A principle is proposed for constructing a transducer for detecting the position of interfaces between layers, the dielectric constant, and the amount of fuel in three-layer media. Sensor structures in the form of an electromagnetic cavity excited at three characteristic frequencies are developed, along with an algorithm for conversion of primary data from coarse measurements at these frequencies. The transducer provides high measurement accuracy.

We consider an application of power indices, which take into account preferences of agents for coalition formation proposed for an analysis of power distribution in elected bodies to reveal most powerful (central) nodes in networks. These indices take into account the parameters of the nodes in networks, a possibility of group influence from the subset of nodes to single nodes, and intensity of short and long interactions among the nodes. Some properties of the indices are discussed. Various applications are presented for the network of countries – those of religion, migration, foreign claims, conflicts, exchange of students, food export-import, etc.

This paper designs an allotment mechanism for a limited amount of an infinitely divisible good (resource) among a finite number of agents under transferable utility. The mechanism is efficient in the sense of total agents’ utility maximization. As a solution, we introduce an adaptation of the Groves–Ledyard “quadratic government” that was initially suggested for the problem of public good.

Dynamic quenching of the intensity of dual-band fluorescence pulses is modelled using numerical solutions of the equations for the population matrix of a model molecule with five states. The state with the highest energy is assumed to be resonantly excited by light and two other excited states that are populated by subsequent relaxation processes are assumed to be the initial states for molecular transitions with emission of dual-band fluorescence photons. The model parameters for the molecule are chosen to match the typical parameters of molecules with intramolecular proton phototransfer. Quenching is treated as a consequence of nonradiative decay of the excited states of the fluorescing molecule owing to collisions with quenchant molecules. Examples of different dual-band fl uorescence quenching mechanisms for the model molecule are given, depending on the decay of particular excited states of the molecule involving nonradiative intramolecular transitions or transitions into states of the quenchant molecules. Keywords mathematical modelling fluorescence quenching dual-band fluorescence pulses intramolecular hydrogen bond proton phototransfer