Journal of Physical Mathematics & its Applications
Journal of Physical Mathematics & its Applications is an open access peer-reviewed journal from the publishers of Scientific Research and Community (SRC) which publishes articles in the form of written, video and power-point presentations from the arena of Physical Mathematics & its Applications. The journal focuses to build up accessing the complete content of articles freely from online for reader’s perusal. Article acceptance will be in the form of research, review, analysis, magazines, editorials, opinion, communications, mini-review, short communications, picturized, book review, video type and power point presentations (PPTS). Articles can be submitted through online from https://www.onlinescientificresearch.com/submit-online or can send through an e-mail with attachment for physicalmathematics@onlinescientificresearch.info
Mathematical Modeling Applied to Combustion Processes: Advances in the Theory of Combustion Modeling
Combustion modeling theory is an area of science that focuses on developing mathematical and computational models to describe and predict combustion processes, which occur when a fuel reacts with an oxidant, usually oxygen in the air. In this research, thermodynamic concepts, kinetic models and fluid mechanics models are applied to model an ideal combustion process in a combustion chamber of a jet engine in order predict the temperature variations in the combustor caused by the injection of hot gases into the chamber and by combustion.
Copyright (c) 2026 Journal of Physical Mathematics & its Applications
This article explores the deep structural constraints governing algebraic composition and argues that the universe cannot be fundamentally commutative or associative. Starting from Hurwitz’s classical theorem, which classifies real normed division algebras and restricts them to four cases-ℝ, ℂ, ℍ, and ????-we show that multiplicative coherence is an extraordinarily rare geometric property. The Cayley-Dickson construction is then analyzed as a controlled extension of this framework, revealing a systematic trade-off between expressivity and structural stability: as dimension increases, commutativity, associativity, and eventually divisibility is necessarily lost. Beyond abstract algebra, the article connects these mathematical results to concrete everyday experiences, illustrating non-commutativity through the order of ordinary actions (socks and shoes) and non-associativity through musical composition, where grouping determines meaning. These examples are not merely pedagogical metaphors, but manifestations of the same structural logic governing algebraic systems. We argue that non-commutativity and non-associativity should not be understood as defects, but as signatures of a world rich enough to sustain meaning, interaction, and transformation. From this perspective, stable algebraic structures correspond to rare equilibrium states, while most cognitive, physical, and creative processes operate in regimes where structure is dynamic rather than fixed. The article thus proposes a unifying interpretation in which mathematics functions as a geometry of possibilities, explaining why certain forms of simplicity are forbidden and why complexity is a necessary condition for the emergence of a meaningful universe.
BIM 2.0 in Project Development Construction Execution and Supervision
Building Information Modeling (BIM) 2.0 represents a significant evolution in construction project management, integrating additional dimensions such as time (4D), costs (5D), and sustainability (6D). Its adoption has transformed collaboration between stakeholders in the AEC (Architecture, Engineering, and Construction) sector, enabling real-time data-driven decision-making and improving project energy efficiency and sustainability. Recent studies indicate that BIM 2.0 implementation can reduce construction costs by up to 20% and lead times by 15%. Regarding the Methodology, this article is based on a systematic review of Scopus-indexed literature (Q1) and representative case studies between 2019 and 2023. BIM 2.0 applications were analyzed in LEED certified projects and energy efficiency standards, using energy simulation tools and advanced 3D modeling. Performance metrics such as CO₂ emission reduction, resource optimization, and risk management were evaluated. Addressing the Results and Discussion, we can say that the implementation of BIM 2.0 demonstrated a 30% improvement in energy efficiency in net-zero buildings and a 25% reduction in carbon emissions during the construction phase. Interoperability with AI and IoT enabled real-time monitoring of energy consumption and early detection of design conflicts. However, challenges such as the lack of software standardization and the shortage of skilled labor persist, affecting 40% of the analyzed projects. In the Conclusions section, we determined that BIM 2.0 is consolidated as a key tool for sustainable construction, facilitating the integration of emerging technologies and improving project lifecycle management. Investment in professional training and protocol standardization is recommended to maximize its potential. Future research should address the integration of blockchain and digital twins to optimize data security and traceability.
Mathematical Examination of MHD Slip Oscillatory Blood Flow Through an Artery in the Presence of a Magnetic Field
In this study, we investigated the mathematical examination of MHD slip oscillatory blood flow through an artery in the presence of a magnetic field. The process involves the development of dimensional mathematical models representing the flow in the form of a partial differential equation and scaling the model using some quantities where the governing models were made dimensionless and some pertinent parameters, such as the Hartman number and Womersley number, were obtained. The dimensionless governing model was perturbed and reduced to ODE. Method: The perturbed ODE was solved using the Laplace Method (LM), where the function representing the flow was obtained, and we performed numerical simulation using Wolfram Mathematica, version 12. The results reveal that the Hartman number and Womersley numbers influence the blood flow, flow rate, and shear stress, respectively. In conclusion, we have been able to derive a mathematical model that represents the problem, solve it analytically using the Laplace method, and carry out numerical simulation.
Quartic Equation and Proportion of Physical Reality
Considering a qurtic equation as polynomial of the 4th order with non-zero coefficients a,b,c,d & e can be considered as a sum of partial equations. In order to express coefficients of these equations with the help of functional dependence on a given parameter K, solution of individual partial equations can be found, using the numerical values for the sizes of regular 4-dimesinal polyhedron surfaces will then determine their volume ratios. These ratios will also be matching the mass ratios of fundamental particles of the physical realm as for example is the mass ratio of a proton and an electron or the mass ratio of Higgs boson and an electron including the Planck and the electron mass ratio. These mass proportionality in physical realm in terms of elementary particles then enables the solution of partial equations to determine black hole the final “gravity” after the collapse of two mass objects. By these proportions the most massive objects are determined whereas from the initial mass of two objects the mass of gravitationally collapsed object can also be established. From those equations a new elementary particle representing the dark matter could be found with likelihood of finding other particles that could explain the essence of dark energy. On the bases of gravitational objects represented by a black hole, the property of those initial objects that exclude collapse into singularity could be determined.
Application of the Radical Method in Solving Indeterminate Equations (Groups)
Fermat’s last theorem was proposed by the 17th-century French mathematician Pierre de Fermat. He asserted that when the integer n > 2, there was no positive integer solution for the xn + yn = zn equation. However, Fermat did not write down his proof, while his other conjectures contributed greatly to mathematics. Therefore, it inspired many mathematicians’ interests in this conjecture. Their corresponding work enriched number theory and promoted its development. In 1995, Wiles proved that the theorem was valid when n > 2. However, his process of proof is tediously long. It is said that only a few world-class masters can understand it, which is confusing. A Perfect cuboid, also known as a perfect box, refers to a cuboid whose edge lengths, diagonals of faces, and body diagonals are all integers. The mathematician Euler once speculated that a perfect rectangle might not exist. No one in the mathematical world has allegedly found a perfect cuboid. Meanwhile, no one has been able to prove that it does not exist. Whats a Hellen triangle? A Helen triangle is a triangle whose sides and areas are rational numbers. For thousands of years, triangles and their geometric properties have been studied intensively and thoroughly. With the understanding of Hellen triangles, people have found Hellen triangles with three integer heights and with three integer angle bisectors. However, Hellen triangles with three integer midlines have yet to be found. After several years of research, the author discovered that the above three problems had commonalities and could be demonstrated using the same method. The same algebraic structure is the key to solving these three problems, such as the equations y=x3 +ax2 +bx+c and y=x+3)3+a(x+3)2+b(x+3)+c are algebraically isomorphic. These two equations represent the same curve and are essentially indistinguishable. The above three problems can be solved with this property easily and concisely.
Copyright (c) 2025 Journal of Physical Mathematics & its Applications
Weeding Rake Design, Fabrication and Performance Evaluation
This study focused on the design, fabrication, and performance evaluation of a hand-push weeding rake equipped with a single front wheel. The device was developed to provide a cost-effective and environmentally friendly alternative to herbicide application for smallholder farmers. Performance evaluation was conducted across three soil types (sandy, loamy, and clay), with measurements of operational time, weeding efficiency, and human energy expenditure. The results indicated that soil type significantly influenced performance. Sandy soil required the least operational time (12.8 min) and energy input (245.3 kJ) but achieved moderate efficiency (87.6%). Loamy soil recorded the highest efficiency (92.4%) with intermediate energy expenditure (312.7 kJ). Conversely, clay soils presented the greatest operational resistance, leading to higher time (21.8 min), lower efficiency (79.6%), and higher energy demand (358.1 kJ). Statistical analysis using ANOVA confirmed significant differences (p < 0.0001) in all measured parameters across soil types. Tukey’s post-hoc tests further revealed that all pairwise soil comparisons were statistically significant. The findings demonstrate that the single-wheel weeding rake is best suited for loamy soils, though it can function effectively in sandy soils with reduced efficiency. Clay soils remain a challenge due to higher energy requirements. While the study was limited to controlled test plots, the results underscore the potential of this tool as a low-cost, sustainable, and ergonomic alternative to chemical weed control methods for small-scale farming systems.
