Best proximity pair results for relatively nonexpansive mappings in geodesic spaces

Given $A$ and $B$ two nonempty subsets in a metric space, a mapping $T : A \cup B \rightarrow A \cup B$ is relatively nonexpansive if $d(Tx,Ty) \leq d(x,y) \text{for every} x\in A, y\in B.$ A best proximity point for such a mapping is a point $x \in A \cup B$ such that $d(x,Tx)=\text{dist}(A,B)$. In this work, we extend the results given in [A.A. Eldred, W.A. Kirk, P. Veeramani, Proximal normal structure and relatively nonexpansive mappings, Studia Math., 171 (2005), 283-293] for relatively nonexpansive mappings in Banach spaces to more general metric spaces. Namely, we give existence results of best proximity points for cyclic and noncyclic relatively nonexpansive mappings in the context of Busemann convex reflexive metric spaces. Moreover, particular results are proved in the setting of CAT(0) and uniformly convex geodesic spaces. Finally, we show that proximal normal structure is a sufficient but not necessary condition for the existence in $A \times B$ of a pair of best proximity points

Averaged alternating reflections in geodesic spaces

We study the nonexpansivity of reflection mappings in geodesic spaces and apply our findings to the averaged alternating reflection algorithm employed in solving the convex feasibility problem for two sets in a nonlinear context. We show that weak convergence results from Hilbert spaces find natural counterparts in spaces of constant curvature. Moreover, in this particular setting, one obtains strong convergence.Comment: 13 pages; some typos correcte

Measuring the Taylor rule's performance

Using a recently developed econometric technique to determine how the original Taylor rule and subsequent variations perform using different measures of inflation, output and unemployment. We found that the rule remains relevant today, despite the changes wrought by globalization, financial market innovations and technological advances.

Forecasting the end of the global recession: did we miss the early signs?

This paper looks at the term-structure literature to identify early signs predicting recessionary patterns in the U.S. and other developed economies. Based on the National Bureau of Economic Research (NBER) and Economic Cycle Research Institute (ECRI) recession dates, we define the probability of recession as a function of the traditional yield spread, plus a forward-looking measure of growth expectations, namely the output gap growth spread. For other countries, we extend the model and make it additionally dependent on the probability of recession in the U.S. Our results indicate that most of the a-posteriori official recession dates could have been forecast as early as April 2009, when the first green shoots of recovery appeared in the U.S. data. Overall, the term-structure versions we apply allow us to signal recessions earlier and more accurately than traditional term-structure models and most professional forecasters.Forecasting ; Macroeconomics - Econometric models ; International finance

Globalization and the changing nature of the U.S. economy's influence in the world

Global economic integration may have made other countries more dependent on each other and weakened their initial responses to U.S. economic fluctuations.Globalization ; Economic conditions - United States ; International trade ; Financial crises

In the eye of the storm: gasoline markets after the hurricanes

Hurricane Katrina, 2005 ; Gasoline ; Gas industry ; Petroleum industry and trade

The relative performance of alternative Taylor rule specifications

We look at how well several alternative Taylor rule specifications describe Federal Reserve policy decisions in real time, using the newly developed Giacomini and Rossi (2007) test for non-nested model selection in the presence of (possible) parameter instability. Further, we isolate those Taylor rule features that are most important for achieving relatively strong real-time performance. A second-order partial adjustment version of the Koenig (2004a) model performs consistently better than alternative specifications. Key features of this rule are the partial adjustment of the federal funds rate toward an equilibrium rate that depends on the unemployment rate and forward-looking inflation measures.Taylor's rule ; Real-time data ; Monetary policy - United States ; Forecasting

Gasoline content regulation as a trade barrier: do boutique fuels discourage fuel imports?

This paper examines the impact of Clean Air Act Amendments of 1990 (CAAA) environmental regulations on U.S. motor gasoline import patterns. Following the damage to U.S. petroleum refining infrastructure from hurricanes Katrina and Rita, the federal government provided temporary relief for several weeks from so-called boutique fuel specifications designed to improve air quality in certain regions of the country. These temporary waivers increased marketers’ ability to sell gasoline originally destined for specific regional markets into a greater number of markets. We hypothesize that these same waivers also encouraged gasoline imports more than increased prices would have alone. We test our hypothesis using two analyses. The first consists of a simple transfer function analysis designed to separate price effects (and thus effects of refinery closures) from the effects of regulatory relief. The second analysis consists of a natural experiment comparing the primary recipient of regulatory relief—the Gulf Coast gasoline market— to the rest of the United States. Both analyses suggest that the CAAA-related specifications prevent a substantial amount of gasoline imports from entering the United States under normal circumstances.

Comparación de liberación de fluoruro de diferentes cementos para bandas ortodoncicas

Objetivo: Comparar el flúor liberado de diferentes cementos para bandas ortodóncicas y su capacidad de recarga. Materiales y Métodos: Cinco cementos indicados para bandas ortodóncicas fueron evaluados para analizar su liberación de fluoruro y capacidad de recarga los cuales considero un ionómeros de vidrio convencional G1:(GC Fuji Ortho Band Shofu) cemento de ionómeros de vidrio modificado con resina G2:(Optiband Ultra), ionómeros de vidrio reforzado con resina G3:(Multi-Cure Band), cemento de resina compuesta modificado con poliácido G4:(Transbond Plus LC Band) y ionómero de vidrio convencional G5:(Ketac Cem). Las lecturas de concentración de fluoruro se llevaron a cabo durante 30 días usando un electrodo selectivo de ion fluoruro (modelo 1011, Hanna Instruments, EE. UU.) y un potenciómetro (modelo 3222, Hanna Instruments). Se realizaron mediciones apartir de 24 horas, 48 horas, 5,10 y 30 días. Después de este período, las muestras se recargaron con enjuague bucal con flúor (Colgate plax , 2500ppm). Se determinó la cantidad de fluoruro liberado durante 3 días. Resultados: en general, todos los materiales presentaron una mayor liberación de flúor en las primeras 24 horas; G1 (Shofu) mostró una mayor liberación de flúor en este período en comparación con los demás cementos. Por otro lado, G5 (Ketac Cem) presentó la liberación de flúor más constante hasta el décimo día. Conclusión: G1 (Shofu) liberó mayores concentraciones de fluoruro, aunque no se encontraron diferencias significativas. G1 (Shofu) y G4 (Trasbond) posterior a la recarga mostraron en las primeras 24 h una liberación de fluoruro mejorada y sostenida pero después de las 48 horas esta fue decreciente.Proyecto PAPIIT: IA204516

Effective numerical computation of p(x)−p(x)-Laplace equations in 2D

In this article we implement a method for the computation of a nonlinear elliptic problem with nonstandard growth driven by the $p(x)-$Laplacian operator. Our implementation is based in the {\em decomposition--coordination} method that allows us, via an iterative process, to solve in each step a linear differential equation and a nonlinear algebraic equation. Our code is implemented in {\sc MatLab} in 2 dimensions and turns out to be extremely efficient from the computational point of view.Comment: 9 pages, 5 figure