136 research outputs found
Searches for HCl and HF in comets 103P/Hartley 2 and C/2009 P1 (Garradd) with the Herschel space observatory
HCl and HF are expected to be the main reservoirs of fluorine and chlorine
wherever hydrogen is predominantly molecular. They are found to be strongly
depleted in dense molecular clouds, suggesting freeze-out onto grains in such
cold environments. We can then expect that HCl and HF were also the major
carriers of Cl and F in the gas and icy phases of the outer solar nebula, and
were incorporated into comets. We aimed to measure the HCl and HF abundances in
cometary ices as they can provide insights on the halogen chemistry in the
early solar nebula. We searched for the J(1-0) lines of HCl and HF at 626 and
1232 GHz, respectively, using the HIFI instrument on board the Herschel Space
Observatory. HCl was searched for in comets 103P/Hartley 2 and C/2009 P1
(Garradd), whereas observations of HF were conducted in comet C/2009 P1. In
addition, observations of HO and HO lines were performed in C/2009
P1 to measure the HO production rate. Three lines of CHOH were
serendipitously observed in the HCl receiver setting. HCl is not detected,
whereas a marginal (3.6-) detection of HF is obtained. The upper limits
for the HCl abundance relative to water are 0.011% and 0.022%, for 103P and
C/2009 P1, respectively, showing that HCl is depleted with respect to the solar
Cl/O abundance by a factor more than 6 in 103P, where the error is
related to the uncertainty in the chlorine solar abundance. The marginal HF
detection obtained in C/2009 P1 corresponds to an HF abundance relative to
water of (1.80.5) 10, which is approximately consistent
with a solar photospheric F/O abundance. The observed depletion of HCl suggests
that HCl was not the main reservoir of chlorine in the regions of the solar
nebula where these comets formed. HF was possibly the main fluorine compound in
the gas phase of the outer solar nebula.Comment: Accepted for publication in Astronomy & Astrophysic
HIFI observations of warm gas in DR21: Shock versus radiative heating
The molecular gas in the DR21 massive star formation region is known to be
affected by the strong UV field from the central star cluster and by a fast
outflow creating a bright shock. The relative contribution of both heating
mechanisms is the matter of a long debate. By better sampling the excitation
ladder of various tracers we provide a quantitative distinction between the
different heating mechanisms. HIFI observations of mid-J transitions of CO and
HCO+ isotopes allow us to bridge the gap in excitation energies between
observations from the ground, characterizing the cooler gas, and existing ISO
LWS spectra, constraining the properties of the hot gas. Comparing the detailed
line profiles allows to identify the physical structure of the different
components. In spite of the known shock-excitation of H2 and the clearly
visible strong outflow, we find that the emission of all lines up to > 2 THz
can be explained by purely radiative heating of the material. However, the new
Herschel/HIFI observations reveal two types of excitation conditions. We find
hot and dense clumps close to the central cluster, probably dynamically
affected by the outflow, and a more widespread distribution of cooler, but
nevertheless dense, molecular clumps.Comment: Accepted for publication by A&
Weighted composition operators on Korenblum type spaces of analytic functions
[EN] We investigate the continuity, compactness and invertibility of weighted composition operators W-psi,W-phi: f -> psi(f circle phi) when they act on the classical Korenblum space A(-infinity) and other related Frechet or (LB)-spaces of analytic functions on the open unit disc which are defined as intersections or unions of weighted Banach spaces with sup-norms. Some results about the spectrum of these operators are presented in case the self-map phi has a fixed point in the unit disc. A precise description of the spectrum is obtained in this case when the operator acts on the Korenblum space.This research was partially supported by the research project MTM2016-76647-P and the grant BES-2017-081200.Gomez-Orts, E. (2020). Weighted composition operators on Korenblum type spaces of analytic functions. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 114(4):1-15. https://doi.org/10.1007/s13398-020-00924-1S1151144Abramovich, Y.A., Aliprantis, C.D.: An invitation to operator theory. Graduate Studies in Mathematics. Amer. Math. Soc., 50 (2002)Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator in the Fréchet spaces and . Glasgow Math. J. 59, 273–287 (2017)Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator on Korenblum type spaces of analytic functions. Collect. Math. 69(2), 263–281 (2018)Albanese, A.A., Bonet, J., Ricker, W.J.: Operators on the Fréchet sequence spaces . Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113(2), 1533–1556 (2019)Albanese, A.A., Bonet, J., Ricker, W.J.: Linear operators on the (LB)-sequence spaces . Descriptive topology and functional analysis. II, 43–67, Springer Proc. Math. Stat., 286, Springer, Cham (2019)Arendt, W., Chalendar, I., Kumar, M., Srivastava, S.: Powers of composition operators: asymptotic behaviour on Bergman, Dirichlet and Bloch spaces. J. Austral. Math. Soc. 1–32. https://doi.org/10.1017/S1446788719000235Aron, R., Lindström, M.: Spectra of weighted composition operators on weighted Banach spaces of analytic funcions. Israel J. Math. 141, 263–276 (2004)Bierstedt, K.D., Summers, W.H.: Biduals of weighted Banach spaces of analytic functions. J. Austral. Math. Soc., Ser. A, 54(1), 70–79 (1993)Bonet, J.: A note about the spectrum of composition operators induced by a rotation. RACSAM 114, 63 (2020). https://doi.org/10.1007/s13398-020-00788-5Bonet, J., Domański, P., Lindström, M., Taskinen, J.: Composition operators between weighted Banach spaces of analytic functions. J. Austral. Math. Soc., Ser. A, 64(1), 101–118 (1998)Bourdon, P.S.: Essential angular derivatives and maximum growth of Königs eigenfunctions. J. Func. Anal. 160, 561–580 (1998)Bourdon, P.S.: Invertible weighted composition operators. Proc. Am. Math. Soc. 142(1), 289–299 (2014)Carleson, L., Gamelin, T.: Complex Dynamics. Springer, Berlin (1991)Cowen, C., MacCluer, B.: Composition Operators on Spaces of Analytic Functions. CRC Press, Boca Raton, FL (1995)Contreras, M., Hernández-Díaz, A.G.: Weighted composition operators in weighted Banach spacs of analytic functions. J. Austral. Math. Soc., Ser. A 69, 41–60 (2000)Eklund, T., Galindo, P., Lindström, M.: Königs eigenfunction for composition operators on Bloch and spaces. J. Math. Anal. Appl. 445, 1300–1309 (2017)Hedenmalm, H., Korenblum, B., Zhu, K.: Theory of Bergman Spaces. Grad. Texts in Math. 199. Springer, New York (2000)Jarchow, H.: Locally Convex Spaces. Teubner, Stuttgart (1981)Kamowitz, H.: Compact operators of the form . Pac. J. Math. 80(1) (1979)Korenblum, B.: An extension of the Nevanlinna theory. Acta Math. 135, 187–219 (1975)Köthe, G.: Topological Vector Spaces II. Springer, New York Inc (1979)Lusky, W.: On the isomorphism classes of weighted spaces of harmonic and holomophic functions. Stud. Math. 75, 19–45 (2006)Meise, R., Vogt, D.: Introduction to functional analysis. Oxford Grad. Texts in Math. 2, New York, (1997)Montes-Rodríguez, A.: Weighted composition operators on weighted Banach spaces of analytic functions. J. Lond. Math. Soc. 61(3), 872–884 (2000)Queffélec, H., Queffélec, M.: Diophantine Approximation and Dirichlet series. Hindustain Book Agency, New Delhi (2013)Shapiro, J.H.: Composition Operators and Classical Function Theory. Springer, New York (1993)Shields, A.L., Williams, D.L.: Bounded projections, duality and multipliers in spaces of analytic functions. Trans. Amer. Math. Soc. 162, 287–302 (1971)Zhu, K.: Operator Theory on Function Spaces, Math. Surveys and Monographs, Amer. Math. Soc. 138 (2007
A Pettis-Type Integral and Applications to Transition Semigroups
Motivated by applications to transition semigroups, we introduce the notion
of a norming dual pair and study a Pettis-type integral on such pairs. In
particular, we establish a sufficient condition for integrability. We also
