Investigation of the Operational and Technological Reliability of the Small-size Internal Threading Process

The article presents the results of research in the direction of improving technological equipment for internal threading of parts in a flexible automated production. Methods for assessing the operational and technological reliability of a flexible manufacturing module (FMM) of thread processing are considered, which can be used as the basis for the developed method of synthesis of its elements. It is proposed to consider the technological system of the flexible manufacturing module (FMM) of thread processing as a system in which transitions from state to state occur under the action of the simplest flows with parameters of the transition probabilities of a continuous Markov chain. The developed mathematical model describing the state of the FMM taking into account the failures of the functioning of its elements, parametric failures, as well as taking into account the recovery after these types of failures, makes it possible to reflect the influence on the operation of the module of the parameters of the flows of failures and restorations of the tool, machine tool, fixture, loading device. The solution of the obtained systems of equations of final probabilities allows for given (or experimentally obtained) intensities of failure streams (functioning and parametric) for FMM threading to obtain the values of the probability of failure-free operation, as well as the probabilities of finding the system in an inoperative state due to corresponding failures. The measures taken make it possible to solve the synthesis problem at the level of structural and layout optimization, so that at the stage of parametric synthesis to determine the elements that are vulnerable according to the developed criterion, the improvement of which will lead to the creation of the most efficient system.

Equalities and inequalities for several variables mappings

In this paper, some special mappings of several variables such as the multicubic and the multimixed quadratic–cubic mappings are introduced. Then, the systems of equations defining a multicubic and a multimixed quadratic–cubic mapping are unified to a single equation. Under some mild conditions, it is shown that a multimixed quadratic–cubic mapping can be multiquadratic, multicubic and multiquadratic–cubic. Furthermore, by applying a known fixed-point theorem, the Hyers–Ulam stability of multimixed quadratic–cubic, multiquadratic, multicubic and multiquadratic–cubic are studied in non-Archimedean normed spaces.

Toward a Logic of the Organism: A Process Philosophical Consideration

Mathematical models applied in contemporary theoretical and systems biology are based on some implicit ontological assumptions about the nature of organisms. This article aims to show that real organisms reveal a logic of internal causality transcending the tacit logic of biological modeling. Systems biology has focused on models consisting of static systems of differential equations operating with fixed control parameters that are measured or fitted to experimental data. However, the structure of real organisms is a highly dynamic process, the internal causality of which can only be captured by continuously changing systems of equations. In addition, in real physiological settings kinetic parameters can vary by orders of magnitude, i.e., organisms vary the value of internal quantities that in models are represented by fixed control parameters. Both the plasticity of organisms and the state dependence of kinetic parameters adds indeterminacy to the picture and asks for a new statistical perspective. This requirement could be met by the arising Biological Statistical Mechanics project, which promises to do more justice to the nature of real organisms than contemporary modeling. This article concludes that Biological Statistical Mechanics allows for a wider range of organismic ontologies than does the tacitly followed ontology of contemporary theoretical and systems biology, which are implicitly and explicitly based on systems theory.

Proposing Algorithm Using YOLOV4 and VGG-16 for Smart-Education

In this paper, we propose an algorithm to identify and solve systems of high-order equations. We rely on traditional solution methods to build algorithms to solve automated equations based on deep learning. The proposal method includes two main steps. In the first step, we use YOLOV4 (Kumar et al. 2020; Canu, 2020) to recognize equations and letters associated with the VGG-16 network (Simonyan and Zisserman, 2015) to classify them. We then used the SymPy model to solve the equations in the second step. Data are images of systems of equations that are typed and designed by ourselves or handwritten from other sources. Besides, we also built a web-based application that helps users select an image from their devices. The results show that the proposed algorithm is set out with 95% accuracy for smart-education applications.

Multirate linearly-implicit GARK schemes

Many complex applications require the solution of initial-value problems where some components change fast, while others vary slowly. Multirate schemes apply different step sizes to resolve different components of the system, according to their dynamics, in order to achieve increased computational efficiency. The stiff components of the system, fast or slow, are best discretized with implicit base methods in order to ensure numerical stability. To this end, linearly implicit methods are particularly attractive as they solve only linear systems of equations at each step. This paper develops the Multirate GARK-ROS/ROW (MR-GARK-ROS/ROW) framework for linearly-implicit multirate time integration. The order conditions theory considers both exact and approximative Jacobians. The effectiveness of implicit multirate methods depends on the coupling between the slow and fast computations; an array of efficient coupling strategies and the resulting numerical schemes are analyzed. Multirate infinitesimal step linearly-implicit methods, that allow arbitrarily small micro-steps and offer extreme computational flexibility, are constructed. The new unifying framework includes existing multirate Rosenbrock(-W) methods as particular cases, and opens the possibility to develop new classes of highly effective linearly implicit multirate integrators.

Transformation Method for Solving System of Boolean Algebraic Equations

: In recent years, various methods and directions for solving a system of Boolean algebraic equations have been invented, and now they are being very actively investigated. One of these directions is the method of transforming a system of Boolean algebraic equations, given over a ring of Boolean polynomials, into systems of equations over a field of real numbers, and various optimization methods can be applied to these systems. In this paper, we propose a new transformation method for Solving Systems of Boolean Algebraic Equations (SBAE). The essence of the proposed method is that firstly, SBAE written with logical operations are transformed (approximated) in a system of harmonic-polynomial equations in the unit n-dimensional cube Kn with the usual operations of addition and multiplication of numbers. Secondly, a transformed (approximated) system in Kn is solved by using the optimization method. We substantiated the correctness and the right to exist of the proposed method with reliable evidence. Based on this work, plans for further research to improve the proposed method are outlined.