On Finding a Solution of One Problem for the Heat Equation of on a Semi-Axis
The presented article is devoted to finding a solution to one problem for a heat equation with discontinuous coefficients on the semiaxis. Applying an integral transformation to the problem, a boundary value problem is constructed for an ordinary differential equation depending on a complex parameter. In this case, it is assumed that the solution to the problem found at infinity is bounded. Since the coefficient of the equation is discontinuous, the solution to the problem is found in both finite and infinite intervals. In the general solutions found in both intervals, there are constants that are independent of each other. Although in the problem the number of boundary and associated conditions is three, the number of constants involved in the solution is four. This can lead to violation of the uniqueness of the solution to the problem. To eliminate this discrepancy, it is necessary to choose one of the found constants equal to zero, using the condition that the solution is bounded at infinity. The other three constants are found from the boundary and associated conditions and taken into account in the solution of an ordinary differential equation with discontinuous coefficients. The article shows that the solution of an ordinary differential equation with discontinuous coefficients is a meramorphic function on the complex plane. The singular points found for solving the problem are pole-type singular points located in a strip containing an imaginary axis. In the paper, the expansion theorem is proved and the solution of the problem is constructed in the form of a contour integral. The absolute and uniform convergence of the found contour integral for the solution is shown, which means the substantiation of the formal solution of the original problem.
Counting the Number of Even and Odd AUNU Permutations with Occurrences of 123- Pattern
Permutation groups are important tools in enumerating combinatorial objects. In AUNU permutation, the first element counted as one and its length is a prime number. This paper concerned with the counting system of AUNU permutations which contain certain subsequences to obtain some new algebraic theoretic consequences. The number of even and odd of such permutations is determined and the involutions among the counted elements. Bijections are also determined between the sets of such permutations and other combinatorial objects. A discussion was presented of lattices whose maximum length chains correspond to AUNU permutations. The results in this paper complement previous work by the Authors. We also obtained generating functions and for the number of even (respectively odd) AUNU permutations on n letters containing exactly r=1occurrence of 123 avoiding permutation.
Pattern Occurrences in words and Permutations
Restricted Permutation and Symmetric Prmutation
Conservation of Heat Energy for Derivation of One-Dimensional Heat Equation and its Analytical Solution
This article deals with the derivation of the one-dimensional heat equation and explores its analytical solutions, specifically focusing on Dirichlet boundary value and initial value problems associated with this particular partial differential equation. The primary objective of this study is to investigate the solution for the one-dimensional heat equation, which serves as a prominent example of a partial differential equation. To achieve this, the method of separation of variables is utilized to obtain the analytical solution. The heat equation, renowned for its effectiveness in analyzing the dynamic flow of heat within solids, has stood the test of time as a powerful tool for several centuries. Lastly, we have taken a model example and solve it using the stated method and also mesh plot is displayed using Python software.
Problem of Rational Distances from a Point to the Vertices of a Unit Square on a Plane and Its Application to Control Theory
Among the unsolved problems of mathematics there are those whose hidden meaning turns out to be many times more important and instructive than solutions of these problems themselves. Most likely, this is exactly the case with the problem of rational distances from a point to the vertices of a unit square on a plane, if you approach it not quite from the frontal side.
