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In this paper, we extend Guo and Xia’s necessary condition which has been presented by Guo and Xia (Fuzzy optimizat Decis Mak 5: 33–47, 2006) in order to study the finitely many constraints of fuzzy relation inequalities and optimize a linear objective function on this region which is defined by the fuzzy max–min operator. The new condition provides a means for removing the unnecessary paths resulting from Guo and Xia’s paths. Also, an algorithm and two numerical examples are offered to abbreviate and illustrate the steps of the resolution process of the problem. [ABSTRACT FROM AUTHOR]

degenerate parabolic system of equations of two-phase multicomponent filtration is considered. It is shown that this system can be treated as a system of conservation laws and the notions developed in the corresponding theory, such as hyperbolicity, shock waves, Hugoniot relations, stability conditions, Riemann problem, entropy, etc., can be applied to this system. The specific character of the use of such notions in the case of multicomponent filtration is demonstrated. An example of two-component mixture is used to describe the specific properties of solutions of the Riemann problem. [ABSTRACT FROM AUTHOR]

We consider the control problem for a group containing a given number of uninformed agents; this is a consensus problem. An agent's model is defined by a two-dimensional integrator. The purpose of this work is to synthesize a decentralized smooth law of the agents' motion in a multiagent system that would let us construct and support a prescribed configuration of the group of agents. The considered group should follow the leader, either real or virtual. Informational links between agents are given by a communications digraph. The work shows numerical results for various initial conditions and various desired trajectories. [ABSTRACT FROM AUTHOR]

We determine necessary conditions under which integrable vector evolution equations of third order admit Miura-type transformations. For equations integrable on the n-dimensional sphere, we obtain first-order differential substitutions. [ABSTRACT FROM AUTHOR]

In this paper we study fair division problems with the special feature that there exists only one transferable good that everyone likes. This good will be used to compensate some individuals for their differences in other non-transferable resources (like talents or handicaps). In this context we test the traditional no-envy solution and we verify that: 1) its ethical content can be a matter of discussion, and 2) frequently it does not select a non-empty set of allocations. We propose an extension of this criterion that partially solves the existence problem while also retaining the main ethical properties of the preceding solution. [ABSTRACT FROM AUTHOR]