A double ambiguity has been charged against Rawls’s difference PRINCIPLE (DP). Is it Maximin, Leximin, or something else? Usually, following A. Sen, scholars identify DP with the so-called Leximin. One argues here that one has to distinguish 1° the Leximin, 2° the Maximin (as rule of justice formally analogous to the maximin rule of decision), represented by the figure in L of the perfectly substitutable goods, and 3° the genuine DP. When the augmentation of inequality benefits the worse off, only Pareto-strong improvements are permitted. Leximin would also permit Pareto-weak improvements too (after the first MAXIMUM D), where only the richest improves: from (2, 3) to (2, 5), say. This is forbidden by DP. With two classes, unlike Maximin, DP has no curve of indifference and is always decisive, as Leximin is. For undecisive Rules of Justice, which admit indifferent curves, I propose to add a lexically secondary rule, to break ties. That move is able to clarify the links and the differences between on the one hand Maximin alone, with its typical indifference curves in L, and on the other hand, the DP properly understood and the Leximin, which both have no indifferent curves. With two classes of persons (best off/worse off), DP appears more egalitarian than Leximin, because it's secondary rule is MinIn (Minimization of Inequality). But the intuition behind the distinction is that it cannot possible “fair” that only the best off improves in a productive social cooperation.

MAXIMUM of the Renyi entropy and the Tsallis entropy are generalization of the MAXIMUM entropy for a larger class of Shannon entropy. In this paper we introduce the MAXIMUM Renyi entropy and some of the attributes of distributions which have MAXIMUM Renyi entropy investigated. The form of distributions with MAXIMUM Renyi entropy is power so we state some properties of these distributions and we have a new form of the Renyi entropy. After pointing the topics of minimum Renyi divergence, some other points in this relation have been discussed. An another form of Renyi divergence have also obtained. Therefore we discussed some of the economic applications of the MAXIMUM entropy. Meanwhile, the review of the Csiszar information measure, the general form of distributions with minimum Renyi divergence have obtained.

A long time ago, since the launch of the first artificial satellite in 1957, controling attitude of satellites has been considered by the designers and engineers of aerospace industry. Considering the importance of this issue various methods of control in response to this need have been presented and analyzed until now. In this paper, we propose and analyze a three-axis optimal control on the six-dimensional system which describes the kinetic and kinematic equations of a satellite subjected to deterministic external perturbations which induce chaotic motion. At first, the chaotic behavior of system using Lyapunov exponents (LE) and numerical simulations is investigated when no control is affected. Then, a three-axis optimal control is presented by the Pontryagin MAXIMUM PRINCIPLE (PMP). This optimal control stabilizes the satellite attitude around the equilibrium point of origin. Finally, we give some simulation results to visualize the effectiveness and feasibility of the proposed method.

Accurate estimation of runoff for a watershed is a very important issue in water resources management. In this study, the monthly runoff was estimated using the rainfall information and conditional probability distribution model based on the PRINCIPLE of MAXIMUM entropy. The information of monthly rainfall and runoff data of Kasilian River basin from 1960 to 2006 were used for the development of model. The model parameters were estimated using the prior information of the watershed such as mean of rainfall, runoff and their covariance. Using the developed model, monthly runoff was estimated for different values of runoff coefficient, return period, , at different probability levels of rainfall for the basin under study. Results showed that the developed model estimates runoff for all return periods satisfactorily if the runoff coefficient value is taken 0.6. Also, it is observed that at a particular probability level and runoff coefficient, the estimated runoff decreases as return period increases. However, the rate of change of runoff decreases slightly as return period increases.

Hydrological cycle is directed into thermodynamic non-equilibrium state and MAXIMUM entropy production through thermodynamic processes. Therefore, it is possible to understand and describe hydrological cycle through computation of entropy production rate and the MAXIMUM entropy production PRINCIPLE (MEP). Based on MEP, if there are sufficient degrees of freedom within a system, it will adopt a steady state at which entropy production is maximized under existing restrictions. This PRINCIPLE can help to estimate the hydrological components and parameters without need for detailed understanding of watershed characteristics. Due to the importance of this issue in the science of hydrological modeling and the lack of Persian resources in this field, the present study examines the hydrological cycle from a thermodynamic point of view using valid scientific sources. In this study, the hydrological cycle is considered as a thermodynamic system and the method of calculating entropy production rate by components of water balance is presented. Also, how to estimate hydrological components using the MEP PRINCIPLE is explained in a simple example. Overall, the MEP PRINCIPLE holds great promise for equipping us with a better understanding of the organization of hydrological processes within the Earth system and development of the models based on non-equilibrium thermodynamic.