Test Examples Research Articles

The $ m $-weak group inverse for rectangular matrices

<abstract><p>An extension of the $ m $-weak group inverse (or $ m $-WGI) on the set of rectangular matrices is provided to solve some systems of matrix equations. The extension is termed as the $ W $-weighted $ m $-WGI (or $ W $-$ m $-WGI). The $ W $-$ m $-WGI presents a new, wider class of generalized inverses which involves some already defined generalized inverses, such as the $ m $-WGI, $ W $-weighted weak group, and $ W $-weighted Drazin inverse. Basic properties and diverse characterizations are proved for $ W $-$ m $-WGI. Several expressions for computing $ W $-$ m $-WGI are proposed in terms of known generalized inverses and projectors, as well as its limit and integral representations. The $ W $-$ m $-WGI class is utilized to solve some linear matrix equations and express their general solutions. Some new properties of the weighted generalized group inverse and recognized properties of the $ W $-weighted Drazin inverse are obtained as corollaries. Numerical and symbolic test examples are presented to verify the obtained results.</p></abstract>

Some numerical methods for solving fractional partial difference equations in the discrete domain

This paper proposes a method for solving fractional partial difference equations using discrete Sumudu transformation. Some properties of discrete Sumudu transformation were used. The applications of the test examples for the initial value problems of fractional partial difference equations were tested using two methods: the successive approximation method. The second, homotopy perturbation, was proven efficient with the proposed method.

A Double‐Layer Optimization Method for Cascading Failure Prevention Considering Transient Stability

In recent years, in order to reduce the damage from the blackout accident, the demand of the power system for its basic resistance ability has gradually increased. Therefore, this paper proposes a double‐layer optimization method for the prevention of cascading failure of the power system that takes into account the transient stability constraint for cascading trips that directly lead to the accident. In terms of models, the paper reconstructs an outer model for optimizing the safety margin based on the inner model that solves the safety margin of cascading failure prevention. In terms of algorithms, the paper uses the Extended Particle Swarm Optimization (EPSO) algorithm with higher precision and accuracy to solve the inner model and innovatively introduced the Practical Dynamic Security Region (PDSR), which uses PSASP software for offline calculation and online application, as a dynamic analysis method to quickly realize transient stability constraint to solve the outer model. Three evaluation indexes of the preventive optimization effect can be obtained by this method; dispatchers can plan more flexible and reliable optimal dispatching schemes through these indexes, to comprehensively improve the safety margin of cascading failure prevention in the current operating state and enhance the risk resistance ability of the power grid. This paper has used MATLAB and PSASP to perform simulation analysis using the IEEE39 node system as a test example to verify the effectiveness and superiority of the proposed model and algorithm.

Robust and Chance-Constrained Dispatch Policies for Linear Power Systems

Several methods have recently been proposed to determine optimal feedback control policies for generator dispatch under uncertain grid in-feeds. This work presents and explains two such approaches based on a constrained linear power flow model in a unified notation, a robust method based on linear programming and a chance-constrained one based on polynomial chaos expansions and second order cone programming. This work compares both methods on the same small test example and discusses consequences for long-term grid expansion planning. While the robust method is easier to implement, it is also not more restrictive. For the chance-constrained method, we highlight a serious drawback in reformulations common in the literature. As an aside, we extend the existing formulation to cases where not all disturbances can be measured, and combine it with a robust pre-processing scheme.

О генерации электрического разряда в диэлектрике потоком фотонов

The development of an electric discharge during photon scattering in a dielectric material is considered. A preliminary mathematical model of the discharge process is presented. The model is based on a quantum kinetic equation for quasi-free charge carriers produced by bulk radiation effects and impact ionization. Equations are obtained for the concentration, drift current density, and gas temperature of quasi-free electrons. A test example is considered, confirming that the model does not contradict the known conditions for the formation of an electric discharge.

