Mathematical Model Research Articles

Metacognitive Awareness as a Predictor of Mathematical Modeling Competency Among Preservice Elementary Teachers

<p style="margin-left:28px; text-align:justify">Mathematical modeling offers a promising approach to improving mathematics education. This study aims to determine if the concept of metacognitive awareness in the learning process is associated with mathematical modeling. This study also considers the interaction effect of sex and academic year level on both variables. Focusing the study on preservice elementary teachers might address potential issues and targeted intervention in their preparation program concerning their ability to teach and guide young learners in modeling activities. The research sample includes 140 preservice elementary teachers at Central Luzon State University, Philippines. Data collection used an adapted metacognitive awareness inventory and a validated researcher-made mathematical modeling competency test aligned with the K-12 mathematics curriculum in the Philippines. Results revealed that the preservice elementary teachers had a high metacognitive awareness and mathematical modeling competency, ranging from 22 to 31 out of 36 points. Besides, Factorial ANOVA indicates that academic year level positively affects both variables regardless of sex, and stepwise regression analysis unveiled that information management, declarative knowledge, and planning significantly predict 41.4% of the mathematical modeling competency variance. This suggests that developing metacognitive awareness supports preservice elementary teachers in performing modeling tasks that improve their competency level in mathematics.</p>

Modeling and sensitivity analysis of a supersonic inductive Magnetohydrodynamic (MHD) generator

This study presents the supersonic inductive Magnetohydrodynamic (SIMHD) generator and simulates its model through the use of COSMOL Multiphysics. This generator, as an inductive MHD generator, is suggested to address the problems associated with the conventional MHD generator. Since the proposed generator does not require a moving part to convert thermal energy to electrical energy, it is categorized as a direct energy convertor. The SIMHD generator consists of a converging-diverging duct and is divided into two sections at the diverging part by means of a diaphragm. Both of these sections are diverging, which makes it possible to obtain a high Mach number. In this regard, the performance of the SIMHD generator is studied by its mathematical modeling and numerical simulation using the finite element method. In addition, a sensitivity analysis is carried out on the design parameters. The results indicate that the proposed SIMHD duct design will increase the speed from 160 to 1300 m⁄s, and decrease the temperature from 2100 to 1300 K. Moreover, considering a charge generation equation, the produced power for the resistive load 50 Ω equals 25.3 kW. This generator also has the potential to be used in scramjets and ramjets.

A digital twin model of the axial temperature field of a DC cable for millisecond calculations

The most important features of digital twin technology for transmission and transformation equipment are symbiotic evolution and state prediction. In constructing the digital twin model for DC cables, the transient and steady-state temperature fields need to be considered comprehensively in the modeling process to consider the multi-physical field coupling, mathematical model, operational data, and environmental conditions in specific cases, which makes it difficult to satisfy the real-time requirements of the digital twin. To solve this problem, in this paper, a digital twin technology architecture for DC cables is proposed, and a neural network learning model is constructed to minimize the latency due to the complexity of the model simulation. Moreover, an efficient digital twin model that is based on the model-driven approach is developed for the fast computation of the axial temperature field of DC cables. The use of the Sequence-to-Sequence residual neural network algorithm for the reduced-order multi-physics field coupling modeling reduces the computational time and ensures as much accuracy as possible up to the finite element model simulation. The simulation results show that the use of the digital twin model reduces the simulation time from 275 s to 0.56 s, and the relative error between the accuracy of the digital twin model and the finite element model for the axial temperature field of the DC cable is 0.46 %. Finally, verification of the reasonableness and feasibility of the proposed method is carried out via an experimental platform according to the standard of CIGRE TB496. In particular, the maximum value of the DC cable temperature is verified to have a small error compared with the result of the Sequence-to-Sequence calculation under specific working conditions.