Distance From a Point to the Vertices of a Square
Entomotherapy Assessment of Medicinal Insects Within Abeokuta Metropolis
This study investigates the use of medicinal insects in traditional healing practices within Abeokuta Metropolis, Ogun State, Nigeria. The research aims to catalog various insects utilized in medicinal applications, document preparation methods and administration techniques, and explore the cultural beliefs surrounding entomotherapy. Using a survey research design, 150 participants were randomly selected from the Abeokuta area, yielding insights into the preserved traditional knowledge of entomotherapy. The findings recorded that a significant majority (125 out of 150) authenticated the effectiveness of medicinal insects, with family (65%) and community elders (21%) identified as primary sources of knowledge transmission. Oral ingestion emerged as the predominant method of administration (38.4%), while some respondents reported challenges in using these insects. Notably, the community displays divided opinions regarding the preservation of this knowledge, highlighting the need for structured efforts to document and promote traditional practices. The study shed more light on the effectiveness of entomotherapy and emphasizes the importance of intergenerational learning in maintaining traditional ecological knowledge. Based on these findings, recommendations include developing community-based documentation programs, promoting intergenerational knowledge transfer, addressing challenges faced by users, integrating traditional knowledge with modern healthcare, and raising awareness about the cultural value of medicinal insects. These actions can enhance understanding and utilization of insect-derived remedies, contributing to innovative healthcare solutions.
Traditional Knowledge and Therapeutic Uses
The True Schwarzschild Radius: Explaining Why Matter Falls into Black Holes
The Schwarzschild radius (RS) has long been interpreted as the “size” of a black hole, often leading to the common but misleading notion that matter falling into a black hole must traverse a spherical surface of radius RS before crossing the event horizon. However, by applying the Schwarzschild metric to itself, we discover a paradox: at R = RS, the metric predicts a collapse of distance to zero and an infinite spacetime curvature, revealing that RS is not a true physical radius but rather a collapse threshold defined in pre-black hole geometry. In this work, we use a thought experiment with a solar-mass object to analyze how spacetime distorts as the object collapses toward its Schwarzschild radius. By constructing a series of concentric shells just above RS and applying the Schwarzschild metric, we demonstrate that each shell’s apparent radius shrinks dramatically sometimes to less than one Planck length. This insight highlights that the Schwarzschild radius marks the boundary at which spacetime itself begins to fold, but it is not the actual, observable size of a black hole. Furthermore, we propose that in a fully collapsed state, the Planck length grows to match the Schwarzschild radius, creating a consistent spacetime structure that reconciles the metric’s behavior at the event horizon. This perspective challenges the notion that time freezes at the event horizon and provides a new understanding of how matter can continue to fall into black holes despite extreme spacetime curvature. Our analysis suggests that RS should be treated as a theoretical collapse thresh- old rather than a physical surface. Recognizing this distinction may deepen our understanding of black holes, the nature of spacetime, and the dynamics of matter falling into these cosmic phenomena.
Mathematical Modeling and Stability Analysis of Cholera Transmission Dynamics with Environmental Sanitation and Treatment Interventions
Cholera remains a persistent public health challenge despite significant advancements in medicine and hygiene. Understanding its transmission dynamics is essential for effective control and eradication. This study develops a compartmental mathematical model to analyze the spread of Vibrio cholerae, incorporating key control measures such as treatment, natural recovery, reinfection, and environmental sanitation. The model is formulated as a system of nonlinear differential equations, representing different population compartments. A key component of the analysis is the derivation of the basic reproduction number (R0) ,which serves as a threshold indicator for disease persistence. Stability analysis reveals that: If (R0 <1) , the disease-free equilibrium is globally asymptotically stable, indicating eventual cholera eradication. If (R0 >1) an endemic equilibrium exists, signifying sustained cholera transmission within the population. Sensitivity analysis identifies the most influential parameters affecting (R0) , highlighting that increasing treatment rates and improving sanitation significantly reduce disease spread. The fourth order Runge–Kutta numerical scheme is implemented in MAPLE 21 to generate the numerical solutions, which demonstrate that, timely treatment, and environmental sanitation accelerates the reduction of R0, moving the system toward the disease-free state.
Ulianov Elliptic Cryptography: A Real-Number-Based Asymmetric Encryption Model
Traditional cryptographic algorithms such as RSA and ECC rely on the computational difficulty of problems like prime factorization and discrete logarithms. However, these systems are increasingly vulnerable in the face of emerging quantum computing technologies, which can efficiently solve these problems using algorithms like Shor’s. Ulianov Elliptic Cryptography (UEC) introduces a fundamentally new approach based on non-invertible real-number functions and high-entropy embedding techniques, offering resistance to both classical and quantum attacks. This paper presents the theoretical foundation of UEC, its key components, and a security analysis that demonstrates its robustness.
