We have developed and discussed the theory and applications of a physicalmathematical model of the dynamics of rain attenuation and have tested it as a rain attenuation prediction model in slant paths. Other parameters, however, such as fade durations and rates of change of fades, can be calculated. The main physical input is the 1-min rain rate time series of a site, which is converted to a rain rate space series along horizontal or slant paths by using an estimate of the storm translation speed v method known as "synthetic storm technique." However, the long-term predictions are found to be insensitive to v. The vertical structure of precipitation is modeled with two layers. The model was tested against the probability distributions of rain long-term 11.6-GHz attenuation collected at the three Italian stations (Fucino, Gera Lario, and Spino d'Adda) during the SIRIO propagation experiment (13 years of data) for which concurrent rain rate time series are available. In the outage probability range 10 -! to 5x10-3% defined the prediction error E = ( Ap -A m ) / A m (where A and A are respectively Itl p ' the measured and predicted rain attenuations, dB),
Statistics of languages are usually calculated by counting characters, words, sentences, word rankings. Some of these random variables are also the main "ingredients" of classical readability formulae. Revisiting the readability formula of Italian, known as GULPEASE, shows that of the two terms that determine the readability index G-the semantic index C G , proportional to the number of characters per word, and the syntactic index G F , proportional to the reciprocal of the number of words per sentence-G F is dominant because G C is, in practice, constant for any author throughout seven centuries of Italian Literature. Each author can modulate the length of sentences more freely than he can do with the length of words, and in different ways from author to author. For any author, any couple of text variables can be modelled by a linear relationship y mx = , but with different slope m from author to author, except for the relationship between characters and words, which is unique for all. The most important relationship found in the paper is that between the short-term memory capacity, described by Miller's "7 ∓ 2 law" (i.e., the number of "chunks" that an average person can hold in the short-term memory ranges from 5 to 9), and the word interval, a new random variable defined as the average number of words between two successive punctuation marks. The word interval can be converted into a time interval through the average reading speed. The word interval spreads in the same range as Miller's law, and the time interval is spread in the same range of short-term memory response times. The connection between the word interval (and time interval) and short-term memory appears, at least empirically, justified and natural, however, to be further investigated. Technical and scientific writings (papers, essays, etc.
This paper reports a statistical relationship between 1 s averaged rain attenuation (A, in decibels) and standard deviation (sigma, in decibels) of simultaneous tropospheric scintillation in 1 s intervals, derived from high resolution (50 samples/s) experimental 19.77 GHz attenuation time series recorded at Spino d'Adda (45.4°N) in a 30.6° slant path to satellite Olympus during an observation time of approximately 1 year. During rain the relationship between scintillation and rain attenuation, suitably separated, can be fit by the power law formula derivable from a turbulent thin layer model
The purpose of the paper is to extend the general theory of translation to texts written in the same language and show some possible applications. The main result shows that the mutual mathematical relationships of texts in a language have been saved or lost in translating them into another language and consequently texts have been mathematically distorted. To make objective comparisons, we have defined a “likeness index”—based on probability and communication theory of noisy binary digital channels-and have shown that it can reveal similarities and differences of texts. We have applied the extended theory to the New Testament translations and have assessed how much the mutual mathematical relationships present in the original Greek texts have been saved or lost in 36 languages. To avoid the inaccuracy, due to the small sample size from which the input data (regression lines) are calculated, we have adopted a “renormalization” based on Monte Carlo simulations whose results we consider as “experimental”. In general, we have found that in many languages/translations the original linguistic relationships have been lost and texts mathematically distorted. The theory can be applied to texts translated by machines. Because the theory deals with linear regression lines, the concepts of signal-to-noise-ratio and likenss index can be applied any time a scientific/technical problem involves two or more linear regression lines, therefore it is not limited to linguistic variables but it is universal.
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