ОДНОВИМІРНА ЗГОРТКОВА МОДЕЛЬ НЕЙРОННОЇ МЕРЕЖІ ДЛЯ ОБРОБЛЕННЯ СИГНАЛІВ З АМПЛІТУДНОЮ МОДУЛЯЦІЄЮ БАГАТЬОХ СКЛАДОВИХ

The processing of radio signals using artificial neural networks (ANNs) has great potential for research, which can be explained by the adaptability of ANNs to various transmission conditions and the ability to detect abstract patterns of changes in signal parameters. The article reviews the works of other authors devoted to different ways of using ANNs for processing radio signals. Taking into account the information in the reviewed works, the research task was formed, which consists in developing an optimized ANN model for radio signal processing. Signals with amplitude modulation of many components (AMMC) were chosen to form training samples for ANN. The choice of modulation type is justified by greater energy efficiency compared to other widely used digital modulation types, such as quadrature amplitude modulation. Mathematic basis of AMMC signal generation is described. The process of finding the coordinates of three component 8-AMMC signal constellation is explained, the formation of signals in the time plane based on the found coordinates is explained as well as their discretization and the addition of white noise. An iterative algorithm for generating initial data for ANN based on the described ratios is proposed. The general structure of one-dimensional convolutional neural network is considered. Functions of individual neurons, connections between them, the formation of layers and the convolution operation are described mathematically. On the basis of the previously given ratios, a final display of the network was formed. Specific dimensions and activation functions for layers are selected. The use of convolutional layers is justified by time invariance. Based on the reviewed mathematical models, selected activation functions and dimensions, a neural model was formed. The process of validating the effectiveness of the formed neural model is described, which is based on comparing the symbolic error probabilities of the proposed and reference models at different signal-to-noise ratios. The validation results are presented. The advantages of the obtained model over the previously proposed purely recurrent model and the AMMC reference receiver are explained.

ДОСЛІДЖЕННЯ ОСОБЛИВОСТЕЙ ОБРОБЛЕННЯ СИГНАЛІВ ДИНАМІЧНИХ ЦІЛЕЙ В БОРТОВИХ РУХОМИХ ІМПУЛЬСНИХ РАДІОЛОКАТОРАХ

The characteristic features of coherent (quasi-coherent) and incoherent accumulation and detection of signals received from the radio air (reflected from a passive dynamic target) are considered, which are an additive mixture of a useful component and a possible "noise-like" interference with the added "own" noise of the receiving path in airborne mobile pulse radars air base. It is assumed that the random components of the input signal are adequately described by a normal (or close to it) distribution law, and the signal (during the accumulation interval) is harmonic, the period of which is uniquely related to the Doppler frequency shift in the received signal. Necessary and sufficient conditions for coherent (quasi-coherent) and incoherent effective signal accumulation are formulated, analytical and graphical dependencies are given for determining the output ratio "signal /(noise+interference)" at different multiplicities of coherent and incoherent accumulation in both time and spectral domains. A mathematical model based on the system modeling package "System View" was developed and investigated, which demonstrates, by means of adequate simulation and statistical averaging, the peculiarities and quantitative differences of the results of coherent and incoherent accumulations at various, in particular low, but practically significant, input ratios "signal /( noise+interference)", as well as from the multiplicity of accumulation, that is, the number of received signals during the permissible interval of accumulation.

Estimation of landfill gas emissions at the solid waste disposal site of low-population regions with LandGEM and tabasaran–rettenberger mathematical models

ABSTRACT In developing countries, solid waste most commonly ultimately ends up is landfill. Landfill sites release significant amounts of air pollutants, such as methane (CH4) and carbon dioxide. It is thus important to reduce, control, and recycle these gases. In this study, we aimed to calculate gas emissions and energy production from landfill sites serving low-population areas. Future landfill gas production was estimated using LandGEM and Tabasaran – Rettenberger models, based on population and waste volume predictions. In both models, total amount of landfill gas and CH4 produced reached their highest values in 2035. According to the LandGEM model, this will amount to 11,230 and 3,179 Mg/year, respectively, while the Tabasaran – Rettenberger model predicted 14,986 and 4,014 Mg/year, respectively. The volume of landfill gas calculated using the Tabasaran – Rettenberger model was 3.730 million m3/year for 2021, while this was 2.544 million m3/year using the LandGEM model. In 2021, 84007 Mg of waste was disposed of at the landfill site. According to data from the electricity generation plant at the site, the electrical energy generated in 2021 was 5,309 kWh. Comparing the results from these two models with actual landfill data, the Tabasaran – Rettenberger model came closest to the estimate. Therefore, the Tabasaran – Rettenberger model can be used to estimate the potential for gas production at landfill sites in cities with similar waste components.