Two-Way Contingency Table Analysis for Casualty Due to Road Traffic Crashes
Road traffic crash is an event on the road that is wished never to occur. Much more scared and worrisome is casualty due to road traffic crash. As a nation it is important to know where casualty due to road traffic crash occurs the most for appropriate interventions. This study aimed at investigating whether there is significant relationship between geo political regions in Nigeria and outcome of road traffic crash, where the target outcome is the casualty due to road traffic crashes. Data on number of casualties and non-casualties for each geopolitical region of Nigeria from the year 2016 to 2022 was collected and presented in a 6×2 contingency table. Pearson Chi Square test and Likelihood Ratio Chi Square test for independence were used to determine whether there is relationship between the geopolitical region and outcome of road traffic crash. Result revealed that there is significant relationship between the two categorical variables. To determine significant associations in the 6×2 contingency table, 15 possible local 2×2 tables were derived from the 6×2 contingency table, and odds ratio as a measure of association was employed. Results revealed that significantly, the odds ratio for each of the 15 possible local 2×2 tables are not equal to 1. Conclusively, the geopolitical region with the least casualties due to road traffic crashes in Nigeria is South East. Higher than South East region is South South region. Higher than South South region is South West Region. Higher than South West region is North West region. Higher than North West region is North East Region. The geopolitical region with the greatest casualties due to road traffic crash in Nigeria is North Central. Generally, the Northern region of Nigeria suffered higher casualties than the Southern region. More attention needs be given to stop the higher casualties suffered in the Northern region of Nigeria and particularly, in the North Central region.
Contribution of the Teachers Collaborative Work to Innovative Context in Training Course to Promote Knowledge in Professional Practice of Statistical Education in Basic Education
Statistical literacy and reasoning are prominent in international curriculum documents as an objective in teaching and learning of students. But this promotion in basic education is poorly consolidated in teachers’ practices due to lack of their knowledge. Thus, the adoption of collaborative work in innovative teachers training is defended as essential to promote their necessary knowledge and professional development of statistical literacy and reason practices, to promote teaching and students learning. Thus, this qualitative and interpretative research is pertinent, aiming to understand the contribution of the approaches considered in this teacher training using a collaborative context to promote their statistical knowledge and professional practice of students’ teaching. This study results show that the collaborative context carried out in the training course contributed to the necessary improvement in knowledge and professional teachers practices development of statistical literacy. So, this study is relevant to support international teachers from this educational community in their necessary experiences to provide the teaching of Statistics in innovative work of the collaborative context of the teachers training, to support their development and knowledge to understanding practices to improve educational contexts.
Professional Practice in the Early Years
Statistical Literacy and Reason Education
Advancing Physical Mathematics and its Applications
Physical Mathematics and its Applications is a rapidly evolving field that bridges theoretical physics and advanced mathematical frameworks. As we continue to cultivate a platform for rigorous research and innovative discoveries, our journal has played a pivotal role in fostering scholarly discourse, disseminating cuttingedge findings, and strengthening interdisciplinary collaborations. This editorial highlights the key achievements of the journal and underscores its significance in the global academic landscape.
UC Factorization and Inversion of Tridiagonal Matrices
Tridiagonal matrix inversion using a UC factorization decomposition of classic tridiagonal matrices is presented in this paper. Further we provide two algorithms to measure the runtimes of both algorithms and how to validate the effectiveness of our decomposition method. All of this serves as foundation for a couple of points of interest.
Theoretical Foundations of the Physical-Mathematical Model of the Non-Stationary Combustion Process of Solid Fuel and Derivation of Methods for the Calculation of Non-Stationary Velocity
This study investigates the physico-chemical processes in the gas phase, considering the methods for calculating of burning rate of solid propellant and physico-mathematical model of non-stationary combustion of solid fuel, we study the equation for heat propagation in the k–phase, the specification of the initial and bounday condition, the fundamental solution of the heat conduction equation in the k–phase is obtained. We consider the equation for calculating non-stationary combustion velocity, the stationary combustion velocity in the presence of catalysts in the fuel composition, the method for calculating constants. We investigate the analytical solution of the linearized integral equation for the burning rate, we determine the particular solutions of the linearized integral equation and we found the numerical and approximate solutions of the nonlinear integral equation for the burning velocity.
