Mathematical Strategies Research Articles

Normalized solutions for Chern–Simons–Schrödinger system with mixed dispersion and critical exponential growth

This paper focuses on the existence of normalized solutions for the Chern–Simons–Schrödinger system with mixed dispersion and critical exponential growth. These solutions correspond to critical points of the underlying energy functional under the ‐norm constraint, namely, . Under certain mild assumptions, we establish the existence of nontrivial solutions by developing new mathematical strategies and analytical techniques for the given system. These results extend and improve the results in the existing literature.

Effect of Application of Model for Inclusive and Compulsory Participation Strategy for Teaching and Learning Mathematics on Students’ Learning Outcomes

Effect of Application of Model for Inclusive and Compulsory Participation Strategy for Teaching and Learning Mathematics on Students’ Learning Outcomes

Identifying queer discourses and navigational strategies in mathematics for undergraduate STEM students

IntroductionWhile research has explored racialized and gendered discourses in mathematics, there is a gap in understanding the experiences of Queer students and the discourses related to sexual identity in mathematics. This study aims to identify the discourses about mathematics that Queer STEM students describe in relation to their Queer identity and how they navigate these discourses.MethodsUsing phenomenology, individual interviews were conducted with 17 Queer STEM students at four universities in the United States. The interviews explored their life histories, experiences in mathematics, and responses to vignettes depicting mathematical scenarios. Grounded theory was leveraged to analyze the interviews to build a framework for Queer discourses and navigational strategies.ResultsSeven Queer discourses in mathematics were identified with underlying notions of exclusion and irrelevancy. The most prevalent discourses cast Queer identity as being irrelevant (erasure), unseen (heteronormative), or discriminated against (marginalized) in mathematics. At the same time there were some beliefs that Queer identity acceptance was unknown (ambiguous) was treated equally (normalized) or was accepted and even valued in math. Key findings from the study help theory build an exclusion-irrelevancy space to network together mathematical discourses and highlight how Queer marginalization is acted upon based on notions of rightful presence and not mathematical success.DiscussionThis study highlights the need to recognize and address the marginalization of Queer students in mathematics. By understanding the discourses and navigational strategies employed by these students, educators can create more inclusive and equitable STEM environments. It is critical to recognize and build upon the unique strengths of Queer students in mathematics, rather than focusing only on the challenges they face.

ONLINE MATHEMATICS LEARNING STRATEGY APPROACH: TEACHING METHODS AND LEARNING ASSESSMENT

The primary focus of this research is to develop strategies aimed at identifying effective methods applicable to online mathematics instruction and assessment. Teaching through distance education has many challenges, requiring educators' adeptness in utilizing e-learning platforms for both instructional delivery and assessment purposes. This study adopts a literature review methodology, drawing upon various previous studies relevant to this subject matter. The research findings reveal several online mathematical strategies and assessment techniques envisioned to adequately measures students' capacity to discern complex issues and employ critical thinking to resolve mathematical problems. The important role of the educator as a facilitator is underscored in crafting learning materials synchronized to the needs of students navigating the online platform. In this context, online mathematics instructional strategies are intricately intertwined with pedagogical dimensions and the appropriateness of utilized media and assessment modalities. Emphasizing interactive, creative, and innovative learning emerges as a critically important characteristic, particularly within the realm of online mathematics instruction

근거이론에 의한 과학고등학교 기회균등전형 학생의 수학 학습 경험 연구

This study applies the grounded theory research method to closely understand the difficulties experienced and the coping mechanisms employed by students admitted to science high schools through the equal opportunity admission system in their mathematics learning. Specifically, in-depth interviews were conducted with eight graduating third-year students from a science high school, and the collected data along with the participants' math learning journals were analyzed following the procedures of grounded theory. The findings revealed that all participants experienced academic burnout in relation to their mathematics studies. The timing, pace of entering burnout, and recovery varied among the participants. Although this academic burnout seemed to naturally resolve to a significant extent during the third year due to reasons such as early graduation of top-tier students, some participants remained in a state of burnout. Based on the results of analyzing the difficulties and coping strategies in mathematics learning from the perspective of students in the equal opportunity admission system, this study proposes implications for the guidance and program development for these students.

