2,348 research outputs found

    Tensor product representation of Kothe-Bochner spaces and their dual spaces

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    We provide a tensor product representation of Kothe-Bochner function spaces of vector valued integrable functions. As an application, we show that the dual space of a Kothe-Bochner function space can be understood as a space of operators satisfying a certain extension property. We apply our results in order to give an alternate representation of the dual of the Bochner spaces of p-integrable functions and to analyze some properties of the natural norms that are defined on the associated tensor products.First and third authors are supported by grant MTM201453009-P of the Ministerio de Economia y Competitividad (Spain). Second and fourth authors are supported by grant MTM2012-36740-C02-02 of the Ministerio de Economia y Competitividad (Spain).Calabuig, JM.; Jiménez Fernández, E.; Juan Blanco, MA.; Sánchez Pérez, EA. (2016). Tensor product representation of Kothe-Bochner spaces and their dual spaces. Positivity. 20(1):155-169. https://doi.org/10.1007/s11117-015-0347-3S155169201Bochner, S.: Integration von Funktionen, deren Werte die Elemente eines Vectorraumes sind. Fundamenta Mathematicae 20, 262–276 (1933)Calabuig, J.M., Delgado, O., Juan, M.A., Sánchez, E.A.: Pérez, On the Banach lattice structure of Lw1L^1_w L w 1 of a vector measure on a δ\delta δ -ring. Collect. Math. 65, 6567–85 (2014)Calabuig, J.M., Delgado, O., Sánchez Pérez, E.A.: Factorizing operators on Banach function spaces through spaces of multiplication operators. J. Math. Anal. Appl. 364(1), 88–103 (2010)Calabuig, J.M., Gregori, P., Sánchez, E.A.: Pérez, Radon-Nikodým derivatives for vector measures belonging to Köthe function spaces. J. Math. Anal. Appl. 348, 469–479 (2008)Cerdà, J., Hudzik, H., Mastyło, M.: Geometric properties of Köthe-Bochner spaces. Math. Proc. Cambridge Philos. Soc. 120(3), 521–533 (1996)Chakraborty, N.D., Basu, S.: Spaces of p-tensor integrable functions and related Banach space properties. Real Anal. Exchange 34, 87–104 (2008)Chakraborty, N.D., Basu, S.: Integration of vector-valued functions with respect to vector measures defined on δ\delta δ -rings. Ill. J. Math. 55(2), 495–508 (2011)Defant, A., Floret, K.: Tensor norms and operator ideals. North-Holland, Amsterdam (1993)Delgado, O., Juan, M.A.: Representation of Banach lattices as Lw1L^{1}_{w} L w 1 spaces of a vector measure defined on a δ\delta - δ - ring. Bull. Belgian Math. Soc. 19, 239–256 (2012)Diestel, J., Uhl, J.J.: Vector measures. Am. Math. Soc, Providence (1977)Dobrakov, I.: On integration in Banach spaces, VII. Czechoslovak Math. J. 38, 434–449 (1988)García-Raffi, L.M., Jefferies, B.: An application of bilinear integration to quantum scattering. J. Math. Anal. Appl. 415, 394–421 (2014)Gregori Huerta, P.: Espacios de medidas vectoriales. Thesis, Universidad de Valencia, ISBN:8437060591 (2005)Jefferies, B., Okada, S.: Bilinear integration in tensor products. Rocky Mt. J. Math. 28, 517–545 (1998)Lewis, D.R.: On integrability and summability in vector spaces. Ill. J. Math. 16, 294–307 (1972)Lin, P.-K.: Köthe-Bochner function spaces. Birkhauser, Boston (2004)Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces II. Springer, Berlin (1979)Okada, S., Ricker, W.J., Sánchez Pérez, E.A.: Optimal Domains and integral extensions of operators acting in function spaces. Operator Theory Advances and Applications, vol. 180. Birkhäuser, Basel (2008)Pallu de La Barriére, R.: Integration of vector functions with respect to vector measures. Studia Univ. Babes-Bolyai Math. 43, 55–93 (1998)Rodríguez, J.: On integration of vector functions with respect to vector measures. Czechoslovak Math. J. 56, 805–825 (2006

