The objective of this article is to derive the necessary optimality conditions, known as Pontryagin's MINIMUM PRINCIPLE, for fuzzy optimal control problems based on the concepts of differentiability and integrability of a fuzzy mapping that may be parameterized by the left and right-hand functions of its a-level sets.

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.

The traditional method for studying non-stationary signals is spectrogram based on the short-time Fourier transform (STFT). The well known limitation of the STFT is the inherent trade-off between time and frequency resolution. The Wigner-Ville (WV) distribution has the best time-frequency resolution, but its draw back is generating cross-terms. The matching pursuit (MP) distribution based on using the Gaussian atom is always positive, does not include crossterm, and has convenient resolution. In this paper, we have shown in addition to the known properties, the MP distribution can also remove the additive noise inherently. On the other words, we are able to remove the noise just by limiting the algorithm iterations and without paying any additional cost. Although the MP distribution based on using the Gaussian atoms is always positive and it has convenient resolution, according to the MP the time marginal and the frequency marginal will not be obtained accurately. In this paper, it has been shown that by implementing the MINIMUM cross entropy (MCE) technique according to the MP distribution as a priory positive distribution, the new extracted distribution has the most similarity to the MP distribution and it also satisfies the correct time and frequency marginal.

In this paper, a novel and practical approach is proposed to solve the fuzzy optimal control (FOC) using an improved multi-layer perceptron (IMLP) network along with the Pontryagin MINIMUM PRINCIPLE (PMP).

In this paper, finding Dynamic Load Carrying Capacity (DLCC) of flexible link manipulators in point to-point motion was formulated as an optimal control problem. The finite element method was employed for modelling and deriving the dynamic equations of the system. The study employed indirect solution of optimal control for system motion planning. Due to offline nature of the method, many difficulties such system nonlinearities and all types of constraints can be catered for and implemented easily. The application of Pontryagin’s MINIMUM PRINCIPLE to this problem was resulted in a standard two-point boundary value problem (TPBVP), solved numerically. Then, the formulation was developed to find the maximum payload and corresponding optimal path. The main advantage of the proposed method is that the various optimal trajectories can be obtained with different characteristics and different maximum payloads. Therefore, the designer can select a suitable path among the numerous optimal paths. In order to verify the effectiveness of the method, a simulation study considering a two-link flexible manipulator was presented in details.

The approach based on the constitutionalization of criminal institutions is one of the most effective strategies for organizing the discourses aimed at safeguarding fundamental rights and freedoms of citizens against the state power. Aiming at alleviating the damage caused by unnecessary imprisonment and systematizing the Iranian judicial procedures in selection of this punishment necessitates finding a solution in this regard in legislative and judicial criminal policy-making levels. Doing so, constitutionalization of adopting the "MINIMUM legal punishment of imprisonment" and recognizing this approach as a "legal PRINCIPLE" is one of the strategies that can play a pivotal role in realization of the foregoing goals. In this article, through relying on the PRINCIPLE of criminal minimalism, the way of applying this PRINCIPLE in the selection of imprisonment in Iranian and French legal systems as well as Islamic jurisprudence is studied comparatively.

Introduction: In this study, we analyze the optimal intervention strategies that lead to reducing the effects of the COVID-19 pandemic by artificial neural networks (ANNs). Our aim is to investigate the effects of optimal control strategies, such as the implementation of government intervention, testing, and vaccination policies during outbreaks.Methods: We utilized a controlled SIDAREV model to study the progression of the COVID-19 pandemic. Using Pontryagin's MINIMUM PRINCIPLE (PMP) for the SIDAREV model, we defined an unconstrained minimization problem. Applying the Hamiltonian conditions, we approximated the obtained ordinary differential equations (ODE) using ANNs. We utilized the multilayer perceptron (MLP) to obtain the approximate solution of the states and co-states functions.Results: We observed the effects of optimal control strategies, and to show the efficiency of the proposed method, we compared it with the Runge-Kutta method through some examples.Conclusion: Using a mathematical model that simulates the behavior of the Covid-19 disease, we can examine the effects of controllers such as government interventions, tests and vaccinations with the neural network method. The results show that this method is useful in solving the problem of optimal control of infectious diseases.

Leaf stripe disease (LSD) of grapevine, which was previously known as esca complex disease, is one of the most important and destructive trunk diseases of grapevines. Phaeoacremonium MINIMUM is the PRINCIPLE hyphomycete associated with disease. Chemical control of LSD has proven difficult, meanwhile, application of biological control agents for disease management have been promising. The aim of present study was to evaluate inhibitory potentiol of three Trichoderma species sincluding one commercial product (Trichoderma harzianum T22) and two endophytic isolates, T. longibrachiatum and T. brevicompactum, against four isolates of Pm. MINIMUM with opposite mating type (two MAT1-1 and two MAT1-2 isolates) using dual culture, volatile and non-volatile metabolite assays. The results of this study showed that all three species of the antagonist had significant inhibitory effect on the growth of Pm. MINIMUM, in comparison to the control. In dual culture assay, T. harzianum T22 showed the highest potential in the inhibition of the Pm. MINIMUM growth, with 76. 53 percent growth inhibition, in comparison to the two other antagonists. In volatile metabolites assay, significant differences were observed among the antagonists in growth inhibition of the Pm. MINIMUM. In non-volatile compounds assay, T. brevicompactum with 75. 46 percent growth inhibition of pathogen, showed the highest control potential in comparison with the other two species. Non-volatile compounds of T. longibrachiatum and T. harzianum T22 showed 46. 93 and 17. 67 percent inhibition on colony growth, respectively. Evaluation of the inhibitory effects of these antagonists on the opposite mating types of Pm. MINIMUM showed that volatile compounds of T. longibrachiatum were more effective on MAT1-1 (48. 74% growth inhibition) compared to MAT1-2 (35. 10 growth inhibition). Overall, the results of this study reveal T. brevicompactum as an effective antagonist against Pm. MINIMUM; hence, further evaluation of its biocontrol properties and efficacy in disease control under greenhouse and field condition remain to be studied.