Comprehensive analysis of COVID-19 transmission dynamics: mathematical modeling, stability analysis, and optimal control strategies

This paper presents a mathematical model for comprehensively analyzing the transmission dynamics of COVID-19. We investigate the model’s various properties, such as positivity, boundedness, and the existence and uniqueness of solutions. Additionally, we calculate the basic reproductive number, denoted as R 0, to gauge the epidemic’s potential spread. Furthermore, we conduct a stability analysis to understand the long-term behavior of the model. Furthermore, we devised an optimal control strategy to effectively curb disease transmission. Using graphical analysis, we assess the impact of secondary infection rates and quarantine rates across different population groups. Finally, we compare our proposed numerical scheme with the well-known RK-4 scheme, emphasizing the NSFD scheme’s ability to maintain positivity, unlike the RK-4 scheme. Our numerical simulations offer strong evidence supporting the theoretical findings, demonstrating the effectiveness of our results.

Mathuiz-B Android-Based Application Program to Overcome Dissimilarity in Mathematics Fields of Sabilurrosyad Islamic Junior High School Students

Sabilurrosyad Islamic Middle School is a junior high school in the village of Karangbesuki. The geography school is located on the edge of Malang City and far away from the center of Malang City. Students entering junior high school are big children from local public elementary school graduates. Sabilurrosyad Islamic Middle School is the school that found its students with diverse ability different academics. _ Problems faced _ partner is different competence academic field mathematics in students new Sabilurrosyad Islamic Middle School. Based on the results analysis situation and SWOT analysis, the team devoted the public to the solution by creating and giving application edugames (MATHUIZ-B) that can used by schools. For participants assigned to educate new order capabilities, cognitive students can be uniform with standard junior high school level. The method of this community activity begins with preparation, making the Mathuiz-B application, outreach to teachers and principals of Sabilurrosyad Middle School, and Submission of the application so that service partners can use it. On activities devotion public, team devotion will provide an application manual book and a book regarding successful strategies for learning mathematics for entering junior high school.

Mathematical Model and Optimal Control Strategy for the Dynamics of Hepatitis B Virus Disease Incorporating Treatment Failure and Advanced Stage Compartments

In this paper, mathematical model for the dynamic of Hepatitis B virus infection was developed taking into cognizance the effect of rate of progression to the end stage (cirrhosis and HCC) by individuals who experience treatment failure in the treatment class and chronically infected class. In order to track the transmission of these diseases, the basic reproduction number which determines the rate of new secondary infection when an infected individual is introduced into a totally susceptible population was computed by next generation matrix method (NGM). The stability of the disease-free equilibrium point was also investigated using Routh-Hurwitz Criterion and the result proven to be Locally Asymptotically Stable (LAS) when the basic reproduction number less than unity. The global stability was also investigated by Castillo-Chavez method and the results show that the model is Globally Asymptotically (GAS) when reproduction number is less than unity. Sensitivity analysis was carried out on the parameters of the reproduction number, using forward normalized sensitivity index to ascertain those parameters of high impact on the reproduction number to aid the incorporation of the control variables appropriately. Numerical simulation was also carried using Forward-backward Runge-Kutta fourth order scheme to study the effect of these control strategies on the dynamics of the model and the results shows that the best strategy to implement to help eradicate HBV disease in the system is strategy E which is the combination of effective condom use, HBV vaccination, HBV Treatment and Behavioral change

Belonging Matters: Amplifying Teachers’ Voices in Schools

This research commentary illuminates teachers’ insights that help examine the nuanced relationship between spaces and situations that describe the impact of fostering belongingness and elevating their voices. Data includes results from a qualitative survey, which was a convenience sample across the southern region of the United States. The findings highlight the need for creating environments that cultivate a sense of belonging and empower teachers. By elevating the voices of teachers, our intention was to underscore the significance of acknowledging what they express and the emotions they navigate daily inside and outside of their classrooms. We conclude with some call-to-action strategies for mathematics teacher educators as they work alongside teachers and other stakeholders to elevate the educational experience for teachers and students alike.

The Ethnomathematical Approach Through The Methodology: Contextualization, Decontextualization and Recontextualization (CDR) and Its Contribution to The Learning of: Arithmetic, Geometry and Algebra

Objective: The objective of this article is to investigate the applicability of the CDR Method within the Ethnomathematics approach, in order to make possible the optimization and improvement of the teaching of the main branches of mathematics in Ecuador. This topic has been the product of several investigations carried out at the Institute for Research in Ethnosciences of the Central University of Ecuador, IIEC-UCE, particularly in the area of Ethnomathematics. Theoretical Framework: under a theoretical and practical frame of reference, with the purpose of showing the possibility of achieving a meaningful, coherent, environmentally sensitive and contextualized learning in the geopolitical reality. It is considered that the main contribution will be to support the construction of an own episteme and identity with the Andean ancestral roots. As for the methodology, we worked with focus groups formed by students of the cycle called General Basic Education. Method: It is proposed to investigate the applicability of the Ethnomathematical approach through the methodology: Contextualization, Decontextualization and Recontextualization, CDR and its contribution to the learning of arithmetic, geometry and algebra. The stages are described and the cyclical relationship that exists in a dialectical, systematic and propositive process that aims to make a disruption with the traditional algorithmic, decontextualized and memorized methodology that is usually used in the educational system is shown. The use of this method is proposed. Results and Discussion: The results obtained are considered satisfactory and it was observed that the CDR can be adopted by teachers interested in changing their teaching methods in the classroom, in addition, it is easily adaptable to different educational levels and areas of knowledge such as: History, Chemistry, Arts, Medicine, among others. Implications of the research: The research aims to provoke a cause-effect situation, where the causality is based on the deficiency of mathematics education in the country and the effect that would produce the approach of contextualization in the different facets: historical, social, political, etc., to produce meaningful learning. Originality/Value: It is considered original because it presents a new approach to mathematics education; CDR is both a disruptive strategy for learning mathematics in connection with the environment, the Andean episteme and its unique ontology. It IS also an axiological alternative insofar as it incorporates the Andean ethos as a referential philosophical framework.

Generating mathematical strategies shows evidence of a serial order effect

This study investigated whether performance on a mathematical strategy-generating task showed evidence for a serial order effect (decreasing fluency but increasing originality and creativity of strategies over time). One-hundred and fifty-five undergraduate students generated as many strategies as they could to solve a three-digit subtraction problem for 8 min, and the resulting strategies were evaluated using fluency and originality indexes that were heavily informed by research on creativity. Results showed evidence for a serial order effect, such that strategy fluency decreased across the working period, but later strategies were rated as more original/creative. These results demonstrates that classroom practices that encourage strategy generation can be a useful tool to help students think more creatively in mathematics.

Mathematical modeling and optimal control strategies to limit the spread of fowl pox in poultry

This paper presents a mathematical model aimed at elucidating the dynamics of fowl pox transmission within poultry populations. The model focuses on implementing control strategies to manage the spread of the disease, considering two primary modes of transmission: direct contact and transmission via mosquitoes. Our objective is to enhance understanding of disease propagation and to propose a control strategy aimed at minimizing the number of infected birds Ib(t) and increasing the number of recovered birds Rb(t) during the time interval t0,tf, while also minimizing the costs associated with implementing the control strategy. The proposed mathematical framework facilitates the integration of various control strategies to effectively manage fowl pox transmission dynamics. By employing Pontryagin’s maximum principle, efficient control measures are identified to mitigate the spread of the disease. Finally, numerical simulations are performed to verify the theoretical analysis using MATLAB.

Problem Solving Strategies in Mathematics of Students in the of Primary Level: Basis for Strategic Study Guide

Mathematical problem solving ability refers to the thinking ability and problem solving ability that students show in solving mathematical problems, which is a very important ability in mathematics learning. However, because traditional mathematics teaching focuses on teaching basic concepts and algorithms and neglects the cultivation of students' problem-solving skills, many students are unable to begin to apply what they have learned to real-life problems. The Chinese government attaches great importance to the cultivation of students' mathematical ability in the educational reform for students. As China's society continues to develop and progress, we are paying more and more attention to how students use their knowledge to solve problems and how students can improve their problem-solving skills at the primary and secondary school levels.