A non-isolated extended voltage gain quadratic boost converter with reduced device voltage stress and continuous input current

ABSTRACT This article presents an improved model of a high voltage gain DC-DC converter topology. The voltage gain of the proposed topology is extended using a newly structured cascaded boost converter with voltage doubler cells along with the Super Luo structure in the network. The ultimate aim is to improve the output voltage gain of the proposed converter to a higher level with a lower duty cycle. Additionally, the design considerations minimize the voltage stress of the components (diodes, capacitors, and semiconductor switches) compared to the conventional topology. Moreover, the proposed topology ensures a continuous input current to the structure. Mathematical modeling is developed using steady-state analysis, and the results are analyzed using the MATLAB/Simulink. Finally, the proposed converter provides a high gain, that is, 10, at a lower duty cycle of 0.32 with reduced voltage stress on the components.

Digital marketing business models: Key stages, types and trends of development

The main goal of the article is to formalize the key business models of marketing of modern companies and substantiate the key stages, types and trends of development. The relevance and need to pay significant attention to the marketing digital business model when organizing a business is substantiated. Using structural and logical analysis and criticism of scientific research, the essence, advantages and disadvantages are determined, the main blocks, stages and key elements of the structure of business models of modern companies are argued. It has been proven that marketing digital business models serve as a logical and visual plan for organizing all business processes of companies from production, marketing, sales and logistics to building a hierarchy of profitability. The key development trends are substantiated and the most popular business models of business organization in modern conditions are structured on the basis of scientific generalization, structural and logical analysis and mathematical modeling. Practical significance is characterized by the fact that the marketing business models of world-class companies are generalized and structured, taking into account their specifics and characteristics. Practical recommendations and key stages of building a company’s business model and its implementation into reality have been formed to achieve strategic business goals.

Analysis of the Interaction Effects of Electromagnetic Fields with Major Living Tissues—One Health Concept Numerical Evaluation Strategy

The well-being and sociability of individuals have always been part of modernity. The development of new technologies that meet these aspirations is receiving increasing attention. Thus, strengthening the desired objectives of these technologies and minimizing their undesirable side effects is the subject of growing commitment. The present contribution aims, in this context, to evaluate and analyze the desired and undesirable effects of the interaction of electromagnetic fields with living tissues in general. These are routines based on mathematical modeling reinforcing the expected functions as well as those of control and protection against undesirable effects. These adverse effects correspond to the “One Health” concept, which encompasses the health of animals, plants and humans, as well as ecological disorders created by human activity. First, in this article, the interactions of electromagnetic fields with tissues are analyzed, involving their thermal biological effects of desired and undesired exposures. The roles of blood and sap fluids in bio-affected tissues are then analyzed. Secondly, the equations governing electromagnetics and bio-heat, as well as their coupled solution are studied. Third, the thermal behavior of tissues and the adverse effects of exposure are examined. Next, monitoring and defending the effects of exposures are discussed. This contribution, supported by a review of the literature, illustrates routines for mathematical modeling of the generalized interaction of electromagnetic fields with living tissues.

Dynamic analysis of drag-based vibratory swimmers using higher-order averaging

This paper discusses the mathematical modeling, dynamic analysis, and design optimization of a class of drag-based vibratory swimmers using averaging. A typical swimmer of this class consists of a surface or subsurface main body, an oscillatory mass inside the body, and a rigid fin attached to the main body using torsional springs and immersed in water. This paper takes advantage of third-order averaging techniques for dynamic analysis and design optimization of the swimmer for high frequencies. The averaged dynamics are used for determining the optimum stiffness of the springs for maximizing the average speed of the swimmer for high-frequency motion of the oscillatory mass. Experimental results confirm the general response of the mathematical model.