introduce and study a class of semigroups on such dual pairs which are an
abstract version of transition semigroups. Using our results, we give
conditions ensuring that a semigroup consisting of kernel operators has a
Laplace transform which also consists of kernel operators. We also provide
conditions under which a semigroup is uniquely determined by its Laplace
transform.Comment: Incorporated referee's comments; final versio
Gas morphology and energetics at the surface of PDRs: new insights with Herschel observations of NGC 7023
We investigate the physics and chemistry of the gas and dust in dense
photon-dominated regions (PDRs), along with their dependence on the
illuminating UV field. Using Herschel-HIFI observations, we study the gas
energetics in NGC 7023 in relation to the morphology of this nebula. NGC 7023
is the prototype of a PDR illuminated by a B2V star and is one of the key
targets of Herschel. Our approach consists in determining the energetics of the
region by combining the information carried by the mid-IR spectrum (extinction
by classical grains, emission from very small dust particles) with that of the
main gas coolant lines. In this letter, we discuss more specifically the
intensity and line profile of the 158 micron (1901 GHz) [CII] line measured by
HIFI and provide information on the emitting gas. We show that both the [CII]
emission and the mid-IR emission from polycyclic aromatic hydrocarbons (PAHs)
arise from the regions located in the transition zone between atomic and
molecular gas. Using the Meudon PDR code and a simple transfer model, we find
good agreement between the calculated and observed [CII] intensities. HIFI
observations of NGC 7023 provide the opportunity to constrain the energetics at
the surface of PDRs. Future work will include analysis of the main coolant line
[OI] and use of a new PDR model that includes PAH-related species.Comment: Accepted for publication in Astronomy and Astrophysics Letters
(Herschel HIFI special issue), 5 pages, 5 figure
First results on Martian carbon monoxide from Herschel/HIFI observations
We report on the initial analysis of Herschel/HIFI carbon monoxide (CO)
observations of the Martian atmosphere performed between 11 and 16 April 2010.
We selected the (7-6) rotational transitions of the isotopes ^{13}CO at 771 GHz
and C^{18}O at 768 GHz in order to retrieve the mean vertical profile of
temperature and the mean volume mixing ratio of carbon monoxide. The derived
temperature profile agrees within less than 5 K with general circulation model
(GCM) predictions up to an altitude of 45 km, however, show about 12-15 K lower
values at 60 km. The CO mixing ratio was determined as 980 \pm 150 ppm, in
agreement with the 900 ppm derived from Herschel/SPIRE observations in November
2009.Comment: Accepted for publication in Astronomy and Astrophysics (special issue
on HIFI first results); minor changes to match published versio
On the Construction of Quantum Field Theories with Factorizing S-Matrices
The subject of this thesis is a novel construction method for interacting
relativistic quantum field theories on two-dimensional Minkowski space. The
input in this construction is not a classical Lagrangian, but rather a
prescribed factorizing S-matrix, i.e. the inverse scattering problem for such
quantum field theories is studied.
For a large class of factorizing S-matrices, certain associated quantum
fields, which are localized in wedge-shaped regions of Minkowski space, are
constructed explicitely. With the help of these fields, the local observable
content of the corresponding model is defined and analyzed by employing methods
from the algebraic framework of quantum field theory.
The abstract problem in this analysis amounts to the question under which
conditions an algebra of wedge-localized observables can be used to generate a
net of local observable algebras with the right physical properties. The answer
given here uses the so-called modular nuclearity condition, which is shown to
imply the existence of local observables and the Reeh-Schlieder property.