The selections and differences in mathematical problem-posing strategies of junior high school students

To illustrate the selections and differences in mathematical problem-posing (MPP) strategies of junior high school students, this study constructs a theoretical framework for mathematical problem-posing strategies and then conducts an empirical study through a survey of 1653 Chinese junior high school students. The results show that students prioritize accepting the given information to pose mathematical problems, while few choose to change the given information. Most students used chaining, and very few students used symmetry to pose mathematical problems. From a developmental perspective, excluding the number of problems, there were grade differences in the selectivity of MPP strategies among students in grades 7, 8, and 9. Still, for each grade, accepting the given information and chaining were the most used strategies in the category therein. More than 77.56% (1282 students) chose category B to pose further mathematical problems after accepting or changing the given information to pose mathematical problems. The results of path analysis illustrate that there are two main routes of the evolution of the selections of the strategies of MPP of junior high school students: the first one is from category A to category B, and the second one is after the students use changing the given information, they are present with the selection of strategies, either use symmetry or chaining. The results may have important implications for the teaching and learning of problem-posing.

Magnetohydrodynamics tangent hyperbolic nanofluid flow across a vertical stretching surface using Levengberg-Marquardt back propagation artificial neural networks

This analysis uses the Levenberg-Marquardt back propagation artificial neural networks (LM-BP-ANNs) approach to demonstrate the mathematical strategy of neural networks for the simulation of MHD Tangent hyperbolic nanofluid (THNF) flow consisting of motile microorganisms through a vertically extending surface. The fluid flow is being investigated in terms of exponential heat source/sink, thermal radiation, and magnetic field. The modeled equations are relegated to the ordinary system of differential equations by substituting similarity variables. The ND-solve approach is applied for the modeled equations to numerically handle and generate a dataset. Several activities, including testing, verification, and training, are performed by creating a scheme for various fluid problems using reference data sets. The precision of LM-BP-ANNs is evaluated using mean square error, curve fitting error histogram, and the regression analysis plot. Furthermore, graphs are used to analyze flow parameters for concentration, momentum, and energy profiles. It has been observed that the velocity field declines as the magnetic field grows stronger. The THNF model for energy, mass, and momentum equations is tested, authenticated, and trained within an average of 10−9. The LM-BP-ANNs accomplish the highest accuracy, with a target date and absolute error reference values in the 10−4 to 10−5 range.

Evolving engineering education: online vs. in-person capstone projects compared (EEE-OIPC)

This study examines the effectiveness of online and face-to-face (F2F) instructional methods in Capstone Senior Design (CSD) projects within Electrical Engineering (EE) and Mechanical Engineering (ME). It explores how each mode influences student success and learning outcomes, addressing the need for adaptable teaching strategies in science, technology, engineering, and mathematics (STEM) education. A comprehensive assessment was conducted, which included project evaluations, advisor feedback, and self-peer reviews. This multifaceted approach aimed to gauge the relative efficacy of online versus F2F modalities in supporting educational outcomes. The findings indicated that both online and F2F modalities achieved parity on several metrics. However, F2F settings significantly enhanced teamwork and collaboration among students. In contrast, online environments excelled in advisor evaluations, suggesting effective mentorship despite less consistent teamwork and project execution. The results emphasize the potential benefits of integrating online and traditional pedagogies to improve educational strategies and student learning experiences. The study highlights the importance of developing online instructional strategies that better mimic the collaborative advantages of F2F instruction. It also underscores the need for a holistic approach to curriculum development to prepare STEM students effectively for future challenges.

Enhancing riverine load prediction of anthropogenic pollutants: Harnessing the potential of feed-forward backpropagation (FFBP) artificial neural network (ANN) models