Using interpretative structure model and analytical network process for optimum site selection of airport locations in Delta Egypt

Abstract Airports are among the constructions that must meet international standards and specifications established by the International Civil Aviation Organization (ICAO). Some of these parameters and criteria include topography, environmental, and operating circumstances. Navigation operations are also affected by terrain and human barriers, while noise, infrastructure, and weather factors affect the environment around airports. This article investigates using the interpretative structure model (ISM) and analytical network process (ANP) together as a new technique to select and determine the optimum site selection for constructing new international airports in the Nile Delta, Egypt. The criteria used (16 international criteria) are selected depending on the standards of the ICAO, field surveys, and previous studies. Nile Delta, Egypt, is chosen as a case study because it suffers from the lack of international airports and has a population of approximately 23 million. Therefore, new international airports must be established to serve this region, boost tourism, improve transportation, and stimulate commercial traffic. The results using the suggested new technique are compared with the traditional used methods for site selection, such as fuzzy-analytic hierarchy process. Landsat 8 images are used in this research. A quality test using the area under the curve and the receiver operating characteristic curve was applied to evaluate the new technique for site selection of international airports, depending on calculating the highest suitability index for each proposed site. From the quality tests, it is deduced that the suggested method (ISM–ANP) for airport site selection is more accurate than any other traditional method. ArcGIS 10.5 software is used to draw the final digital maps containing the proposed resulted sites. As a result, three new locations for the construction of international airports were found and selected throughout the research region (Delta Nile, Egypt) based on the used mathematical models. Therefore, the proposed novel method for determining the locations of international airports is thought to be effective and feasible, and it can be used to determine the locations of any development projects in general, particularly in developing countries, which benefits the decision-makers in making the right decisions.

A Mathematical Logistic Model Describes Both Global CO2 Emissions and its Accumulation in the Atmosphere

A single kinetic model, of a logistic nature, is able to describe two different phenomena: the global emission of CO2 due to the combustion of fossil fuels and the observed accumulation of CO2 in the atmosphere. Unexpectedly, the analysis of the experimental data clearly shows that the two rates of emission and accumulation are almost exactly in phase and differ by a constant factor. The fraction of CO2 that accumulates in the atmosphere is constantly equal to 65% of the emissions. The same percentage also applies to the rate of change of the two phenomena, i.e., the accelerations.

Rock fines breakage by flow-induced stresses against drag: geo-energy applications

The paper presents a strength-failure mechanism for colloidal detachment by breakage and permeability decline in reservoir rocks. The current theory for permeability decline due to colloidal detachment, including microscale mobilisation mechanisms, mathematical and laboratory modelling, and upscaling to natural reservoirs, is developed only for detrital particles with detachment that occurs against electrostatic attraction. We establish a theory for detachment of widely spread authigenic particles due to breakage of the particle-rock bonds, by integrating beam theory of particle deformation, failure criteria, and creeping flow. Explicit expressions for stress maxima in the beam yield a graphical technique to determine the failure regime. The core-scale model for fines detachment by breakage has a form of maximum retention concentration of the fines, expressing rock capacity to produce breakable fines. This closes the governing system for authigenic fines transport in rocks. Matching of the lab coreflood data by the analytical model for 1D flow exhibits two-population particle behaviour, attributed to simultaneous detachment and migration of authigenic and detrital fines. High agreement between the laboratory and modelling data for 16 corefloods validates the theory. The work is concluded by geo-energy applications to (i) clay breakage in geological faults, (ii) typical reservoir conditions for kaolinite breakage, (iii) well productivity damage due to authigenic fines migration, and (iv) feasibility of fines breakage in various geo-energy extraction technologies.

