Maharam-type kernel representation for operators with a trigonometric domination

[EN] Consider a linear and continuous operator T between Banach function spaces. We prove that under certain requirements an integral inequality for T is equivalent to a factorization of T through a specific kernel operator: in other words, the operator T has what we call a Maharam-type kernel representation. In the case that the inequality provides a domination involving trigonometric functions, a special factorization through the Fourier operator is given. We apply this result to study the problem that motivates the paper: the approximation of functions in L2[0, 1] by means of trigonometric series whose Fourier coefficients are given by weighted trigonometric integrals.This research has been supported by MTM2016-77054-C2-1-P (Ministerio de Economia, Industria y Competitividad, Spain).Sánchez Pérez, EA. (2017). Maharam-type kernel representation for operators with a trigonometric domination. Aequationes Mathematicae. 91(6):1073-1091. https://doi.org/10.1007/s00010-017-0507-6S10731091916Calabuig, J.M., Delgado, O., Sánchez Pérez, E.A.: Generalized perfect spaces. Indag. Math. 19(3), 359–378 (2008)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, 88–103 (2010)Delgado, O., Sánchez Pérez, E.A.: Strong factorizations between couples of operators on Banach function spaces. J. Convex Anal. 20(3), 599–616 (2013)Dodds, P.G., Huijsmans, C.B., de Pagter, B.: Characterizations of conditional expectation type operators. Pacific J. Math. 141(1), 55–77 (1990)Flores, J., Hernández, F.L., Tradacete, P.: Domination problems for strictly singular operators and other related classes. Positivity 15(4), 595–616 (2011). 2011Fremlin, D.H.: Tensor products of Banach lattices. Math. Ann. 211, 87–106 (1974)Hu, G.: Weighted norm inequalities for bilinear Fourier multiplier operators. Math. Ineq. Appl. 18(4), 1409–1425 (2015)Halmos, P., Sunder, V.: Bounded Integral Operators on $$L^2$$ L 2 Spaces. Springer, Berlin (1978)Kantorovitch, L., Vulich, B.: Sur la représentation des opérations linéaires. Compositio Math. 5, 119–165 (1938)Kolwicz, P., Leśnik, K., Maligranda, L.: Pointwise multipliers of Calderón- Lozanovskii spaces. Math. Nachr. 286, 876–907 (2013)Kolwicz, P., Leśnik, K., Maligranda, L.: Pointwise products of some Banach function spaces and factorization. J. Funct. Anal. 266(2), 616–659 (2014)Kuo, W.-C., Labuschagne, C.C.A., Watson, B.A.: Conditional expectations on Riesz spaces. J. Math. Anal. Appl. 303, 509–521 (2005)Lindenstrauss, J., Tzafriri, L.: Classical Banach Spaces II. Springer, Berlin (1979)Maharam, D.: The representation of abstract integrals. Trans. Am. Math. Soc. 75, 154–184 (1953)Maharam, D.: On kernel representation of linear operators. Trans. Am. Math. Soc. 79, 229–255 (1955)Maligranda, L., Persson, L.E.: Generalized duality of some Banach function spaces. Indag. Math. 51, 323–338 (1989)Neugebauer, C.J.: Weighted norm inequalities for averaging operators of monotone functions. Publ. Mat. 35, 429–447 (1991)Okada, S., Ricker, W.J., Sánchez Pérez, E.A.: Optimal Domain and Integral Extension of Operators Acting in Function Spaces. Operator Theory: Adv. Appl., vol. 180. Birkhäuser, Basel (2008)Rota, G.C.: On the representation of averaging operators. Rend. Sem. Mat. Univ. Padova. 30, 52–64 (1960)Sánchez Pérez, E.A.: Factorization theorems for multiplication operators on Banach function spaces. Integr. Equ. Oper. Theory 80(1), 117–135 (2014)Schep, A.R.: Factorization of positive multilinear maps. Ill. J. Math. 28(4), 579–591 (1984)Schep, A.R.: Products and factors of Banach function spaces. Positivity 14(2), 301–319 (2010

