Forecasting Problems for Economic Macroparameters

The article deals with problems of forecasting of economic macroparameters on the basis of the principle of «subjective multideterminism», i.e. an expert account of maximal amount of interrelated «objective» and «subjective» causes. A description is given of the system of support of decision-making in forecasting the level of inflation and gross domestic product on the basis of the tree solution method.

Method of Finding Hamilton Routes in Transport Network

This article discusses a solution method for Hamilton Problem, which either finds the task's solution, or indicates that the task is unsolvable. Offered method has significantly smaller requirements for computing resources than known algorithms.

Representations of Inverse Functions by the Integral Transform with the Sign Kernel

Mathematics Subject Classification: Primary 30C40

The Inflation Index Prognosis Based on the Method of Decision-Marking “Tree”

The description of the support system for marking decision in terms of prognosing the inflation level based on the multifactor dependence represented by the decision – marking “tree” is given in the paper. The interrelation of factors affecting the inflation level – economic, financial, political, socio-demographic ones, is considered. The perspectives for developing the method of decision – marking “tree”, and pointing out the so- called “narrow” spaces and further analysis of possible scenarios for inflation level prognosing in particular, are defined.

On some Modifications of the Nekrassov Method for Numerical Solution of Linear Systems of Equations

A modification of the Nekrassov method for finding a solution of a linear system of algebraic equations is given and a numerical example is shown.

Numerical Solution of Fractional Diffusion-Wave Equation with two Space Variables by Matrix Method

Mathematics Subject Classi¯cation 2010: 26A33, 65D25, 65M06, 65Z05.

Case-based Reasoning Method for Real-time Expert Diagnostics Systems

The method of case-based reasoning for a solution of problems of real-time diagnostics and forecasting in intelligent decision support systems (IDSS) is considered. Special attention is drawn to case library structure for real-time IDSS (RT IDSS) and algorithm of k-nearest neighbors type. This work was supported by RFBR.

Solving Ratio-Dependent Predator-Prey System with Constant Effort Harvesting using Variational Iteration Method

Due to wide range of interest in use of bio-economic models to gain insight into the scientific management of renewable resources like fisheries and forestry,variational iteration method (VIM) is employed to approximate the solution of the ratio-dependent predator-prey system with constant effort prey harvesting.The results are compared with the results obtained by Adomian decomposition method and reveal that VIM is very effective and convenient for solving nonlinear differential equations.

Using Sensitivity as a Method for Ranking the Test Cases Classified by Binary Decision Trees

Usually, data mining projects that are based on decision trees for classifying test cases will use the probabilities provided by these decision trees for ranking classified test cases. We have a need for a better method for ranking test cases that have already been classified by a binary decision tree because these probabilities are not always accurate and reliable enough. A reason for this is that the probability estimates computed by existing decision tree algorithms are always the same for all the different cases in a particular leaf of the decision tree. This is only one reason why the probability estimates given by decision tree algorithms can not be used as an accurate means of deciding if a test case has been correctly classified. Isabelle Alvarez has proposed a new method that could be used to rank the test cases that were classified by a binary decision tree [Alvarez, 2004]. In this paper we will give the results of a comparison of different ranking methods that are based on the probability estimate, the sensitivity of a particular case or both.

Randomized Parallelization – a New Method for Solving Hard Combinatorial Problems

A new method for solving some hard combinatorial optimization problems is suggested, admitting a certain reformulation. Considering such a problem, several different similar problems are prepared which have the same set of solutions. They are solved on computer in parallel until one of them will be solved, and that solution is accepted. Notwithstanding the evident overhead, the whole run-time could be significantly reduced due to dispersion of velocities of combinatorial search in regarded cases. The efficiency of this approach is investigated on the concrete problem of finding short solutions of non-deterministic system of linear logical equations.

Recognition on Finite Set of Events: Bayesian Analysis of Generalization Ability and Classification Tree Pruning

The problem of recognition on finite set of events is considered. The generalization ability of classifiers for this problem is studied within the Bayesian approach. The method for non-uniform prior distribution specification on recognition tasks is suggested. It takes into account the assumed degree of intersection between classes. The results of the analysis are applied for pruning of classification trees.

An Interactive Method of Linear Mixed Integer Multicriteria Optimization

The paper describes a learning-oriented interactive method for solving linear mixed integer problems of multicriteria optimization. The method increases the possibilities of the decision maker (DM) to describe his/her local preferences and at the same time it overcomes some computational difficulties, especially in problems of large dimension. The method is realized in an experimental decision support system for finding the solution of linear mixed integer multicriteria optimization problems.

Classification-Based Method of Linear Multicriteria Optimization

The paper describes a classification-based learning-oriented interactive method for solving linear multicriteria optimization problems. The method allows the decision makers describe their preferences with greater flexibility, accuracy and reliability. The method is realized in an experimental software system supporting the solution of multicriteria optimization problems.

Solution of Space-Time Fractional Schrödinger Equation Occurring in Quantum Mechanics

Dedicated to Professor A.M. Mathai on the occasion of his 75-th birthday. Mathematics Subject Classi¯cation 2010: 26A33, 44A10, 33C60, 35J10.

Acceleration of Convergence in Dontchev’s Iterative Method for Solving Variational Inclusions

2000 Mathematics Subject Classification: 47H04, 65K10.