STOCHASTIC GALERKIN METHOD AND PORT-HAMILTONIAN FORM FOR LINEAR FIRST-ORDER ORDINARY DIFFERENTIAL EQUATIONS

We consider linear first-order systems of ordinary differential equations (ODEs) in port-Hamiltonian (pH) form. Physical parameters are remodeled as random variables to conduct an uncertainty quantification. A stochastic Galerkin projection yields a larger deterministic system of ODEs, which does not exhibit a pH form in general. We apply transformations of the original systems such that the stochastic Galerkin projection becomes structure-preserving. Furthermore, we investigate meaning and properties of the Hamiltonian function belonging to the stochastic Galerkin system. A large number of random variables implies a high-dimensional stochastic Galerkin system, which suggests itself to apply model order reduction (MOR) generating a low-dimensional system of ODEs. We discuss structure preservation in projection-based MOR, where the smaller systems of ODEs feature pH form again. Results of numerical computations are presented using two test examples.

Numerical modeling of surface subsidence due to compaction of soil with fine inclusions

A mathematical model of filtration consolidation of an inhomogeneous soil mass was formed taking into account the change in the size of the area during the compaction process. The inhomogeneity is considered as the presence of fine inclusions (geobarriers) the physical and mechanical characteristics of which differ from those of the main soil. From a mathematical viewpoint, the model is described by a one-phase Stefan problem that has a kinematic boundary condition on the upper moving boundary as its component. The purpose of the research is to find out the effect of fine inclusion on the dynamics of subsidence of the soil surface in the process of compaction. The change in the dimensions of the solution area is physically determined by the change in the volume of the pores of the porous medium in the process of dissipating excess pressure. If the permeability of the geobarrier is low, it affects the dynamics of consolidation processes and, accordingly, the magnitude of subsidence. Finite element solutions of the initial-boundary value problem for the nonlinear parabolic equation in the heterogeneous region with the conjugation condition of non-ideal contact were found. Numerical time discretization methods, a method for determining the change in the position of the upper boundary at discrete moments of time, and an algorithm for determining the physical and mechanical characteristics of a porous medium depending on the degree of consolidation are given. A number of test examples were considered, and the effect of a thin inclusion on the dynamics of the change in the position of the upper boundary of the problem solution area was investigated.

Development of an express risk assessment in tender participation for contracting construction organizations in civil and agro-industrial construction

Participation in a tender is an integral part of the activities of contracting construction organizations. The difficulty lies in the fact that contractors have to make a decision on participation or non-participation in the tender quite quickly from the moment the customer posts information about the procurement. Incorrect decisions made by the contractor at this stage lead to lost profits, financial losses, ineffectiveness, loss of reputation and other unpleasant consequences. To level out this situation, the paper describes existing approaches to assessing the risks of participation in tender activities, which can protect the contractor from participating in unwanted procurement. In order to assess the feasibility of participating in a procurement, the authors propose the development of an algorithm for express risk assessment of a contractor's participation in a tender, which suggests, under limited time, to make a reasonable decision on the need to participate in a particular tender. This requires a qualitative and quantitative assessment of the contractor’s main risks, which are combined into two main groups: the risk of loosing the tender and the risk of future losses. The authors propose methods for assessing risks and classifying them as high, medium and low levels. The paper provides an example of practical testing of the proposed express assessment.

PyPGCF: A Python Software for Phylogenomic Analysis, Species Demarcation, Identification of Core, and Fingerprint Proteins of Bacterial Genomes That Are Important for Plants.

This computational protocol describes how to use pyPGCF, a python software package that runs in the linux environment, in order to analyze bacterial genomes and perform: (i) phylogenomic analysis, (ii) species demarcation, (iii) identification of the core proteins of a bacterial genus and its individual species, (iv) identification of species-specific fingerprint proteins that are found in all strains of a species and, at the same time, are absent from all other species of the genus, (v) functional annotation of the core and fingerprint proteins with eggNOG, and (vi) identification of secondary metabolite biosynthetic gene clusters (smBGCs) with antiSMASH. This software has already been implemented to analyze bacterial genera and species that are important for plants (e.g., Pseudomonas, Bacillus, Streptomyces). In addition, we provide a test dataset and example commands showing how to analyze 165 genomes from 55 species of the genus Bacillus. The main advantages of pyPGCF are that: (i) it uses adjustable orthology cut-offs, (ii) it identifies species-specific fingerprints, and (iii) its computational cost scales linearly with the number of genomes being analyzed. Therefore, pyPGCF is able to deal with a very large number of bacterial genomes, in reasonable timescales, using widely available levels of computing power.

A Physical Basis of Predicting the Magnitude and Failure Time of a Forthcoming Earthquake

Let T and M be, respectively, the precursor time of a certain precursor and the magnitude of a forthcoming earthquake. Observations may lead to a relationship of T versus M in a form of log(T)=a+bM. In this study, we will explore the intrinsic physics of the log(T)−M relationship. Based on the log(T)−M relationships of two different precursors from observed data, we propose a method of predicting the magnitude and failure time of a forthcoming earthquake. A testing example based on the log(T)−M relationships inferred from the data of presiemic radon concentration anomalies and gamma-ray emission changes observed at respective monitoring stations in Taiwan is given in this study. Results confirm a high possibility of predicting the magnitude and failure time of a forthcoming earthquake just from the observed occurrence times of two different precursors based on their log(T)−M relationships.

Numerical algorithm for solving parabolic identification problem with mixed boundary condition

A source identification problem for a parabolic equation with mixed boundary condition is studied. Stability estimates for the solution of identification problem with mixed boundary conditions are obtained. Numerical algorithm for solving this inverse problem are proposed. Stability estimates for difference schemes are established. The numerical result in test example is presented.

Robust finite difference scheme for the non-linear generalized time-fractional diffusion equation with non-smooth solution

The present paper aims to develop a stable multistep numerical scheme for the non-linear generalized time-fractional diffusion equations (GTFDEs) with non-smooth solutions. Mesh grading technique is used to discretize the temporal direction, which results in 2−α order of convergence (0<α<1). The spatial direction is discretized using a second order difference operator and the non-linear term is approximated using Taylor’s series. Theoretical stability and convergence analysis is established in the L2-norm. Moreover, some random noise perturbations are added to investigate the numerical stability of the developed scheme. Finally, numerical simulations are performed on three test examples to verify the robustness and efficiency of the scheme.

Analysis of Stability and Oscillations of Porous Power and Sigmoid Functionally Graded Sandwich Plates by the R-Function Method

In this paper, the R-function method is used for the first time to study the stability and oscillations of porous functionally graded (FG) sandwich plates with a complex geometric shape. It is assumed that the outer layers of the plate are made of functionally graded materials (FGM), and the filler is isotropic, namely ceramic. The differential equations of motion were obtained using the usual first-order shear deformation theory with a given shear coefficient (FSDT). Two models of porosity distribution according to the power (P-law) and sigmoid (S-law) laws were studied. Analytical expressions for calculating the effective mechanical characteristics of FG materials with even and uneven porosity distribution were obtained. The proposed approach takes into account the fact that the subcritical state of the plate can be heterogeneous, and therefore, first of all, the stresses in the middle plane of the plate are determined, and then the eigenvalue problem is solved in order to find the critical load. To determine the critical load and plate frequencies, the Ritz method was used along with the R-function method. The developed algorithms and software are tested on test examples and compared with known results obtained using other methods. A number of problems of stability and oscillations of the FG of porous sandwich plates with a complex geometric shape for various layer stacking schemes, various boundary conditions and laws of porosity distribution have been solved.

Simultaneous identification of the solely time‐dependent potential and source control terms from known moisture moments

Pseudo‐parabolic equations are commonly used as mathematical models in mechanics, biology, and physics to address various applied problems. One particular application involves describing moisture transfer dynamics in subsoil layers using pseudo‐parabolic equations. This manuscript examines the inverse problem (IP) of identifying the moisture transfer function, along with the time‐varying potential and source control terms, in a linear pseudo‐parabolic equation from known moisture moments. We prove the existence of a unique solution to the inverse problem for sufficiently small times by employing the contraction principle. The inverse problem is reformulated as a nonlinear least‐squares minimization problem, with the unknowns subjected to simple bounds. To guarantee stability, the Tikhonov regularization technique is utilized. For the numerical discretization, we develop the Crank–Nicolson finite‐difference method to solve the direct problem. To solve the nonlinear least‐squares minimization problem, we utilize the built‐in subroutine lsqnonlin from the MATLAB optimization toolbox. We present and thoroughly discuss numerical outcomes for a benchmark test example, providing insights into the performance and effectiveness of the proposed methodology.

Comparing Test Methods in ABCtronics: An Example of Global Urban Air Quality Result Testing

This article explores the importance of the methods in quality control in the semiconductor industry. Three test methods in ABC tronics, a semiconductor company from Case-ABCtronics: Manufacturing, Quality Control, and Client Interfaces, will be used to test the data comes from an air quality database available on Kaggle. These data initially taken from Numbeo as an aggregation of user voting. The results of the three different methods are analyzed to draw their respective conclusion, that is whether the investigation report will be accepted or not. In the comparison of three methods, the new testing method is more likely to reject the entire result, and individual chip testing method is a most recommended test method with several advantages. The article emphasizes the usefulness of the findings for other manufacturers in the industry who are looking to improve their quality control measures and maintain high standards of product quality.

Application of the Double Approximation Method for Constructing Stiffness Matrices of Volumetric Finite Elements

Introduction. When numerically solving problems of elasticity theory in a three-dimensional formulation by the finite element method, finite elements (FE) in the form of parallelepipeds, prisms and tetrahedra are used. Regularly, the construction of stiffness matrices of volumetric FE is based on the principle of isoparametricity, which involves the Lagrange polynomials to approximate the geometry and displacements. In computational practice, the most widespread FE are the so-called multilinear isoparametric FE with a linear law of approximation of displacements. The main disadvantage of these elements lies in the “locking” effect when modulating bending deformations. Moreover, the error of the numerical solution increases drastically in the case when the structure, in comparison to conventional deformations, undergoes significant displacements as a rigid whole. Long-term experience in solving problems of deformable solid mechanics by the finite element method has shown that existing volumetric FE have slow convergence, specifically, when modeling bending deformations of plates and shells. This study aims at constructing stiffness matrices of multilinear volumetric FE of increased accuracy allowing for rigid displacements based on the double approximation method.Materials and Methods. The mathematical apparatus of the double approximation method based on the principle of a separate representation of the distribution functions of displacements and deformations inside the element, was used to construct the stiffness matrices of volumetric FE. The storage and processing of the resulting system of equations was implemented in algorithmic terms of sparse matrices. Software development and computational experiments were carried out using the Microsoft Visual Studio 2013 64-bit computing platform and the Intel ® Parallel Studio XE 2019 compiler with the integrated Intel ® Visual Fortran Composer XE 2019 text editor. Visualization of the calculation results was performed using the descriptor graphics of the MATLAB computer mathematics package. A large eight-node SOLID185 CE of the ANSYS Mechanical software complex was used as a test sample.Results. Mathematical tool and software were developed to study the stress-strain state of massive structures under various types of external actions. The authorized application software package was verified on test examples with known analytical solutions. It has been shown that the constructed FE accurately satisfy the basic requirements for finite element modeling of spatial problems of elasticity theory.Discussion and Conclusion. The performed testing of the developed mathematical and program toolkit has shown that the finite elements constructed on the basis of the double approximation method can successfully compete with similar SOLID185 volumetric elements of the ANSYS Mechanical software complex. The proposed elements can be integrated into domestic import-substituting software systems that implement the finite element method in the form of the displacement method.

