orlicz and -Bloch spaces. Appl. Math. Comp. 218, 3441â3450 (2011)Dineen, S.: Complex Analysis in Locally Convex Spaces, vol. 57. North-Holland Math. Studies, Amsterdam (1981)Girela, D., MĂĄrquez, M.A.: Superposition operators between spaces and Hardy spaces. J. Math. Anal. Appl. 364, 463â472 (2010)Grosse-Erdmann, K.-G.: A weak criterion for vector-valued holomorphic functions. Math. Proc. Camb. Publ. Soc. 136, 399â41 (2004)Harutyunyan, A., Lusky, W.: On the boundedness of the differentiation operator between weighted spaces of holomorphic functions. Studia Math. 184, 233â247 (2008)Langenbruch, M.: Continuation of Gevrey regularity for solutions of partial differential operators. In: Functional Analysis (Trier, 1994), pp. 249â280. de Gruyter, Berlin (1996)Levin, B.Ya.: Lectures on Entire Functions. Translations of Mathematical Monographs, vol. 150, Amer. Math. Soc., Providence (1996).Lusky, W.: On weighted spaces of harmonic and holomorphic functions. J. Lond. Math. Soc. 51, 309â320 (1995)Lusky, W.: On the isomorphism classes of weighted spaces of harmonic and holomorphic functions. Studia Math. 175, 19â45 (2006)Pommerenke, Ch.: Boundary Behaviour of Conformal Maps. Springer, Berlin (1992)Ramos FernĂĄndez, J.C.: Bounded superposition operators between weighted Banach spaces of analytic functions. Preprint, Available from http://arxiv.org/abs/1203.5857Shields, A.L., Williams, D.L.: Bounded projections, duality and multipliers in spaces of analytic functions. Trans. Am. Math. Soc. 162, 287â302 (1971)VukotiÄ, D.: Integrability, growth of conformal maps, and superposition operators, Technical Report 10. Aristotle University of Thessaloniki, Department of Mathematics (2004)Xiong, C.: Superposition operators between spaces and Bloch-type spaces. Complex Var. Theory Appl. 50, 935â938 (2005)Xu, W.: Superposition operators on Bloch-type spaces. Comput. Methods Funct. Theory 7, 501â507 (2007)Zhu, K.: Operator Theory in Function Spaces, 2nd edn. Am. Math. Soc., Providence (2007
Role of the nonperturbative input in QCD resummed Drell-Yan -distributions
We analyze the role of the nonperturbative input in the Collins, Soper, and
Sterman (CSS)'s -space QCD resummation formalism for Drell-Yan transverse
momentum () distributions, and investigate the predictive power of the CSS
formalism. We find that the predictive power of the CSS formalism has a strong
dependence on the collision energy in addition to its well-known
dependence, and the dependence improves the predictive power
at collider energies. We show that a reliable extrapolation from perturbatively
resummed -space distributions to the nonperturbative large region is
necessary to ensure the correct distributions. By adding power
corrections to the renormalization group equations in the CSS formalism, we
derive a new extrapolation formalism. We demonstrate that at collider energies,
the CSS resummation formalism plus our extrapolation has an excellent
predictive power for and production at all transverse momenta . We also show that the -space resummed distributions provide a good
description of Drell-Yan data at fixed target energies.Comment: Latex, 43 pages including 15 figures; typos were correcte
Unification, KK-thresholds and the top Yukawa coupling in F-theory GUTs
In a class of F-theory SU(5) GUTs the low energy chiral mass spectrum is
obtained from rank one fermion mass textures with a hierarchical structure
organised by U(1) symmetries embedded in the exceptional E_8 group. In these
theories chiral fields reside on matter `curves' and the tree level masses are
computed from integrals of overlapping wavefuctions of the particles at the
triple intersection points. This calculation requires knowledge of the exact
form of the wavefuctions. In this work we propose a way to obtain a reliable
estimate of the various quantities which determine the strength of the Yukawa
couplings. We use previous analysis of KK threshold effects to determine the
(ratios of) heavy mass scales of the theory which are involved in the
normalization of the wave functions. We consider similar effects from the
chiral spectrum of these models and discuss possible constraints on the
emerging matter content. In this approach, we find that the Yukawa couplings
can be determined solely from the U(1) charges of the states in the
`intersection' and the torsion which is a topological invariant quantity. We
apply the results to a viable SU(5) model with minimal spectrum which satisfies
all the constraints imposed by our analysis. We use renormalization group
analysis to estimate the top and bottom masses and find that they are in
agreement with the experimental values.Comment: 28 pages, 2 figure
Fuchs versus Painlev\'e
We briefly recall the Fuchs-Painlev\'e elliptic representation of Painlev\'e
VI. We then show that the polynomiality of the expressions of the correlation
functions (and form factors) in terms of the complete elliptic integral of the
first and second kind,
and , is a straight consequence of the fact that the differential
operators corresponding to the entries of Toeplitz-like determinants, are
equivalent to the second order operator which has as solution (or,
for off-diagonal correlations to the direct sum of and ). We show
that this can be generalized, mutatis mutandis, to the anisotropic Ising model.
