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In this paper, based on the discrete lifetime distribution, the residual and past of the Tsallis and Renyi extropy are introduced as new measures of information. Moreover, some of their properties and their relation to other measures are discussed. Furthermore, an example of a uniform distribution of the obtained models is given. Moreover, the softmax function can be used as a discrete probability distribution function with a unity sum. Thus, applying those measures to the softmax function for simulated and real data is demonstrated. Besides, for real data, the softmax data are fit to a convenient ARIMA model. [ABSTRACT FROM AUTHOR]

In this study, eight configurations of oval and flat tubes in annular finned-tube thermal devices are examined and compared with the conventional circular tube. The objective is to assess the effect of tube flatness and axis ratio of the oval tube on thermal-flow characteristics of a three-row staggered bank for Re (2600 ≤ Re ≤ 10,200). It has been observed that the thermal exchange rate and Colburn factor increase according to the axis ratio and the flatness, where O1 and F1 provide the highest values. O1 produces the lowest friction factor values of all the oval tubes at all Re, and F4 gives 13.2–18.5% less friction than the other tube forms. In terms of performance evaluation criterion, all of the tested tubes outperformed the conventional circular tube (O5), with O1 and F1 obtaining the highest values. The global performance criterion of O1 has been found to be 9.6–45.9% higher as compared to the other oval tube geometries at lower values of Re, and the global performance criterion increases with the increase in flatness. The F1 tube shape outperforms all the examined tube designs; thus, this tube geometry suggests that it be used in energy systems. [ABSTRACT FROM AUTHOR]

Statistical and artificial neural network models are applied to forecast the quantum scheme of a three-level atomic system (3LAS) and field, initially following a photon added negative binomial distribution (PANBD). The Mandel parameter is used to detect the photon statistics of a radiation field. Explicit forms of the PANBD are given. The prediction of the Mandel parameter, atomic probability of the 3LAS in the upper state, and von Neumann entropy are obtained using time series and artificial neural network methods. The influence of probability success photons and the number of added photons to the NBD are examined. The total density matrix is used to compute and analyze the time evolution of the initial photonic negative binomial probability distribution that governs the 3LAS–field photon entanglement behavior. It is shown that the statistical quantities are strongly affected by probability success photons and the number of added photons to the NBD. Also, the prediction of quantum entropy is achieved by the time series and neural network. [ABSTRACT FROM AUTHOR]