Vol 29, No 4 (2018)

The article considers a three-dimensional inverse problem to determine the conductivity distribution in a three-dimensional body embedded in a layered conducting medium. A uniqueness theorem is proved for the class of layered bodies with finitely many layers where conductivity is observed only in the direction of the layer.

The article examines the basic concepts of reversible circuit design, focusing mainly on existing models of fault-tolerant circuits and testing methods. A new approach is proposed to the synthesis of fault-tolerant reversible elements using fault-tolerant coding of signals in a polarized Hamming space.

We consider a wireless sensor network (WSN) in the form of a chain of sensors with several sinks. Chiasserini–Garetto conditions are imposed on the functioning of the network nodes and the transmission environment. The number of network nodes is assumed in the thousands. A parallel simulation model is constructed to estimate the WSN performance parameters. Computer experiments conducted on a BlueGene/P supercomputer show good scalability of the model.

We consider a game-theoretical model of defense in which the opponents use several types of infinitelydivisible attack and defense weapons. The defender (first player) payoff is the probability of destroying each attack weapon by at least one of the defense weapons. It is assumed that defense deploys at least one unit of each type of weapons. The optimal defense strategy is a pure maximin strategy, and the optimal mixed attack strategy involves choosing only one of the available attack weapons with certain probabilities. The search for optimal player strategies is reduced to the solution of linear programs.

We carry out a numerical investigation of the nonlinear heat equation with a volume heat source that describes combustion with a nonzero background temperature. The problem is considered in cylindrical coordinates assuming radial symmetry. Combustion processes have been studied in both isotropic and anisotropic media. Various types of combustion processes have been identified in the form of thermal dissipative structure, in particular, when combustion is localized in one direction and the combustion region expands in the other direction. Structures form on a nonzero background under certain supercritical perturbations of the background temperature, while subcritical initial disturbances decay and relax to background temperatures. The observed blowups depend on the relations among the parameters describing the power dependence on temperature, thermal conductivity, and the highest order expansion term in the volume heat source.

The following problem is considered: specify a Boolean function of n variables such that every bilinear (polylinear) function is reduced, on a certain number of tuples of the specified function, to a unique bilinear (polylinear) function that is identical with the specified function on these tuples. We show that this is feasible for bilinear functions and for polylinear functions with a fixed number of parentheses k, starting with some n , and we can restrict the analysis to a sequence of functions with definition domain of cardinality O(n).

The affiliation of the third author Ke Wang is Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P.R. China.

The second author Shiheng Wang and the third author Ke Wang are both corresponding authors.