The behavior of real exchange rates: the case of Japan

The study examines the convergence rate of mean reversion by contrasting the estimated half-life of real exchange rate (RER). We employ an extensive monthly consumer price index (CPI)-based product price’s panel for Japan (the U.S. as the num´eraire). We find that the disaggregated RERs are persistent due to the cross-sectional dependence problems. By controlling common correlated effects, the estimated half-life for all goods may fall to as low as 2.54 years, below the consensus view of 3 to 5 years summarized by Rogoff (1996). After correcting the small-sample bias, the estimated half-life of deviations from purchasing power parity (PPP) increase by 1.03 year. Our findings also support that the half-life of mean reversion of RER is about 3.55 years for traded goods, about 0.11 year lower than non-traded goods. We also show that traded goods and non-traded goods perform distinct distributions of persistence

Limit of Fractional Power Sobolev Inequalities

We derive the Moser-Trudinger-Onofri inequalities on the 2-sphere and the 4-sphere as the limiting cases of the fractional power Sobolev inequalities on the same spaces, and justify our approach as the dimensional continuation argument initiated by Thomas P. Branson.Comment: 17 page

Some higher order isoperimetric inequalities via the method of optimal transport

In this paper, we establish some sharp inequalities between the volume and the integral of the $k$-th mean curvature for $k+1$-convex domains in the Euclidean space. The results generalize the classical Alexandrov-Fenchel inequalities for convex domains. Our proof utilizes the method of optimal transportation.Comment: 21 page

A kinetic study on the lime-heat treatment of corn for masa production

An objective method to predict the optimum cooking time of corn for tortilla production does not exist. Since nixtamalization (lime-heat treatment) is the most important step in the preparation of tortillas, the changes in the corn kernel during this period should be analyzed for the development of an optimal tortilla-making process. This study presents a mathematical model for quantitatively analyzing the kinetics of water diffusion and starch gelatinization during the nixtamalization process;Corn was cooked with and without calcium hydroxide, according to traditional processing steps. The temperature of the cooking solution, the amount of water absorbed by the corn, and the extent of starch gelatinization in the corn were monitored throughout the process. The data were quantitatively analyzed using the mathematical model that was developed based on the principles of diffusion and chemical reaction kinetics. The simplex pattern search scheme was used to locate the optimum rate parameters, which were used to calculate the extent of starch gelatinization. The calculated degree of gelatinization was then compared with that experimentally determined;The result shows that the developed mathematical model is useful for simulating the changes that take place during water-cooking and lime-cooking of corn. The calculated degree of starch gelatinization in corn, based on the quantitative analysis of water uptake data, was highly correlated with those data experimentally determined;Comparison among the responses of nine cultivars of corn to lime-heat treatment showed that the sensitivity of the diffusion process and of the gelatinization reaction to temperature change was the same for the nine corn samples studied. The results also show that the values of diffusivity, D[subscript]0, and the reaction rate constant, K[subscript]0, determine the differences in water uptake and starch gelatinization among samples;According to the stickiness values of masa, the range of degree of starch gelatinization for the preparation of suitable masa dough was between 14 and 20%. Twenty to 30 min cooking time for the sample studied was found to produce this degree of starch gelatinization

On fractional GJMS operators

We describe a new interpretation of the fractional GJMS operators as generalized Dirichlet-to-Neumann operators associated to weighted GJMS operators on naturally associated smooth metric measure spaces. This gives a geometric interpretation of the Caffarelli--Silvestre extension for $(-\Delta)^\gamma$ when $\gamma\in(0,1)$, and both a geometric interpretation and a curved analogue of the higher order extension found by R. Yang for $(-\Delta)^\gamma$ when $\gamma>1$. We give three applications of this correspondence. First, we exhibit some energy identities for the fractional GJMS operators in terms of energies in the compactified Poincar\'e--Einstein manifold, including an interpretation as a renormalized energy. Second, for $\gamma\in(1,2)$, we show that if the scalar curvature and the fractional $Q$-curvature $Q_{2\gamma}$ of the boundary are nonnegative, then the fractional GJMS operator $P_{2\gamma}$ is nonnegative. Third, by assuming additionally that $Q_{2\gamma}$ is not identically zero, we show that $P_{2\gamma}$ satisfies a strong maximum principle.Comment: 38 pages. Final version, to appear in Communications on Pure and Applied Mathematic