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Purpose – The COVID-19 pandemic is a new crisis in the world that caused many restrictions, from personal life to social and business. In this situation, the most vulnerable groups such as refugees who are living in the camps are faced with more serious problems. Therefore, a system dynamic approach has been developed to evaluate the effect of applying different scenarios to find out the best response to COVID-19 to improve refugees’ health and education. Design/methodology/approach – The interaction of several health and education factors during an epidemic crisis among refugees leads to behavioral responses that consequently make the crisis control a complex problem. This research has developed an SD model based on the SIER model that responds to the public health and education system of Syrian refugees in Turkey affected by the COVID-19 virus and considered three policies of isolation, social distance/hygiene behavior and financial aid using the available data from various references. Findings – The findings from the SD simulation results of applying three different policies identify that public health and education systems can increase much more by implementing the policy of social distance/hygiene behavior, and it has a significant impact on the control of the epidemic in comparison with the other two responses. Originality/value – This paper contributes to humanitarian organizations, governments and refugees by discussing useful insights. Implementing the policy of social distance and hygiene behavior policies would help in a sharp reduction of death in refugees group. and public financial support has improved distance education during this pandemic.

We consider the Dirac equation written in polar form, without any external potential but equipped with a non-zero tensorial connection, and we find a new type of solution that is localized around the origin with a decreasing exponential behavior in the radial coordinate.

Heat transfer in counterflow heat exchangers is modeled by using transport and balance equations with the temperatures of cold fluid, hot fluid, and metal pipe as state variables distributed along the entire pipe length. Using such models, boundary value problems can be solved to estimate the temperatures over all the length by means of measurements taken only at the boundaries. Conditions for the stability of the estimation error given by the difference between the temperatures and their estimates are established by using a Lyapunov approach. Toward this end, a method to construct nonlinear Lyapunov functionals is addressed by relying on a polynomial diagonal structure. This stability analysis is extended in case of the presence of bounded modeling uncertainty. The theoretical findings are illustrated with numerical results, which show the effectiveness of the proposed approach.

State observers for systems having Lipschitz nonlinearities are considered for what concerns the stability of the estimation error by means of a decomposition of the dynamics of the error into the cascade of two systems. First, conditions are established in order to guarantee the asymptotic stability of the estimation error in a noise-free setting. Second, under the effect of system and measurement disturbances regarded as unknown inputs affecting the dynamics of the error, the proposed observers provide an estimation error that is input-to-state stable with respect to these disturbances. Lyapunov functions and functionals are adopted to prove such results. Third, simulations are shown to confirm the theoretical achievements and the effectiveness of the stability conditions we have established.

The optimal handling of level sets associated to the solution of Hamilton-Jacobi equations such as the normal flow equation is investigated. The goal is to find the normal velocity minimizing a suitable cost functional that accounts for a desired behavior of level sets over time. Sufficient conditions of optimality are derived that require the solution of a system of nonlinear Hamilton-Jacobi equations. Since finding analytic solutions is difficult in general, the use of numerical methods to obtain approximate solutions is addressed by dealing with some case studies in two and three dimensions.