    Impacts of climate change on plant diseases – opinions and trends

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    There has been a remarkable scientific output on the topic of how climate change is likely to affect plant diseases in the coming decades. This review addresses the need for review of this burgeoning literature by summarizing opinions of previous reviews and trends in recent studies on the impacts of climate change on plant health. Sudden Oak Death is used as an introductory case study: Californian forests could become even more susceptible to this emerging plant disease, if spring precipitations will be accompanied by warmer temperatures, although climate shifts may also affect the current synchronicity between host cambium activity and pathogen colonization rate. A summary of observed and predicted climate changes, as well as of direct effects of climate change on pathosystems, is provided. Prediction and management of climate change effects on plant health are complicated by indirect effects and the interactions with global change drivers. Uncertainty in models of plant disease development under climate change calls for a diversity of management strategies, from more participatory approaches to interdisciplinary science. Involvement of stakeholders and scientists from outside plant pathology shows the importance of trade-offs, for example in the land-sharing vs. sparing debate. Further research is needed on climate change and plant health in mountain, boreal, Mediterranean and tropical regions, with multiple climate change factors and scenarios (including our responses to it, e.g. the assisted migration of plants), in relation to endophytes, viruses and mycorrhiza, using long-term and large-scale datasets and considering various plant disease control methods

    Back reaction effects on the dynamics of heavy probes in heavy quark cloud

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    We holographically study the effect of back reaction on the hydrodynamical properties of N=4\mathcal{N} = 4 strongly coupled super Yang-Mills (SYM) thermal plasma. The back reaction we consider arises from the presence of static heavy quarks uniformly distributed over N=4\mathcal{N} = 4 SYM plasma. In order to study the hydrodynamical properties, we use heavy quark as well as heavy quark-antiquark bound state as probes and compute the jet quenching parameter, screening length and binding energy. We also consider the rotational dynamics of heavy probe quark in the back-reacted plasma and analyse associated energy loss. We observe that the presence of back reaction enhances the energy-loss in the thermal plasma. Finally, we show that there is no effect of angular drag on the rotational motion of quark-antiquark bound state probing the back reacted thermal plasma.Comment: 29 pages, 21 figure

    Accreting Millisecond X-Ray Pulsars

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    Accreting Millisecond X-Ray Pulsars (AMXPs) are astrophysical laboratories without parallel in the study of extreme physics. In this chapter we review the past fifteen years of discoveries in the field. We summarize the observations of the fifteen known AMXPs, with a particular emphasis on the multi-wavelength observations that have been carried out since the discovery of the first AMXP in 1998. We review accretion torque theory, the pulse formation process, and how AMXP observations have changed our view on the interaction of plasma and magnetic fields in strong gravity. We also explain how the AMXPs have deepened our understanding of the thermonuclear burst process, in particular the phenomenon of burst oscillations. We conclude with a discussion of the open problems that remain to be addressed in the future.Comment: Review to appear in "Timing neutron stars: pulsations, oscillations and explosions", T. Belloni, M. Mendez, C.M. Zhang Eds., ASSL, Springer; [revision with literature updated, several typos removed, 1 new AMXP added

    Identification of multiple root disease resistant wheat germplasm against cereal nematodes and dryland root rot and their validation in regions of economic importance

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    História da literatura portuguesa coordenada por Giulia Lanciani - primeiras páginas de um total pp. 7-108)História literária do século XVIII portuguêsGoverno de Portuga

    Quark Number Susceptibility with Finite Chemical Potential in Holographic QCD

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    We study the quark number susceptibility in holographic QCD with a finite chemical potential or under an external magnetic field at finite temperature. We first consider the quark number susceptibility with the chemical potential. We observe that approaching the critical temperature from high temperature regime, the quark number susceptibility divided by temperature square develops a peak as we increase the chemical potential, which confirms recent lattice QCD results. We discuss this behavior in connection with the existence of the critical end point in the QCD phase diagram. We also consider the quark number susceptibility under the external magnetic field. We predict that the quark number susceptibility exhibits a blow-up behavior at low temperature as we raise the value of the magnetic field. We finally spell out some limitations of our study.Comment: 25 pages, 3 figures, published versio

    Enumerating Pathways of Proton Abstraction Based on a Spatial and Electrostatic Analysis of Residues in the Catalytic Site

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    The pathways of proton abstraction (PA), a key aspect of most catalytic reactions, is often controversial and highly debated. Ultrahigh-resolution diffraction studies, molecular dynamics, quantum mechanics and molecular mechanic simulations are often adopted to gain insights in the PA mechanisms in enzymes. These methods require expertise and effort to setup and can be computationally intensive. We present a push button methodology – Proton abstraction Simulation (PRISM) – to enumerate the possible pathways of PA in a protein with known 3D structure based on the spatial and electrostatic properties of residues in the proximity of a given nucleophilic residue. Proton movements are evaluated in the vicinity of this nucleophilic residue based on distances, potential differences, spatial channels and characteristics of the individual residues (polarity, acidic, basic, etc). Modulating these parameters eliminates their empirical nature and also might reveal pathways that originate from conformational changes. We have validated our method using serine proteases and concurred with the dichotomy in PA in Class A β-lactamases, both of which are hydrolases. The PA mechanism in a transferase has also been corroborated. The source code is made available at www.sanchak.com/prism
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