Higher order symmetrizer and application to an unusual transport equation

We study a class of stationary transport equation with nonlocal low-order tems We obtain the existence and uniqueness of a solution in sobolev spaces     

Homogeneous and non-homogeneous boundary value problems for first order linear hyperbolic systems arising in fluid-mechanics (Part I)

We prove t h e existence and the uniqueness of differentiable and strong solutions for aclass of non-homogeneous boundary value problems for first order linear hyperbolic systems arising from the dynamics of compressible non-viscous fluids . The method provides.the existence of differentiable solutions without resorting to strong or weak solutions. A necessary and sufficient condition for the existence of solutions for the non-homogeneous problem is proved. I t consists of an explicitrelationship between the boundary values of u and those of the data f . Strong solutions are obtained without this supplementary assumption. See Theorems 3.1, 4.1, 4 . 2 , 4.3 and Corollary 4.4; see also Remarks 2.1 and 2.4. In this paper we consider equation (3.1) below. In the forthcoming part II we prove similar results for the corresponding evolution problem.     

Homogeneous and non-homogeneous boundary value problems for first order linear hyperbolic systems arising in fluid mechanics (Part II)

We prove the existence and the uniqueness of differentiable and strong solutions for a class of boundary value problems for first order linear hyperbolic systems arising from the dynamics of compressible non-viscous fluids. In particular necessary and sufficient conditions for the existence of solutions for the non-homogeneous problem are studied; strong solutions are obtained without this supplementary condition. See Theorems3.2, 3.9, 4.1, 4.2 and Corollary 4.3; see also the discussion after Theorem 4.1. In particular we don't assume the boundary space to be maximal non-positive and the boundary matrix to be of constant rank on the boundary. In this paper we prove directly the existence of differentiable solutions without resort to weak or strong solutions. An essential tool will be the introduction of a space Z of regular functions verifying not only the assigned boundary conditions but also some suitable complementary boundary conditions; see also the introduction of Part I of this work [I].     

Comparative Study of Antioxidant and Pro-Oxidant Properties of Homoleptic and Heteroleptic Copper Complexes with Amino Acids,Dipeptides and 1,10-Phenanthroline: The Quest for Antitumor Compounds

In a search for new antitumoral agents, a series of homoleptic copper(II) complexes with amino acids and dipeptides, as well as heteroleptic complexes containing both dipeptides and 1,10-phenanthroline, were studied. Furthermore, a single-crystal structure containing alanyl-leucinato ([Cu₃(AlaLeu)₃(H₂O)₃(CO₃)]·PF₆·H₂O), which is the first homotrinuclear carbonato-bridged copper(II) complex with a dipeptide moiety, is presented. To assess possible antitumor action mechanisms, we focused on the comparative analysis of pro- and antioxidant behaviors. Pro-oxidant activity, in which the reactive oxygen species (ROS) formed by the reaction of the complexes with H₂O₂ produce oxidative damage to 2-deoxy-d-ribose, was evaluated using the TBARS method. Additionally, the antioxidant action was quantified through the superoxide dismutase (SOD)-like activity, using a protocol based on the inhibitory effect of SOD on the reduction of nitrobluetetrazolium (NBT) by the superoxide anion generated by the xanthine/xanthine oxidase system. Our findings show that Cu–amino acid complexes are strong ROS producers and moderate SOD mimics. Conversely, Cu–dipeptide–phen complexes are good SOD mimics but poor ROS producers. The activity of Cu–dipeptide complexes was strongly dependent on the dipeptide. A DFT computational analysis revealed that complexes with high SOD-like activity tend to display a large dipole moment and condensed-to-copper charge, softness and LUMO contribution. Moreover, good ROS producers have higher global hardness and copper electrophilicity, lower copper softness and flexible and freely accessible coordination polyhedra.     

Navier–Stokes Equations with Shear Thinning Viscosity. Regularity up to the Boundary

In this paper we consider a class of stationary Navier–Stokes equations with shear dependent viscosity, in the shear thinning case p < 2, under a non-slip boundary condition. We are interested in global (i.e., up to the boundary) regularity results, in dimension n = 3, for the second order derivatives of the velocity and the first order derivatives of the pressure. As far as we know, there are no previous global regularity results for the second order derivatives of the solution to the above boundary value problem. We consider a cubic domain and impose the non-slip boundary condition only on two opposite faces. On the other faces we assume periodicity, as a device to avoid effective boundary conditions. This choice is made so that we work in a bounded domain Ω and simultaneously with a flat boundary. The extension to non-flat boundaries is done in the forthcoming paper [7], by following ideas introduced by the author, for the case p > 2, in reference [5]. The results also hold in the presence of the classical convective term, provided that p is sufficiently close to the value 2.      

Dynamic effects in inefficiency: Evidence from the Colombian banking sector

Firms face a continuous process of technological and environmental changes that requires them to make managerial decisions in a dynamic context. However, costs and constraints prevent firms from making instant adjustments towards optimal conditions and may cause inefficiency to persist in time. We propose a dynamic inefficiency specification that captures differences in the adjustment costs among firms and non-persistent effects of inefficiency heterogeneity. The model is fitted to a ten year sample of Colombian banks. The new specification improves model fit and have effects on efficiency estimations. Overall, Colombian banks present high inefficiency persistence but important differences between institutions are found. In particular, merged banks present low adjustment costs that allow them to recover rapidly efficiency losses derived from merging processes.     

Post processing of solution and flux for the nodal mimetic finite difference method

We develop and analyze a post processing technique for the family of low‐order mimetic discretizations based on vertex unknowns for the numerical treatment of diffusion problems on unstructured polygonal and polyhedral meshes. The post processing works in two steps. First, from the nodal degrees of freedom, we reconstruct an elemental‐based vector field that approximates the gradient of the exact solution. Second, we solve a local problem for each mesh vertex associated with a scheme degree of freedom to determine a post processed normal flux that is conservative and divergence preserving. Theoretical results and numerical experiments for two‐dimensional (2D) and 3D benchmark problems show optimal convergence rates. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 336–363, 2015