The best constant for the centered maximal operator on radial decreasing functions

We show that the lowest constant appearing in the weak type (1,1) inequality satisfied by the centered Hardy-Littlewood maximal operator on radial integrable functions is 1.Comment: corrected typo

Lower bounds for the centered Hardy-Littlewood maximal operator on the real line

Let $10$ such that for each $f\in L^p(\mathbb{R})$, the centered Hardy-Littlewood maximal operator $M$ on $\mathbb{R}$ satisfies the lower bound $\|Mf\|_{L^p(\mathbb{R})}\ge (1+\varepsilon_p)\|f\|_{L^p(\mathbb{R})}$.Comment: accepted manuscrip

Evaluation of the changes in working limits in an automobile assembly line using simulation

The aim of the work presented in this paper consists of the development of a decision-making support system, based on discrete-event simulation models, of an automobile assembly line which was implemented within an Arena simulation environment and focused at a very specific class of production lines with a four closed-loop network configuration. This layout system reflects one of the most common configurations of automobile assembly and preassembly lines formed by conveyors. The sum of the number of pallets on the intermediate buffers, remains constant, except for the fourth closed-loop, which depends on the four-door car ratio (x) implemented between the door disassembly and assembly stations of the car body. Some governing equations of the four closed-loops are not compatible with the capacities of several intermediate buffers for certain values of variable x. This incompatibility shows how the assembly line cannot operate in practice for x0,97 in a stationary regime, due to the starvation phenomenon or the failure of supply to the machines on the production line. We have evaluated the impact of the pallet numbers circulating on the first closed-loop on the performance of the production line, translated into the number of cars produced/hour, in order to improve the availability of the entire manufacturing system for any value of x. Until the present date, these facts have not been presented in specialized literature. © 2012 American Institute of Physics

Effect of solidification rate on pore connectivity of aluminium foams and its consequences on mechanical properties

This study evaluates the influence of solidification rate on the generation and control of pore connectivity of closed-cell aluminium foams. Additionally, it gives the experimental support to evaluate and model the effect of this pore connectivity on the mechanical properties. A collection of AlSi10 foams produced via powder metallurgy route, with porosities between 0.65 and 0.85, were examined. During production, applied heating conditions were the same in all cases but the cooling conditions were varied in order to promote different solidification rates in a wide range (from -1 to -15 K/s). Structural characterisation was performed by gas pycnometry and X- ray microtomography while the mechanical properties were evaluated by microhardness measurements and uniaxial compression tests. Results showed a clear reduction of pore connectivity when increasing the solidification rate. The consequence is a prominent improvement of the foam strength over the one expected from just the matrix refinement. Further analysis on this relationship between the pore connectivity and the mechanical properties, has allowed to propose a correction to the theoretical model for collapse strength in closed cell foams to consider such contribution and predict more accurate results

Boundedness and unboundedness results for some maximal operators on functions of bounded variation

We characterize the space $BV(I)$ of functions of bounded variation on an arbitrary interval $I\subset \mathbb{R}$, in terms of a uniform boundedness condition satisfied by the local uncentered maximal operator $M_R$ from $BV(I)$ into the Sobolev space $W^{1,1}(I)$. By restriction, the corresponding characterization holds for $W^{1,1}(I)$. We also show that if $U$ is open in $\mathbb{R}^d, d >1$, then boundedness from $BV(U)$ into $W^{1,1}(U)$ fails for the local directional maximal operator $M_T^{v}$, the local strong maximal operator $M_T^S$, and the iterated local directional maximal operator $M_T^{d}\circ ...\circ M_T^{1}$. Nevertheless, if $U$ satisfies a cone condition, then $M_T^S:BV(U)\to L^1(U)$ boundedly, and the same happens with $M_T^{v}$, $M_T^{d} \circ ...\circ M_T^{1}$, and $M_R$.Comment: 15 page

Direct Benzene Hydroxylation with Dioxygen Induced by Copper Complexes : Uncovering the Active Species by DFT Calculations

Acord transformatiu CRUE-CSICThe direct oxidation of benzene into phenol using molecular oxygen at very mild temperatures can be promoted in the presence of the copper complex TpCu(NCMe) in the homogeneous phase in the presence of ascorbic acid as the source of protons and electrons. The stoichiometric nature, relative to copper, of this transformation prompted a thorough DFT study in order to understand the reaction pathway. As a result, the dinuclear species TpCu(μ-O)(μ-OH)CuTpis proposed as the relevant structure which is responsible for activating the arene C-H bond leading to phenol formation