Impact of nitrogenous fertilizers on carbonate dissolution in small agricultural catchments: Implications for weathering CO2 uptake at regional and global scales

The goal of this study was to highlight the occurrence of an additional proton-promoted weathering pathway of carbonate rocks in agricultural areas where N-fertilizers are extensively spread, and to estimate its consequences on riverine alkalinity and uptake of CO2 by weathering. We surveyed 25 small streams in the calcareous molassic Gascogne area located in the Garonne river basin (south-western France) that drain cultivated or forested catchments for their major element compositions during different hydrologic periods. Among these catchments, the Hay and the Montousse´, two experimental catchments, were monitored on a weekly basis. Studies in the literature from other small carbonate catchments in Europe were dissected in the same way. In areas of intensive agriculture, the molar ratio (Ca + Mg)/HCO3 in surface waters is significantly higher (0.7 on average) than in areas of low anthropogenic pressure (0.5). This corresponds to a decrease in riverine alkalinity, which can reach 80% during storm events. This relative loss of alkalinity correlates well with the NO3 content in surface waters. In cultivated areas, the contribution of atmospheric/soil CO2 to the total riverine alkalinity (CO2 ATM-SOIL/HCO3) is less than 50% (expected value for carbonate basins), and it decreases when the nitrate concentration increases. This loss of alkalinity can be attributed to the substitution of carbonic acid (natural weathering pathway) by protons produced by nitrification of Nfertilizers (anthropogenic weathering pathway) occurring in soils during carbonate dissolution. As a consequence of these processes, the alkalinity over the last 30 years shows a decreasing trend in the Save river (one of the main Garonne river tributaries, draining an agricultural catchment), while the nitrate and calcium plus magnesium contents are increasing. We estimated that the contribution of atmospheric/soil CO2 to riverine alkalinity decreased by about 7–17% on average for all the studied catchments. Using these values, the deficit of CO2 uptake can be estimated as up to 0.22–0.53 and 12–29 Tg1 yr1 CO2 on a country scale (France) and a global scale, respectively. These losses represent up to 5.7–13.4% and only 1.6–3.8% of the total CO2 flux naturally consumed by carbonate dissolution, for France and on a global scale, respectively. Nevertheless, this loss of alkalinity relative to the Ca + Mg content relates to carbonate weathering by protons from N-fertilizers nitrification, which is a net source of CO2 for the atmosphere. This anthropogenic CO2 source is not negligible since it could reach 6–15% of CO2 uptake by natural silicate weathering and could consequently partly counterbalance this natural CO2 sink

The forgotten monoid

We study properties of the forgotten monoid which appeared in work of Lascoux and Schutzenberger and recently resurfaced in the construction of dual equivalence graphs by Assaf. In particular, we provide an explicit characterization of the forgotten classes in terms of inversion numbers and show that there are n^2-3n+4 forgotten classes in the symmetric group S_n. Each forgotten class contains a canonical element that can be characterized by pattern avoidance. We also show that the sum of Gessel's quasi-symmetric functions over a forgotten class is a 0-1 sum of ribbon-Schur functions.Comment: 13 pages; in version 3 the proof of Proposition 3 is correcte

Nilpotent bicone and characteristic submodule of a reductive Lie algebra

The nilpotent bicone of a finite dimensional complex reductive Lie algebra g is the subset of elements in g x g whose subspace generated by the components is contained in the nilpotent cone of g. The main result of this note is that the nilpotent bicone is a complete intersection. This affirmatively answers a conjecture of Kraft-Wallach concerning the nullcone. In addition, we introduce and study the characteristic submodule of g. The properties of the nilpotent bicone and the characteristic submodule are known to be very important for the understanding of the commuting variety and its ideal of definition. In order to study the nilpotent bicone, we introduce another subvariety, the principal bicone. The nilpotent bicone, as well as the principal bicone, are linked to jet schemes. We study their dimensions using arguments from motivic integration. Namely, we follow methods developed in http://arxiv.org/abs/math/0008002v5 .Comment: 48 pages. Remark 8 has been modified; one sentence was not correct. We thank Kari Vilonen for pointing out this erro

