Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.

In this paper, the degree to which Persian orthography deviates from transparency is quantified and evaluated. We investigate the relations between graphemes and phonemes in Persian, in which the writing system is not fully representative of the spoken language, mostly due to the omission of the short-vowel graphemes. We measure the degree of the Persian orthographic system transparency using a heuristic mathematical model. We apply the same measures to orthographic systems of other languages and compare the results to those obtained for Persian. The results show a relatively high degree of transparency in Persian when it comes to writing, but a low degree of transparency when it comes to reading. We also consider models that avoid the problems related to the short vowels in Persian and these models demonstrate a considerable decrease of the uncertainty in the Persian orthographic system.

Whereas the logistic curve can be used to model the increase in the percentage of periphrastic do in several types of English sentences, a different fit to the data for affirmative declaratives is needed. Two possible fits are considered in this paper, both based on a generalized logistic differential equation with a time-dependent coefficient. Linear and piecewise constant coefficients are used. Linguistic and practical implications of the two approaches are discussed.