On Seiffert-like means

We investigate the representation of homogeneous, symmetric means in the form M(x,y)=\frac{x-y}{2f((x-y)/(x+y))}. This allows for a new approach to comparing means. As an example, we provide optimal estimate of the form (1-\mu)min(x,y)+ \mu max(x,y)<= M(x,y)<= (1-\nu)min(x,y)+ \nu max(x,y) and M((x+y)/2-\mu(x-y)/2,(x+y)/2+\mu(x-y)/2)<= N(x,y)<= M((x+y)/2-\nu(x-y)/2,(x+y)/2+\nu(x-y)/2) for some known means

Constructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization

In this paper, we propose a general framework for constructing IGA-suitable planar B-spline parameterizations from given complex CAD boundaries consisting of a set of B-spline curves. Instead of forming the computational domain by a simple boundary, planar domains with high genus and more complex boundary curves are considered. Firstly, some pre-processing operations including B\'ezier extraction and subdivision are performed on each boundary curve in order to generate a high-quality planar parameterization; then a robust planar domain partition framework is proposed to construct high-quality patch-meshing results with few singularities from the discrete boundary formed by connecting the end points of the resulting boundary segments. After the topology information generation of quadrilateral decomposition, the optimal placement of interior B\'ezier curves corresponding to the interior edges of the quadrangulation is constructed by a global optimization method to achieve a patch-partition with high quality. Finally, after the imposition of C1=G1-continuity constraints on the interface of neighboring B\'ezier patches with respect to each quad in the quadrangulation, the high-quality B\'ezier patch parameterization is obtained by a C1-constrained local optimization method to achieve uniform and orthogonal iso-parametric structures while keeping the continuity conditions between patches. The efficiency and robustness of the proposed method are demonstrated by several examples which are compared to results obtained by the skeleton-based parameterization approach

The fallacy in productivity decomposition

This paper argues that the typical practice of performing growth decompositions based on log-transformed productivity values induces fallacious conclusions: using logs may lead to an inaccurate aggregate growth rate, an inaccurate description of the microsources of aggregate growth, or both. We identify the mathematical sources of this log-induced fallacy in decomposition and analytically demonstrate the questionable reliability of log results. Using firm-level data from the French manufacturing sector during the 2009-2018 period, we empirically show that the magnitude of the log-induced distortions is substantial. Depending on the definition of accurate log measures, we find that around 60-80% of four-digit industry results are prone to mismeasurement. We further find significant correlations of this mismeasurement with commonly deployed industry characteristics, indicating, among other things, that less competitive industries are more prone to log distortions. Evidently, these correlations also a affect the validity of studies that investigate the role of industry characteristics in productivity growth

TECHNOLOGICAL ADAPTATION TO RESOURCE SCARCITY IN THE U.S. LUMBER INDUSTRY

This paper provides an econometric investigation of the role of a renewable natural resource, sawlogs, in the production of lumber over the period 1950-1974. The economic scarcity of sawlogs is confirmed. Within a given production technology, the potential for substitution among capital, labor and sawlog inputs is greatly restricted but not impossible. Technological change has been strongly labor-saving but has had a negligible effect on wood requirements. Consequently, the real price of lumber has risen, stimulating development of substitute wood products. Continued decline of the industry is anticipated.Research and Development/Tech Change/Emerging Technologies, Resource /Energy Economics and Policy,

welfare cost of business cycles when markets are incomplete

This paper analyzes the welfare effects of business cycles when workers face uninsurable idiosyncratic labor income risk that has a cyclical component. In accordance with the recent literature, this paper assumes that eliminating business cycles amounts to integrating out aggregate shocks (the integration principle) and that idiosyncratic shocks and aggregate shocks are stochastically independent (the independence assumption). This paper provides two arguments why the previous literature has underestimated the welfare costs of business cycles. First, the welfare cost of business cycles are in general indeterminate, and the previous literature has only reported the lower bound that is consistent with the data. In a simple example calibrated to match the observed cyclical variations in displacement probabilities, the lower bound is .35 percent of average consumption and the upper bound is 1.39 percent (using log-utility). Second, the previous literature has only focused on cyclical variations in job displacement (unemployment) probabilities, but neglected cyclical variations in the average income loss of displaced workers. In a simple calibrated example, the introduction of cyclical variations in the average income loss of displaced workers increases the lower bound from .35 percent of average consumption to .94 percent and the upper bound from 1.39 percent to 1.89 percent (again for log-utility)welfare cost of business cycles, incomplete markets

The Spatial Structure of Young Stellar Clusters. III. Physical Properties and Evolutionary States

We analyze the physical properties of stellar clusters that are detected in massive star-forming regions in the MYStIX project--a comparative, multiwavelength study of young stellar clusters within 3.6 kpc that contain at least one O-type star. Tabulated properties of subclusters in these regions include physical sizes and shapes, intrinsic numbers of stars, absorptions by the molecular clouds, and median subcluster ages. Physical signs of dynamical evolution are present in the relations of these properties, including statistically significant correlations between subcluster size, central density, and age, which are likely the result of cluster expansion after gas removal. We argue that many of the subclusters identified in Paper I are gravitationally bound because their radii are significantly less than what would be expected from freely expanding clumps of stars with a typical initial stellar velocity dispersion of ~3 km/s for star-forming regions. We explore a model for cluster formation in which structurally simpler clusters are built up hierarchically through the mergers of subclusters--subcluster mergers are indicated by an inverse relation between the numbers of stars in a subcluster and their central densities (also seen as a density vs. radius relation that is less steep than would be expected from pure expansion). We discuss implications of these effects for the dynamical relaxation of young stellar clusters.Comment: Accepted for publication in The Astrophysical Journal ; 48 pages, 13 figures, and 6 table