A novel recipe for exactly solving in finite terms a class of special differential Riccati equations is reported. Our procedure is entirely based on a successful resolution strategy quite recently applied to quantum dynamical time-dependent SU(2) problems. The general integral of exemplary differential Riccati equations, not previously considered in the specialized literature, is explicitly determined to illustrate both mathematical usefulness and easiness of applicability of our proposed treatment. The possibility of exploiting the general integral of a given differential Riccati equation to solve an SU(2) quantum dynamical problem, is succinctly pointed out.

We develop a new approach to the study of subgroups in the Cremona group. Namely, we consider the class of differential equations $y''=F(x,y)$ with rational right parts and its symmetry group. This group is a subgroup in the Cremona group of birational automorphisms of $\mathbb{C}^2$, which makes it possible to apply for their study methods of differential invariants and geometric theory of differential equations. Also, using algebraic methods in the theory of differential equations we obtain a global classification for such equations instead of local classifications for such problems provided by Lie, Tresse and others.

The paper is devoted to a methodology oriented to eliciting professional skills of a team of human-operators of a technological plant by applying system identification techniques. Within the frameworks, the aim is to derive an input/output model that might reflect the actual level of group professional competences and skills. Deriving the required input/output model is based on applying such a kind of the “proxy”, that is indirect, variables as the time. Namely, there is applied the time that is needed to the team of human-operators to make a decision on the plant process behavior using information provided by information sources distributed over an information & control board, such as, say, group view displays (GVD). In turn, these times are proposed to be fixed by use of eye trackers. Obtained in such a manner and calculated by use of data of observation of actual algorithm of experienced human-operator team performance, the model characteristics represent a tool for evaluation of human-operator team experience.

A method is proposed to support management policy design and verification in complex cyber-physical & human systems (CPHS). A hierarchy of interconnected formal models is built to provide the multi-faceted view of the conflict situation lying in the core of a certain management problem. Game-theoretical analysis reveals the problem and mechanism design suggests the alternative management policy. Its efficiency is verified by multi-agent simulations and gaming experiments with experts. The approach is illustrated using the examples of two market manipulation issues arising on the Russian wholesale electricity market.

Based on the interdisciplinary approach covering the analysis of cognitive mapping practices and modern approaches to comprehending mental processes in cognitive science, the cognitive approach to the analysis of processes of identification of objects, situations, etc. is proposed, taking account of cognitive aspects that affect validity of the end results. The approach is capable to explain the traditional reducing sight of methodologists at cognitive processes of identification and to fix some conditions at which the reducing vision generates risks for validity of end results. Some proposals to increase identification validity based on verification follow from the models within the approach. The approach was developed and successfully tested with reference to cognitive mapping of complex and ill structured situations, where and when cognitive issues of identification are brightly expressed and cannot be ignored in view of validity of the end results.