Concentration in vanishing adiabatic exponent limit of solutions to the Aw–Rascle traffic model

In this paper, we study the phenomenon of concentration and the formation of delta shock wave in vanishing adiabatic exponent limit of Riemann solutions to the Aw–Rascle traffic model. It is proved that as the adiabatic exponent vanishes, the limit of solutions tends to a special delta-shock rather than the classical one to the zero pressure gas dynamics. In order to further study this problem, we consider a perturbed Aw–Rascle model and proceed to investigate the limits of solutions. We rigorously proved that, as the adiabatic exponent tends to one, any Riemann solution containing two shock waves tends to a delta-shock to the zero pressure gas dynamics in the distribution sense. Moreover, some representative numerical simulations are exhibited to confirm the theoretical analysis.

Atomic Decomposition and Boundedness of Operators on Weighted Hardy Spaces

In this article, we establish a new atomic decomposition for , where the decomposition converges in -norm rather than in the distribution sense. As applications of this decomposition, assuming that T is a linear operator bounded on and 0 < p ≤ 1, we obtain (i) if T is uniformly bounded in -norm for all w-p-atoms, then T can be extended to be bounded from to ; (ii) if T is uniformly bounded in -norm for all w-p-atoms, then T can be extended to be bounded on ; (iii) if T is bounded on , then T can be extended to be bounded from to .

Bias in American Ornithologists' Union Bird Names

Ornithology has developed bodies to make collective decisions on the taxonomy, scientific names, and common names of birds. This tradition within ornithology assists with communication and reduces confusion. For North and Central America, a committee of the American Ornithologists' Union standardizes the taxonomy and nomenclature of all the birds that naturally occur within that area. This paper makes the point that this activity has been dominated by members from the United States, with insufficient attention paid to the appropriate use of the term "American" or to the concerns of citizens of countries other than the USA. As a result, the term "American" is used inappropriately as a synonym for North American in a geographic distribution sense. In addition, the terms "Canadian" and "Mexican" are used very sparingly or not at all in the English common name for species that occur in those countries. Suggestions are made with regards to the membership of the nomenclature committee and for remedying this problem with English common names.

CONVERGENCE IN DISTRIBUTION OF THE PERIODOGRAM OF CHAOTIC PROCESSES

In this work we analyze the convergence in distribution sense of the periodogram function (to the spectral density function) based on a time series of a stationary process Xt = (φ ◦ Tt)(X0) obtained from the iterations of a continuous transformation T invariant for an ergodic probability μ and a continuous function φ taking values in ℝ. We only assume a certain rate of convergence to zero for the autocovariance coefficient of the stochastic process, i.e. we assume there exist C > 0 and β > 2 such that |γX(h)| ≤ C|h|-β, for all h ∈ ℕ, where γX(h) = ∫(φ ◦ Th)(x) φ(x)dμ(x) - (∫ φ(x)dμ(x))2 is the h-autocovariance of the process. Our result applies to the case of exponential decay of correlation (or covariance), as it happens for a continuous expanding transformation T on the circle and a Holder potential φ. It can also be applied to the case when the transformation T has a fixed point with derivative equal to one.

A COMPUTER PROGRAM TO OBTAIN THE WEIGHTS OF A TIME‐DOMAIN WAVE‐SHAPING FILTER WHICH IS OPTIMUM IN AN ERROR‐DISTRIBUTION SENSE

The program presented in this paper (Appendix A) computes the weights of a time‐domain wave‐shaping filter F which will transform a given input signal into a desired output signal in an optimum “error‐distribution” sense (see Mereu, 1976).