Till now, different constitutive models have been applied to model the hot deformation flow curves of different materials. In this research, the hot deformation flow stress of API X65 pipeline steel was modeled using the power law equation with strain dependent constants. The results was compared with the results of the other previously examined constitutive equations including the Arrhenius equation, the equation with the peak stress, peak strain and four constants and the equation developed based on a power function of Zener-Hollomon parameter and a third order polynomial function of strain power a constant number. Root mean square error (RMSE) criterion was used to assess the performance of the understudied models. It was observed that the power law equation with strain dependent constants has a better performance (lower RMSE) than that of the other understudied constitutive equations except for the equation with the peak stress, peak strain and four constants. The overall results can be used for the mathematical simulation of hot deformation processes.

In this study, we use a newly proposed method based on the software structure of the maple, called the Khaters method, and will be introducing exponential, hyperbolic, and trigonometric solutions for one of the Schrö dinger equations, called the nonlinear Schrö dinger equation with the dual power law nonlinearity. Given the widespread use of the Schrö dinger equation in physics and engineering, solving this equation is very important with the above method, which includes a large variety of solutions. Schrö dinger's nonlinear equation is a partial differential equation that plays a significant role in modern physics. ...

In this paper, the homotopy analysis method (HAM) is considered to obtain the solution of the Schrodinger equation with a power law nonlinearity. For this purpose, a theorem is proved to show the convergence of the series solution obtained from the proposed method. Also, an example is solved to illustrate the efficiency of the mentioned algorithm and the h-curve is plotted to determine the region of convergence.

In this paper, a novel risk-based, two-objective (technical and economical) optimal reactive power dispatch method in a wind-integrated power system is proposed which is more consistent with operational criteria.  The technical objective includes the minimization of the new voltage instability risk index. The economical objective includes cost minimization of reactive power generation and active power loss. The proposed voltage instability risk employs a hybrid possibilistic (Delphi-Fuzzy)-probabilistic approach that takes into consideration the operator’s experience, the wind speed and demand forecast uncertainties when quantifying the risk index. The decision variables are the reactive power resources of the system. To solve the problem, the modified multi-objective particle swarm optimization algorithm with sine and cosine acceleration coefficients is utilized. The method is implemented on the modified IEEE 30-bus system. The proposed method is compared with those in the previously published literature, and the results confirm that the proposed risk index is better at estimating the voltage instability risk of the system, especially in cases with severe impact and low probability. In addition, according to the simulation results compared to typical security-based planning, the proposed risk-based planning may increase the security and economy of the system due to better utilization of system resources.

Law is the most important rule and norm in modern life, which regulates the state’s relations with the citizens and the citizens with each other. Every law belongs to a legal system, and it is not unreasonable to say that the value of a legal system depends on the efficiency and quality of the law. The law quality is further determined in the formal and pre-legislative stages, in which the language of the law is of greater importance than in the other stages. All members of society communicate with the law through language. Language plays a constructive role in the functioning of law since the legislator expresses his intentions through words. Thus, it becomes clear that language and law are deeply related. The way language is used in law reflects the quality of the law. Accordingly, explaining the role of language in the legal system helps to know how language works and is used in law and becomes a roadmap to properly writing the law. As a result, this research introduced the knowledge of forensic linguistics through documentary methods and explained the importance of language in the legal system.

The purpose of this article is to examine the effect of political power on rule of law as a basis for economic development. Political power consists of two key components: power transition and power distribution. Power might be centralized in the hands of a small group or distributed among different groups. Power transition is also distinguished by democratic or non-democratic power. In the present study, the application of descriptive-analytical approach provides evidence that centralized political power leads to the violation of citizens’,rights by the politicians. Conversely, decentralized political power restricts the politicians and consequently, prevents the violation of legal rights. Then, the application of an empirical approach and the analysis of 102 countries’,data reveal that intensification in political power concentration will reduce the rule of law quality. In addition, the results indicate that controlling the power distribution effect will remarkably reduce the power transition’, s effect on the quality of rule of law. Sensitivity analysis also demonstrates the results’,stability after changing the dependent variable, adding other control variables and using the instrumental variable method.

In this paper, using the Lie group analysis method, we study the group invariant of the Foam Drainage equation. It shows that this equation can be reduced to ODE. Also we apply the Lie-group classical, and the nonclassical method due to Bluman and Cole to deduce symmetries of the Foam Drainage equation. and we prove that the nonclassical method applied to the equation leads to new reductions, which cannot be obtained by Lie classical symmetries. Also this paper shows how to construct directly the local conservation laws for this equation.

In this paper, river regime equations through developing of unit stream power equation and based on data of Sistan and Karaj Rivers were derived. At the first step, methods and out-comes of former researchers are classified. On the next step, based on dimensional analysis, unit stream power as a function of river flow parameters including suspended sediment load and specific gravity of particles is developed. Using the unit stream power equation and Sistan and Karaj Rivers' data, regime equations are derived for these rivers. Finally, the results derived from regime equations are compared with the field data and regime equations of the other researchers. A good agreement was observed between field data and values resulted from developed regime equations in this research.