Investigation of the transient change of the cutting force during the milling of C45 and X5CrNi18-10 steel taking into account the dynamics of the electro-mechanical measuring system

AbstractThe possible methods of determining the cutting force—due to the great practical importance of knowing the force—have long been and are still intensively studied areas of cutting theory. In milling, cutting is a series of successive short material removals. During force measurement in such cases, the transient process that can be detected at the beginning of the process can influence the nature of the entire cutting cycle. The present study reports on the research, the aim of which was to explore the dynamic process of cutting force measurement in intermittent cutting. The measurements were made during face milling of C-steel and highly alloyed steel (X5CrNi 18–10). The milling head contained a single insert, with which the disturbing interaction of the multiple cutting edges was eliminated. As a result of the work, a method suitable for examining the close relationship between the initial transient nature of the milling cycle and the decay, as well as a mathematical model for the decay process, was developed. The model was validated with cutting experiments and measurements. The achieved results can be used to better understand the process of chip removal and to determine the actual power requirements of milling works.

The research on the failure mechanism and dynamic reliability of lubricated clearance

In the operation of mechanisms with lubricated clearances, uncertain parameters such as the temperature of lubricant, driving speed, and clearance value will lead to dynamic variations for oil film thickness of lubricated clearance. The lubrication may fail when the oil film thickness of bearing surfaces is insufficient, thereby significantly affecting the performance of the mechanism. This paper presents a novel method for the dynamic reliability of lubricated clearances by improved response surface method (IRSM). Firstly, the mathematical model of lubricated clearance is established, and the oil film load of lubricated clearance is defined, then the dynamic model of mechanism considering lubricated clearances is built through Lagrange method. Secondly, considering the failure mechanism of the lubricated clearance, the surrogate model is established using the IRSM with minimum oil film thickness as the failure criterion. Finally, taking the 9-link mechanism with multiple lubricated clearances as a numerical example, the dynamic minimum oil film thickness of the lubricated clearance considering uncertain parameters is computed. The reliability of the lubricated clearance is investigated by the surrogate model, and the applicability of the model is verified by the Monte Carlo method (MCM). The results demonstrate that the IRSM has higher accuracy compared to the traditional response surface method (TRSM). This paper provides a theoretical basis for the study of failure mechanism and reliability of lubricated clearances, and also has practical significance for engineering applications.

Auto‐Pressurized Multi‐Stage Tesla‐Valve Type Microreactors in Carbon Monoliths Obtained Through 3D Printing: Impact of Design on Fluid Dynamics and Catalytic Activity

AbstractThe present research exploits an innovative methodology for producing auto‐pressurized carbon microreactors with a precise and controlled structure analyzing the influence of their design on the fluid dynamics and their catalytic performance. Carbon monoliths with Tesla‐valve shape channels (Tesla, T, and modified Tesla, Tm) are synthesized through the combination of 3D printing and sol–gel process and further probed as Ni/CeO2 supports on CO2 methanation. The experimental results and mathematical modeling corroborated the improved performance obtained through the complex design compared to a conventional one. In addition to chaotic fluid flow induced by the deviation in flow direction, which improves the reagents‐active phase interaction, local pressure increases due to convergence of flows may enhance the Sabatier reaction according to Le Châtelier's principle. Conversely to straight channels, T and Tm are not affected by flow rate and presented chemical control. Tesla‐valve with curved angle (Tm) improved the mass transfer, achieving higher conversion and ≈30% reaction rate increase regarding right angle (T). Thus, this auto‐pressurized multi‐stage Tesla‐valve monolith opens the gate to design specific and advanced functional materials for multitude chemical reactions where not only the reactant‐active phase contact can be maximized but also the reaction conditions can be controlled to maximize the reaction kinetics.

Physical Model of Inclusions Removal at Static Steel–Slag Interface

Inclusions are one of the important factors affecting the cleanliness of molten steel. The current optimization of inclusion removal methods mainly focuses on promoting inclusions to float to the slag–steel interface so that the inclusions can be absorbed and removed by the refining slag. However, the research on the floating removal of inclusions cannot be carried out directly in the ladle, so methods such as mathematical models and physical models were developed. This article uses silicone oil to simulate the slag layer; polypropylene particles; and aluminum oxide particles to simulate inclusions to establish a water model experiment. By changing the viscosity of silicone oil and the diameter of particles, the factors affecting the movement of inclusions at the slag–steel interface were explored. Based on the water model, a mathematical model of the floating behavior of inclusions at the slag–steel interface was constructed, and parameters such as particle diameter and interfacial tension in the water model experiment were studied by the mathematical model for calculation. Both the mathematical model and the water model experimental results show that after the viscosity of silicone oil increases from 0.048 Pa·s to 0.096 Pa·s, the dimensionless displacement and terminal velocity of the particles decreases. When the diameter of the same particle increases, the dimensionless displacement and terminal velocity increases. The dimensionless displacement of polypropylene particles of the same diameter is larger than that of aluminum oxide particles, and the terminal velocity is smaller than that of aluminum oxide particles. This is attributed to the better overall three-phase wettability of polypropylene particle. When the liquid level increases, the dimensionless displacement and terminal velocity of particles under the same conditions show only slight differences (less than 10%).

