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Том 40, № 1 (2016)
- Год: 2016
- Статей: 7
- URL: https://journals.rcsi.science/0278-6419/issue/view/10795
Article
A hybrid scheme of the discrete sources method for analyzing boundary value problems of nano-optics
Аннотация
The problem of the diffraction of a plane linearly polarized wave on a nanodimensional elongated particle located on a permeable substrate is considered. A hybrid scheme of the discrete sources method with allowance for particle geometry is used to construct the solution. The proposed scheme is substantiated mathematically with certain constraints on particle thickness. Numerical results illustrating the capabilities of the method are presented.
1-9
Planning computations in a multiprocessor system with unfixed parameters
Аннотация
The problem of constructing a feasible preemptive multiprocessor schedule is considered for a case where directive intervals are assigned, processors can have arbitrary performance, and the amount of tasks depends linearly on the volume of additional resources allocated for them. In cases where a feasible schedule is not found with an allocated volume of additional resources, the problem of optimally correcting the directive intervals is considered. The solution is based on an analysis of the necessary and sufficient conditions of a feasible schedule’s existence.
41-46
Special modes in a two-sector economy model with an integral utility function
Аннотация
In this work, we study a two-sector economic model with the Cobb–Douglas production function on an infinite planning horizon where the utility function is a functional of an integral form and a Lagrangian of a logarithmic type. A one-dimensional equation is obtained that depends only on the coefficients of elasticity and amortization, and determines the possible special modes. The special modes are described in analytical form.
10-18
A distributed replicator system corresponding to a bimatrix game
Аннотация
Reaction–diffusion type replicator systems are investigated for the case of a bimatrix. An approach proposed earlier for formalizing and analyzing distributed replicator systems with one matrix is applied to asymmetric conflicts. A game theory interpretation of the problem is described and the relation between dynamic properties of systems and their game characteristics is determined. The stability of a spatially homogeneous solution for a distributed system is considered and a theorem on maintaining stability is proved. The results are illustrated with two-dimensional examples in the case of distribution.
19-27
On quasi-universal word functions
Аннотация
A method for constructing quasi universal “simple form” functions in the class of word functions is proposed. The method is used to construct an explicit superposition basis in the class of functions that can be computed in polynomial time.
28-34
A multistage exchange trading model with asymmetric information and elements of bargaining
Аннотация
A modification of the discrete multistage exchange trading model with risky securities is considered. At each stage of trading, the players place their integer bids. One of the players knows the real price, while the other knows only its probability distribution. The transaction price is defined as a convex combination of the proposed bids with some given coefficient. The solution to an infinitely long game is obtained.
35-40
Compression of underdetermined data in a 7-piece chess table
Аннотация
Block compression algorithms used for solving the problem of 7-piece chess endings are presented. The algorithms are based on data reordering before compression, the RE-PAIR compression algorithm, and use of the so-called underdetermined value method.
47-52