In the analysis of the concrete models, this condition is proven for a large
family of S-matrices, including the scattering operators of the Sinh-Gordon
model and the scaling Ising model as special examples. The so constructed
models are then investigated with respect to their scattering properties. They
are shown to solve the inverse scattering problem for the considered
S-matrices, and a proof of asymptotic completeness is given.Comment: PhD thesis, Goettingen university, 2006 (advisor: D. Buchholz) 153
pages, 10 figure
The Cesàro operator on Korenblum type spaces of analytic functions
[EN] The spectrum of the CesA ro operator , which is always continuous (but never compact) when acting on the classical Korenblum space and other related weighted Fr,chet or (LB) spaces of analytic functions on the open unit disc, is completely determined. It turns out that such spaces are always Schwartz but, with the exception of the Korenblum space, never nuclear. Some consequences concerning the mean ergodicity of are deduced.The research of the first two authors was partially supported by the projects MTM2013-43540-P and MTM2016-76647-P. The second author gratefully acknowledges the support of the Alexander von Humboldt Foundation.Albanese, A.; Bonet Solves, JA.; Ricker, WJ. (2018). The Cesàro operator on Korenblum type spaces of analytic functions. Collectanea mathematica. 69(2):263-281. https://doi.org/10.1007/s13348-017-0205-7S263281692Albanese, 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.: Montel resolvents and uniformly mean ergodic semigroups of linear operators. Quaest. Math. 36, 253–290 (2013)Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator in growth Banach spaces of analytic functions. Integral Equ. Oper. Theory 86, 97–112 (2016)Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator in the Fréchet spaces ℓ p + and L p - . Glasgow Math. J. 59, 273–287 (2017)Albanese, A.A., Bonet, J., Ricker, W.J.: The Cesàro operator on power series spaces. Stud. Math. doi: 10.4064/sm8590-2-2017Aleman, A.: A class of integral operators on spaces of analytic functions, In: Proceedings of the Winter School in Operator Theory and Complex Analysis, Univ. Málaga Secr. Publ., Málaga, pp. 3–30 (2007)Aleman, A., Constantin, O.: Spectra of integration operators on weighted Bergman spaces. J. Anal. Math. 109, 199–231 (2009)Aleman, A., Peláez, J.A.: Spectra of integration operators and weighted square functions. Indiana Univ. Math. J. 61, 1–19 (2012)Aleman, A., Persson, A.-M.: Resolvent estimates and decomposable extensions of generalized Cesàro operators. J. Funct. Anal. 258, 67–98 (2010)Aleman, A., Siskakis, A.G.: An integral operator on H p . Complex Var. Theory Appl. 28, 149–158 (1995)Aleman, A., Siskakis, A.G.: Integration operators on Bergman spaces. Indiana Univ. Math. J. 46, 337–356 (1997)Barrett, D.E.: Duality between A ∞ and A - ∞ on domains with nondegenerate corners, Multivariable operator theory (Seattle, WA, 1993), pp. 77–87, Contemporary Math. Vol. 185, Amer. Math. Soc., Providence (1995)Bierstedt, K.D., Bonet, J., Galbis, A.: Weighted spaces of holomorphic functions on bounded domains. Mich. Math. J. 40, 271–297 (1993)Bierstedt, K.D., Bonet, J., Taskinen, J.: Associated weights and spaces of holomorphic functions. Stud. Math. 127, 137–168 (1998)Bierstedt, K.D., Meise, R., Summers, W.H.: A projective description of weighted inductive limits. Trans. Am. Math. Soc. 272, 107–160 (1982)Bierstedt, K.D., Summers, W.H.: Biduals of weighted Banach spaces of analytic functions. J. Aust. Math. Soc. (Ser. A) 54, 70–79 (1993)Bonet, J., Domański, P., Lindström, M., Taskinen, J.: Composition operators between weighted Banach spaces of analytic functions. J. Aust. Math. Soc. (Ser. A) 64, 101–118 (1998)Diestel, J., Jarchow, H., Tonge, A.: Absolutely Summing Operators. Cambridge University Press, Cambridge (1995)Domenig, T.: Composition operators on weighted Bergman spaces and Hardy spaces. Atomic Decompositions and Diagonal Operators, Ph.D. Thesis, University of Zürich (1997). [Zbl 0909.47025]Domenig, T.: Composition operators belonging to operator ideals. J. Math. Anal. Appl. 237, 327–349 (1999)Dunford, N., Schwartz, J.T.: Linear Operators I: General Theory. 