卷 41, 编号 1 (2017)

A principle of consistency for grid operators that ensures grid-operator inhomogeneous boundary-value problems are posed well is considered. Grid analogs of first-order differential operators and boundary operators that are consistent in the sense of fulfilling the grid analogs of integral relations are constructed on an irregular triangular grid. These relations are corollaries to the divergence theorem for vector fields that are the product of a scalar by a vector, the vector product of vectors, or the interior product of a vector by a dyadic. In each grid relation, one function is defined at the nodes; the other, in cells. Construction is performed using a grid-operator interpretation of the corollaries to the integral relations, which hold if one of the functions is a piecewise-linear interpolant to the nodal grid function, and the other is the piecewise-constant interpolant of the cell grid function.

The construction of an estimator for a signal function from noisy data is considered. The technique depends on minimizing the probability of exceeding the maximum error in calculating the wavelet coefficients for a given critical value. In a model with additive Gaussian noise, the order of the loss function is estimated in a class of Lipschitz regular functions.

The Germeyer “defense–attack” model is modified to allow for an echeloned defence system in a given direction. The model is a special case of the terminal-type discrete optimal control problem, and it can be solved using the subgradient-descent method. The posed control problem refines the resource level-distribution problem for a given direction, counting more general constraints with allowance for the action abilities of defense tools at various borders.

We study certain simple models of confidential databases in cloud computing systems. In the framework of these models we introduce a concept of deductive security for queries to such databases, find necessary and sufficient conditions of deductive security, and describe some classes of queries which satisfy these requirements.