Speech tested for Zipfian fit using rigorous statistical techniques

Zipf’s law describes the relationship between the frequencies of words in a corpus and their rank. Its most basic form is a simple series, indicating that the frequency of a word is inverselyproportional to its rank:1/2, 1/3, 1/4,...The past two decades have seen the emergence of usage-based and cognitive approaches to language study. A key observation of these approaches, along with the importance of frequency, is that speech differs in substantial and structural ways from writing. Yet, except for a few older analyses performed on very small corpora, most studies of Zipf’s law have been done on written corpora. Further, a judgement of Zifianness in much of this work is based on loose and informal criteria. In fact, sophisticated statistical techniques have been developed for curve fitting in recent years in the mathematics and physics literature. These include the use of the Kolmogorov-Smirnov statistic, along with maximum likelihood estimation to generate p-values and the use of the complementary error function for normal distributions. The latter helps determine if a corpus, failing a Zipfian fit, might be better described by another distribution. In this paper, we will:Show that three corpora of recorded speech follow a power law distribution using rigorous statis- tical techniques: Buckeye, Santa Barbara, MiCaseDescribe preliminary results showing that the techniques outlined in this paper may be useful in the diagnoses of those conditions that can include disordered speech.Explain how to do the analyses described in this paper.Explain how to download and use the R/Python code we have written and packaged as the Zipf Tool Kit

Pertechnetate/Perrhenate Surface Complexation on Bamboo Engineered Biochar

The work deals with the evaluation of biochar samples prepared from Phyllostachys Viridiglaucescens bamboo. This evaluation consists of the characterization of prepared materials’ structural properties, batch and dynamic sorption experiments, and potentiometric titrations. The batch technique was focused on obtaining basic sorption data of 99mTcO4− on biochar samples including influence of pH, contact time, and Freundlich isotherm. ReO4−, which has very similar chemical properties to 99mTcO4−, was used as a carrier in the experiments. Theoretical modeling of titration curves of biochar samples was based on the application of surface complexation models, namely, so called Chemical Equilibrium Model (CEM) and Ion Exchange Model (IExM). In this case it is assumed that there are two types of surface groups, namely, the so-called layer and edge sites. The dynamic experimental data of sorption curves were fitted by a model based on complementary error function erfc(x).

Diffusion coefficient calculated by complementary error function for the sublimation diffusion of disperse dye

In order to find a simple and reliable method for the calculation of the diffusion coefficient, the correlation equation of concentration and distance in the form of complementary error function was derived from solving an ordinary differential equation of the diffusion equation. A disperse dye in paste was treated at 170°C–190°C for 3–4 h for the sublimation diffusion into polyethylene terephthalate using a film roll method. Quadratic regression analysis on the profile of dye concentration–distance was used to determine the surface concentration. The diffusion coefficient of each layer was calculated by obtaining the variable value of the complementary error function from the ratio of the mean dye concentration of each layer to the surface concentration. From linear regression analysis on the Arrhenius plot of the logarithm of the diffusion coefficient versus the reciprocal of absolute temperature, the correlation coefficient for the diffusion of 3 h was 0.9978 and that of 4 h was 0.9991. Thus, it was expected that the diffusion coefficients determined by the equation of complementary error function adopted in this experiment were reliable. The activation energy of diffusion for 3 h was 30.5 kcal mol−1 and that for 4 h was 27.4 kcal mol−1.