The singled-out second order linear differential operator being replaced
by an isomonodromic system of two third-order linear partial differential
operators associated with , the Jacobi's form of the complete elliptic
integral of the third kind (or equivalently two second order linear partial
differential operators associated with Appell functions, where one of these
operators can be seen as a deformation of ). We finally explore the
generalizations, to the anisotropic Ising models, of the links we made, in two
previous papers, between Painlev\'e non-linear ODE's, Fuchsian linear ODE's and
elliptic curves. In particular the elliptic representation of Painlev\'e VI has
to be generalized to an ``Appellian'' representation of Garnier systems.Comment: Dedicated to the : Special issue on Symmetries and Integrability of
Difference Equations, SIDE VII meeting held in Melbourne during July 200
The motion of the 2D hydrodynamic Chaplygin sleigh in the presence of circulation
We consider the motion of a planar rigid body in a potential flow with
circulation and subject to a certain nonholonomic constraint. This model is
related to the design of underwater vehicles.
The equations of motion admit a reduction to a 2-dimensional nonlinear
system, which is integrated explicitly. We show that the reduced system
comprises both asymptotic and periodic dynamics separated by a critical value
of the energy, and give a complete classification of types of the motion. Then
we describe the whole variety of the trajectories of the body on the plane.Comment: 25 pages, 7 figures. This article uses some introductory material
from arXiv:1109.321
Three-term recurrence relations for systems of Clifford algebra-valued orthogonal polynomials
Recently, systems of Clifford algebra-valued orthogonal polynomials have been studied from different points of view. We prove in this paper that for their building blocks there exist some three-term recurrence relations, similar to that for orthogonal polynomials of one real variable. As a surprising byproduct of own interest we found out that the whole construction process of Clifford algebra-valued orthogonal polynomials via Gelfand-Tsetlin basis or otherwise relies only on one and the same basic Appell sequence of polynomials.This work was supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications of the University of Aveiro, the CMAT - Research Centre of Mathematics of the University of Minho and the FCT - Portuguese Foundation for Science and Technology (âFundação para a CiËencia e a Tecnologiaâ), within projects PEst-OE/MAT/UI4106/2014 and PEst-OE/MAT/UI0013/2014.info:eu-repo/semantics/publishedVersio
Equilibrium configurations of fluids and their stability in higher dimensions
We study equilibrium shapes, stability and possible bifurcation diagrams of
fluids in higher dimensions, held together by either surface tension or
self-gravity. We consider the equilibrium shape and stability problem of
self-gravitating spheroids, establishing the formalism to generalize the
MacLaurin sequence to higher dimensions. We show that such simple models, of
interest on their own, also provide accurate descriptions of their general
relativistic relatives with event horizons. The examples worked out here hint
at some model-independent dynamics, and thus at some universality: smooth
objects seem always to be well described by both ``replicas'' (either
self-gravity or surface tension). As an example, we exhibit an instability
afflicting self-gravitating (Newtonian) fluid cylinders. This instability is
the exact analogue, within Newtonian gravity, of the Gregory-Laflamme
instability in general relativity. Another example considered is a
self-gravitating Newtonian torus made of a homogeneous incompressible fluid. We
recover the features of the black ring in general relativity.Comment: 42 pages, 11 Figures, RevTeX4. Accepted for publication in Classical
and Quantum Gravity. v2: Minor corrections and references adde
Harmonic analysis and hypercomplex function theory in co-dimension one
Fundamentals of a function theory in co-dimension one for Clifford algebra valued functions over ân+1 are considered. Special attention is given to their origins in analytic properties of holomorphic functions of one and, by some duality reasons, also of several complex variables. Due to algebraic peculiarities caused by non-commutativity of the Clifford product, generalized holomorphic functions are characterized by two different but equivalent properties: on one side by local derivability (existence of a well defined derivative related to co-dimension one) and on the other side by differentiability (existence of a local approximation by linear mappings related to dimension one). As important applications, sequences of harmonic Appell polynomials are considered whose definition and explicit analytic representations rely essentially on both dual approaches.The work of the first, second and fourth authors was supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for
Science and Technology (âFCT-Fundação para a CiĂȘncia e Tecnologiaâ), within project PEst-OE/MAT/UI4106/2013. The work of the second author was supported by Portuguese funds through the CMAT - Centre of Mathematics and FCT within the Project UID/MAT/00013/2013
Frame dragging and bending of Light in Kerr and Kerr-(anti) de Sitter spacetimes
The equations of general relativity in the form of timelike and null
geodesics that describe motion of test particles and photons in Kerr spacetime
are solved exactly including the contribution from the cosmological constant.
We then perform a systematic application of the exact solutions obtained to the
following cases. The exact solutions derived for null, spherical, polar and
non-polar orbits are applied for the calculation of frame dragging
(Lense-Thirring effect) for the orbit of a photon around the galactic centre,
assuming that the latter is a Kerr black hole for various values of the Kerr
parameter including those supported by recent observations. Unbound null polar
orbits are investigated, and an analytical expression for the deviation angle
of a polar photon orbit from the gravitational Kerr field is derived. In
addition, we present the exact solution for timelike and null equatorial
orbits. In the former case, we derive an analytical expression for the
precession of the point of closest approach (perihelion, periastron) for the
orbit of a test particle around a rotating mass whose surrounding curved
spacetime geometry is described by the Kerr field. In the latter case, we
calculate an exact expression for the deflection angle for a light ray in the
gravitational field of a rotating mass (the Kerr field). We apply this
calculation for the bending of light from the gravitational field of the
galactic centre for various values of the Kerr parameter and the impact factor.Comment: LaTeX file, 45 pages 1 figure, typos fixed, v3 published in Classical
and Quantum Gravity 22 (2005) 4391-442
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