Mathematical Software Research Articles

Reactive powder concrete beam design using a mathematical software to reduce costs

AbstractReactive powder concrete is widely recognized for its remarkable mechanical characteristics and resilience, rendering it an ideal option for structural uses that include heavy loads. However, the intricate interaction of numerous material and geometric aspects makes constructing reactive powder concrete beams extremely difficult. By using MATLAB to provide an optimized design framework for beams, this research tackles these issues. Particle swarm optimization and evolutionary algorithms are two of the advanced techniques used in the study to solve the optimization problem. It also includes constraints other one as structural requirements and material limitations. Results demonstrate that MATLAB-based optimization facilitates effective design, lowering costs and material consumption, with potential for more applications in the building sector.

Thermoelastic field analysis using Differential Transform under Moore-Gibson-Thompson Theory

Abstract Heat conduction has many applications in engineering fields. There are
various heat conduction models have been studied in the last few years.The main objective of this research is to study the effect of MGT model on thermoelastic problem . Also, offer a strong tool-the DifferentialTransform Method- for solving the governing partial differential equations with a simpler computation load than existing approaches.This paper presents the mathematical model describing the Moore–Gibson–Thompson (MGT) equation in rectangular plate. This MGT equation is modified into the heat conduction in the rectangular plate. Thermoelastic phenomena play a significant role in heat conduction, particularly in materials that experience both thermal and mechanical stresses. Thus the thermoelastic properties of rectangular plates were also studied using the two-dimensional mathematical model under MGT heat conduction.Goodier’s function and Boussinesq harmonic functions techniques have been used to obtain the thermal stresses in rectangular plates. The results have been discussed using graphs drawn by the mathematical software MATLAB.

Heat transfer analysis of hybrid nanofluid under the effects of surface roughness along with velocity and thermal slips

AbstractSurface roughness has a great impact on the peristaltic motion of nanofluid flow and plays an important role in engineering, manufacturing, and material sciences. During tissue engineering, imaging techniques, implant surface finish, surgical instrument texture, and tissue engineering, and so forth. This study explores the effects of electrical double layers, surface roughness, velocity slip, and thermal slip to investigate the heat transfer rate of cobalt and alumina nanoparticles with water through uniform and nonuniform horizontal tubes. In the present study, the Jeffrey nanofluid flow model is chosen to investigate the heat transfer phenomenon of hybrid nanofluids based on alumina and cobalt nanoparticles suspension in water. The effects of electroosmosis, surface roughness, viscous dissipation, heat source/sink parameter, velocity, and thermal slips are also under consideration during the peristaltic motion of hybrid nanofluid in uniform and nonuniform tubes. The mathematical software MATHEMATICA 13.3 is utilized to find the exact solution and graphical results to investigate the complicated flow behavior. It is noticed that the velocity near the walls of the tube is lower for the surface roughness parameter and higher in the core part. The behavior of velocity for the remaining parameter is the opposite. The temperature of the current fluid flow increases for all parameters except the surface roughness parameter. The effects of velocity for hybrid nanofluid are prominent as compared with nanofluid in the core part. The temperature profile and heat transfer rate for hybrid nanofluids are lower as compared with nanofluids, which shows the cooling effects. This study is beneficial for hyperthermia, gene therapy, drug delivery, and tissue engineering.

Optimization of carbon emission in an integrated machine-piece scheduling and vehicle routing problem and its solution using MOPSO and NSGAII metaheuristic algorithms

The growth of the global economy is accompanied by significant energy consumption, and greenhouse gas emissions create various problems such as global warming and environmental degradation. To protect the environment, governments are seeking to reduce carbon emissions. Production systems that operate solely based on economic factors in the workshop only consider problems such as production speed, cost, and processing time. Two aspects can be effective in saving energy and reducing emissions at the production planning level: using routing to find the shortest path for collecting workpieces to the workshop, and turning off machines with long idle times and restarting them at the appropriate time. If the workshop production problem is combined with vehicle routing, a new problem arises. According to the research conducted so far, an integrated mathematical model for production routing has not been designed in a situation where the routing is before the production workshop. In this research, this bi-objective model is introduced, and it is solved using the augmented epsilon-constraint (AEC) method. The proposed mixed-integer linear programming model of this research includes three dimensions: environmental, social (customer satisfaction), and economic simultaneously. Given the high complexity of the mathematical model, MATLAB software and MOPSO and NSGA-II algorithms were used to solve it at higher dimensions. Seven evaluation criteria were used to compare the two proposed algorithms, and the results show that the MOPSO algorithm performs better. The findings suggest that minimizing pollution may involve sacrificing on-time delivery to customers. Consequently, decision-makers must carefully weigh the trade-off between reducing environmental impact and maintaining satisfactory delivery performance, ultimately deciding on an acceptable pollution level.

MATRİSLƏR VƏ ONLAR ÜZƏRİNDƏ ƏMƏLLƏRİN ÖYRƏDİLMƏSİNDƏ İSTİFADƏ EDİLƏN PRAKTİK MƏZMUNLU MƏSƏLƏLƏR SİSTEMİNDƏ İKT-NİN TƏTBİQİ

The article is devoted to practical applications of mathematics. The use of matrices in the spheres of economics, medicine, programming, psychology and other sciences shows that they play an important role not only in mathematics, but also in all spheres of our life. The article shows ways to use mathematical packages and MS Excel to perform operations on matrices. This, on the one hand, directs students' attention to the essence of the issue, reduces additional calculations, and on the other hand, leads to the development of their skills in working with ICT.

Novel dynamics of the fractional KFG equation through the unified and unified solver schemes with stability and multistability analysis

Abstract The nonlinear fractional Klein–Fock–Gordon (KFG) equation represents an advanced theoretical physics and applied mathematical tool that provides a more extraordinary framework for studying fields with complex and non-standard behaviors. Here, we aim to delve into the new wave profiles of this fractional KGF equation. Initially, this system is successfully converted into an ordinary differential equation (ODE) with the help of wave conversion, and the ODE is solved through the unified and unified solver techniques for the first time. In addition, the 3D and 2D plots of these solutions are drawn using a mathematical software package for different parameters with different values. Therefore, some unique waveforms can be found in these solutions. Moreover, stability and multistability analyses are prepared and shown graphically to confirm the converging limitations of appropriate parameters. This work will be practiced more effectively in future research on nonlinear partial differential models.

Modified Hermite Wavelet Discrete Matrix Approach for the Brusselator Chemical Model

AbstractThe primary goal of this study is to create a wavelet collocation technique that can be used to solve nonlinear fractional order systems of ordinary differential equations, which are equations that arise in modeling problems related to auto‐catalytic chemical reactions. Using the Hermite wavelet collocation method (HWCM), the system of nonlinear ordinary differential equations of integer and fractional order is numerically solved. The nonlinear Brusselator system is transformed into an algebraic equation system using the collocation method and the fractional derivative operational matrices. The Newton‐Raphson method is used to solve these algebraic equations, and the approximate values of the derived unknown coefficients are substituted. Through the numerical examples, the method's computational effectiveness and correctness are illustrated with various model constraints. A numerical comparison is made between the current approach ND solver, RK method, and Haar wavelet method (HWM). The efficiency and reliability of the developed strategy's performance are shown in graphs and tables. The created Hermite wavelet collocation method is resilient and has good accuracy compared to current methods found in the literature. Numerical computations are performed through Mathematica, a mathematical software.

Experimental study on radiational characteristics and nursing care of a novel radioisotope 188Re memory alloy esophageal stent.

Radioactive esophageal stent, known for inhibiting tumor growth and delaying restenosis in malignant esophageal tumors, presents challenges due to potent radiation, leading to side effects. This study aims to support the clinical use of 188Re radioactive esophageal stent. The 188Re stent with 128MBq initial activity was placed in a biomimetic esophageal membrane. Radiation absorption doses were measured by thermoluminescence and calculated using mathematical software. Under simulated positioning, the stent was implanted in the esophagus of an experimental pig, followed by the feeding of Kangfuxin solution and nursing care (KFX-RT). Non-implanted and implanted-only pigs served as normal (CR) and experimental (RT) controls. Blood samples collected on days 7 and 21 were analyzed for inflammatory factors (TGF-β1, TNF-α, IL-6) using enzyme-linked immunosorbent assay. Esophageal tissue cells were assessed for deoxyribonucleic acid index (DI) and subdiploid content through flow cytometry. Absorbed doses at 0.5mm and 5mm reference points were 223.91cGy and 20.55cGy, respectively, with 92.64% absorbed within a 1mm thickness. Radiation dose significantly decreased at 6.5mm, with only 4.72% absorbed at depths ≥6.5mm. On days 7 and 21, levels of inflammatory factors, DI and subdiploid content were significantly increased in the KFX-RT and RT groups compared to the CR group, while all levels in the KFX-RT group were significantly lower than in the RT group. The 188Re esophageal stent exhibits high radiation absorption in superficial tissues and low absorption in deeper tissues. Kangfuxin solution combined with nursing care alleviates radiation-induced inflammatory damage.

Fast heuristics for the time‐constrained immobile server problem

AbstractWe propose easy‐to‐implement heuristics for time‐constrained applications of a problem referred to in the literature as the facility location problem with immobile servers, stochastic demand, and congestion, the service system design problem, or the immobile server problem (ISP). The problem is typically posed as one of allocating capacity to a set of M/M/1 queues to which customers with stochastic demand are assigned with the objective of minimizing a cost function composed of a fixed capacity‐acquisition cost, a variable customer‐assignment cost, and an expected‐waiting‐time cost. The expected‐waiting‐time cost results in a nonlinear term in the objective function of the standard binary programming formulation of the problem. Thus, the solution approaches proposed in the literature are either sophisticated linearization or relaxation schemes, or metaheuristics. In this study, we demonstrate that an ensemble of straightforward, greedy heuristics can rapidly find high‐quality solutions. In addition to filling a gap in the literature on ISP heuristics, new stopping criteria for an existing cutting plane algorithm are proposed and tested, and a new mixed‐integer linear model requiring no iterating algorithm is developed. In many cases, our heuristic approach finds solutions of the same or better quality than those found by exact methods implemented with expensive, state‐of‐the‐art mathematical programming software, in particular a commercial nonlinear mixed‐integer linear programming solver, given a five‐minute time limit.

Зависимость потенциала на рельсах от сопротивления заземляющего устройства тяговой подстанции и параметров рельсовой линии

Purpose: to analyse the dependence of the potential on rails on the track coordinate at different values of conductivity of the grounding device of the traction substation (g0 = 0 S, 10 S, 25 S, 50 S). Methods: the analysis was carried out on the developed substitution diagram of the traction rail network section using the method of nodal potentials. The calculation was implemented in Mathcad 15 mathematical package. Selection of initial data was carried out taking into account the values established in the current normative documentation. Results: an equivalent substitution scheme of the traction rail network on a double-track section has been developed, in which each homogeneous section of the rail line is replaced by an equivalent U-shaped quadrupole. This allows to transform an electric circuit with distributed parameters into a circuit with concentrated parameters. If it is necessary to simulate transverse or longitudinal asymmetry of traction current in a section, such a section is replaced by a three-wire substitution diagram in which the earth conductor is taken into account. To improve the accuracy of the modelling results, the inter-track jumpers are taken into account, and the number of nodal potentials is increased to 7. It is established that the highest modulus value of voltage on rails is observed near the traction substation. It has been determined that the voltage value on rails near the traction substation decreases when the conductivity of the earthing device increases. Practical significance: values of rail-ground potential at different values of conductivity of grounding device of traction substation for tracks of both directions of traffic — even and odd tracks — are determined. The value of conductivity of the traction substation grounding device at which it is safe for the personnel to stay on the rails near the traction substation has been determined. The obtained results can be recommended for practical use in railway transport.

The use of computer modeling in the educational process based on the example of studying Coulomb’s law

Abstract The study analyzes computer modeling tools intended for use in educational and scientific contexts. The concept of modeling as a method of research and a teaching tool is examined, the emphasis is placed on computer modeling. It is shown how physical laws, particularly Coulomb’s law, can be studied through modeling. The study uses pre-made simulators, spreadsheets, mathematical packages, as well as our own software in Object Pascal and Python. Experimental testing has confirmed the effectiveness of computer modeling in teaching natural sciences. A survey of students and teachers showed interest in further use of simulation tools in the educational process.

On Locally Symmetric Polynomial Metrics: Riemannian and Finslerian surfaces

In the paper we investigate locally symmetric polynomial metrics in special cases of Riemannian and Finslerian surfaces. The Riemannian case will be presented by a collection of basic results (regularity of second root metrics) and formulas up to Gauss curvature. In case of Finslerian surfaces we formulate necessary and sufficient conditions for a locally symmetric fourth root metric in 2D to be positive definite. They are given in terms of the coefficients of the polynomial metric to make checking the positive definiteness as simple and direct as possible. Explicit examples are also presented. The situation is more complicated in case of spaces of dimension more than two. Some necessary conditions and an explicit example are given for a positive definite locally symmetric polynomial metric in 3D. Computations are supported by the MAPLE mathematics software (LinearAlgebra).

Bifurcation, chaotic behaviors and solitary wave solutions for the fractional Twin-Core couplers with Kerr law non-linearity

The main purpose of this article is to analyze the bifurcation, chaotic behaviors, and solitary wave solutions of the fractional Twin-Core couplers with Kerr law non-linearity by using the planar dynamical system method. This equation has profound physical significance and application value in the areas of optics and optical communication. Firstly, the traveling wave transformation is applied to convert the beta-derivative Twin-Core couplers with Kerr law non-linearity into the ordinary differential equations. Secondly, phase portraits and Poincaré sections of two-dimensional dynamical system and its perturbation system are plotted by using mathematical software. For different initial values, the planar phase diagram and three-dimensional phase diagram in red and blue are plotted, respectively. Finally, the solitary wave solutions of the fractional Twin-Core couplers with Kerr law non-linearity are obtained by using theory of planar dynamical system. In addition, three-dimensional graphs, two-dimensional graphs, and the contour graphs of the solitary wave solutions are drawn.

Numerical and Symbolic Analysis for Mathematical Problem-Solving with Maple

This study explores the versatile capabilities of Maple, a widely used mathematical software, in addressing a wide range of numerical and symbolic computations essential for scientific and engineering applications. The researchers investigated Maple's diverse suite of tools, including numerical integration, nonlinear equation solving, polynomial interpolation, symbolic integration, and various numerical methods. Through an in-depth literature review, illustrated case studies, and detailed performance evaluations, the paper demonstrates the effectiveness and accuracy of Maple's computational approaches in dealing with complex problems in various areas of applied mathematics. This study's findings underscored Maple's tremendous value as a reliable and comprehensive software package for researchers, scientists, and professionals involved in advanced mathematical analysis and scientific computing. Furthermore, the paper highlighted Maple's versatility in creating high-quality three-dimensional plots, crucial for visualizing and analyzing complex mathematical and scientific data. Using either sets or lists, the ability to display multiple surfaces in a single three-dimensional plot showcases Maple's power in data visualization and communicating complex ideas. By positioning Maple as a powerful platform for solving versatile mathematical problems, this study highlights the software's indispensable role in advancing scientific discoveries and engineering innovations.

Peristaltic Flow of Jeffrey Fluid in an Inclined Porous Tube with Multi-Thrombosis

The fact that multiple thrombosis opposes blood flow and flow is rare in blood vessels is refined to a normal condition with catheter application. The inner surface of the circular blood arteries may not be smooth in the majority of diseased instances. Additionally, the small blood vessel peristalsis mechanism is formed. In this paper, we discuss a mathematical model for the flow of biological fluid (blood) in a circular tube with multi-thrombosis considered under peristaltic wave propagation. The blood flow in this tube is restricted due to the many thromboses present, and the flow is redesigned with the aid of a catheter. We model this non-Newtonian blood flow issue for Jeffrey fluid. In most pathological cases, the inner surface of the circular blood vessels may not be smooth. Further, the mechanism of the peristalsis is established for small blood vessels. Because of this biological phenomenon, the peristaltic movement of Jeffrey fluid in a porous annulus with slip is examined. Equations that govern energy and momentum are solved exactly, and graphical interpretation is made using mathematical software. Streamline graphs show the many thromboses that increase in height. The wall shear stress graphs show a sinusoidally advancing wave with peaks and dips of different amplitudes. This tube's unique crest and trough amplitude are caused by the presence of multiple thromboses. We obtained the impact of the pressure gradient on the permeability parameter (β). The pressure gradient falls as the permeability parameter rises.

INFORMATION SYSTEM FOR ASSESSING THE LEVEL OF HUMAN CAPITAL MANAGEMENT

The article offers conceptual foundations for formalizing the process of assessing a level of human capital (HC) management at the enterprise using mathematical and computer modeling based on neural network technologies. The methodological approach for assessing the level of human capital management has been improved. This allows the use of neural network tools to identify accurately and reasonably the level of HC management with the help of self-learning multilayer perceptron. The weight coefficients of such a network were calculated. An appropriate artificial neural network – a multilayer perceptron – was built using the mathematical software MatLab and it was successfully diagnosed. The improved mathematical model for assessing the level of HC management at the enterprise makes it possible to display transparently a set of input parameters on a set of output solutions, to decompose such a process, and to simplify the procedure of its formalization. The designed neural network allows us to determine quickly and accurately the level of HC management at the enterprise. The conceptual approach proposed by the authors has several significant advantages over existing alternative methods: accuracy of assessment; taking into account a wide range of various evaluation parameters of impact; high speed of making decisions and self-learning ability. The proposed approach was successfully implemented to assess the level of HC management at 24 domestic enterprises. The information system "HC" developed by the authors allows to calculate the estimated parameters of the evaluation process; to determine the level of HC management based on the mathematical apparatus of the multilayer perceptron. Such estimates correlate with the estimates obtained by the experts of these enterprises which indicates the adequacy of the approach proposed by the authors. Therefore, the proposed information system for assessing the level of management of the HC allows accurate implementation of such a process with minimal time and money costs.

Effects of Geogebra use on the Academic Performance of Students in Mathematics in Public Secondary Schools in Rwanda

This study examines the impact of GeoGebra, a dynamic mathematics software, on the academic performance of students in mathematics at a public secondary school in Nyaruguru District, Rwanda. Specifically, it explores GeoGebra’s use in mathematics, its effects on student performance, and the correlation between its usage and academic outcomes. A sample of 7,916 participants was surveyed, including 69 math teachers, 309 students, and three headteachers. Data were collected through questionnaires, interviews, and observations, using purposive, stratified, and simple random sampling. The study revealed that 87.4% of participants agreed that GeoGebra enhanced students’ mathematical problem-solving abilities, while 94.1% agreed that it improved class participation. Additionally, 89.9% noted improvement in mathematics exam and test performance, with 91.3% observing better homework completion rates. GeoGebra use correlated with higher test scores and increased engagement in mathematical analysis, including trigonometry, transformations, and equation-solving. Although correlations with some outcomes were statistically minor (p > 0.05), the tool consistently supported mathematical independence and exploration. GeoGebra’s interactive features, including graphs, charts, and 3D models, facilitate students’ understanding of complex concepts, fostering improved memory and problem-solving skills. It enables collaborative learning, which promotes critical thinking, and highlights real-world applications of mathematics, increasing engagement. Personalized feedback features allow students to progress at their own pace, suggesting GeoGebra as an effective tool for enhancing mathematical comprehension and performance in secondary education.

Spatial Epidemiology and Its Role in Prevention and Control of Swine Viral Disease

Spatial epidemiology offers a comprehensive framework for analyzing the spatial distribution and transmission of diseases, leveraging advanced technical tools and software, including Geographic Information Systems (GISs), remote sensing technology, statistical and mathematical software, and spatial analysis tools. Despite its increasing application to swine viral diseases (SVDs), certain challenges arise from its interdisciplinary nature. To support novices, frontline veterinarians, and public health policymakers in navigating its complexities, we provide a comprehensive overview of the common applications of spatial epidemiology in SVD. These applications are classified into four categories based on their objectives: visualizing and elucidating spatiotemporal distribution patterns, identifying risk factors, risk mapping, and tracing the spatiotemporal evolution of pathogens. We further elucidate the technical methods, software, and considerations necessary to accomplish these objectives. Additionally, we address critical issues such as the ecological fallacy and hypothesis generation in geographic correlation analysis. Finally, we explore the future prospects of spatial epidemiology in SVD within the One Health framework, offering a valuable reference for researchers engaged in the spatial analysis of SVD and other epidemics.

STRUCTURE OF THE AUTOMATED CONTROL SYSTEM OF TECHNOLOGICAL PARAMETERS OF TREATMENT FACILITIES OF THE CITY SEMEY

Increasing the efficiency of control of treatment facilities can be achieved by automation of control at the stages of observation, collection, processing and analysis of information by means of mathematical data analysis packages, implementation of automated control systems of technological processes.This article is devoted to the issues of technical modernization of automatic control system of water disposal in Semey city. The need to modernize the concept of building the ACS has arisen in connection with the technical re-equipment of production and introduction of new energy-saving technologies in it.The hypothesis of the research suggests the possibility of improving the efficiency of wastewater treatment facilities of Semey city through the use of modern methods of collection and transmission of technological parameters to the control panel of the dispatcher in order to make operational decisions on the management of technological and technological process of wastewater treatment based on monitoring of equipment operation. Due to the complexity of the whole complex of treatment facilities, the main sewage pumping station (GKNS-2) and air blower pumping station (ABPS) were selected as objects for the development of automated control system of technological parameters (ACS TP).The article considers the proposed structural scheme of the automated system of control of technological parameters of treatment facilities of Semey city, gives a description of each level of the system and the principle of their interaction.

Students’ Knowledge of Integration of GeoGebra in Mathematics Classes in Uganda

GeoGebra, an open-source Dynamic Mathematics Software (DMS), has emerged as a transformative tool in mathematics education, allowing students and teachers to visualize, explore, and manipulate geometric concepts in dynamic virtual environments. This study investigated the students’ knowledge of integration of GeoGebra in mathematics classes in lower secondary schools in Rwampara District, Southwestern Uganda. The objectives of this study were to identify the most abstract geometrical concepts posing challenges to students, examine the impact of GeoGebra training on the identified abstract concepts, and assess the relationship between students' attitudes and the integration of GeoGebra. This study utilized a quantitative approach, employing quasi-experimental and cross-sectional survey designs. Data were collected from 103 students using questionnaires and pre-and post-tests to evaluate the impact of GeoGebra software intervention. Independent samples t-test, Pearson's linear correlation, and descriptive statistics such as means, standard deviations, and frequencies were employed as data analysis methods. The study found that the students identified rotational transformation as the most abstract geometrical concept. The pre-test results indicated that respondents had similar baseline knowledge of rotational transformation. However, after the GeoGebra intervention, the post-test results showed that the difference in mean scores between the experimental and control groups was statistically significant. Additionally, the experimental group demonstrated a positive attitude towards the software. The study concluded that while rotational transformation posed a significant challenge for students, GeoGebra significantly improved their conceptual understanding and performance in this geometry concept. The study recommended that teachers should strongly consider integrating GeoGebra into their ICT-based teaching and learning resources to help improve students' conceptual understanding, motivation, attitude, and achievement in rotational transformations and other geometric concepts