High H2S concentration abatement in a biotrickling filter: start-up at controlled pH and effect of the EBRT on O2/H2S supply ratio

In this study, a biotrickling filter reactor was set up and used to treat high concentrations of gaseousH2S. Inoculation was carried out at an inlet H2S concentration of 1,000 ppmv (27.8 g H2S m-3 h-1)and sludge from a municipal wastewater treatment plant (MWWTP) was used as inoculum. After 3days, removal efficiency (RE) above 98 % was achieved even after the loading rate (LR) wasincreased up to 55.6 g H2S m-3 h-1 (2,000 ppmv). Operation at such LR, with an empty bed residencetime (EBRT) of 180 s and controlled pH of 6.5-7 was carried out during 3 months. The start-upphase, the effect of decreasing EBRTs at constant inlet concentration and the composition of theprocess end-products in relation to the supplied O2/H2S ratio were studied. Also, a carbon massbalance under steady state conditions was calculated.Peer ReviewedPostprint (published version

Linearizing torsion classes in the Picard group of algebraic curves over finite fields

We address the problem of computing in the group of $\ell^k$-torsion rational points of the jacobian variety of algebraic curves over finite fields, with a view toward computing modular representations.Comment: To appear in Journal of Algebr

Fibonacci numbers and self-dual lattice structures for plane branches

Consider a plane branch, that is, an irreducible germ of curve on a smooth complex analytic surface. We define its blow-up complexity as the number of blow-ups of points necessary to achieve its minimal embedded resolution. We show that there are $F_{2n-4}$ topological types of blow-up complexity $n$, where $F_{n}$ is the $n$-th Fibonacci number. We introduce complexity-preserving operations on topological types which increase the multiplicity and we deduce that the maximal multiplicity for a plane branch of blow-up complexity $n$ is $F_n$. It is achieved by exactly two topological types, one of them being distinguished as the only type which maximizes the Milnor number. We show moreover that there exists a natural partial order relation on the set of topological types of plane branches of blow-up complexity $n$, making this set a distributive lattice, that is, any two of its elements admit an infimum and a supremum, each one of these operations beeing distributive relative to the second one. We prove that this lattice admits a unique order-inverting bijection. As this bijection is involutive, it defines a duality for topological types of plane branches. The type which maximizes the Milnor number is also the maximal element of this lattice and its dual is the unique type with minimal Milnor number. There are $F_{n-2}$ self-dual topological types of blow-up complexity $n$. Our proofs are done by encoding the topological types by the associated Enriques diagrams.Comment: 21 pages, 16 page

The semigroup of a space curve singularity

The semigroup of values of a space curve singularity is an invariant of the singularity. We analyze the complexity of this invariant, in order to describe the geometric invariants of the sequence of infinitely near points of the curve necessary to determine the generators of the semigroup. We give several approaches and examples using Hamburger–Noether matrices to describe the infinitely near points of the curve

Linear precision for toric surface patches

We classify the homogeneous polynomials in three variables whose toric polar linear system defines a Cremona transformation. This classification also includes, as a proper subset, the classification of toric surface patches from geometric modeling which have linear precision. Besides the well-known tensor product patches and B\'ezier triangles, we identify a family of toric patches with trapezoidal shape, each of which has linear precision. B\'ezier triangles and tensor product patches are special cases of trapezoidal patches

On the stability of tetrahedral relative equilibria in the positively curved 4-body problem

We consider the motion of point masses given by a natural extension of Newtonian gravitation to spaces of constant positive curvature. Our goal is to explore the spectral stability of tetrahedral orbits of the corresponding 4-body problem in the 2-dimensional case, a situation that can be reduced to studying the motion of the bodies on the unit sphere. We first perform some extensive and highly precise numerical experiments to find the likely regions of stability and instability, relative to the values of the masses and to the latitude of the position of three equal masses. Then we support the numerical evidence with rigorous analytic proofs in the vicinity of some limit cases in which certain masses are either very large or negligible, or the latitude is close to zero.Comment: 32 pages, 6 figure

The cone of curves and the Cox ring of rational surfaces given by divisorial valuations

We consider surfaces X defined by plane divisorial valuations v of the quotient field of the local ring R at a closed point p of the projective plane P-2 over an arbitrary algebraically closed field k and centered at R. We prove that the regularity of the cone of curves of X is equivalent to the fact that v is non-positive on Op(2) (P-2 \ L), where L is a certain line containing p. Under these conditions, we characterize when the characteristic cone of X is closed and its Cox ring finitely generated. Equivalent conditions to the fact that v is negative on Opt (P-2 \ L) k are also given. (C) 2015 Published by Elsevier Inc.Supported by Spain Ministry of Economy MTM2012-36917-C03-03 and Universitat Jaume I P1-1B201502.Galindo Pastor, C.; Monserrat Delpalillo, FJ. (2016). The cone of curves and the Cox ring of rational surfaces given by divisorial valuations. Advances in Mathematics. 290:1040-1061. https://doi.org/10.1016/j.aim.2015.12.015S1040106129

Filtrations by complete ideals and applications

Infinitely near base points and Enriques' unloading procedure are used to construct filtrations by complete ideals of C{x, y}. It follows a procedure for getting generators of the integral closure of an ideal

Singularities of plane curves

Comprehensive and self-contained exposition of singularities of plane curves, including new, previously unpublished results