Density, adhesion and stiffness of warm mix asphalts

XI Congreso de Ingeniería del Transporte (CIT 2014)This study presents the results of different laboratory tests related to the density, adhesion (sensitivity to water test) and rigidity (resilient module) of bituminous mixtures, manufactured at three different temperatures (160 °C, 140 °C and 120 °C), with three additives: a surfactant made up of different amino substances, a paraffin obtained by the Fisher-Tropsch synthesis process which is totally soluble in bitumen, and a synthetic zeolite in powder form which causes the bitumen to micro-foam,. Test samples have been compacted by impact, according to the Marshall method, and kneading, according to gyratory machine. To evaluate these properties an asphalt concrete mixture has been chosen, with a binder, B-50/70, and a maximum size of aggregates of 16 mm, which is usually placed in the surface layer of the pavement. The densities obtained by the two compaction methods are easy to reach. Densities will decrease if the temperature of manufacturing is lower. All mixtures compacted by gyratory machine at different temperatures displayed very good behavior of water sensitivity; but not all mixtures compacted by impact achieved this. The additives improve the adhesion between aggregate and binder. The stiffness moduli decreased in all mixtures for both types of compaction when the temperature was higher, and this reduction is less pronounced in the mixes manufactured with the gyratory compactor. Mixtures with additives tend to reduce the module, except paraffin.This paper is based on the results for the Fenix Project. The development of the Fenix Project was possible thanks to the financial contribution of the Center for Technological and Industrial Development (CDTI) within the framework of the Ingenio 2010 programme, through the CENIT Programme

Reactivation of Fault Systems by Compartmentalized Hydrothermal Fluids in the Southern Andes Revealed by Magnetotelluric and Seismic Data

In active volcanic arcs such as the Andean volcanic mountain belt, magmatically‐sourced fluids are channelled through the brittle crust by faults and fracture networks. In the Andes, volcanoes, geothermal springs and major mineral deposits have a spatial and genetic relationship with NNE‐trending, margin‐parallel faults and margin‐oblique, NW‐trending Andean Transverse Faults (ATF). The Tinguiririca and Planchón‐Peteroa volcanoes in the Andean Southern Volcanic Zone (SVZ) demonstrate this relationship, as their spatially associated thermal springs show strike alignment to the NNE‐oriented El Fierro Thrust Fault System. We constrain the fault system architecture and its interaction with volcanically sourced hydrothermal fluids using a combined magnetotelluric (MT) and seismic survey that was deployed for 20 months. High conductivity zones are located along the axis of the active volcanic chain, delineating fluids and/or melt. A distinct WNW‐trending cluster of seismicity correlates with resistivity contrasts, considered to be a reactivated ATF. Seismicity occurs below 4 km, suggesting activity is limited to basement rocks, and the cessation of seismicity at 9 km delineates the local brittle‐ductile transition. As seismicity is not seen west of the El Fierro fault, we hypothesize that this structure plays a key role in compartmentalizing magmatically‐derived hydrothermal fluids to the east, where the fault zone acts as a barrier to cross‐fault fluid migration and channels fault‐parallel fluid flow to the surface from depth. Increases in fluid pressure above hydrostatic may facilitate reactivation. This site‐specific case study provides the first three‐dimensional seismic and magnetotelluric observations of the mechanics behind the reactivation of an ATF

Wanted dead or alive : high diversity of macroinvertebrates associated with living and ’dead’ Posidonia oceanica matte

The Mediterranean endemic seagrass Posidonia oceanica forms beds characterised by a dense leaf canopy and a thick root-rhizome ‘matte’. Death of P. oceanica shoots leads to exposure of the underlying matte, which can persist for many years, and is termed ‘dead’ matte. Traditionally, dead matte has been regarded as a degraded habitat. To test whether this assumption was true, the motile macroinvertebrates of adjacent living (with shoots) and dead (without shoots) matte of P. oceanica were sampled in four different plots located at the same depth (5–6 m) in Mellieha Bay, Malta (central Mediterranean). The total number of species and abundance were significantly higher (ANOVA; P<0.05 and P<0.01, respectively) in the dead matte than in living P. oceanica matte, despite the presence of the foliar canopy in the latter. Multivariate analysis (MDS) clearly showed two main groups of assemblages, corresponding to the two matte types. The amphipods Leptocheirus guttatus and Maera grossimana, and the polychaete Nereis rava contributed most to the dissimilarity between the two different matte types. Several unique properties of the dead matte contributing to the unexpected higher number of species and abundance of motile macroinvertebrates associated with this habitat are discussed. The findings have important implications for the conservation of bare P. oceanica matte, which has been generally viewed as a habitat of low ecological value.peer-reviewe

Regional Genetic Structure in the Aquatic Macrophyte Ruppia cirrhosa Suggests Dispersal by Waterbirds

The evolutionary history of the genus Ruppia has been shaped by hybridization, polyploidisation and vicariance that have resulted in a problematic taxonomy. Recent studies provided insight into species circumscription, organelle takeover by hybridization, and revealed the importance of verifying species identification to avoid distorting effects of mixing different species, when estimating population connectivity. In the present study, we use microsatellite markers to determine population diversity and connectivity patterns in Ruppia cirrhosa including two spatial scales: (1) from the Atlantic Iberian coastline in Portugal to the Siculo-Tunisian Strait in Sicily and (2) within the Iberian Peninsula comprising the Atlantic-Mediterranean transition. The higher diversity in the Mediterranean Sea suggests that populations have had longer persistence there, suggesting a possible origin and/or refugial area for the species. The high genotypic diversities highlight the importance of sexual reproduction for survival and maintenance of populations. Results revealed a regional population structure matching a continent-island model, with strong genetic isolation and low gene flow between populations. This population structure could be maintained by waterbirds, acting as occasional dispersal vectors. This information elucidates ecological strategies of brackish plant species in coastal lagoons, suggesting mechanisms used by this species to colonize new isolated habitats and dominate brackish aquatic macrophyte systems, yet maintaining strong genetic structure suggestive of very low dispersal.Fundacao para a Cincia e Tecnologia (FCT, Portugal) [PTDC/MAR/119363/2010, BIODIVERSA/0004/2015, UID/Multi/04326/2013]Pew FoundationSENECA FoundationMurcia Government, Spain [11881/PI/09]FCT Investigator Programme-Career Development [IF/00998/2014]Spanish Ministry of Education [AP2008-01209]European Community [00399/2012]info:eu-repo/semantics/publishedVersio

Lack of association of the CIITA -168A→G promoter SNP with myasthenia gravis and its role in autoimmunity

<p>Abstract</p> <p>Background</p> <p>The major histocompatibility complex class II transactivator (CIITA) regulates MHC class II gene expression. A promoter SNP -168A→G (rs3087456) has previously been shown to be associated with susceptibility to several immune mediated disorders, including rheumatoid arthritis (RA), multiple sclerosis (MS) and myocardial infarction (MI). Myasthenia gravis (MG) is an autoimmune disorder which has previously been shown to be associated with polymorphisms of several autoimmune predisposing genes, including <it>IL-1</it>, <it>PTPN22</it>, <it>TNF-α </it>and the <it>MHC</it>. In order to determine if allelic variants of rs3087456 increase predisposition to MG, we analyzed this SNP in our Swedish cohort of 446 MG patients and 1866 controls.</p> <p>Results</p> <p>No significant association of the SNP with MG was detected, neither in the patient group as a whole, nor in any clinical subgroup. The vast majority of previous replication studies have also not found an association of the SNP with autoimmune disorders.</p> <p>Conclusions</p> <p>We thus conclude that previous findings with regard to the role of the <it>CIITA </it>-168A→G SNP in autoimmunity may have to be reconsidered.</p

Assessing the trophic ecology of three sympatric squid in the marine ecosystem off the Patagonian Shelf by combining stomach content and stable isotopic analyses

Squid species are important components of the Southern Atlantic Ocean ecosystems, as they prey on a wide range of crustaceans, fish and cephalopods. As a result of this trophic interaction and their high abundance, they are considered reliable indicators of energy transfer and biomass in the food web. We identified Illex argentinus, Doryteuthis gahi and Onykia ingens as the most important squid species interacting on the Patagonian shelf, and used isotope analysis and stomach content identification to assess the feeding ecology and interaction of these squids in the ecosystem. Our results describe trophic interactions by direct predation of O. ingens and I. argentinus on D. gahi, and a trophic overlap of the three squid, and indicate a higher trophic level and differences in the foraging areas for mature and maturing D. gahi inferred through δ15N and δ13C concentrations. These differences were related to the segregation and different habitat of large mature D. gahi and suggest a food enrichment of C and N based on feeding sources other than those used by small maturing D. gahi and I. argentinus and O. ingens.Versión del editor1,484

Continuation for thin film hydrodynamics and related scalar problems

This chapter illustrates how to apply continuation techniques in the analysis of a particular class of nonlinear kinetic equations that describe the time evolution through transport equations for a single scalar field like a densities or interface profiles of various types. We first systematically introduce these equations as gradient dynamics combining mass-conserving and nonmass-conserving fluxes followed by a discussion of nonvariational amendmends and a brief introduction to their analysis by numerical continuation. The approach is first applied to a number of common examples of variational equations, namely, Allen-Cahn- and Cahn-Hilliard-type equations including certain thin-film equations for partially wetting liquids on homogeneous and heterogeneous substrates as well as Swift-Hohenberg and Phase-Field-Crystal equations. Second we consider nonvariational examples as the Kuramoto-Sivashinsky equation, convective Allen-Cahn and Cahn-Hilliard equations and thin-film equations describing stationary sliding drops and a transversal front instability in a dip-coating. Through the different examples we illustrate how to employ the numerical tools provided by the packages auto07p and pde2path to determine steady, stationary and time-periodic solutions in one and two dimensions and the resulting bifurcation diagrams. The incorporation of boundary conditions and integral side conditions is also discussed as well as problem-specific implementation issues

Learning curves of basic laparoscopic psychomotor skills in SINERGIA VR simulator

Purpose: Surgical simulators are currently essential within any laparoscopic training program because they provide a low-stakes, reproducible and reliable environment to acquire basic skills. The purpose of this study is to determine the training learning curve based on different metrics corresponding to five tasks included in SINERGIA laparoscopic virtual reality simulator. Methods: Thirty medical students without surgical experience participated in the study. Five tasks of SINERGIA were included: Coordination, Navigation, Navigation and touch, Accurate grasping and Coordinated pulling. Each participant was trained in SINERGIA. This training consisted of eight sessions (R1–R8) of the five mentioned tasks and was carried out in two consecutive days with four sessions per day. A statistical analysis was made, and the results of R1, R4 and R8 were pair-wise compared with Wilcoxon signed-rank test. Significance is considered at P value <0.005. Results: In total, 84.38% of the metrics provided by SINERGIA and included in this study show significant differences when comparing R1 and R8. Metrics are mostly improved in the first session of training (75.00% when R1 and R4 are compared vs. 37.50% when R4 and R8 are compared). In tasks Coordination and Navigation and touch, all metrics are improved. On the other hand, Navigation just improves 60% of the analyzed metrics. Most learning curves show an improvement with better results in the fulfillment of the different tasks. Conclusions: Learning curves of metrics that assess the basic psychomotor laparoscopic skills acquired in SINERGIA virtual reality simulator show a faster learning rate during the first part of the training. Nevertheless, eight repetitions of the tasks are not enough to acquire all psychomotor skills that can be trained in SINERGIA. Therefore, and based on these results together with previous works, SINERGIA could be used as training tool with a properly designed training program