Assessing riverine pollutant loads is a more realistic method for analysing point and non-point anthropogenic pollution sources throughout a watershed. This study compares numerous mathematical modelling strategies for estimating riverine loads based on the chosen water quality parameters: Biochemical Oxygen Demand (BOD), Chemical Oxygen Demand (COD), Suspended Solids (SS), and Ammoniacal Nitrogen (NH3–N). A riverine load model was developed by employing various input variables including river flow and pollutant concentration values collected at several monitoring sites. Among the mathematical modelling methods employed are artificial neural networks with feed-forward backpropagation algorithms and radial basis functions. The classical multiple linear regression (MLR) statistical model was used for the comparison. Four widely used statistical performance assessment metrics were adopted to evaluate the performance of the various developed models: the root mean square error (RMSE), mean absolute error (MAE), mean relative error (MRE), and coefficient of determination (R2). The considerable number of errors (with RMSE, MAE, and MRE) discovered in estimating riverine loads using the multiple linear regression (MLR) statistical model can be attributed to the nonlinear relationship between the independent variables (Q and Cx) and dependent variables (W). The feed-forward neural network model with a backpropagation algorithm and Bayesian regularisation training algorithm outperformed the radial basis neural network. This finding implies that, in addition to suspended sediment loads, riverine loads may be predicted using an artificial neural network using pollutant concentration (Cx) and river discharge (Q) as input variables. Other geographical and temporal fluctuation characteristics that may impact river water quality, on the other hand, may be incorporated as input variables to enhance riverine load prediction. Finally, riverine load analyses were successfully conducted to reduce the riverine load.

New analysis of VSC-based modular multilevel DC-DC converter with low interfacing inductor for hybrid LCC/VSC HVDC network interconnections

The integration of multiterminal hybrid HVDC grids connecting LCC- and VSC-based networks faces several technical challenges such as DC fault isolation, ensuring multi-vendor interoperability, managing high DC voltage levels, and facilitating high-speed power reversal without interruptions. The two-stage DC-DC converter emerges as a key solution to address these challenges. By implementing the modular multilevel converter (MMC) structure, the converter's basic topology includes half-bridge sub-modules on the VSC side and full-bridge sub-modules on the LCC side. However, while this topology has been discussed in the literature, its connection to an LCC-based network with controlled current magnitude lacks detailed analysis regarding operational challenges, control strategies under various scenarios, and design considerations. This paper fills this gap by providing comprehensive mathematical analysis, design insights, and control strategies for the modular DC-DC converter to regulate DC voltage on the LCC-HVDC side. Additionally, the proposed control scheme minimizes the interfacing inductor between the two bridges, ensuring uninterrupted power flow during reversal and effective handling of DC faults. Validation through Control-Hardware-in-the-Loop testing across diverse operational and fault scenarios, along with a comparative analysis of different converters, further strengthens the findings.© 2017 Elsevier Inc. All rights reserved.

Optimal Energy Management Strategy for Repeat Path Operating Fuel Cell Hybrid Tram

This study focuses on minimizing fuel consumption of a fuel cell hybrid tram, operated with electric power from both the fuel cell stack and the energy storage system, by optimizing energy distribution between distinct energy sources. In the field of fuel cell hybrid system application, dealing with real-world optimal control implementation becomes more important. Some ‘online control’ strategies optimize energy management by measuring the current battery’s state and planning for future cycles. However, its dependence on stochastic processes remains a limitation for adapting ‘online control’ even when driving in the same way. In order to optimize energy distribution robustly during the tram’s repetitive cycle operation, we develop a practical control map with a fuel cell hybrid tram simulation model and conduct energy distribution. The control map is based on a mathematical equivalent consumption minimization strategy (ECMS) equation reflecting the characteristics of the fuel cell stack and electric cells. The comparison of fuel consumption with another practical control strategy optimized for a specific railway cycle shows that the suggested map-based optimal control achieves a reduction in fuel consumption while satisfying a boundary condition.

Stable determination of an impedance obstacle by a single far-field measurement

We establish sharp stability estimates of logarithmic type in determining an impedance obstacle in R2 . The obstacle is the polygonal shape and the surface impedance parameter is non-zero constant. We establish the stability results using a single far-field pattern, constituting a longstanding problem in the inverse scattering theory. This is the first stability result in the literature in determining an impedance obstacle by a single far-field measurement. The stability in simultaneously determining the obstacle and the boundary impedance is established in terms of the classical Hausdorff distance. Several technical novelties and developments in the mathematical strategy developed for establishing the aforementioned stability results exist. First, the stability analysis is conducted around a corner point in a micro-local manner. Second, our stability estimates establish explicit relationships between the obstacle’s geometric configurations and the wave field’s vanishing order at the corner point. Third, we develop novel error propagation techniques to tackle singularities of the wave field at a corner with the impedance boundary condition.