2nd Printing. Wiley Interscience Publ., New York (1964)Edwards, R.E.: Functional Analysis. Theory and Applications. Holt, Rinehart and Winston, New York, Chicago San Francisco (1965)Grothendieck, A.: Topological Vector Spaces. Gordon and Breach, London (1973)Hedenmalm, H., Korenblum, B., Zhu, K.: Theory of Bergman Spaces. Graduate Texts in Mathematics, vol. 199. Springer, New York (2000)Jarchow, H.: Locally Convex Spaces. Teubner, Stuttgart (1981)Korenblum, B.: An extension of the Nevanlinna theory. Acta Math. 135, 187–219 (1975)Krengel, U.: Ergodic Theorems. de Gruyter Studies in Mathematics, vol. 6. Walter de Gruyter Co., Berlin (1985)Lusky, W.: On the isomorphism classes of weighted spaces of harmonic and holomorphic functions. Stud. Math. 175(1), 19–40 (2006)Meise, R., Vogt, D.: Introduction to Functional Analysis. Clarendon Press, Oxford (1997)Melikhov, S.N.: (DFS )-spaces of holomorphic functions invariant under differentiation. J. Math. Anal. Appl. 297, 577–586 (2004)Persson, A.-M.: On the spectrum of the Cesàro operator on spaces of analytic functions. J. Math. Anal Appl. 340, 1180–1203 (2008)Pietsch, A.: Nuclear Locally Convex Spaces. Springer, Berlin (1972)Shields, A.L., Williams, D.L.: Bounded projections, duality and multipliers in spaces of analytic functions. Trans. Am. Math. Soc. 162, 287–302 (1971)Siskakis, A.: Volterra operators on spaces of analytic functions—a survey. In: Proceedings of the First Advanced Course in Operator Theory and Complex Analysis, Univ. Sevilla Serc. Publ., Seville, pp. 51–68 (2006
Extendibility of bilinear forms on banach sequence spaces
[EN] We study Hahn-Banach extensions of multilinear forms defined on Banach sequence spaces. We characterize c(0) in terms of extension of bilinear forms, and describe the Banach sequence spaces in which every bilinear form admits extensions to any superspace.The second author was supported by MICINN Project MTM2011-22417.DANIEL CARANDO; Sevilla Peris, P. (2014). Extendibility of bilinear forms on banach sequence spaces. Israel Journal of Mathematics. 199(2):941-954. https://doi.org/10.1007/s11856-014-0003-9S9419541992F. Albiac and N. J. Kalton, Topics in Banach Space Theory, Graduate Texts in Mathematics, Vol. 233, Springer, New York, 2006.R. Arens, The adjoint of a bilinear operation, Proceedings of the American Mathematical Society 2 (1951), 839–848.R. Arens, Operations induced in function classes, Monatshefte für Mathematik 55 (1951), 1–19.R. M. Aron and P. D. Berner, A Hahn-Banach extension theorem for analytic mappings, Bulletin de la Société Mathématique de France 106 (1978), 3–24.S. Banach, Sur les fonctionelles linéaires, Studia Mathematica 1 (1929), 211–216.S. Banach, Théorie des opérations linéaires, (Monogr. Mat. 1) Warszawa: Subwncji Funduszu Narodowej. VII, 254 S., Warsaw, 1932.D. Carando, Extendible polynomials on Banach spaces, Journal of Mathematical Analysis and Applications 233 (1999), 359–372.D. Carando, Extendibility of polynomials and analytic functions on l p, Studia Mathematica 145 (2001), 63–73.D. Carando, V. Dimant and P. Sevilla-Peris, Limit orders and multilinear forms on lp spaces, Publications of the Research Institute for Mathematical Sciences 42 (2006), 507–522.J. M. F. Castillo, R. García, A. Defant, D. Pérez-García and J. Suárez, Local complementation and the extension of bilinear mappings, Mathematical Proceedings of the Cambridge Philosophical Society 152 (2012), 153–166.J. M. F. Castillo, R. García and J. A. Jaramillo, Extension of bilinear forms on Banach spaces, Proceedings of the American Mathematical Society 129 (2001), 3647–3656.P. Cembranos and J. Mendoza, The Banach spaces ℓ ∞(c 0) and c 0(ℓ ∞) are not isomorphic, Journal of Mathematical Analysis and Applications 367 (2010), 461–463.A. Defant and K. Floret, Tensor Norms and