TAAC'2012, Section Two: Applied Mathematics and System Analysis

The paper refers to the investment decision-making process for the financial manager when this process requires the evaluation of the revenues and expenses related to the investments, with the financial mathematical methods and approaches. The financial manager provides the selection of the project that produces more revenues than its capital investment is. There are some methods for the evaluation of the project expediency and various methods may be used for these issues as well. The paper considers the following methods for investment projects' evaluation: \begin{itemize} \item Net Present Value - NPV; \item Internal Rate of Return - IRR; \item Payback Period - PP; \item Profitable Index - PI. \end{itemize} Generally, the above mentioned methods are equally convenient for obtaining the normal project. Herewith Each method has its own advantages and disadvantages that should be familiar for the financial manager and should be used in decision-making process.

A new nonparametric test for two samples based on order statistics is suggested. Test can be computed for small samples with small computation complexity. Statistics probabilities and algorithm for calculation are given. A classification criteria based on the statistics is proposed.

The plane laminar convective flow of viscous fluid in a enclosure rectangular region has been considered. Mathematical model has been formulated in dimensionless variables as stream function, vorticity and temperature. Numerical results have been obtained by the R-functions and Galerkin methods.

Filtration flow under floodbed in presence of waterproof areas (lenses) is considered. The numerical method based on combination of superposition principle, Ritz's method and the method of R-functions, is used for solution of this problem.

The question of weak solvability of the ultraslow diffusion equation with the Caputo fractional derivative is studied. The main result is obtained by employing Galerkin's method. The solution is also proved to be continious.

Various methods of solving dynamic transshipment problems are considered in this paper.The dynamic transshipment problem can be convertedtothe large classic transshipment problem and solved with various general methods (\ref{aba:fig1}). The primal support method based on the concept of the support program is used in this work \cite{TransProb}. The advantages of this method are its simplicity and ability of effective computer realization on a basis of list structures. The disadvantage of the static model is the lack of the dynamics because all network parameters are considered fixed and known in advance. Also this approach doesn't take into account the time required to move the flow between nodes. Another approach to solving dynamic network flow problems is to convert them to discrete optimal control problems. To choose a better approach it is necessary to find out the scope of their applicability, that is to determine such parameters as number of arcs, nodes and time periods.

Nowadays heterogenous IP networks (HIPN) became the most common mean of information exchange. Rapid growth of information infrastructures using and providing software and hardware for such networks emerges the problem of control optimization for these networks. Considering HIPN as complex control object we provide a method for generation of control statements that are (sub-)optimal in terms formulated by network administrator. These methods use combinatorial optimization approaches such as Genetic Algorithms and Stochastic Hopfield Network (Boltzmann machine).

The task of mass transfer of the body of revolution with uniform translational flow is considered. A numerical method for its solution, based on the joint use of the R-functions structural method of V. L. Rvachev, Ukraine NAS academician, for constructing the structure of the boundary problem solution and the Galerkin-Petrov projection method for approximating the indeterminate components of the structure, is proposed.

Diffraction problem of a plane monochromatic electromagnetic E-polarized wave on pre-fractal gratings consisting of a finite number of slits located in parallel planes above the shield have been considered in this work. This problem leads to several boundary singular integral equations (SIE) on the set of intervals, with additional conditions. Discrete mathematical model of integral equations on the basis of an effective numerical method of discrete singularities (MDS) have been constructed. Future prospects in this field of research is the study of problems in the theory of diffraction by periodic and bounded gratings with impedance boundary conditions, the construction of discrete mathematical models of the problems and numerical experiments based on them, the numerical solution using MDS for periodic gratings lying on a dielectric substrate.

A new version of the Structural Dynamic Economic Model SDEM \cite{Barth, Weber} treats the growth of a closed economy driven by conflict of interests of two actors: entrepreneurs and wage-earners. The model is a differential equation system with indirect control, describing a control strategy adopted by entrepreneurs. Depending on the strategy both cases of economic dynamics are possible: steady growth and business cycles. The linear and nonlinear versions of the model are considered and compared. The results of numerical simulation are presented and analyzed.

We present an evolved version of Chen's (2008) viral coefficient. By doing so, we tackle some shortcomings of the simplified viral coefficient model: (1) lack of time component, (2) lack of carrying capacity, and (3) duplicate problem. Our model is based on invitations sent by individuals to one another in a finite social network and can be used to determine the viral growth of visitors in a website at a specific time. By using logistic function and basic theory of finance, the model focuses on website visits that are easily measurable, discrete events, and constitute the starting point for more advanced type of conversions, such as sales.

In the paper we offer explicit and implicit scheme a functional-discrete method (FD-method) for solving nonlinear Klein-Gordon equation. Also we consider the problem of computational complexity of the algorithm for solving the given problem.

The paper considers a method of determining a solution to the Vehicle Routing Problem with Hard Time Windows which can be used in the Probabilistic Tabu Search Algorithm as the lower bound for the formation of the neighborhood of the potential solutions. If the objective function is independent of the vehicle idle before entering the next destination, the solution is an optimum of the original problem.

In this article staged model of mixed economy. It is offers a modification of the tax system in this model. We introduce a set of differentiation profitable enterprises into four groups according to income level. A distributed calculation of the interest tax rate for each group of firms separately. Analyze the influence of the proposed changes on the model of a mixed economic system as a whole.

The purpose of this article is two folds: 1) to correct errors and extend the results obtained in Teneng (2012) and 2) to fit the normal inverse Gaussian distribution to foreign exchange daily closing prices using the open software package R. We observe that daily closing prices (12/04/2008 - 07/08/2012) of CHF/JPY, AUD/JPY, GBP/JPY, NZD/USD, QAR/CHF, QAR/EUR, SAR/CHF, SAR/EUR, TND/CHF AND TND/EUR are excellent fits while EGP/EUR and EUR/GBP are good fits with a Kolmogorov-Smirnov test p-value of 0.062 and 0.08 respectively. It was impossible to estimate normal inverse Gaussian parameters (by maximum likelihood; computational problem) for JPY/CHF but CHF/JPY was an excellent fit. Thus, while the stochastic properties of an exchange rate can be completely modeled with a probability distribution in one direction, it may be impossible the other way around\footnote{Research was supported by Estonian Science Foundation grant number 8804 and Estonian Doctoral School in Mathematics and Statistics.}.

Systems with a saddle matrix often arise in many applications in science and engineering, such as constrained optimization problems or approximations by mixed finite element method of differential equations with partial derivatives. An incomplete generalized Cholesky factorization of a saddle matrix of certain type is obtained. This factorization is used to build a preconditioner of systems with the saddle matrix.

In the work has been developed approaches to decision-making in holding's strategic management and its business units. Holding's strategic management based on the most popular and effective modern methodology - a system of key performance indicators (KPI). Management of the functioning and development of the holding consists of the following stages: strategic analysis, monitoring activities, forecasting activities, updating KPI's system.