The paper provides mathematical analysis of sensitivity of different combination rules in the DS/AHP method when an alternative is added to the set of decision alternatives while solving foresight problems. Different cases of rank reversals are defined and two sets of conditions for these cases using the method DS/AHP are considered. Rank reversals are illustrated when the DS/AHP method is used to solve practical problem of critical technologies of energy conservation and power efficiency evaluation in Ukraine. It is shown that the DS/AHP method is not sensitive to exclusion (or addition) of an irrelevant decision alternative from (or to) the set of decision alternatives.

The iterative reconstruction methods of the wavefront
phase estimation from a set of discrete phase slope measurements have been
considered. The values of the root-mean-square difference between the
reconstructed and original wavefront have been received for Jacobi, Gauss-Seidel,
Successive over-relaxation and Successive over-relaxation with Simpson
Reconstructor methods. The method with the highest accuracy has been defined.

This paper deals with the calculation of a vector of reliable weights of decision
alternatives on the basis of interval pairwise comparison judgments of experts.
These weights are used to construct the ranking of decision alternatives and to
solve selection problems, problems of ratings construction, resources allocation
problems, scenarios evaluation problems, and other decision making problems. A
comparative analysis of several popular models, which calculate interval
weights on the basis of interval pairwise comparison matrices (IPCMs), was
performed. The features of these models when they are applied to IPCMs with
different inconsistency levels were identified. An algorithm is proposed which
contains the stages for analyzing and increasing the IPCM inconsistency,
calculating normalized interval weights, and calculating the ranking of
decision alternatives on the basis of the resulting interval weights. It was
found that the property of weak order preservation usually allowed identifying
order-related intransitive expert pairwise comparison judgments. The correction
of these elements leads to the removal of contradictions in resulting weights
and increases the accuracy and reliability of results.

Abstract:
The
paper proposes a new method of dynamic VaR and CVaR risk measures forecasting.
The method is designed for obtaining the forecast estimates of risk measures
for volatile time series with long range dependence. The method is based on the
heteroskedastic time series model. The FIGARCH model is used for volatility
modeling and forecasting. The model is reduced to the AR model of infinite
order. The reduced system of Yule-Walker equations is solved to find the
autoregression coefficients. The regression equation for the autocorrelation
function based on the definition of a long-range dependence is used to get the autocorrelation
estimates. An optimization procedure is proposed to specify the estimates of
autocorrelation coefficients. The procedure for obtaining of the forecast
values of dynamic risk measures VaR and CVaR is formalized as a multi-step
algorithm. The algorithm includes the following steps: autoregression
forecasting, innovation highlighting, obtaining of the assessments for static
risk measures for residuals of the model, forming of the final forecast using
the proposed formulas, quality analysis of the results. The proposed method is
applied to the time series of the index of the Tokyo stock exchange. The
quality analysis using various tests is conducted and confirmed the high
quality of the obtained estimates.

Abstract:
We consider the homogenization of an elliptic spectral problem with a large potential stated in a thin cylinder with a locally periodic perforation. The size of the perforation gradually varies from point to point. We impose homogeneous Neumann boundary conditions on the boundary of perforation and on the lateral boundary of the cylinder. The presence of a large parameter $1/\varepsilon$ in front of the potential and the dependence of the perforation on the slow variable give rise to the effect of localization of the eigenfunctions. We show that the $j$th eigenfunction can be approximated by a scaled exponentially decaying function that is constructed in terms of the $j$th eigenfunction of a one-dimensional harmonic oscillator operator.

Abstract:
We consider a homogenization of elliptic spectral problem stated in a perforated domain, Fourier boundary conditions being imposed on the boundary of perforation. The presence of a locally periodic coefficient in the boundary operator gives rise to the effect of a localization of the eigenfunctions. Moreover, the limit behaviour of the lower part of the spectrum can be described in terms of an auxiliary harmonic oscillator operator. We describe the asymptotics of the eigenpairs and derive the estimates for the rate of convergence.

Abstract:
We consider the homogenization of a singularly perturbed self-adjoint fourth order elliptic equation with locally periodic coefficients, stated in a bounded domain. We impose Dirichlet boundary conditions on the boundary of the domain. The presence of large parameters in the lower order terms and the dependence of the coefficients on the slow variable give rise to the effect of localization of the eigenfunctions. We show that the $j$th eigenfunction can be approximated by a rescaled function that is constructed in terms of the $j$th eigenfunction of fourth or second order order effective operators with constant coefficients, depending on the large parameters.

Abstract:
Transient properties of different physical systems with metastable states perturbed by external white noise have been investigated. Two noise-induced phenomena, namely the noise enhanced stability and the resonant activation, are theoretically predicted in a piece-wise linear fluctuating potential with a metastable state. The enhancement of the lifetime of metastable states due to the noise, and the suppression of noise through resonant activation phenomenon will be reviewed in models of interdisciplinary physics: (i) dynamics of an overdamped Josephson junction; (ii) transient regime of the noisy FitzHugh-Nagumo model; (iii) population dynamics.

Abstract:
Many single and three-phase converters are well developed, and covered up in most of electric markets. It is used in many applications in power systems and machine drives. However, an exact definite output signal from the dc side still not recognized. The waveforms of output voltage and current demonstrate an imperfect dc signal and constitute losses, harmonic distortion, low power factor, and observed some ripples. An approximately perfect rectifier bridge is the aim of this research. Perhaps it gives the ability to identify the parameters of the converter to obtain, as much as possible, a perfect dc signal with less ripple, high power factor and high efficiency. Design is implemented by simulation on Power Simulator PSIM, and practically, a series regulator LM723 is applied to provide regulating output voltage. Comparisons of both simulation and hardware results are made to observe differences and similarities.

Abstract:
One of the problems in the development of mathematical theory of the genetic code (summary is presented in [1], the detailed—to [2]) is the problem of the calculation of the genetic code. Similar problem in the world is unknown and could be delivered only in the 21st century. One approach to solving this problem is devoted to this work. For the first time a detailed description of the method of calculation of the genetic code was provided, the idea of which was first published earlier [3]), and the choice of one of the most important sets for the calculation was based on an article [4]. Such a set of amino acid corresponds to a complete set of representation of the plurality of overlapping triple gene belonging to the same DNA strand. A separate issue was the initial point, triggering an iterative search process all codes submitted by the initial data. Mathematical analysis has shown that the said set contains some ambiguities, which have been founded because of our proposed compressed representation of the set. As a result, the developed method of calculation was reduced to two main stages of research, where at the first stage only single-valued domains were used in the calculations. The proposed approach made it possible to significantly reduce the amount of computation at each step in this complex discrete structure.