Natural connection between Gelfond-Leontyev generalized derivation operators (GDO) and  Brenke polynomials is established. Operator extension criterion commuting with GDO up to continuous H(G) space is derived. Domain class when characteristic function of the complex convolution operator always has zero type, is described. Hypercyclic and random nature of the generalized complex convolution has been proved.

The method of amplitude characteristic estimation for the cantilever bean of the variable rigidity on the basis of the analysis of Fredholm integral equation of the second kind is presented. The determination method of rigidity changing on the basis of Cauchy sequence analysis.

Presentation algorithm of the closed contour in sceletons collection is presented. Sceletons collection represents sequence of segments which connect circle centers.  Circles fit into the generated contour segment. The major direction of algorithm usage is text information processing without setting up the certain type face.

Existence conditions and calculation modes of the exact balanced solution within the limits of international trade model are considered with the theory of graphs application.

Warmth calculations of carbides and nitrides oxidation of some metals as elements of wearproof coverings define probability of formation corresponding oxide base metals under the cutting conditions. Proofness indicator (volume factor) of connections is introduced for the first time to estimate efficiency of coverings from nitrides, carbides and aluminides, formed oxides, under the cutting conditions.  Experimental data of oxidation of pure metals, double alloys, including aluminides, allow to consider that the efficiency of aluminides of Ti, Fe, Cu, Nb, Zr, Ni, correlates with their proofness indicators values.  Research of cutting firm alloys with coverings of TiC, TiN and Al2O3 in the air and in nitrogen atmosphere have confirmed  efficiency of these coverings under the  retardation (shortstop) of  tribochemical contact reactions.

Parcels taken as a principle of a situation assessment and knowledge formation for an intelligent control system are specified. The method of system training is offered - Generalized Knowledge Mining for Technological System (GKM TS). Its main principles and features are shown.

Some aspects of the defuzzification method in fuzzy expert information processing in the expert system for technological regulation of the machines are considered. An example of the method implementation is given in the article.

A structural construction scheme for the hardware-software control complex of transmission pipeline electrochemical anticorrosion protection equipment is offered. Performance features of the complex under test operation according to the developed algorithms with the use of fuzzy logic methods.

Calculation method for three-D rigidity coefficient of the elements of hydraulic drive machines is offered. Description of the stand for field research of the stiffness properties of the hydraulic systems pipelines, including three-D rigidity coefficient, is presented.

The scientifically based algorithm of process and equipment of hairpins with thin-walled details characterization is considered. The results of the chosen and calculated parameters of process and equipment are presented.

Research results of the ultrasonic surface decontamination of the medical instrument in the complex with the structural material transformations occurring under the influence of ultrasonic vibrations are presented. The research work is aimed at the effective ultrasonic machinery modes selection.

A behavioral model of rheological  bodies (viscoelastic material, configuration or system) under load control action, operating in the predetermined fashion for a time, is offered.

Lagrange approach to solving problems of heat power plants hydraulic systems dynamics is stated. The calculations and experimental research data of starting-up processes  of jet and vane pumps by filling hydraulic line canals of model plant with liquid are named.

A survey of enterprise development models as a single socio-ecological-economic system that takes into account the interaction of production and environment is made.

The problem of macro-economic importance of service industries and service economy development, as well as economic trends of service industries development in RF, and their dynamic growth factors  are analysed. The Russian service practice innovations are featured.

In connection with the transition of Rostov Region to an innovative type of development, the regional authority organs need to introduce new methods and forms into the regional control system that will satisfy modern tendencies and allow to realize regional economic development control more effectively. The article is about description of contents and conditions of regional management by innovations resources.

The place and role of innovations in the postindustrial period are analyzed. The current state and problems of the innovative sector of the Russian economy are evaluated. Stimulation factors of the enterprises innovative activity are studied.

Development of the pharmacy market of the Russian Federation causes severe competition among various pharmacy organizations. It results in progressive amalgamation of small-scale and medium-sized pharmacy enterprises.

Segmentation of competitors by revealing and ranging strategic grouping barriers of  the retail trade enterprises with food products is considered.

Modeling training is analyzed. It allows to define goals, contents and training stages. Professional competencies development involves modeling methodological knowledge and implementation of the information models in the evolutive training and information technology teaching at the preschool, propaedeutic, basic, specialized, vocational stages.

Opportunities of forming theoretical knowledge, practical skills, and control, taking into account levels of information-technological training levels at every teaching stage for college students.

The basic semiotic terms – sign, symbol, emblem – are analyzed. Generalization of the existing notions allows to state that signs are things, objects, or phenomena which denote other  things, objects, or phenomena. Symbol can be considered a variety of sign, it is socially significant, emotionally expressive, and polysemous. Emblem is a  variety of sign with great semantic substantiation.