Copyright (c) 2024 Journal of Physical Mathematics & its Applications
Newtonian Mechanics Extension (to Arbitrary Speeds) and its Relation to Special Relativity in Complex Model
Complex Euclidean C3 model for “para-space”, as an alternative to the real Minkowski’s M4 space-time model for special relativity (SR) was introduced. As it turned out, in the SR theory of the complex model, velocities can be defined with no use of time and so time (no more the primitive notion!) can be defined within the theory of 3-D complex model. The complex C3 model, initially thought of as the model for special relativity (SR), turned out to possess deep unifying properties as being able to model both SR and classical Newtonian mechanics. The latter classic theory of the C3 model can also be extended to arbitrary high, but finite, speeds while the “Galilean speed of light” turns out to be infinite. The latter property clearly explains the universality of speed of light phenomenon. This became possible since all the SR phenomena one recovers from the unobserved complex Newtonian simply by taking real parts from underlying complex (para)physical quantities. This unifying property of the theory of the complex model, hypothetically, can be extended also to quantum mechanics so that all the three mechanics can, possibly, be unified as one theory of the complex C3 para-space model. Besides the unifying properties, use of this complex model dramatically simplifies the underlying physical theories especially (if this hypothesis is true) the quantum mechanics. The related to this complex approach ontological problems of existence of the unobserved physical objects and phenomena in C3 – R3 were addressed in the Appendix.
The Advanced Conjectures for the Prime Number Theorem
This paper examines the distribution of the prime numbers using epidemiological statistical methods. First, we will show more advanced conjectures of the prime number theorem in two forms. One is, like conventional conjecture, when drawn on coordinates, it becomes a curve. However, we aim for the curve to pass through the center of the dispersion of the prime counting function. And we obtain the results worthy of publication in this regard. The other one is what we call the corridors for the prime number theorem. As x increases, a larger proportion of π(x) gathers in what we call the main corridor. Next, we will clarify the process of acquiring this theory. Initially, we will clarify how the basic form of the conjecture is determined. Then, we will describe the process of obtaining the value for α used in this conjecture. Through this, we can share the results and origins of these conjectures. At the end, we declare our achievement, even though we acknowledge that this is only a prediction rather than a proof.
The CAT’s Tail: Unraveling Five Signatures in the CMB Spectrum
This article elucidates the Cosmic Antiproton Tomography (CAT) model’s unique perspective on the Cosmic Microwave Background (CMB), highlighting specific signatures that reveal more about the early universe’s structure than previously understood. The fundamental CAT, derived from the antiproton annihilations, aligns closely with the CMB’s observed spectrum. However, its true significance lies in the additional granularity provided by CAT harmonics, offering deeper insights into the universe’s early dynamics and structure.
Stable Proximal Dynamical System for Mixed Variational Inequalities in Hilbert Spaces
In this paper we focus on solving mixed variational inequalities by proximal fixed-time dynamical systems, in which the solution of the proximal dynamical system is uniquely described and converges to the solution of the associated mixed variational inequality under the assumptions of strong monotonicity and Lipschitz continuity on the operator in the variational inequality, where the time of convergence is finite and is uniformly bounded for all initial conditions. The proposed technique can be reduced to the fixed-time stable projected dynamical system and results can still be applied even with relaxing the assumption of strong monotonicity. The modified continuous-time proximal dynamical system is designed to solve convex minimizing problems on a (possibly infinite-dimensional) Hilbert spaces. Finally, some qualitative properties with fixed-time stability of equilibrium points to the proposed scheme for solving continuous-time nonsmooth convex optimization problems or, in a general setting mixed variational inequalities are presented.
The Transport of Species of Structures along the Braid Group
The purpose of this paper is to present in an introductory was the notion of transport of t-structures of a given species. The letter t symbolizes a braid with m strands that is performed on each element of [U]m. The transport will therefore be unique on each element of [U]m up to isomorphism because a braid is an isotopy class. This paper contains the basic concepts of the combinatorial theory of species of t-structures. We begin with some general considerations on the notion of t-structure, everywhere present in mathematics and theoretical computer science. These preliminary considerations lead us in a natural manner to the fundamental concept of species of structures. The definition of species puts the emphasis on the transport of t-structures along bijections of Bm.
