Agricultural systems in Amazonia depend on the management of mycorrhizal fungi.

A large number of useful tropical plant species are dependent on mycorrhizal fungi. Without the fungal symbionts they show growth depression and lower tolerance to biotic and abiotic stresses. In plant production systems, common management practices normally result in symbiosis deficits. In tropical regions where the system of shifting cultivation is practiced, the fallow period was thought to have a positive regulating effect on the mycorrhizal situation. It's showed that between three and eight years of fallow there is an increase of the inoculum potential in the soils but the effectivity of the fungal populations remains very low in comparison to the populations from natural sites. The need to manage the mycorrhizal fungi in situ in the field is discussed

Time-Fractional Optimal Control of Initial Value Problems on Time Scales

We investigate Optimal Control Problems (OCP) for fractional systems involving fractional-time derivatives on time scales. The fractional-time derivatives and integrals are considered, on time scales, in the Riemann--Liouville sense. By using the Banach fixed point theorem, sufficient conditions for existence and uniqueness of solution to initial value problems described by fractional order differential equations on time scales are known. Here we consider a fractional OCP with a performance index given as a delta-integral function of both state and control variables, with time evolving on an arbitrarily given time scale. Interpreting the Euler--Lagrange first order optimality condition with an adjoint problem, defined by means of right Riemann--Liouville fractional delta derivatives, we obtain an optimality system for the considered fractional OCP. For that, we first prove new fractional integration by parts formulas on time scales.Comment: This is a preprint of a paper accepted for publication as a book chapter with Springer International Publishing AG. Submitted 23/Jan/2019; revised 27-March-2019; accepted 12-April-2019. arXiv admin note: substantial text overlap with arXiv:1508.0075

Pion emission from the T2K replica target: method, results and application

The T2K long-baseline neutrino oscillation experiment in Japan needs precise predictions of the initial neutrino flux. The highest precision can be reached based on detailed measurements of hadron emission from the same target as used by T2K exposed to a proton beam of the same kinetic energy of 30 GeV. The corresponding data were recorded in 2007-2010 by the NA61/SHINE experiment at the CERN SPS using a replica of the T2K graphite target. In this paper details of the experiment, data taking, data analysis method and results from the 2007 pilot run are presented. Furthermore, the application of the NA61/SHINE measurements to the predictions of the T2K initial neutrino flux is described and discussed.Comment: updated version as published by NIM

NA61/SHINE facility at the CERN SPS: beams and detector system

NA61/SHINE (SPS Heavy Ion and Neutrino Experiment) is a multi-purpose experimental facility to study hadron production in hadron-proton, hadron-nucleus and nucleus-nucleus collisions at the CERN Super Proton Synchrotron. It recorded the first physics data with hadron beams in 2009 and with ion beams (secondary 7Be beams) in 2011. NA61/SHINE has greatly profited from the long development of the CERN proton and ion sources and the accelerator chain as well as the H2 beamline of the CERN North Area. The latter has recently been modified to also serve as a fragment separator as needed to produce the Be beams for NA61/SHINE. Numerous components of the NA61/SHINE set-up were inherited from its predecessors, in particular, the last one, the NA49 experiment. Important new detectors and upgrades of the legacy equipment were introduced by the NA61/SHINE Collaboration. This paper describes the state of the NA61/SHINE facility - the beams and the detector system - before the CERN Long Shutdown I, which started in March 2013

Measurement of negatively charged pion spectra in inelastic p+p interactions at plabp_{lab} = 20, 31, 40, 80 and 158 GeV/c

We present experimental results on inclusive spectra and mean multiplicities of negatively charged pions produced in inelastic p+p interactions at incident projectile momenta of 20, 31, 40, 80 and 158 GeV/c ($\sqrt{s} =$ 6.3, 7.7, 8.8, 12.3 and 17.3 GeV, respectively). The measurements were performed using the large acceptance NA61/SHINE hadron spectrometer at the CERN Super Proton Synchrotron. Two-dimensional spectra are determined in terms of rapidity and transverse momentum. Their properties such as the width of rapidity distributions and the inverse slope parameter of transverse mass spectra are extracted and their collision energy dependences are presented. The results on inelastic p+p interactions are compared with the corresponding data on central Pb+Pb collisions measured by the NA49 experiment at the CERN SPS. The results presented in this paper are part of the NA61/SHINE ion program devoted to the study of the properties of the onset of deconfinement and search for the critical point of strongly interacting matter. They are required for interpretation of results on nucleus-nucleus and proton-nucleus collisions.Comment: Numerical results available at: https://edms.cern.ch/document/1314605 Updates in v3: Updated version, as accepted for publicatio

Measurement of Production Properties of Positively Charged Kaons in Proton-Carbon Interactions at 31 GeV/c

Spectra of positively charged kaons in p+C interactions at 31 GeV/c were measured with the NA61/SHINE spectrometer at the CERN SPS. The analysis is based on the full set of data collected in 2007 with a graphite target with a thickness of 4% of a nuclear interaction length. Interaction cross sections and charged pion spectra were already measured using the same set of data. These new measurements in combination with the published ones are required to improve predictions of the neutrino flux for the T2K long baseline neutrino oscillation experiment in Japan. In particular, the knowledge of kaon production is crucial for precisely predicting the intrinsic electron neutrino component and the high energy tail of the T2K beam. The results are presented as a function of laboratory momentum in 2 intervals of the laboratory polar angle covering the range from 20 up to 240 mrad. The kaon spectra are compared with predictions of several hadron production models. Using the published pion results and the new kaon data, the K+/\pi+ ratios are computed.Comment: 10 pages, 11 figure

A time-fractional Borel-Pompeiu formula and a related hypercomplex operator calculus

In this paper we develop a time-fractional operator calculus in fractional Clifford analysis. Initially we study the $L_p$-integrability of the fundamental solutions of the multi-dimensional time-fractional diffusion operator and the associated time-fractional parabolic Dirac operator. Then we introduce the time-fractional analogues of the Teodorescu and Cauchy-Bitsadze operators in a cylindrical domain, and we investigate their main mapping properties. As a main result, we prove a time-fractional version of the Borel-Pompeiu formula based on a time-fractional Stokes' formula. This tool in hand allows us to present a Hodge-type decomposition for the forward time-fractional parabolic Dirac operator with left Caputo fractional derivative in the time coordinate. The obtained results exhibit an interesting duality relation between forward and backward parabolic Dirac operators and Caputo and Riemann-Liouville time-fractional derivatives. We round off this paper by giving a direct application of the obtained results for solving time-fractional boundary value problems.The work of M. Ferreira, M.M. Rodrigues and N. Vieira was supported by Portuguese funds through CIDMA-Center for Research and Development in Mathematics and Applications, and FCT–Fundação para a Ciência e a Tecnologia, within project UID/MAT/04106/2019. The work of the authors was supported by the project New Function Theoretical Methods in Computational Electrodynamics / Neue funktionentheoretische Methoden für instationäre PDE, funded by Programme for Cooperation in Science between Portugal and Germany (“Programa de Ações Integradas Luso-Alemãs 2017” - DAAD-CRUP - Acção No. A-15/17 / DAAD-PPP Deutschland-Portugal, Ref: 57340281). N. Vieira was also supported by FCT via the FCT Researcher Program 2014 (Ref: IF/00271/2014).publishe