We introduced the basic classes of curves (1) on which approximation is conducted and obtained constructive characteristic of analogue of Lipschitz class on curves in a complex plane in integral metrics. For that we proved an inverse theorem and to get a constructive characteristic for the analogue of Lipschitz class of order α on the curves (1) in a complex plane in the metric Lp(Γ), i.e. for the class Hpa(Γ) (P > 1) and 0 < α < 1.. The obtained result is a solution the analogue of J.L. Walsh problem related to Jackson-Bernstein classic theorem.

This study describes a procedure employing Gaussian elimination method in matrix algebra to balance chemical equations from easy to relatively complex chemical reactions. The result shows that 4 atom of Carbon (C), 14 atoms of Oxygen (O), and 12 atoms of Hydrogen (H) each on both the reactants and products makes the chemical equation balance. This result satisfies the law of conservation of matter and confirms that there is no contradiction to the existing way(s) of balancing chemical equations. The practical superiority of the matrix procedure as the most general tool for balancing chemical equations is demonstrable. In other words, the mathematical method given here is applicable for all possible cases in balancing chemical equations.

This article is devoted to the description of the mechanism of the transformation of negative entropy (negentropy) coming into the system from outside, into information by doubling bits of information originally presented in the system. The present investigation uses the model of one-dimensional chain of bi-stable elements which is connected with the nearest neibours. The bifurcative character of this phenomenon is revealed.

Fuzzy numbers play a fundamental role in fuzzy mathematics, analogous to the role played by the ordinary numbers in classical mathematics. In this work we use the Triangular Fuzzy Numbers for the verification of a chosen decision and we give an example illustrating our results in practice. In order to check the creditability of our new fuzzy method, the outcomes of its application are compared in our example with the corresponding outcomes of two traditional methods, the calculation of the mean values and the use of the GPA index.

Both the optimization and equilibrium principles turn out to be more akin to common sense than to science. They have been postulated as describing markets, but lack the required empirical underpinning. Optimization is not a magic cure. In order to particularly circumvent some of the technical obstacles for a control problem, it turns out to be practically effective to reduce the system dynamics to a system of ordinary differential equations of considerably higher dimension, such an approach might replace a theoretical difficulty by a greatly increased computational problem.