Optimal control for cooperative systems involving fractional Laplace operators

In this work, the elliptic $2\times 2$ 2 × 2 cooperative systems involving fractional Laplace operators are studied. Due to the nonlocality of the fractional Laplace operator, we reformulate the problem into a local problem by an extension problem. Then, the existence and uniqueness of the weak solution for these systems are proved. Hence, the existence and optimality conditions are deduced.

Methodology of Functional and Technical Evaluation of Cooperative Intelligent Transport Systems and Its Practical Application

In the area of smart cities, great emphasis is placed on many different fields such as energetics, information systems, and transportation. All of these should lead to a simplification of life thanks to smart technologies. If we talk about the transportation field, the main issues related to this area are safety, traffic efficiency, or the environment. Another condition is the successful acceptance of any new technology by its users. Cooperative systems prove to be a suitable solution for these issues, especially in urban areas. Today, pilot implementations of cooperative systems in European countries are being carried out. However, before they are put into full operation, they need to be tested, evaluated, and assessed. This article focuses on the latter two points, i.e., evaluation and assessment of the cooperative systems. For this purpose, a methodology was created, which describes the procedure chosen in the evaluation and assessment of cooperative systems in the Czech Republic and a demonstration of its use by example. The methodology is focused on three main areas, which in this case are functional evaluation, user acceptance, and impact assessment. For the area of user acceptance, the main source was questionnaires, impact assessment relied on measured data while functional evaluation was based on discussions with the drivers, evaluating the cooperative systems, the measured data, and the expert observations. All collected and measured data were then processed and some of the results of the evaluation of the selected service are presented at the end of this article.

Concluding remarks

This concluding chapter highlights one physiological principle that shines through the discussion of human physiology: the emergence of control through the cooperative, collective action of different entities. Studying physiology is about more than gaining facts. It is also about gaining an outlook that can see, analyse, and appreciate the action of cooperative systems. It is an outlook that fully acknowledges the importance of understanding at the molecular level, but that can still retain a focus on what the molecules are for. In this respect, physiology connects more than most with our deepest questions about what it is to be human.

Stability of a Three-Species Cooperative System with Time Delays and Stochastic Perturbations

Considering the impacts of time delays and different kinds of stochastic perturbations, we propose two three-species delayed cooperative systems with stochastic perturbations in this paper. We establish the sufficient criteria of the asymptotical stability and stability in probability by constructing a neutral stochastic differential equation and some suitable functionals. The impacts of time delays and stochastic perturbations to the system dynamics are revealed by some numerical simulations at the end.

Symmetry results for p-Laplacian systems involving a first-order term

In this paper we obtain symmetry and monotonicity results for positive solutions to some p-Laplacian cooperative systems in bounded domains involving first-order terms and under zero Dirichlet boundary condition.