Kinematically excited beam vibrations under random perturbations

There is numerous information in the technical and scientific literature that often the sources of forced kinematically excited oscillations have a clearly expressed random nature. Kinematically excited vibrations of beams are considered. Their sources are random disturbances. Steady (in a probabilistic sense) vibrations of beams are studied. As a consequence, the transverse vibrations of the beam will also be random, and it becomes necessary and expedient to switch to stochastic motion models.&#x0D; Introduction. For a random perturbation process, a spectral matrix is specified. Initial conditions for the equations are not required. The boundary conditions are similar to those used for free and kinematically excited deterministic oscillations. The task is to find the spectral matrix of the random field of beam deviations and dispersion for a given spectral matrix. The question of determining the mathematical expectation is not raised. It is argued that it can be easily reduced to known deterministic problems.&#x0D; Methods. To carry out specific calculations, a model of kinematic disturbances is used in the form of a vector N-dimensional stationary random process with stationary connected components that have hidden periodicities (characteristic frequencies). A test example was completed to determine the dispersion and standard deviation of displacements. The numerical integration step was adopted after numerical experiments. When performing calculations, the parity of the integrand was taken into account. The lower limit of integration is taken to be zero, followed by doubling of the final result.&#x0D; Results. For small values of the broadband parameter, the results of the stochastic and deterministic problems differ little. Examples are presented that are stochastic analogs of harmonic oscillations. For beams under kinematic harmonic disturbances, test examples were performed to determine dispersions and standard deviations.&#x0D; The discussion of the results. The results of calculations in the article are presented by curves having numbers that coincide with the numbers of the matrices. The first matrix corresponds to the absolute correlation of disturbances. The second matrix corresponds to the absolute correlation between the first and third, second and fourth disturbances, while these pairs are absolutely uncorrelated. The third matrix describes random perturbations when the indicated pairs, being perfectly positively correlated within, are absolutely perfectly negatively correlated between pairs. The fourth curve corresponds to the case of ideal correlation of the first three disturbances with each other, while the movements of the fourth support are in antiphase with them. In the latter case, the movements of the outer supports are in antiphase with the movements of the middle ones, which favors the greatest bending of the beam. Therefore, the elastic line has a curvature that is significantly greater than the others.

Cadets’ Listening Skills Development by Means of iSpring QuizMaker Computer Program

New educational paradigm requires the implementation of effective training aids to improve cadets’ foreign language communicative competence. For this reason, the search for new tools for development of key skills is a top problem of theory and practice of teaching foreign languages. The paper substantiates the didactic potential of e-learning tools for the development of certain skills and control of mastering material by cadets. The author touches upon the issues of teaching foreign languages cadets using a modern digital tool – iSpring QuizMaker, which is an additional program for Microsoft PowerPoint. The teaching staff use it to create interactive tests and e-books. In general, the computer program is designed to upgrade and intensify the learning process at the Yaroslavl Higher Military School of Air Defense. The emphasis is made on the possibility to create interactive tests for listening comprehension. The variability of exercises is the main advantage of this program and makes the process more effective and efficient. This function allows to develop cadets’ listening comprehension skills for different purposes. The author provides the examples of iSpring Suite interactive tests in the study of the topic «Top 5 U.S. fighters today» with the second-year cadets of the Yaroslavl Higher Military School of Air Defense.

SOLUTION OF PHYSICALLY NONLINEAR PROBLEMS OF DEFORMATION OF MASSIVE AND THIN-WALLED PRISMATIC BODIES

The results of a numerical study on test examples of the convergence of the developed version of the semi-analytical method of finite elementsare presented. A comparison of machine time and accuracy of solving elastic and plastic problems obtained on the basis of finite elements with variableand averaged mechanical parameters was performed.The convergence of the finite element method and the semianalytical finite element method in the calculation of prismatic bodies loaded with localized and distributed external influences was studied. An effective numerical approach to the study of arbitrarily loaded massive and thin-walled prismatic bodies of complex shape, the deformation of which can pass beyond theelastic limit of the material, is being developed based on the finite element moment scheme and the semianalytical variant of the finite element method. Due to the representation of displacements by polynomials and the use of iterative methods of solving systems of equations, this approach is developed in relation to the calculation of objects with arbitrary boundary conditions on the ends, which made it possible to expand the area of effective application of the semi-analytical method of finite elements to a new class ofproblems.A number of new complex problems of elastic and elastic-plastic deformation of massive and thinwalled prismatic bodies, which have an independentapplied value, have been solved.

Information Security of Microsystems. Microcontroller

Methodological and practical aspects of testing microcontrollers for resistance to power analysis reengineering are considered. A model of quantitative assessment of durability is proposed, based on the construction of a relative parameter variance diagram of an operation with data. Within the framework of the model, a criterion has been introduced that allows comparing the durability of various devices. The key provisions of the methodology for testing devices on the power consumption channel have been developed. Using the example of testing one of the microcontrollers, the procedure for determining the resistance to extracting internal memory data is presented. Based on the results of the analysis, conclusions are formulated about the possibility of safe operation with this microcontroller in information systems.