Inverse scattering for vowel articulation with frequency-domain data

An inverse scattering problem is analyzed for vowel articulation in the human vocal tract. When a unit amplitude, monochromatic, sinusoidal volume velocity is sent from the glottis towards the lips, various types of scattering data are used to examine whether the cross sectional area of the vocal tract can uniquely be determined by each data set. Among the data sets considered are the absolute value of the pressure measured at a microphone placed at some distance from the lips, the pressure at the lips, and the transfer function from the glottis to the lips. In case of nonuniqueness, it is indicated what additional information may be used for the unique determination.Comment: 29 pages, 9 figure

A theoretical approach for Pareto-Zipf law

We suggest an analytical approach for Pareto-Zipf law, where we assume random multiplicative noise and fragmentation processes for the growth of the number of citizens of each city and the number of the cities, respectively.Comment: 6 pages 2 figures and dated for IJMPC Volume 19 presumably issue

A new model for competition between many languages

Time evolutions of number of cities, population of cities, world population, and size distribution of present languages are studied in terms of a new model, where population of each city increases by a random rate and decreases by a random division. World population and size distribution of languages come out in good agreement with the available empirical data.Comment: 6 pages 5 figure