Membrane properties revealed by spatiotemporal response to a local inhomogeneity

We study theoretically the spatiotemporal response of a lipid membrane submitted to a local chemical change of its environment, taking into account the time-dependent profile of the reagent concentration due to diffusion in the solution above the membrane. We show that the effect of the evolution of the reagent concentration profile becomes negligible after some time. It then becomes possible to extract interesting properties of the membrane response to the chemical modification. We find that a local density asymmetry between the two monolayers relaxes by spreading diffusively in the whole membrane. This behavior is driven by intermonolayer friction. Moreover, we show how the ratio of the spontaneous curvature change to the equilibrium density change induced by the chemical modification can be extracted from the dynamics of the local membrane deformation. Such information cannot be obtained by analyzing the equilibrium vesicle shapes that exist in different membrane environments in light of the area-difference elasticity model.Comment: 11 pages, 4 figure

Kernel Inverse Regression for spatial random fields

In this paper, we propose a dimension reduction model for spatially dependent variables. Namely, we investigate an extension of the \emph{inverse regression} method under strong mixing condition. This method is based on estimation of the matrix of covariance of the expectation of the explanatory given the dependent variable, called the \emph{inverse regression}. Then, we study, under strong mixing condition, the weak and strong consistency of this estimate, using a kernel estimate of the \emph{inverse regression}. We provide the asymptotic behaviour of this estimate. A spatial predictor based on this dimension reduction approach is also proposed. This latter appears as an alternative to the spatial non-parametric predictor

Orthogonal involutions on central simple algebras and function fields of Severi-Brauer varieties

An orthogonal involution $\sigma$ on a central simple algebra $A$, after scalar extension to the function field $\mathcal{F}(A)$ of the Severi--Brauer variety of $A$, is adjoint to a quadratic form $q_\sigma$ over $\mathcal{F}(A)$, which is uniquely defined up to a scalar factor. Some properties of the involution, such as hyperbolicity, and isotropy up to an odd-degree extension of the base field, are encoded in this quadratic form, meaning that they hold for the involution $\sigma$ if and only if they hold for $q_\sigma$. As opposed to this, we prove that there exists non-totally decomposable orthogonal involutions that become totally decomposable over $\mathcal{F}(A)$, so that the associated form $q_\sigma$ is a Pfister form. We also provide examples of nonisomorphic involutions on an index $2$ algebra that yield similar quadratic forms, thus proving that the form $q_\sigma$ does not determine the isomorphism class of $\sigma$, even when the underlying algebra has index $2$. As a consequence, we show that the $e_3$ invariant for orthogonal involutions is not classifying in degree $12$, and does not detect totally decomposable involutions in degree $16$, as opposed to what happens for quadratic forms

The Arason invariant of orthogonal involutions of degree 12 and 8, and quaternionic subgroups of the Brauer group

Using the Rost invariant for torsors under Spin groups one may define an analogue of the Arason invariant for certain hermitian forms and orthogonal involutions. We calculate this invariant explicitly in various cases, and use it to associate to every orthogonal involution with trivial discriminant and trivial Clifford invariant over a central simple algebra of even co-index a cohomology class $f_3$ of degree 3 with $\mu_2$ coefficients. This invariant $f_3$ is the double of any representative of the Arason invariant; it vanishes when the algebra has degree at most 10, and also when there is a quadratic extension of the center that simultaneously splits the algebra and makes the involution hyperbolic. The paper provides a detailed study of both invariants, with particular attention to the degree 12 case, and to the relation with the existence of a quadratic splitting field.Comment: A mistake pointed out by A. Sivatski in Section 5.3 has been corrected in the new version of this preprin

Saturation spaces for regularization methods in inverse problems

The aim of this article is to characterize the saturation spaces that appear in inverse problems. Such spaces are defined for a regularization method and the rate of convergence of the estimation part of the inverse problem depends on their definition. Here we prove that it is possible to define these spaces as regularity spaces, independent of the choice of the approximation method. Moreover, this intrinsec definition enables us to provide minimax rate of convergence under such assumptionsLinear inverse problems, regularization methods, structural econometrics