Математические методы и модели микроэкономики
The number of papers addressing the forecasting of the infectious disease morbidity is rapidly growing due to accumulation of available statistical data. This article surveys the major approaches for the short-term and the long-term morbidity forecasting. Their limitations and the practical application possibilities are pointed out. The paper presents the conventional time series analysis methods — regression and autoregressive models; machine learning-based approaches — Bayesian networks and artificial neural networks; case-based reasoning; filtration-based techniques. The most known mathematical models of infectious diseases are mentioned: classical equation-based models (deterministic and stochastic), modern simulation models (network and agent-based).
In the article the author considers the factors, governing by people coming in a small business. These factors can vary depending on the social and economic situation. The author estimates an enterprise potential of the Russian society and analyzes the reasons on which people start to attend to business.
The proceedings from the 15th EDAMBA conference, which took place at the University of Economics in Bratislava on 22nd November 2012 have been prepared as a joint refereed publication of participants presenting their papers at the conference. The aim of EDAMBA as an organisation is to promote the exchange of information, to enhance the mobility of PhD candidates, to promote research cooperation and to increase the quality of PhD programmes and to create an environment of excellence with a European perspective while pursuing the existing diversity.
Econometric models of the dependence on various factors of the number of participants of the Unified State Examination, which have scored different points for certain subjects in 2012 and 2013, are considered. The analysis uses data on high and low scores for regions of Russia. Dependences of the number of good and bad Unified State Examination points on the number of students who took part in the exam in different regions are studied. It is shown that, the more the number of participants in the exam in each region, the greater the number of both good and bad ratings in the region. But, as a rule, the number of low grades in a discipline is a concave function, and the number of high grades is a convex function of the number of schoolchildren who took part in the exam.
The computationally efficient method of fitness function evaluation (criterion for chromosomes selection) in genetic algorithms (GA) is discussed in this paper. This method may be used if a single gene modifies chromosome.
Steiner's problem in graphs is solved for the computing optimization. Population is represented as a weighted graph. Vertices of that graph represent chromosomes, edges represent the computational cost of selection criteria recurrent calculation. The GA application for identification of regression models assumes (a) gene is a regressor;
(b) chromosome is the set of regressors in single regression model (subset of all candidates);
(c) population — set of regression models (subset of all possible models); (d) selection criteria — residual sum of squares (RSS); (e) the chromosome modification by modification of one gene corresponds to the forward selection and backward elimination methods of variables (regressors) selection.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.