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Том 41, № 1 (2017)
- Год: 2017
- Статей: 8
- URL: https://journals.rcsi.science/0278-6419/issue/view/10800
Article
Consistent grid operators with the cell-nodal definition of grid functions
Аннотация
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.
1-10
11-13
Asymptotic behavior of the loss function in the multiplicative scaling of the wavelet coefficients of a signal function
Аннотация
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.
14-17
One control problem of a pencil of trajectories
Аннотация
A linear control problemwith a nonsingleton initial set is dealt with. For this problem,we consider the problem of transforming this initial set along trajectories of a linear controlled system into some fixed terminal set in a finite time using a single control. Various aspects of this control problem are studied using the machinery of support functions.
18-24
Multi-level defense system models: overcoming by means of attacks with several phase constraints
Аннотация
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.
25-31
Closure operators with positive connectives and quantifiers
Аннотация
Closure operators based on the logical connectives & and ∨ and the quantifiers ∃ and ∀ and extend the superposition operator are classified. The (&∃∀)-closure operator, which uses only the connective & and both quantifiers, is considered. The basic properties of the (&∃∀)-closure operator are determined. All of the 15 (&∃∀)-closed classes of Boolean functions are found.
32-37
On the deductive security of queries to confidential databases in cloud computing systems
Аннотация
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.
38-43
Ant algorithms for scheduling computations in data centers
Аннотация
An ant colony algorithm is considered for the problem ofmapping requests onto physical resources of data centers. Results from an experimental study of the properties of the algorithm are presented, and it is compared to algorithms that combine greedy strategies and limited searches.
44-50