Operator Ideals, North-Holland Mathematics Studies, Vol. 176, North-Holland Publishing Co., Amsterdam, 1993.A. Defant and C. Michels, Norms of tensor product identities, Note di Matematica 25 (2005/06), 129–166.J. Diestel, H. Jarchow and A. Tonge, Absolutely Summing Operators, Cambridge Studies in Advanced Mathematics, Vol. 43, Cambridge University Press, Cambridge, 1995.D. J. H. Garling, On symmetric sequence spaces, Proceedings of the London Mathematical Society (3) 16 (1966), 85–106.A. Grothendieck, Résumé de la théorie métrique des produits tensoriels topologiques, Bol. Soc. Mat. São Paulo 8 (1953), 1–79.H. Hahn, Über lineare Gleichungssysteme in linearen Räumen, Journal für die Reine und Angewandte Mathematik 157 (1927), 214–229.R. C. James, Bases and reflexivity of Banach spaces, Annals of Mathematics (2) 52 (1950), 518–527.H. Jarchow, C. Palazuelos, D. Pérez-García and I. Villanueva, Hahn-Banach extension of multilinear forms and summability, Journal of Mathematical Analysis and Applications 336 (2007), 1161–1177.W. B. Johnson and L. Tzafriri, On the local structure of subspaces of Banach lattices, Israel Journal of Mathematics 20 (1975), 292–299.P. Kirwan and R. A. Ryan, Extendibility of homogeneous polynomials on Banach spaces, Proceedings of the American Mathematical Society 126 (1998), 1023–1029.J. Lindenstrauss and A. Pełczyński, Absolutely summing operators in Lp-spaces and their applications, Studia Mathematica 29 (1968), 275–326.J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces. II, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], Vol. 97, Springer-Verlag, Berlin, 1979. Function spaces.G. Pisier, Factorization of Linear Operators and Geometry of Banach Spaces, CBMS Regional Conference Series in Mathematics, Vol. 60, Published for the Conference Board of the Mathematical Sciences, Washington, DC, 1986.M. Fernndez-Unzueta and A. Prieto, Extension of polynomials defined on subspaces, Mathematical Proceedings of the Cambridge Philosophical Society 148 (2010), 505–518.W. L. C. Sargent, Some sequence spaces related to the lp spaces, Journal of the London Mathematical Society 35 (1960), 161–171.N. Tomczak-Jaegermann, Banach-Mazur Distances and Finite-Dimensional Operator Ideals, Pitman Monographs and Surveys in Pure and Applied Mathematics, Vol. 38, Longman Scientific & Technical, Harlow, 1989
Herschel measurements of the D/H and 16O/18O ratios in water in the Oort-cloud comet C/2009 P1 (Garradd)
The D/H ratio in cometary water is believed to be an important indicator of
the conditions under which icy planetesimals formed and can provide clues to
the contribution of comets to the delivery of water and other volatiles to
Earth. Available measurements suggest that there is isotopic diversity in the
comet population. The Herschel Space Observatory revealed an ocean-like ratio
in the Jupiter-family comet 103P/Hartley 2, whereas most values measured in
Oort-cloud comets are twice as high as the ocean D/H ratio. We present here a
new measurement of the D/H ratio in the water of an Oort-cloud comet. HDO,
H_2O, and H_2^18O lines were observed with high signal-to-noise ratio in comet
C/2009 P1 (Garradd) using the Herschel HIFI instrument. Spectral maps of two
water lines were obtained to constrain the water excitation. The D/H ratio
derived from the measured H_2^16O and HDO production rates is 2.06+/-0.22 X
10**-4. This result shows that the D/H in the water of Oort-cloud comets is not
as high as previously thought, at least for a fraction of the population, hence
the paradigm of a single, archetypal D/H ratio for all Oort-cloud comets is no
longer tenable. Nevertheless, the value measured in C/2009 P1 (Garradd) is
significantly higher than the Earth's ocean value of 1.558 X 10**-4. The
measured H_2^16O/H_2^18O ratio of 523+/-32 is, however, consistent with the
terrestrial value.Comment: 6 pages with 4 figures and 1 table. Accepted for publication as a
Letter in Astronomy & Astrophysic
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