In the article the Cauchy problem of the Carleman equation is considered. The Carleman system of equations is a model problem of the kinetic theory of gases. It is a discrete kinetic model of one-dimensional gas consisting of identical monatomic molecules. The molecules can have one of two speeds, which have equal values and opposite directions. This system of the equations is quasi-linear hyperbolic system of partial differential equations. There is no analytic solution for this problem in general case. So, the numerical investigation of the Cauchy problem of the Carleman system solution is very important.The paper presents and discusses the results of the numerical investigation of the Cauchy problem for the studied system solution with periodic initial conditions. The dependence of the stabilization time of the solution and the time dependence of energy exchange from small parameter are obtained.The second point of the paper is numerical investigation of the solution of the Cauchy problem with non-periodic initial conditions. The solution stabilization to the equilibrium state is obtained. The solution stabilization time is compared with stabilization time in periodic case.The final point of the paper is numerical investigation of the Cauchy problem with stationary normal processes as initial conditions. The solution to this problem is two stationary stochastic processes for any fixed value of time variable. As a rule, the practical interest is not a stochastic solution but its statistical characteristics. The stochastic solution realization is presented and discussed. The dependence of the mathematical expectation of the solution deviation modulus from equilibrium state is obtained. It demonstrates the process of the solution stabilization.

The use of fractional derivatives for describing and studying the physical processes of stochastic transport has become one of the most popular fields of physics in the recent years, many of the problems of fluid flow in highly-porous (fractal) environments also lead to the need to study boundary value problems for the equations of fractional order.The paper considers one of the boundary value problems for one-dimensional differential equation of fractional order. Using the Fourier method, the solution to this problem was explicitly written. The author also studied the qualitative properties of the solutions of the boundary value problem. It was proved that, in the case of going to infinity, the limit of the decisions recorded in the form of the function and the limit of the derivative of this solution tend to zero.The results can find application in the theory of fluid flow in a fractal environment and in order to simulate changes in temperature.Fractional integrals and derivatives of fractional integral-differential equations find wide application in contemporary studies of theoretical physics, mechanics and applied mathematics. Fractional calculus is a very powerful tool for describing the physical systems, which have memory and are non-local. Many processes in complex systems are non-locality and have long-term memory. The fractional integral operators and the fractional differential operators allow describing some of these properties. The use of fractional calculus will be useful for obtaining the dynamic models, in which integraldifferential operators describe the power of long-term memory and time coordinate and three-dimensional nonlocality for medium and complex processes.

At the present time the nonlinear deformation model based on deformation diagrams of the materials is believed to be the most promising for estimation of stress-strain state of reinforced concrete elements at different stages of their compression: before crack formation, in the process of crack formation, at the stage of cracked element operation, at destruction stage. Reliability of estimates depends largely on accuracy of analytical description of curvilinear diagram of concrete deformation. On the other hand we should remember that the calculated construction may be subject to different loading modes: short-term, long-term or competitive. In this regard the universal character is required from the used deformability diagrams. They should be easily transformed for calculation with different modes.The authors suggest methods of constructing such a deformation diagram using elasticity coefficient. Using the corresponding elasticity coefficients in calculations it is possible to account for different loading modes of structures (for example long-term loading). Such an analytical representation of concrete deformation diagram is more generalpurpose as compared to dependence on European standards.

Underground construction in dense urban areas requires solving many problems, the most important of which is to prevent excessive additional deformations of the bases, which surround the area of the construction of buildings and structures.In order to prevent deviant strains different methods are used in engineering practice. In the recent years our country began to use a very popular abroad method of compensation grouting, which is currently one of the most effective methods of protecting the land-based facilities from the influence of underground facilities. This method has another important advantage, which allows using it rather for stabilizing yield of buildings and structures continuing for various reasons (geological, technological, etc.), or for lifting them if the settlement has exceeded the standard value.The method involves injection of a slowly hardening compensation grouting solution of a definite viscosity, which has a mineral base (suspension), into the foundation soil of the structure, the settlement of which should be controlled or compensated.

An accumulation of defects caused by the action of the loads both man-made and external leads to a decrease in the carrying capacity of the carcass structure during operation of industrial buildings. Most notably this problem manifests itself in the buildings equipped with crane equipment. During operation the columns and crane girders obtain significant deformation, and this entails a reduction in structural stiffness characteristics. At the same time a load factor is enhanced when using heavier equipment. Therefore, the main purpose of this study is to identify the opportunities to ensure the reliability required for an industrial building equipped with overhead cranes. The study has developed a complex of calculation methods, the main task of which is to estimate the residual resource of a specific period of technical system operation, taking into account the random nature of a whole set of disturbances. The analysis of the results obtained by the consistent implementation of these techniques allows tracking the dynamics of changes in the stress-strain state of load-bearing structures of industrial objects in operation.In order to solve the problem of providing rigidity frames and improve the reliability of their safe operation the authors propose constructive measures to slow the rate recorded in the calculation of the bearing capacity loss of the system. For this aim we suggest setting the end face transverse stiffening diaphragms, increasing the rigidity of the column above the crane, arranging some connecting rods in the temperature seam, located in the levels of coating and under crane beams. These measures should be used together, which allows achieving a significant effect in providing transverse rigidity. The coating disk with a sufficiently high horizontal rigidity is able to transfer a portion of the load acting on the transverse frames on transverse end faces of the diaphragm. The binder rods prevent relative lateral displacement of the temperature blocks relative to each other, thereby they put the entire frame under the action of horizontal crane loads into operation. Increasing the stiffness of the column above the crane allows transferring a significant part of the effort to the coating when the bridge crane has close proximity to the coating.The proposed constructions are easy to manufacture and do not require the device holes, which weaken the structure. They can be made not only while erecting the buildings, but also in the already constructed ones by increasing the carrying capacity of the overhead cranes. In this paper we evaluate the effectiveness of the proposed measures to improve the structural rigidity of frameworks on the example of several industrial buildings. The comparative analysis of the results obtained before and after the introduction of affirmative action has shown that their arrangement reduces the horizontal displacements of the frame, in the level of crane girders, and the level of coating, with a larger effect observed in the buildings with heavy-duty overhead cranes. This reduction of displacement involves the growth of bending moments values in above the crane column part and the reduction of the magnitude moments in the under crane part. At the great height under the crane portion of the column in most buildings these changes can save generally significant amounts of steel for the framework.Thus, the proposed technical solutions are aimed not only at extending the safe operation of industrial buildings, but also have a positive effect in case of re-production associated with an increase in the lifting capacity of crane equipment, with little financial cost.

Today great attention is paid to production and research of the mechanical and termal properties of nanocomposites based on polyimides. These polymers are heatresisting and possess the increased mechanical properties in wide range of temperatures. Various nanoparticles are introduced into polyimides: graphite nanotubes and flatparticles, the particles of SiO , the surface of which is modified, the particles of ZrOandmontmorillonite, etc.The authors analyzed the influence of nanoparticles on the glass transition temper-ature T and elastic modulus E of the polyimides based on 1,3-bis-(3,3’,4,4’-dicarboxy-phenoxy)benzene and 4,4’-bis-(4-aminophenoxy)biphenyl, and pyromellitic dianhydride and oxydianiline. Nanoparticles introduced in small amounts are produced of graphite and ZrO . The suggested ratios take into account the chemical structure of the polymer and nanoparticles, as well as the structure of their surface in case of chemical modification; the concentration of nanoparticles and their form, the number of polar groups on the surface. The number of polar groups and nanoparticles’ concentration have the greatest influence on T . The elastic modulus of nanocomposites depending on nanoparticles’ concentration is connected with van der Waals volume of the repeating unit of polymer and nanoparticle.

This article considers some aspects and common problems associated with the organization of parallel calculations in the problems of hydrodynamics. As an example the authors consider the calculation problem of the velocity field in the area of river and sea water mixing and the simulation of sedimentation of terrigenous material.

Basing on life cycle analysis of building materials produced of waste products the authors defined the formation stages of environmental risks of adverse impacts on the environment. The studies have revealed that one of the main environmental risks is the occurrence of secondary emission of pollutants from building materials produced of waste products when used by the end-user, which is not taken into account by the existing regulatory documents defining the environmental safety of construction materials. The questions of prevention of the possible negative impact of the construction materials based on or with addition of production waste while their use on the environment and population as a result of a number of natural and anthropogenic factors, which can lead to negative ecological effects, which are difficult to forecast, are not regulated enough. In the present conditions of the absence of regulatory framework of their ecological safety the wide use of production waste for obtaining construction materials without account for the possible ecological risks may lead to technogenic burden exceeding the acceptable level.The authors defined the main ways to reduce the environmental risks when using the resource potential of waste for the production of building materials by reducing the emissions of these pollutants while reducing their permeability.

The activity of housing services and utilities results in great amounts of waste: sludge of water and wastewater utilities, waste waters of TPPs and recycling water supply. The known ways of such waste utilization are related to production of construction materials and secondary reactants for wastewater treatment. Though the volumes of sludge most often exceed the regional demand in raw materials for local construction materials or coagulants. Moreover sludge as man-made raw material cannot compete with their natural analogues in terms of quality.The basic characteristics of housing and communal services sludge storages were considered from the perspective of their target development. The system of state assessment of sludge storages was represented by the multidimensional data analysis. The waste disposal facilities considered in this study were classified into three groups from the perspective of the feasibility and practicability of their abandoning. An example of the digital matrix of waste disposal facilities’ condition was given. The constructive and technological design of the system of recultivating materials production was given.

In this article the questions of kinematic structure of steady turbulent flow near a solid boundary are considered. It has been established that due to friction the value of the local Reynolds number decreases and always becomes smaller than the critical value of the Reynolds number, which leads to formation of viscous flow near a wall. Velocity profiles for the area of viscous flow with constant and variable shear stress are obtained. The experimental investigations of different authors showed that in this area the flow is of unsteady character, where viscous flow occurs intermittently with turbulent flow. With increasing distance from the wall the flow becomes fully turbulent. In the area where generation and dissipation of turbulence are very intensive, there is a developed turbulent flow with increasing distance from the wall. Dissipation of turbulence is an action of viscous force. The logarithmic velocity profile was obtained by L. Prandtl disregarding the viscous component and the linear variation of the shear stress in the depth flow. The profile parameters C and k were determined from Nikuradze’s experiments. The detailed investigations of Nikuradze’s experiments established the part of the flow where the logarithmic velocity profile is correctly confirmed.This part of the flow was called “Prandtl layer”. The measured velocity distribution above this layer deviates in the direction of greater values. Processing of experimental data revealed that the thickness of the “Prandtl layer”, normalized to the radius of a pipe, depend on a drag coefficient. The formula for determining the thickness of the “Prandtl layer” with the known value of the drag coefficient is obtained. It is shown that the thickness of “Prandtl layer” almost coincides with the boundary layer displacement thickness formed on the wall of the pipe.

The author considers the influences of the forces of viscosity and superficial tension on the discharge ratio in a channel with side narrowing. In the article the equation is presented that takes into account the influence of all the factors: the pressure, the speed of the liquid, liquid density, dynamic viscosity, superficial tension, gravity acceleration, expense per unit of width, width of the course, width of narrowing. Superficial tension and liquid density for the used liquids changed a little.The narrowing in the rectangular tray was achieved by force of flowing liquid between rectangular parallelepipeds, which were attached to the wall of the tray. The dimensions of the rectangular parallelepipeds were: the length L = 200 mm, the width B = 33 mm, and the depth of the mouth b = 34 mm.The findings of the experiment proved that the increase in the Reynolds number causes the increase flow discharge ratio and it approaches the constant value at Re ? 4000.

In 2012 the boundaries of Moscow extended in the direction of Kaluga region. The change in territory boundaries resulted in increasing the area of the city, after that the total population increased. It is supposed, that the majority of the agglomerated population will use the care-giving institutions of the “New Moscow”, that’s why its territory requires the transport system adapted for all the population groups. Special attention should be paid to creation of the constant barrier-free transport system reconstructing the existing junctions and creating new ones answering the modern demands on availability for citizens with limited mobility.The article reviews the development of the transport system on the territory of “New Moscow” basing on the data of Federal State Statistics Service. The suggestions on the barrier-free environment development, multipurpose road junctions are given with account for the number of citizens with disabilities. Only in “New Moscow” there are about1,2 mln of them. The variety of means of transport requires new approaches to organization of transfers from one transport to another. The solution will be in hubs, which will be both available for common and disabled people.

The accumulated experience of constructing technically complicated objects and the modern design technologies in general allow conducting deep analysis of construction technological solutions, though, during the project implementation there usually appears an objective necessity to substitute a wide list of technological equipment by the analogues with most close technological characteristics. In the production process it is a rather timeconsuming and organizationally complicated task, which is firstly connected with the choice of reliable supplier and contractor, logistic coordination, providing the purchase procedure. The enumerated factors critically influence the terms of energy project implementation.In the article special aspects of the construction of power engineering facilities is considered. The authors justified the necessity of the researches on the life cycle period related to preparation for construction operations, during which the project is influenced by a lot of negative factors and circumstances different in their form and intensity. The examples and the definitions of unforeseen events and circumstances, which can influence on the realization of the project, are given. The solution to the problem of risk management in the process of technological equipment supply during the construction of power engineering facilities is given. They allow implementing the goal function in the best way providing the required efficiency.

N the conditions of economical instability accompanying the change of technological modes and generation of «economy of knowledge” the stable competitive advantages of organization may be formed only on an innovative basis. Implementation of innovations in equipment and technology is accompanied, and sometimes even reasoned, by organizational innovations, which are the basis of organizational development of modern enterprises. Although there is a sufficient number of investigations in the field, the problems of justification of the criteria and estimation of organizational innovations’ efficiency don’t have a generally accepted solution, which takes into account the specific character of this type of innovations.In the article the methods of efficiency estimation for organizational innovation on an enterprise are developed. The methods are based on multicriteria optimization of efficiency indicators of organizational communications, which are changing at implementing innovations. The communicational approach is justified, which is the basis for organizational innovations implementation in an enterprise as a social-econoomic system, the key criteria are identified and the algorithm for efficiency estimation for organizational innovations in frames of the communicative approach is developed. Application of the suggested methodological approach contributes to the reasoned planning and implementation of organizational innovations into an enterprise activity.

In modern integrated monitoring systems and systems of automated control of technological processes there are several essential algorithms and procedures for obtaining primary information about an object and its behavior. The primary information is characteristics of static and moving objects: distance, speed, position in space etc. In order to obtain such information in the present work we proposed to use photos and video detectors that could provide the system with high-quality images of the object with high resolution. In the modern systems of video monitoring and automated control there are several ways of obtaining primary data on the behaviour and state of the studied objects: a multisensor approach (stereovision), building an image perspective, the use of fixed cameras and additional lighting of the object, and a special calibration of photo or video detector.In the present paper the authors develop a method of determining the distances to objects by analyzing a series of images using depth evaluation using defocusing. This method is based on the physical effect of the dependence of the determined distance to the object on the image from the focal length or aperture of the lens. When focusing the photodetector on the object at a certain distance, the other objects both closer and farther than a focal point, form a spot of blur depending on the distance to them in terms of images. Image blur of an object can be of different nature, it may be caused by the motion of the object or the detector, by the nature of the image boundaries of the object, by the object’s aggregate state, as well as by different settings of the photo-detector (focal length, shutter speed and aperture).When calculating the diameter of the blur spot it is assumed that blur at the point occurs equally in all directions. For more precise estimates of the geometrical parameters determination of the behavior and state of the object under study a statistical approach is used to determine the individual parameters and estimate their accuracy. A statistical approach is used to evaluate the deviation of the dependence of distance from the blur from different types of standard functions (logarithmic, exponential, linear). In the statistical approach the evaluation method of least squares and the method of least modules are included, as well as the Bayesian estimation, for which it is necessary to minimize the risks under different loss functions (quadratic, rectangular, linear) with known probability density (we consider normal, lognormal, Laplace, uniform distribution). As a result of the research it was established that the error variance of a function, the parameters of which are estimated using the least squares method, will be less than the error variance of the method of least modules, that is, the evaluation method of least squares is more stable. Also the errors’ estimation when using the method of least squares is unbiased, whereas the mathematical expectation when using the method of least modules is not zero, which indicates the displacement of error estimations. Therefore it is advisable to use the least squares method in the determination of the parameters of the function.In order to smooth out the possible outliers we use the Kalman filter to process the results of the initial observations and evaluation analysis, the method of least squares and the method of least three standard modules for the functions after applying the filter with different coefficients.