System Of Canonical Equations Research Articles

METHODS TO SYNCHRONIZE DATA IN A MICROSERVICE ARCHITECTURE

This article discusses the problem of data synchronization methods using microservice architecture. Microservices is a popular and widespread software architecture today. The article reviews three main ways of interaction of microservices. They are event-based communication, interaction through direct HTTP requests and messaging, and also highlights and analyzes their advantages and disadvantages. The main purpose of the article is to analyze and make offer of the optimal option for solving the problem of synchronizing interacting microservices in real time. The optimal solution involves using the Apache Kafka message broker. It publishes data streams and subscriptions to them, as well as stores and processes them. Mathematical modeling of the proposed data synchronization method was described by constructing its state macine, as well as a system of canonical equations.

APPLICATION OF ANALYTICAL SOLUTIONS FOR BENDING BEAMS IN THE METHOD OF MOVEMENT

Introduction: Usually, to analyze statically indeterminate rod systems, the classical displacement method and preprepared tables for two types of rods of the main system are used. A mathematically correct representation of local loads with the use of generalized functions makes it possible to find an accurate solution of the differential equation for the equilibrium of a beam exposed to an arbitrary transverse load. Purpose of the study: We aimed to obtain analytical expressions for functions of deflection, rotation angles, transverse forces, and bending moments depending on four types of local loads for beams with different boundary conditions, so as to apply accurate solutions in the displacement method. Methods: We propose an analytical form of the displacement method to analyze rod structural models. For beams exposed to different types of transverse load (uniformly distributed force, concentrated force, or a couple of forces), accurate analytical solutions were obtained for functions of deflection, bending moments, and transverse forces at different types of beam ends’ restraint. This is possible due to the fact that concentrated load and load in the form of the moment of force can be specified by using unit column functions. By transforming Mohr’s integrals, using integration by parts, we show that the system of canonical equations of the displacement method was obtained based on the Lagrange principle. Results: Based on the analysis of a statically indeterminate frame, the effectiveness of the proposed analytical method is shown as compared with the classical displacement method.

The canonical equations K 66, K 67, K 68 and K 69

AbstractIn this paper we apply the REFORM method for the deduction of the system of canonical equations

ANALYSIS OF A RIGID WALL IN AN ELASTIC WEIGHTY HALF-PLANE

The analysis of stress-strain state of a rigid wall in an elastic weighty half-plane with a broken outline is carried out. To this end, the auxiliary problem of displacements definition in an elastic weighty quarter-plane was solved. Ritz method derived a formula to determine the displacements of elastic flat wedge boundaries in view of its own weight. On the basis of the received expressions the algorithm of displacements definition of a crack in an elastic weighty half-plane with a broken outline is developed. Analytical calculation of a rigid vertical wall located in an elastic weighty half-plane under the influence of a horizontal load, carried out by two methods: by Zhemochkin's method and finite difference method. In the problem statement an elastic half-plane is considered a model of the soil medium, therefore, only compressive normal stresses can arise on the connection of the wall with the elastic base. This assumption implies occurrence of discontinuities soil medium, and leads for the wall to an emergence of two dividing points of boundary conditions. The determination of the boundaries contact of the wall with the elastic half-plane, are not known in advance, is performed by iteratively way at each step set the position of dividing points of boundary conditions and the system of canonical equations of a corresponding method is written. If tensile stresses appear in wall-base contact and/or there is overlap of the crack edges occurs, then proceeds to the next iteration. Analysis of the results shows that the bending moment and shear forces in sections of the rigid wall in a broken weighty half-plane differ slightly from the same diagrams constructed for a rigid wall in an elastic weightless half-plane. The verification of the results of analytical calculation with the results received by using the LIRA 9.6 that implements the finite element method is obtained. The calculation results for the rigid wall in an elastic weighty half-plane obtained by analytical methods, qualitatively consistent with the results based on LIRA 9.6.

The Limiting Spectra of Girko’s Block-Matrix

To analyze the limiting spectral distribution of some random block-matrices, Girko (Random Oper. Stoch. Equ. 8(2), 189–194, 2000) uses a system of canonical equations from (An Introduction to Statistical Analysis of Random Arrays. VSP, Utrecht, 1998). In this paper, we use the method of moments to give an integral form for the almost sure limiting spectral distribution of such matrices.

Hamiltonian formulation and exact solutions of the Bianchi type I spacetime in conformal gravity

We develop a Hamiltonian formulation of the Bianchi type I spacetime in conformal gravity - the theory described by the Lagrangian , which involves the quadratic curvature invariant constructed from the Weyl tensor, in a four-dimensional spacetime. We derive the explicit forms of the super-Hamiltonian and of the constraint expressing the conformal invariance of the theory and we write down the system of canonical equations. To seek out exact solutions of this system we add extra constraints on the canonical variables and we go through a global involution algorithm which eventually leads to the closure of the constraint algebra. The Painlevé approach provides us with a proof of non-integrability, as a consequence of the presence of movable logarithms in the general solution of the problem. We extract all possible particular solutions that may be written in closed analytical form. This enables us to demonstrate that the global involution algorithm has brought forth the complete list of exact solutions that may be written in closed analytical form. We discuss the conformal relationship, or absence thereof, of our solutions with Einstein spaces.

BÉSM-2M computer calculation of beam type structures on elastic foundations (method, algorithm, program)

The approximate method of computing multiple span beams with variable cross section and elastic supports and connections, in any area of contact with the elastic foundation for static loads and temperature variation effects was elaborated by the author at the Leningrad Department of the Gidroproekt. For this purpose a foundation model based on Winkler's hypothesis, an elastic, isotropie medium of finite depth, one of infinite depth (the plane and the space probtems),~and a combined medium (the plane and the space problems) were investigated. The method is based on the general theory of structural mechanics of bar systems with the application of the integral equations of Fredholm and of the methods of numerical analysis. The computational formulas are given in matrix form. The above mentioned method is completely developed in the B-l-10 program for the BESM-2M computer. Let us examine a multiple span beam of variable height h(x) and constant width bb having a portion of its length supported by an elastic foundation and undergoing the influence of a complex of external factors F. The external factors include concentrated and distributed forces Pi, q(x) and moments Mi, m(x), temperature gradients AT(x), initial rotations vl(x) and displacements v~.(x) of the supports and connections, the load on the foundation surface qel(X). We will consider the connections and supports as elastic and completely independent of the foundation (Fig. la). As unknowns we select the normal forces r(x) which appear at the contact between the beam and the foundation and the internal forces xi (0-<i _<n) in the supports and connections. Tim friction on the contact surface is neglected. It we assume that r(x) is a known function, the structure can be considered as a multiple span beam (Fig. lb): We consider the basic system as a cantilever beam with a connection at the right. In the case when there is no connection we introduce fictitious constraints preventing the rotation or the vertical displacement. The rotation angle ~ and the vertical displacement v of the actual constraints will be supplementary unknowns. The reduced system of canonical equations of the mixed method with respect to Xi, ~, and v will be in the most general case 7: