Comparative Effect of UV,UV/H2O2 and UV/H2O2/Fe on Terbuthylazine Degradation in Natural and Ultrapure Water

Different advanced oxidation processes (AOPs) (ultraviolet radiation, hydrogen peroxide photolysis and photo-Fenton) were applied to test the degradation of terbuthylazine in three types of water: (a) ultrapure water, (b) surface water from the Gaditana area (Los Hurones reservoir, Cádiz, Spain) and (c) groundwater from the Tempul spring in Jerez de la Frontera (Cádiz, Spain). The experiments were carried out on a laboratory scale, using two different types of reactors, batch and semi-continuous. In batch reactors, the most efficient process for the experiments carried out with both ultrapure water and underground groundwater was ultraviolet radiation, whereas for surface water from the Gaditana area, the process that obtained the best results was the photolysis of hydrogen peroxide with 2.5 mg L⁻¹ of H₂O₂. In semi-continuous reactors, the most efficient process was the photolysis of hydrogen peroxide with 2.5 mg L⁻¹ of H₂O₂ for all the matrices studied. In both types of reactors, terbuthylazine degradation percentages higher than 90% were achieved; the main difference was in the reaction time, which varied from minutes in the batch reactor to seconds in the semi-continuous reactor. In all the applied AOPs, N-terbutyl-6-hydroxy-N′ethyl-1,3,5-triazine-2,4-diamine (TBA-212) was generated as a reaction intermediate.     

Electronic structure of IPR and non-IPR endohedral metallofullerenes: Connecting orbital and topological rules

The electronic structure of endohedral metallofullerenes is rationalized by connecting the apparently independent orbital and topological rules that explain the stability of this family of fullerenes. The separation of the 12 pentagons of the fullerene, which is maximized in order to minimize the Coulomb repulsion, is found to be correlated with the orbital energies of the cage that accepts the electron transfer from the internal cluster. An explanation for the absence of non-IPR cages in large-size EMFs is also provided.     

A Note on the Legendre Series Solution of the Biharmonic Equation for Cylindrical Problems

The solution of cylindrical problems is addressed. A series solution is considered of the biharmonic equation, in which the series terms of the stress function Φ are expressions based upon Legendre polynomials and logarithmically singular functions. An explicit form of a polynomial supplementing each logarithmically singular part of the series solution is obtained.     

A Lie symmetry approach for the solution of the inverse kinematics problem

In this paper, it is considered the inverse kinematics problem, which is faced from a differential point of view. In particular, it is shown that an asymptotic inverse kinematics can be interpreted as a Lie symmetry of the direct kinematics. A parameterization of all Lie symmetries of the direct kinematics is proposed, and the classical Newton and gradient method are obtained as particular cases.     

Dirac Operators on Hypersurfaces of Manifolds with Negative Scalar Curvature

We give a sharp extrinsic lower bound for the first eigenvaluesof the intrinsic Dirac operator of certain hypersurfaces boundinga compact domain in a spin manifold of negative scalar curvature.Limiting-cases are characterized by the existence, on the domain,of imaginary Killing spinors. Some geometrical applications, as anAlexandrov type theorem, are given.     

On the maximum principle for complete second-order elliptic operators in general domains

This paper is concerned with the maximum principle for second-order linear elliptic equations in a wide generality. By means of a geometric condition previously stressed by Berestycki-Nirenberg-Varadhan, Cabré was very able to improve the classical ABP estimate obtaining the maximum principle also in unbounded domains, such as infinite strips and open connected cones with closure different from the whole space. Now we introduce a new geometric condition that extends the result to a more general class of domains including the complements of hypersurfaces, as for instance the cut plane. The methods developed here allow us to deal with complete second-order equations, where the admissible first-order term, forced to be zero in a preceding result with Cafagna, depends on the geometry of the domain.     

Existence of global attractors for a class of periodic Kolmogorov systems

In this paper we use a continuation argument to prove the existence of global attractors for a class of periodic Kolmogorov systems.     

MGM Optimal convergence for certain (multilevel) structured linear systems

We present a multigrid algorithm to solve linear systems whose coefficient metrices belongs to circulant, Hartley or τ multilevel algebras and are generated by a nonnegative multivariate polynomial f. It is known that these matrices are banded (with respect to their multilevel structure) and their eigenvalues are obtained by sampling f on uniform meshes, so they are ill‐conditioned (or singular, and need some corrections) whenever f takes the zero value. We prove the proposed metod to be optimal even in presence of ill‐conditioning: if the multilevel coefficient matrix has dimension ni at level i, i = 1, … , d, then only ni operations are required on each iteration, but the convergence rate keeps constant with respect to N(n) as it depends only on f. The algorithm can be extended to multilevel Toeplitz matrices too.     

On Hexagonal Structures in Higher Dimensional Theories

We analyze the geometrical background under which many Lie groups relevant to particle physics are endowed with a (possibly multiple) hexagonal structure. There are several groups appearing, either as special holonomy groups on the compactification process from higher dimensions, or as dynamical string gauge groups; this includes groups like SU(2), SU(3), G ₂, Spin(7), O(8) as well as E ₈ and O(32). We emphasize also the relation of these hexagonal structures with the octonion division algebra, as we expect as well eventually some role for octonions in the interpretation of symmetries in High Energy Physics.