Gerogescu-Roegen versus Solow/Stiglitz and the convergence to the Cobb-Douglas

The value of the elasticity of substitution of capital for resources is a crucial element in the debate over whether continual growth is possible. It is generally held that the elasticity has to be at least one to permit continual growth and that there is no way of estimating this outside the range of the data. This paper presents a model in which the elasticity is determined endogenously and may converge to one. It is concluded that the general opinion is wrong: that the possibility of continual growth does not depend on the exogenously given value of the elasticity and that the value of the elasticity outside the range of the data can be studied by econometric methods.

Convergence of the mass-transport steepest descent scheme for the sub-critical Patlak-Keller-Segel model

Variational steepest descent approximation schemes for the modified Patlak-Keller-Segel equation with a logarithmic interaction kernel in any dimension are considered. We prove the convergence of the suitably interpolated in time implicit Euler scheme, defined in terms of the Euclidean Wasserstein distance, associated to this equation for sub-critical masses. As a consequence, we recover the recent result about the global in time existence of weak-solutions to the modified Patlak-Keller-Segel equation for the logarithmic interaction kernel in any dimension in the sub-critical case. Moreover, we show how this method performs numerically in one dimension. In this particular case, this numerical scheme corresponds to a standard implicit Euler method for the pseudo-inverse of the cumulative distribution function. We demonstrate its capabilities to reproduce easily without the need of mesh-refinement the blow-up of solutions for super-critical masses.

Convergence of singular integrals with general measures

We show that L2-bounded singular integrals in metric spaces with respect to general measures and kernels converge weakly. This implies a kind of average convergence almost everywhere. For measures with zero density we prove the almost everywhere existence of principal values.

Evolutionary switch and genetic convergence on rbcL following the evolution of C4 photosynthesis.

Rubisco is responsible for the fixation of CO2 into organic compounds through photosynthesis and thus has a great agronomic importance. It is well established that this enzyme suffers from a slow catalysis, and its low specificity results into photorespiration, which is considered as an energy waste for the plant. However, natural variations exist, and some Rubisco lineages, such as in C4 plants, exhibit higher catalytic efficiencies coupled to lower specificities. These C4 kinetics could have evolved as an adaptation to the higher CO2 concentration present in C4 photosynthetic cells. In this study, using phylogenetic analyses on a large data set of C3 and C4 monocots, we showed that the rbcL gene, which encodes the large subunit of Rubisco, evolved under positive selection in independent C4 lineages. This confirms that selective pressures on Rubisco have been switched in C4 plants by the high CO2 environment prevailing in their photosynthetic cells. Eight rbcL codons evolving under positive selection in C4 clades were involved in parallel changes among the 23 independent monocot C4 lineages included in this study. These amino acids are potentially responsible for the C4 kinetics, and their identification opens new roads for human-directed Rubisco engineering. The introgression of C4-like high-efficiency Rubisco would strongly enhance C3 crop yields in the future CO2-enriched atmosphere.

Price level convergence, purchasing power parity and multiple structural breaks: an application to US cities

This article provides a fresh methodological and empirical approach for assessing price level convergence and its relation to purchasing power parity (PPP) using annual price data for seventeen US cities. We suggest a new procedure that can handle a wide range of PPP concepts in the presence of multiple structural breaks using all possible pairs of real exchange rates. To deal with cross-sectional dependence, we use both cross-sectional demeaned data and a parametric bootstrap approach. In general, we find more evidence for stationarity when the parity restriction is not imposed, while imposing parity restriction provides leads toward the rejection of the panel stationar- ity. Our results can be embedded on the view of the Balassa-Samuelson approach, but where the slope of the time trend is allowed to change in the long-run. The median half-life point estimate are found to be lower than the consensus view regardless of the parity restriction.

Interprovincial disparities in China since the reforms: Convergence or divergence?

This paper investigates the extent of disparities amongst the provinces of China since the economic reform in 1978 up to the most recent year for which data is available. After a brief review of theoretical and in particular recent empirical literature on regional inequality in China it investigates whether or not the dynamic economic growth in China has been coupled with increasing disparities amongst the Chinese provinces. The paper utilises a few models of convergence along the lines of those hypothesised by neoclassical economists. It employs per capita income and per capita consumption to identify the possible absolute and conditional convergence since the economic reforms. The coverage and impact of the disparities in terms of the relative size of population affected are then taken into account in the analysis of inequality in income and consumption.

UK House Prices: Convergence Clubs and Spillovers

This paper uses the log t test to analyse the convergence of house prices across UK regions and the presence of spillovers e ects. We nd that UK house prices can be grouped into four clusters. Moreover we document the dynamics of the house price spillovers across regions.

Known and new results on absolute convergence of Fourier integrals

New sufficient conditions for representation of a function via the absolutely convergent Fourier integral are obtained in the paper. In the main result, Theorem 1.1, this is controlled by the behavior near infinity of both the function and its derivative. This result is extended to any dimension d &= 2.

Human capital spillovers, productivity and regional convergence in Spain

This paper analyses the differential impact of human capital, in terms of different levels of schooling, on regional productivity and convergence. The potential existence of geographical spillovers of human capital is also considered by applying spatial panel data techniques. The empirical analysis of Spanish provinces between 1980 and 2007 confirms the positive impact of human capital on regional productivity and convergence, but reveals no evidence of any positive geographical spillovers of human capital. In fact, in some specifications the spatial lag presented by tertiary studies has a negative effect on the variables under consideration.

Evolutionary and convergence stability for continuous phenotypes in finite populations derived from two-allele models.

The evolution of a quantitative phenotype is often envisioned as a trait substitution sequence where mutant alleles repeatedly replace resident ones. In infinite populations, the invasion fitness of a mutant in this two-allele representation of the evolutionary process is used to characterize features about long-term phenotypic evolution, such as singular points, convergence stability (established from first-order effects of selection), branching points, and evolutionary stability (established from second-order effects of selection). Here, we try to characterize long-term phenotypic evolution in finite populations from this two-allele representation of the evolutionary process. We construct a stochastic model describing evolutionary dynamics at non-rare mutant allele frequency. We then derive stability conditions based on stationary average mutant frequencies in the presence of vanishing mutation rates. We find that the second-order stability condition obtained from second-order effects of selection is identical to convergence stability. Thus, in two-allele systems in finite populations, convergence stability is enough to characterize long-term evolution under the trait substitution sequence assumption. We perform individual-based simulations to confirm our analytic results.

Absolute convergence of Fourier integrals

In this survey, results on the representation of a function as an absolutely convergent Fourier integral are collected, classified and discussed. Certain applications are also given.

Moduli of smoothness and rate of a.e. convergence for some convolution operators

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