Tangent hyperbolic nanofluid flow through a vertical cone: Unraveling thermal conductivity and Darcy–Forchheimer effects

Purpose: This paper demonstrates the way tangent hyperbolic nanofluid flow through a vertical cone is influenced by varying viscosity and varying thermal conductivity. This study also seeks to illustrate the impact of convective boundary conditions on a fluid. The mathematical modeling also takes the Darcy–Forchheimer effect into account. Methodology: Using the appropriate similarity transformation, the fluid problem is reduced into a set of nonlinear ordinary differential equations. These systems of differential equations are evaluated numerically by applying the Optimal Homotopy Asymptotic Method. Findings: The nature of emergent parameters is examined in relation to the temperature distribution, nanoparticle concentration profile, and velocity profile. An increase in variable viscosity corresponds to a decrease in fluid velocity, while enhanced thermal conductivity results in elevated fluid temperature. The skin friction coefficient, Sherwood, and Nusselt numbers are numerically examined for active concerned parameters. These findings can be put into practice in a variety of fields such as polymer cooling systems and medication. Originality: Existing literature has yet to explore the combination of tangent hyperbolic nanofluids with varying viscosity and thermal conductivity under convective boundary conditions.

Association of Age with Dual-Task Objective Cognitive Indicators and Gait Parameters in Older Adults.

Early recognition of dementia like Alzheimer's disease is crucial for disease diagnosis and treatment, and existing objective tools for early screening of cognitive impairment are limited. To investigate age-related behavioral indicators of dual-task cognitive performance and gait parameters and to explore potential objective markers of early cognitive decline. The community-based cognitive screening data was analyzed. Hierarchical cluster analysis and Pearson correlation analysis were performed on the 9-item subjective cognitive decline (SCD-9) scores, walking-cognitive dual-task performance, walking speed, and gait parameters of 152 participants. The significant differences of indicators that may related to cognitive decline were statistically analyzed across six age groups. A mathematical model with age as the independent variable and motor cognition composite score as the dependent variable was established to observe the trend of motor cognition dual-task performance with age. Strong correlation was found between motor cognitive scores and SCD and age. Gait parameters like the mean value of ankle angle, the left-right difference rate of ankle angle and knee angle and the coefficient of variation of gait cycle showed an excellent correlation with age. Motor cognition scores showed a decreasing trend with age. The slope of motor cognition scores with age after 50 years (k = -1.06) was six times higher than that before 50 years (k = -0.18). Cognitive performance and gait parameters in the walking-cognitive dual-task state are promising objective markers that could characterize age-related cognitive decline.

Conditions for introducing property tax in China in terms of replacing land sales revenue – models and verification

ABSTRACT Introducing property tax nationwide has been emphasized as an important reform task in China but has been delayed continuously. This paper pays attention the necessity of local governments’ revenue replacement from selling lands to collecting tax. I have built two mathematic models namely, with and without future cash flow, to determine the conditions for the replacement. Through defining and estimating the determinant and reference variables and applying them to the models, I have investigated the two reasons of the delay in introducing property tax in China. First, the land available for collecting property tax is not large enough yet to replace the sales amount of the land. Second, introducing property tax could result in the decrease of local government revenue in the initial stage. In spite of this reasonable delay, it is obvious that the replacement should take place someday because the land for sales is decreasing while the land for collecting property tax is increasing. The models and variables in this study could be applied and referred to for determining the date of the inevitable replacement.