Оценка зависимости изменения розничных цен на электроэнергию от динамики экзогенных факторов (экономических и правовых характеристик)
Theorems of existence and uniqueness of Cauchy’s problem solution for systems of nonlinear functional and differential equations are proved. During the proof of the theorems the positivity of the Cauchy’s matrix corresponding linear system is used essentially.
The paper addresses the on-line teaching of Calculus using webMathematica interactive electronic tutorials developed by the author. The tutorials are available on the web site http://wm.iedu.ru. It is obvious that e-learning technologies need new pedagogy. It is usually called e-pedagogy. We share and realize the main pedagogical principle of webMathematica based learning. The principle is laid out as follows. To teach mathematics not calculation or math not equal calculating.
In order to reduce the Gibbs phenomenon exhibited by the partial Fourier sums of a periodic function, discontinuous in 0, Driscoll and Fornberg considered so-called singular Fourier-Padé approximants constructed from the Hermite-Padé approximants. Convincing numerical experiments have been obtained by these authors, but no error estimates have been proven so far. In the present paper we study the special case of Nikishin systems and their Hermite-Padé approximants, both theoretically and numerically. We obtain rates of convergence by using orthogonality properties of the functions involved along with results from logarithmic potential theory. In particular, we address the question of how to choose the degrees of the approximants, by considering diagonal and row sequences, as well as linear Hermite-Padé approximants. Our theoretical findings and numerical experiments confirm that these Hermite-Padé approximants are more efficient than the more elementary Padé approximants, particularly around the discontinuity of the goal function.
The task of improving the quality of forecasting returns of financial instruments using multivariate mathematical models: regression models and neural networks was analyzed. To construct a multifactor model of returns used the assumption on the influence of market factors that have a different nature. A linear multivariable regression model was constructed using stepwise inclusion algorithm. The multilayer neural network trained using back-propagation algorithm. The quality of the neural prediction models forecast much higher quality, built with the help of a regression model.