Reactive nitrogen in the Spanish agri-food sector: environmental impact on atmosphere, soils, water and resources.

The presence of reactive species of nitrogen (N) in the biosphere might cause environmental impacts at local, regional and global scales. Nowadays the N flows generated by human activities greatly exceed natural processes, thus a necessity exists of identifying and quantifying the current state of environmental N loads. The aim of this work is to quantify the amount of reactive N used in the Spanish agri-food sector, assessing the related potential environmental impacts and potential uses of resources. Data from a previously calculated N flow analysis in the Spanish agricultural and food production system for the 1996-2000 time period were used. Total anthropogenic N inputs to the systems were calculated. Input and output flows were considered in each economic compartment in order to calculate use efficiency (ratio of useful outputs to total inputs), eco-efficiency (ratio of useful outputs to outputs to the environment) and recycling rate (ratio of flow recycled to an earlier life-cycle compartment divided by total outputs). Environmental impacts were assessed by quantifying the N balance between the economic and the environmental subsystems: water, atmosphere, ecosystems soils and other soils. In this case agricultural soils were also considered an environmental compartment, since they are an important intermediate path to the environment. The impact on resources was evaluated considering the net N imports into the system and legume fixing crops, pastures and forages versus feed and fertilizers within the system. Anthropogenic N inputs are relatively high in Spain, which is a net importer of nitrogen, mainly in fertilizers and food and feed commodities. Environmental compartments receive relative high amounts of reactive nitrogen, especially soils. Furthermore, there was a relative low use of domestic resources, with a low proportion of N recycled within the system

Automorphism group of split Cartan modular curves

Postprint (author's final draft

On It\^{o}'s formula for elliptic diffusion processes

Bardina and Jolis [Stochastic process. Appl. 69 (1997) 83--109] prove an extension of It\^{o}'s formula for $F(X_t,t)$, where $F(x,t)$ has a locally square-integrable derivative in $x$ that satisfies a mild continuity condition in $t$ and $X$ is a one-dimensional diffusion process such that the law of $X_t$ has a density satisfying certain properties. This formula was expressed using quadratic covariation. Following the ideas of Eisenbaum [Potential Anal. 13 (2000) 303--328] concerning Brownian motion, we show that one can re-express this formula using integration over space and time with respect to local times in place of quadratic covariation. We also show that when the function $F$ has a locally integrable derivative in $t$, we can avoid the mild continuity condition in $t$ for the derivative of $F$ in $x$.Comment: Published at http://dx.doi.org/10.3150/07-BEJ6049 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Stochastic delay equations with non-negativity constraints driven by fractional Brownian motion

In this note we prove an existence and uniqueness result for the solution of multidimensional stochastic delay differential equations with normal reflection. The equations are driven by a fractional Brownian motion with Hurst parameter $H>1/2$. The stochastic integral with respect to the fractional Brownian motion is a pathwise Riemann--Stieltjes integral.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ327 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm