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A well-regarded as well as powerful method named the ‘analytic hierarchy process’ (AHP) uses mathematics and psychology for making and analysing complex decisions. This article aims to present a brief review of the consistency measure of the judgments in AHP. Judgments should not be random or illogical. Several researchers have developed different consistency measures to identify the rationality of judgments. This article summarises the consistency measures which have been proposed so far in the literature. Moreover, this paper describes briefly the functional relationships established in the literature among the well-known consistency indices. At last, some thoughtful research directions that can be helpful in further research to develop and improve the performance of AHP are provided as well.

This paper will focus on the transaction costs analysis approach to estimating the level of quality management systems self-organization. It became possible to consider transaction costs in quality management systems with the reclassification of consumer. A suggested classification of consumers includes both “external’ and “internal” consumers and also “hidden” and “latent” consumers. Another approach of accounting costs and consumers data allowed us to analyze quality management systems by the share and the level of self-organization.

This paper considers a linear system of partial differential equations (PDEs) to describe the stress-strain state of a two-phase body under static load, such as water-saturated soil. It investigates the basic properties of a new general differential operator Lame. The equations differ from the classical Lame equations by including first derivatives, which account for the influence of pore water on soil mineral particles. The properties of the generalized Lamé operator are investigated for the application of variational methods to solve the problem. It also describes alternative of the Betti and Clapeyron formulas using strain energy results. The calculus of variations of the Galerkin method is used to solve the minimum functional problem. Properties of bilinear forms are established and a theorem on the existence and uniqueness of the solution of the two-phase equilibrium problem is proved. The finite element method is adapted for a kinematic model that considers excess residual pore pressures. A new stiffness matrix is obtained, which is the sum of two matrices: one for the soil skeleton and one for pore water. The adequacy of the mathematical model of a water-saturated foundation for a natural experiment is shown. The use of Korn's inequality implies limitations on elastic properties (homogeneity, anisotropy) and the geometry of the region (requiring regularity and smooth boundaries). The study illustrates that the methodology of mechanics of a deformable solid can be adapted with appropriate modifications to a two-phase body in a stabilized state. The finite element method is adapted for a kinematic model that considers excess residual pore pressures. A new stiffness matrix is obtained, which is the sum of two matrices: one for the soil skeleton and one for pore water. The finite element method is tested on the Flamand problem. The adequacy of the mathematical model of a water-saturated foundation for a full-scale experiment is shown. The problem of the action of distributed load on a water-saturated heterogeneous foundation was solved using the finite element method and the results were compared with experimental data. The effect of mesh partitioning on the accuracy of the numerical solution is also studied in the finite element method. The maximum discrepancy was no more than 26%.

The democratic welfare government is not only interested in creating educational institutions as infrastructure for education for all, but is also equally keen on quality-oriented, even-handed, and equitable education. In fact, the focus of the Global Agenda SDG 4 is to raise the standard of living and quality of life by ensuring quality and lifelong education irrespective of region, race, religion, color, and caste, etc. Thus, there is a strong focus in India to reach global targets and more importantly, this is due to the necessity of fulfilling the government’s goals on overhauling India’s education system in the context of far-reaching changes that have taken place in terms of economic, social, and scientific areas over a period of last twenty years. The outcome of all these complex issues and critical thinking across stakeholders in social development manifested into policy action called the New Education Policy 2020 (NEP 2020). Therefore, it is critically important to analyze the subject under study as a compact system composed of simultaneous relationships to give a combined effect of the objectives and the framework undertaken for the analysis. Quality of life and education are the variables that are difficult to precisely measure in quantitative terms and hence, the implications and inferences are carefully analyzed on the range of issues that are selected for statistical analysis and structural modeling. By going with our estimates, it seems that though NEP 2020 is a popular and mandated educational policy for educational reforms and for a better future, the expected implementation of the policy would be very difficult in the context of digitalization and for raising the quality of life. In our opinion, remarkable progress on the quality of life can be made possible with flexibility in proper life-long education and training, which can culminate skill, experience, quality of education, and rigidity of the segmented labor market into better opportunities and employment.

Network reliability is one of the most important concepts in this modern era. Reliability characteristics, component significance measures, such as the Birnbaum importance measure, critical importance measure, the risk growth factor and average risk growth factor, and network reliability stability of the communication network system have been discussed in this paper to identify the critical components in the network, and also to quantify the impact of component failures. The study also proposes an efficient algorithm to compute the reliability indices of the network. The authors explore how the universal generating function can work to solve the problems related to the network using the exponentially distributed failure rate. To illustrate the proposed algorithm, a numerical example has been taken.

The subject of this paper is a programmable con trol system for a robotic manipulator. Considering the complex nonlinear dynamics involved in practical applications of systems and robotic arms, the traditional control method is here replaced by the designed Elma and adaptive radial basis function neural network—thereby improving the system stability and response rate. Related controllers and compensators were developed and trained using MATLAB-related software. The training results of the two neural network controllers for the robot programming trajectories are presented and the dynamic errors of the different types of neural network controllers and two control methods are analyzed.

In recent years, there has been an increasing interest in plasma jet numerical simulation. Speed and temperature propagation in axial and radial direction in plasma jet significantly influences on speed and temperature of sprayed material and therefore on coating quality. However, there are few studies concerning plasma jet numerical simulation in modern software systems and they describe a specific problem. It is a wellknown fact that using simple structural components such as plasmatron heads for plasma thermal spraying allows us to increase the quality of zirconium oxide coatings by increasing the speed of spraying particles and decreasing their spread value and allows to increase economic efficiency of the process by increasing the operation factor of spraying material. However, scientists have not studied well the influence of the plasmatron head, which looks like a cone element, and the simulation of a high temperature flow along the channel is not mentioned in publications. Therefore, it is necessary to research the flow of a high temperature current along the channel of the head.

In order to effectively organize the process of agricultural enterprises, it is reasonable to involve management tools to build optimal models of interaction of individual components of the production process. The most significant part concerning the technical and economic efficiency is the technological process. However, the harvesting and postharvesting process is of the highest priority. The current stage of the management paradigm development includes the attraction of mathematical modeling in the organizational process. The construction of mathematical models is necessary at the stage of planning, organization, control, and is aimed at choosing such parameters of the technological process that will ensure the highest economic efficiency. At the same time, the validation process of the optimal parameters of machines and equipment that separate the grain receiving is of the most importance. While solving this problem, it is necessary to consider various efficiency criteria, the main of which are “loss volumes” and “reduced costs”. The criteria for the efficiency of the technical equipment of postharvesting grain process are the permissible values of agrotechnical requirements that consider the time of safe storage of freshly harvested grain mass without pretreatment and grain shatter losses due to its overripe. It is necessary to consider the maximum allowable volumes of losses during the postharvesting technological process. In order to define the best organizational solutions the iteration principle is used until a solution that meets the restrictions on the reduced costs level is found. The mathematical modeling in technological processes is carried out with the involvement of regression models that allow predicting the qualitative indicators of the operation of the pre-cleaning machine. As a result, it is possible to choose such a mode of equipment operation that ensures the production of grain that meets the regulatory requirements for the quality of the resulting product. The novelty of this study lies in the development of optimal ways for combine harvesters functioning. The article presents the methodology and procedure of optimizing the technological process during the postharvesting process of grain. The characteristics received as a result of experiments allow us to organize the technological process in an agricultural enterprise in the most optimal way so that it is economically and technically efficient.

Wind energy is a kind of renewable energy that plays a significant role in remote areas for pumping water. The windmill is also used to generate electricity. The windmill is also known as a wind pump when it is used for pumping water. In this work, the authors proposed a complex hybrid model of an example of combined system (windmill, rechargeable battery and pumping system) to evaluate the system’s performance. System performance was affected by system degradation due to system failure. These factors also affected the profit of the user. Two types of repair facilities for continuous and satisfactory performance of the system were assumed. To illustrate the system modeling using the Gumbel–Hougaard family of the copula, numerical examples were used for the exploration of Markov results of the reliability measures and the profit of the system with the warranty period, with this also being demonstrated graphically.

During digitalization of transport service segment people use modern facilities such as geolocation, M2M connectivity, online payments, customer identification. We can also see a high competition here. The task of car sharing managers is to search for the optimal methods of doing business. As the regulations of business, ecological standards and technology environment of the main players is almost similar because of using the same mobile and cloud resources, it is possible to get a competitive advantage by the development of mobile apps for the employee’s PCs and smartphones of customers. The math model shown in this article is developed for implementing in digital platforms of such kind of business. This gives the opportunity to offer customers more attractive car sharing services and to reduce costs by following the environmental restrictions at the same time.