Mathematical Software Research Articles

Solving numerical method problems with mathematical software: Identifying computational thinking

This research examines the application of students’ computational thinking (CT) in solving numerical method problems through computer software. Data collection involved observing their learning process and conducting tests to evaluate their CT skills within the context of the root approach material using Newton-Raphson method. The results indicate that the use of Microsoft Excel facilitates problem-solving for students and educators when employing Newton-Raphson method. Furthermore, it helps identify aspects or indicators of CT in students’ problem-solving processes. The research findings demonstrate that students with strong mathematical abilities should document their conclusions in the algorithmic aspect. Students with moderate mathematical abilities exhibit all indicators in every aspect of CT when solving problems using Newton-Raphson method. On the other hand, students with weak mathematical skills fail to articulate questions, formulas, or conclusions in the algorithm design aspect, but they do show all indicators in the pattern recognition and abstraction aspects.

COMPUTATIONAL ANALYSIS OF NONLINEARIZED THERMAL RADIATION & LORENTZ FORCE ON UNSTEADY FLOW OF NON-NEWTONIAN FLUID IN POROUS MEDIUM

An extensive analysis of nonlinearized thermal radiation & Lorentz force on an unsteady flow of Non-Newtonian fluid taking the Maxwell model over a permeable nonuniform stretchable sheet in a porous media has been presented. Appropriate analogous transformations are introduced to develop the ordinary differential equations from the fluid flow governing equations. Numerical method Lobatto IIIa is used to solve these ODEs and programmed in mathematical software MATLAB to obtain the graphical and numerical details. The effectiveness of non-linearity in thermal radiation, unsteadiness of the flow and magnetic field on Nusselt number, skin friction, heat & fluid motion are tabulated and represented in graphs with an elaborate discussion of the consequences. It is found that the Lorentz force and nonlinearity in thermal radiation have an adverse impression on the heat propagation throughout the flow. Further, a comparative inspection is also carried out proving the relevance of the current technique.

Finding orientations of supersingular elliptic curves and quaternion orders

AbstractAn oriented supersingular elliptic curve is a curve which is enhanced with the information of an endomorphism. Computing the full endomorphism ring of a supersingular elliptic curve is a known hard problem, so one might consider how hard it is to find one such orientation. We prove that access to an oracle which tells if an elliptic curve is $$\mathfrak {O}$$ O -orientable for a fixed imaginary quadratic order $$\mathfrak {O}$$ O provides non-trivial information towards computing an endomorphism corresponding to the $$\mathfrak {O}$$ O -orientation. We provide explicit algorithms and in-depth complexity analysis. We also consider the question in terms of quaternion algebras. We provide algorithms which compute an embedding of a fixed imaginary quadratic order into a maximal order of the quaternion algebra ramified at p and $$\infty $$ ∞ . We provide code implementations in Sagemath (in Stein et al. Sage Mathematics Software (Version 10.0), The Sage Development Team, http://www.sagemath.org, 2023) which is efficient for finding embeddings of imaginary quadratic orders of discriminants up to O(p), even for cryptographically sized p.

The Method of Elementary Solvers in SPICE

Circuit simulators are fundamentally used for solving electric circuit problems with different degrees of complexity in which node voltages and branch currents are the unknowns. This is fully understandable since they were originally created for this specific task. However, behind the curtains, powerful simulation engines based on a variety of numerical techniques operate so as to always comply with Kirchhoff’s current and voltage laws. In this paper, it is shown how a simple circuital configuration, referred to as the elementary solver, consistent in two behavioral current sources in series, can be used to solve mathematical problems that go beyond electronics. Of course, the intention is not to substitute mathematical packages with well-proven calculus capacity but to increase the scope of circuit simulators for their application in other areas of research or simply for educational purposes. It is worth mentioning that no special programming skills are required (except a basic knowledge of the available tools and language) and, furthermore, that the user can operate exclusively in a graphical environment. It is shown, throughout a series of selected examples, how the method of elementary solvers (MES) works, providing a new and practical dimension to the applicability of circuit simulators.

Solitonic solutions and stability analysis of Benjamin Bona Mahony Burger equation using two versatile techniques

This study aims to explore the precise resolution of the nonlinear Benjamin Bona Mahony Burgers (BBMB) equation, which finds application in a variety of nonlinear scientific disciplines including fluid dynamics, shock generation, wave transmission, and soliton theory. Within this paper, we employ two versatile methodologies, specifically the extended exp(-Ψ(χ))\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\exp (-\\Psi (\\chi ))$$\\end{document} expansion technique and the novel Kudryashov method, to identify the exact soliton solutions of the nonlinear BBMB equation. The solutions we discovered involve trigonometric functions, hyperbolic functions, and rational functions. The uniqueness of this research lies in uncovering the bright soliton, kink wave solution, and periodic wave solution, and conducting stability analysis. Furthermore, the solutions’ graphical characteristics were explored through the utilization of the mathematical software Maple 2022 (https://maplesoft.com/downloads/selectplatform.aspx?hash=61ab59890f2313b2241fde3423fd975e). The system’s physical interpretation is defined through various types of graphs, including contour graphs, 3D-surface graphs, and line graphs, which use appropriate parameter values. These recommended techniques hold significant importance and are applicable in diverse nonlinear evolutionary equations found in the field of nonlinear sciences for illustrating nonlinear physical models.

Analysis of the nonlinear Fitzhugh–Nagumo equation and its derivative based on the Rabotnov fractional exponential function

The Fitzhugh–Nagumo equation is an essential governing equation that explains the process of impulse transmission from the nerves. This work suggests a novel generalized arbitrary-order Fitzhugh–Nagumo equation that is based on the recently developed nonsingular fractional operator. The modified Fitzhugh–Nagumo equation has been generalized using fractional Yang–Abdel–Cattani operator to provide a more accurate representation of the equation with memory effects and non-local behavior. Further, we discussed some interesting and new properties of the proposed fractional operator and the Rabotnov exponential fractional kernel with a modified Sumudu integral transform. In order to solve the proposed nonlinear differential equation, the homotopy perturbation method coupled with the modified Sumudu integral transform technique is implemented to examine the result of a newly proposed Yang–Abdel–Cattani fractional Fitzhugh–Nagumo equation, which converges to the exact solution. The nonlinear terms of this equation are handled in terms of He’s polynomials. The existence and uniqueness of the solution have been demonstrated using the Banach space fixed point theorem. The convergence and error analysis of the suggested technique are also discussed. The findings are expressed in terms of generalized Mittag-Leffler functions. The obtained results are plotted with the help of MATLAB R2016a mathematical software. The results in this work are more accurate, and it is proposed that the new Yang–Abdel–Cattani fractional derivative operator is an effective tool for finding the results of any other nonlinear problems arising in science and engineering. All three problems have been computed for different orders to confirm the significance of the fractionalizing concept in the proposed equation. The increase of the fractional order value ℘ to 1 confirms that our proposed time-fractional Fitzhugh–Nagumo equation in the Yang–Abdel–Cattani sense gets close to the analytic solution.

Comparative Study between Thermo-Mechanical and Inherent Strain Method in Analysing Part Distortion of WAAM Component Using Numerical Simulation

This research investigates the part distortion of WAAM process by utilizing advanced numerical simulation. The WAAM component is made of a stainless steel SS316L deposition layer that is deposited on top of a mild steel S235 substrate plate to create a hollow, rectangular structure with a thin wall. In this study, Goldak's double-ellipsoid was used as the heat source model, and an isotropic hardening rule based on the von-Mises yield criterion was used. MSC Marc/Mentat is utilized as the numerical FE software for this research. The commercial S235 mild steel for substrate and the evolved SS316L was scanned by JMATPRO as the input for material modelling. In order to reduce the computational time of the numerical WAAM process, an Inherent Strain Method (ISM) is proposed for a numerical WAAM simulation in Marc. There are two ISM methods proposed for this study, the first is the analytical ISM based on the calculations and second is the calibration-based ISM using Virtual Calibration Test (VCT). On obtaining the ISM value based on the result of VCT, the mathematical software MATLAB were utilized to find the optimized ISM value. This research has a final purpose to determine which numerical simulation model that has a clear advantage on predicting the component deformation result in term of result accuracy as well as computational time. The expected final outcome of this study is the implementation of ISM method on numerical WAAM simulation is able to predict a part distortion in an accurate manner similar to TMM model with significantly faster computational time. Keywords: WAAM, Part Distortion, Numerical Simulation, Inherent Strain Method, Computational Time.

Electromagnetic transient simulation of power system based on PSCAD calling ADPSS

Abstract As the power system gradually expands into a massive scale, time-varying complex system, the requirements for simulation analysis software are constantly improving, and electromagnetic transient analysis plays a crucial role in the power system. Therefore, to solve the possible limitations of this traditional simulation method, this paper proposes an electromagnetic transient simulation of power systems using PSCAD, called ADPSS. Firstly, according to the basic overview and advantages of the electromagnetic transient analysis program PSCAD/EMTDC and the mathematical model software package ADPSS, the interconnection principle and implementation method between PSCAD/EMTDC and ADPSS are studied, and a simple power system power supply model is established in PSCAD. Then, the principle of PSCAD-ADPSS interface technology is studied. The electromagnetic transient simulation is carried out in the interface environment, and the interface custom components are designed. Finally, by conducting a comparative analysis of the simulation outcomes, it is found that the simulation waveforms obtained in the two simulation environments are almost the same, which shows the effectiveness of PSCAD-ADPSS interface simulation technology in electromagnetic transient analysis and has the potential to enhance the precision and dependability of electromagnetic transient simulation.

CИЛОВОЙ АНАЛИЗ ПЛОСКИХ РЫЧАЖНЫХ МЕХАНИЗМОВ ВЕКТОРНЫМ МЕТОДОМ

An analytical method is presented for force analysis of plain lever mechanisms with one degree of freedom, based on the vector method. Using the example of a two-drive structural group, a method is outlined for finding reaction vectors in all its kinematic pairs, while maintaining the clarity and consistency of the solution inherent in the graphic-analytical method of diagrams of component forces. An original analytical description is given for finding the vectors of tangential and normal components of reactions in kinematic pairs. Application of the proposed method of force analysis makes it possisble to find reaction vectors in kinematic pairs without compiling and solving complex systems of equilibrium equations or graphical construction. Adaptation of the proposed force analysis in modern mathematical packages allows for the study of plain lever mechanisms with one degree of freedom in a short time and with high accuracy.

An application of Rumor Propagation In Google trends

Daley and Kendle’s pioneering mathematical basis for modelling rumor propagation around 1965 has paved a strong platform for researchers to come up with new generalizations for practical scenarios of rumor spreading in social networks. In this study, we use a generalization of original DK model, Ignorant-Spreader-Stifler (ISS) model to analyze the cricket related searches in Sri Lanka on Google.The secondary data used for the study were obtained from Google trends for a five-year period from 2012 to 2017, targeting the three t20 matches held during the period. We introduce two algorithms on Maple mathematical software to estimate the parameters of the ISS model numerically. We observe that the way people search on web about cricket is roughly analogous to spreading a rumour and forecasting is better when modelling with most recent data than considering more data back in time and we also find that the predicting accuracy is significantly equal of the two models built considering the data in 2012 and 2014.

A Low-Rank Matrix Approach to Compute Polynomial Approximations of Smooth Two-Dimensional Functions

Polynomial approximation of smooth functions is becoming increasingly important in fields like numerical analysis and scientific computing. These approximations are vital in models that rely on spectral methods. To reduce the memory costs for large dimensional problems, various methods to provide data-sparse representations have been proposed, including methods based on singular value decomposition, adaptive cross approximation, and matrices with hierarchical low-rank structures, to mention a few. This work presents implementation details on the polynomial approximation of univariate smooth functions through the Polynomial1 class, and of bivariate smooth functions by low-rank matrix representation via the Polynomial2 class. These approaches are explained within Tau Toolbox, a mathematical software library for solving integro-differential problems by the spectral Tau method.

Модели составных гармонических полуволн и связь дискретизации времени с энтропией временных параметров сигналов

The problem of finding the absolute error of stepwise and linear interpolation of the control signal from uniform samples from it using models of composite harmonic half-waves is solved. Previously, during the inspection of the control object, the maximum values of the signal parameters and half-waves are determined: speed, acceleration and sharpness, there are no spectrum parameters. To determine the values of the intervals of uniform sampling of time, two groups of models of "harmonic half-waves" are considered. The first group of models is described by harmonic time functions whose parameters are consistent. The second group of models is described by composite harmonic functions of time, thereby the time parameters of the signals are consistent. It is proved that with an increase in the entropy of the maximum values of the signal parameters, the value of the time sampling interval increases without increasing the interpolation error. Thus, the entropy value of the signal parameters serves as an indicator of their inconsistency. The results of modeling and graphs obtained in the environment of the mathematical package are presented. The results are intended to optimize the loading of input tasks and primary information processing of processors in robust real-time automation systems, for example, used to control high-speed trains when braking in sliding or skidding mode.

The Impact of the Different Types of Dance Cheerleading on the Physical Aspect, Adaptive Ability and Level of Resilience of Middle School Students

The purpose of this study is to compare the effects of different types of dance cheerleading on the physical fitness and health level of junior high school students in Kaili City, and to explore the relationship between its effects on physical fitness, adaptive ability and level of resistance to frustration. The subjects of the investigation included students in the Street Dance Cheerleading group, Jazz Cheerleading group and Flower Ball Cheerleading group, participating in the "Physical Education and Health" course. Through the research design of description-comparison-correlation, the data were collected by questionnaire method and analyzed using mathematical statistics software. The results showed that different types of cheerleading had a significant effect on secondary school students' physical ability, adaptability and level of resistance to frustration. It is recommended that schools and educational organizations should strengthen the promotion of cheerleading activities while paying attention to the differences in gender and types of cheerleading in order to improve the overall physical fitness of students and develop their teamwork spirit.

Assessment of Environmental Risks of a Shallow Water Body during Dredging Works

Introduction. The increasing anthropogenic impact on water bodies necessitates integrated solutions to assess environmental risks. Literature describes the stages of risk assessment, the possibilities of environmental management, and expert analysis, while risk modeling in this field is being investigated. However, the potential for predicting risks to water quality and biodiversity during frequently performed hydraulic engineering works such as dredging has not been fully explored. The relevance and practical significance of such an approach are evident. This study aims to develop a mathematical model and software package that can assess risks to species diversity of the ecosystem of a shallow reservoir ecosystem during work in its water area.Materials and Methods. The starting point for the simulation was a description of the movement of water masses based on the Navier-Stokes equations and the continuity equation at variable density. We used the diffusion-convection equation to predict the transfer of suspended and dissolved particles, as well as to assess the impact of impurities during eutrophication. To create the algorithm, we utilized the terms and definitions defined by the state standard for risk management in emergency situations.Results. To test the solution, we took data on hydro-mechanical work in the port area of Arkhangelsk. We visualized the concentration fields of suspended particles 0, 15, 30 and 45 minutes after the soil was unloaded. It was found that during the settling of the suspension, the area of its distribution expanded significantly, and this was fully consistent with the data of field experiments during dredging. We calculated and tabulated the volumes of contaminated water at soil dumps in three sites (with a single discharge and in total). To assess the risks to the Sea of Azov, we used the maximum concentrations of pollutant (copper) obtained through measurements, modeling and remote sensing of the Earth. In tests to determine the potential danger of the substance, we assumed that its concentration caused a reaction in 50% of organisms. For fish, the potentially dangerous concentration was 4 mg/l with a duration of 96 hours of exposure. For zooplankton — 50 mg/l and 48 hours. For microalgae, 20 mg/l and 72 hours. The normalized risk value Rn ≈ 0.52 was obtained. The risk of copper concentration of 80 µg/l in the waters of the Azov Sea was recognized as significant. A tendency towards increasing salinity and stratification of water masses in terms of oxygen content has been identified, consistent with the findings of expeditionary research.Discussion and Conclusion. The developed approach has allowed us to assess the change in the quality of the waters of the Azov Sea and describe some transformations of the water area. Specifically, we are talking about the distribution of suspended particles and areas of their deposition. These processes can lead to changes in the bottom topography, which in turn can reduce the species diversity of the ecosystem.

Systematic Literatur Review: Software Matematika Geogebra Sebagai Media Belajar Untuk Mengetahui Kemampuan Komputasi Peserta Didik

During the period of compulsory education in Indonesia, which is 12 years, the government requires mathematics as the main learning subject for extracts which will continue to have an impact on people’s lives. The level of ability in a field of science must be measured to obtain valid data for the development of education in Indonesia. The use of Geogebra Mathematics Software in schools in Indonesia is not surprising at this time, technological developments have made the use of Geogebra mathematics software commonplace. This research is a Systematic Literature Review, in this research the author analyzes and compares several articles obtained from the internet or digital databases, for example Semantic Scholar or Sprinter Link. The articles that have been found are then selected according to the title researched, so that several reference articles are obtained. The research results show that the use of Geogebra mathematics software in learning has a great influence on students’ computing abilities. Geogebra is a media with a visual, analytical and numerical approach that can be solved using algorithms that require computational capabilities to operate. There is empathy in computational thinking, namely algorithmic thinking problem solving, pattern recognition, and abstraction and generalization.

Mathematical Software: A Panacea for Improving Senior Secondary School Students’ Retention in Geometrical Constructions

When attempting to address the persistently poor performance of students in mathematics, researchers have typically examined factors such as retention to identify long-term solutions. The objective of this study was to improve the retention of senior secondary school students in geometrical constructions through mathematical software. Despite the many benefits of geometry to both the learner and society, the performance of the students continued to be abysmal. Could it be that the students do not retain what they learn? The research was conducted in Benue State, Nigeria, and was based on John Sweller’s cognitive load theory of multimedia. The study’s design utilised a non-randomised, quasi-experimental control group with a sample size of 457 students. Three objectives, research questions and research hypotheses led the study, with the Geometrical Construction Achievement Test and the Geometrical Construction Retention Test as the instruments for data collection. The mean and standard deviation of descriptive statistics were used to analyse the data that was gathered. The research reveals that retention was higher in the experimental group (Mean = 65.88) than in the control group (Mean = 51.87). The study found a statistically significant improvement in retention (p ˂ 0.05). No gender variations were found when the students were taught with mathematical software. Mathematics teachers’ utilisation of mathematical software as a strategy for teaching geometrical constructions among senior secondary school students was recommended.

Research on the Application of Mathematical Software in Concrete Data Analysis

Research on the Application of Mathematical Software in Concrete Data Analysis

Application of Maple Mathematical Package to Search for Transfer Gear Oscillation Frequencies

Considers direct spectral problem of determination of frequencies of free torsional oscillations of transfer gearbox, component part of power plants with diesel fuel, gearboxes. The gearbox is modeled by a dynamic mechanical system with three degrees of freedom of bearings and gear. The frequency equation of the direct problem was found, according to which numerical calculations were carried out to search for the frequencies of torsional vibrations of the transfer gearbox. To the conclusion of the equation and the search for the frequencies of the gearbox oscillations, a software implementation of transformations using the functionality and libraries of the Maple mathematical package is given.

Geometry learning with dynamic software in pre-service mathematics teacher education: A systematic review

Geometry learning with dynamic software in pre-service mathematics teacher education: A systematic review

FREE UNDAMPED SPATIAL VIBRATIONS OF A ROBOT FOR PROCESS AUTOMATION IN METALLURGY

This paper presents the results of mechano-mathematical modeling of free undamped spatial vibrations of a robot for process automation in metallurgy.A dynamic model of the robot is made. It is studied as a mechanical system with twelve degrees of freedom, contained by seven rigid bodies.Kinetic and potential energy are derived symbolically by using the kinematics study results. The matrices characterizing the mass-inertial and elastic properties of the mechanical system are obtained. The differential equations that describe the free undamped vibrations are derived. They take into account the geometrical, mass, inertial and elastic characteristics of the mechanical system.A compiled calculation algorithm is entered into a standard mathematical software product. Results are obtained in symbolic and graphical form. The natural frequencies and natural mode of a robot with concrete parameters are determined.Results of the study of free undamped vibrations represent a basis for studying of the free damped and forced vibrations of a robot for process automation in metallurgy.