Analysis of Mathematical Ethnomodelling Competency Levels of Grade 12 Learners’ on Lotka-Volterra Model Predator-Prey Problem
Background: Mathematical ethnomodelling is a prerequisite to conceptualising and comprehending mathematical concepts independently through reflective-critical thinking to solve real-world problems. Learners in grade 12 in their final Further Education and Training (FET) Phase examination in one of the examining bodies have demonstrated knowledge of mathematical modelling competencies in the Lotka-Volterra Model, despite a few challenges. Aim: To analyse the level of mathematical modelling competency of grade 12 learners, and how they demonstrate knowledge of understanding when solving the Lotka-Volterra model predator-prey problems. Setting: Data was gathered from 15 grade 12 learners of FET final exams by an examining body in South Africa, these learners were conveniently selected. Method: The research design is qualitative on document analysis of real-world tasks on the Lotka-Volterra model. The data-gathering instrument of the study is the learners’ workings on mathematical modelling tasks. Findings: The results indicated that 9 learners invoked their modelling competencies in the modelling problem of the Lotka-Volterra model to produce mathematical results. A lack of appropriate mathematical knowledge and techniques may also hinder learners operating at Levels 1 and 2 from moving on to the process of mathematization and mathematical working, even if they could simplify and structure the problem. Conclusion: We advise teachers and teacher educators to be aware that if the mathematical model is insufficient or if the learners have a poor grasp of mathematics, they might be unable to arrive at a meaningful solution even though they are aware of a strategy that could be used to a task.
Analytical Study of Random Oscillations of Vibration Protection Devices with an Elliptical Hysteresis Loop for Absorbing Harmful Energies by Non-Linear Mechanical Systems and their Elastic Damping Elements
The paper discusses the analysis of forced random oscillations of a non-linear mechanical system, namely a heavy drilling machine, taking into account the damping ability of the operator (human body) as a mechanical system and the elliptical hysteresis loop of the absorption of harmful energies by the elastic-damping element.
Existence and Uniqueness of the Solution of a Mixed Problem for a Parabolic Equation Under Nonconventional Boundary Conditions
Our research focuses on examining a mixed problem associated with a second-order parabolic equation that features temporal mixing and variable coefficients, subject to non-local and non-self-adjoint boundary conditions. We establish the problem’s unique solvability by imposing specific conditions on the provided data, utilizing a combination of residue and contour integral methods. Additionally, our study produces an explicit analytical solution for addressing the problem at hand.
Global Dynamics of Teaching and Learning Mathematics During the Period of Coronavirus Pandemic: Some Reflections from Nigeria
The paper begins by bringing to the fore the universality of the COVID-19 pandemic and its attendant consequences in all human indices of development health, education, aviation, infrastructure, tourism etc. across every continent, with varying degree of severity. The paper focuses on education sub-index – with a particular reference to Mathematics and how some aspects of Mathematics teaching have been deployed to provide an alternative solution to the dissemination of Mathematics, as well as other forms of knowledge. Thus, in education, teaching and learning Mathematics form the central thrust of knowledge transmission and acquisition in view of its bearing to every field of human endeavour. Therefore, the paper examines various stakeholders critical to the knowledge acquisition and dissemination, by arguing in respect of each stakeholder involved and how each of them is affected by the pandemic. The paper further argues that there is change in the conversation relating to teaching and learning vis-à-vis shift in or complete departure from what the system inherits from inception by ushering-in other teaching and learning possibilities such as the use of video-conferencing gadgets and software(s) like Zoom, Moodle, Skype etc. and even broadcast stations like television and radio. In the end, the paper suggests amongst other things, the need for overhauling the entire education system to allow for the inclusion of digital teaching and learning platforms via electronic means so as to prepare future generations against some potential future pandemics. Other suggestions include the introduction of distance learning as well as Open Educational Resources (OERs) and/or mobile software applications so as to reach out to students remotely since the pandemic had compelled everybody to stay at home. This, the paper argues, cannot be achieved without reviewing the current Mathematics curriculum which had not envisaged, nor had it taken care of this type of problem.
Motion, Velocity and Graphical Representations in GeoGebra
In upper secondary school it is not obvious in which topic of mathematics and physics that graphical explorations in areas such as motion and velocity vs time belong. This article suggests a way of using dynamic graphical explorations in GeoGebra as a way to visualize concepts of motion and velocity vs time.