In order to implement the human-centric manufacturing and sustainability concepts in industry, an important effort should be done in order to model working conditions for human operators and improve them. Several studies have been conducted for mass production assembly lines where short cycle times make the work content highly repetitive. However, the case of low-volume production with long cycle times and different impacts on human operators has been rarely considered in the literature. In this paper, we develop a model to take into account the associated ergonomic risks in assembly lines with long cycle times. An optimization method is also developed in order to schedule tasks and assign the required tasks to a set of human operators taking into account the existing ergonomic risks.

We analytically study proximity and distance properties of various kernels and similarity measures on graphs. This helps to understand the mathematical nature of such measures and can potentially be useful for recommending the adoption of specific similarity measures in data analysis.

A constructive method is proposed for finding finite-dimensional submanifolds in the space of smooth functions that are invariant with respect to flows defined by evolutionary partial differential equations. Conditions for the stability of these submanifolds are obtained. Such submanifolds are constructed for generalized Rapoport–Leas equations that arise in the theory of porous media flows.

Superposition of explicit (analytic) monotone non-increasing shock waves for the KdV-Burgers equation is studied. Initial profile chosen as a sum of two such shock waves gradually transforms into a single shock wave of a somewhat complex yet qualitatively predictable structure. The layered media consist of layers with both dispersion and dissipation and layers with dispersion but without dissipation. In the latter case the waves are described by the KdV equation, while in the former --- by the Kdv-Burgers one. A soliton solution of the KdV equation meeting a layer with dissipation transforms somewhat similarly to a ray of light in air crossing semi-transparent plate. Both nonlinear superposition and the behavior of solitons are demonstrated in detail, modelled numerically and graphically presented.

The coalitional manipulability of 13 majoritarian aggregation schemes (voting rules) is studied by computational experiments. We consider a special case of coalition formation in which all agents of manipulating coalition report the same first-ranked alternative upon manipulation, i.e. a group of agents misrepresents their preferences and they agree that the same alternative will be on the first place of their insincere preferences. We find out that in most cases one of the least manipulable rules in this framework is Minimal Dominant Set, which was not among the least manipulable rules in the case of individual manipulation.