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Том 40, № 3 (2016)
- Год: 2016
- Статей: 8
- URL: https://journals.rcsi.science/0278-6419/issue/view/10798
Article
A comparative analysis of adaptive algorithms in the finite element method for solving the boundary value problem for a stationary reaction-diffusion equation
Аннотация
A new adaptive algorithm is proposed for constructing grids in the hp-version of the finite element method with piecewise polynomial basis functions. This algorithm allows us to find a solution (with local singularities) to the boundary value problem for a one-dimensional reaction-diffusion equation and smooth the grid solution via the adaptive elimination and addition of grid nodes. This algorithm is compared to one proposed earlier that adaptively refines the grid and deletes nodes with the help of an estimate for the local effect of trial addition of new basis functions and the removal of old ones. Results are presented from numerical experiments aimed at assessing the performance of the proposed algorithm on a singularly perturbed model problem with a smooth solution.
97-109
Bankruptcy prevention in multiperiod Markowitz optimization problem
Аннотация
A multiperiod version of the Markowitz optimization problem is considered by assuming that the financial market model is discrete with respect to time and the number of scenarios. Basing on the optimal strategy of securities trading, we find the upper bound of the expected final portfolio value which does not lead to bankruptcy.
110-113
Almost everywhere convergence of a wavelet thresholding risk estimate in a model with correlated noise
Аннотация
The problem of estimating a function in a model with correlated noise by thresholding its wavelet decomposition coefficients is considered. The risk estimate using this approach is shown to be strongly consistent.
114-117
On queue length in a queueing system with Erlang incoming flow
Аннотация
A single-channel queueing system with an Erlang incoming flow and random server unavailability intervals as the system releases is considered. The nonstationary and stationary distributions of queue length are obtained.
118-122
Order of the length of Boolean functions in the class of exclusive-OR sums of pseudoproducts
Аннотация
An exclusive-OR sum of pseudoproducts (ESPP) is a modufo-2 sum of products of affine (linear) Boolean functions. The length of an ESPP is defined as the number of summands in this sum; the length of a Boolean function in the class of ESPPs is the minimum length of an ESPP representing this function. The Shannon length function LESPP(n) on the set of Boolean functions in the class of ESPPs is considered; it is defined as the maximum length of a Boolean function of n variables in the class of ESPPs. It is proved that LESPP(n) = Ɵ (2n/n2). The quantity LESPP(n) also equals the least number l such that any Boolean function of n variables can be represented as a modulo-2 sum of at most l multiaffine functions.
123-127
On maximal subgroups of the group of recursive permutations
Аннотация
The group GR of all permutations belonging to R is considered for any partially recursively closed class of functions R. It is proved that the group GR has a continuum number of maximal subgroups. Examples of constructive maximal subgroups of GR are given.
128-132
Specific properties of canonical separated grammars
Аннотация
A class of canonical separated grammars capable of generating the same languages as general-type separated grammars is considered. The main properties and two criteria of canonical grammars are described. A way of unifying nonterminal symbols and proving the uniqueness of the canonical representation for separated grammars is proposed.
133-140
Static binary analysis of mobile applications for the android platform, according to the requirements of information security
Аннотация
An approach is presented for solving the problem of automatically analyzing mobile applications for the Android platform in light of information security requirements when no source code is available.
141-146