Cognitive function among military veterans with STEM occupations

Dear Editor,There is limited research on the relationship between science,technology,engineering,and mathematics(STEM)occupational history and cognitive function in later life,especially among military veterans,who may be at greater risk for later-life cognitive decline.This study examines a nationally representative sample of military veterans to address this gap in knowledge.

Learning to represent 2D human face with mathematical model

How to represent a human face pattern?While it is presented in a continuous way in human visual system,computers often store and process it in a discrete manner with 2D arrays of pixels.The authors attempt to learn a continuous surface representation for face image with explicit function.First,an explicit model(EmFace)for human face representation is pro-posed in the form of a finite sum of mathematical terms,where each term is an analytic function element.Further,to estimate the unknown parameters of EmFace,a novel neural network,EmNet,is designed with an encoder-decoder structure and trained from massive face images,where the encoder is defined by a deep convolutional neural network and the decoder is an explicit mathematical expression of EmFace.The authors demonstrate that our EmFace represents face image more accurate than the comparison method,with an average mean square error of 0.000888,0.000936,0.000953 on LFW,IARPA Janus Benchmark-B,and IJB-C datasets.Visualisation results show that,EmFace has a higher representation performance on faces with various expressions,postures,and other factors.Furthermore,EmFace achieves reasonable performance on several face image processing tasks,including face image restoration,denoising,and transformation.

A Procedure for Trisecting an Acute Angle (Method 2)

This paper presents an alternate graphical procedure (Method 2), to that presented in earlier publications entitled, “A Procedure for Trisecting an Acute Angle” and “A Key to Solving the Angle Trisection Problem”. The procedure, when applied to the 30˚ and 60˚ angles that have been “proven” to be nottrisectable and the 45˚ benchmark angle that is known to be trisectable, in each case produced a construction having an identical angular relationship with Archimedes’ Construction, as in Section 2 on THEORY of this paper, where the required trisection angle was found to be one-third of its respective angle (i.e. DE’MA = 1/3 DE’CG). For example, the trisection angle for the 30˚, 45˚ and 60˚ angles were 10.00000˚, 15.00000˚, and 20.00000˚, respectively, and Section 5 on PROOF in this paper. Therefore, based on this identical angular relationship and the numerical results (i.e. to five decimal places), which represent the highest degree of accuracy and precision attainable by The Geometer’s Sketch Pad software, one can only conclude that not only the geometric requirements for arriving at an exact trisection of the 30˚ and 60˚ angle (which have been “proven” to be not-trisectable) have been met, but also, the construction is valid for any arbitrary acute angle, despite theoretical proofs to the contrary by Wantzel, Dudley, and others.

Measurement Analysis and Evaluation of Twenty- Five Years of Chinese Mathematics Textbooks: Visual Analysis Based on CiteSpace Knowledge Graph (1999-2024)

At present,textbooks based on core literacy have become the inevitable demands of China’s curriculum reform,and the literacy of textbook goal construction is the key to the implementation of core literacy requirements,which is a huge challenge for textbook compilers.In this paper,we use the visual metrology of the CiteSpace knowledge graph to analyze Chinese mathematics textbooks(1999-2024),hoping to guide the future direction of Chinese mathematics textbook research.

Integration of Mathematics History into Junior Middle School Education: A Pedagogical Approach to Enhance Mathematical Literacy

The integration of the history of mathematics into junior middle school mathematics education represents a significant focus of international research in mathematics and education.The mathematics curriculum standards for compulsory education have emphasized the importance of incorporating the history of mathematics,aiming to gradually integrate it into the mathematics classroom.However,in the practical implementation of junior middle school mathematics education,the effective combination of the history of mathematics with teaching methodologies remains largely unexplored.This article explores the integration of junior middle school mathematics education and the history of mathematics,aiming to provide classroom teaching recommendations for teachers and promote the formation of students’mathematical literacy.

The Past and Future of Aesthetics in Mathematics

This paper explores the connotations of mathematical aesthetics and its connections with art,facilitated by collaboration with Ester,an individual with an artistic professional background.It begins by tracing the historical evolution of aesthetics from the classical pursuit of authenticity to the modern shift toward self-expression in art.The discussion then highlights the similarities in the pursuit of truth between mathematics and art,despite their methodological differences.Through an analysis of aesthetic elements in mathematics,such as lines and function graphs,the article illustrates that the beauty of mathematics is not only manifested in cognitive processes but can also be intuitively expressed through visual arts.The paper further examines the influence of mathematics on the development of art,particularly how Leonardo da Vinci applied mathematical principles to his artworks.Additionally,the article addresses art students’perceptions of mathematics,proposes the customization of math courses for art students,and discusses future trends in the integration of mathematics and art,emphasizing the significance of art therapy and the altruistic direction of art.Lastly,the authors use a poster to visually convey the idea that the beauty of mathematics can be experienced through the senses.

Curriculum Reform of Higher Vocational Mathematics Under the Background of Digital Transformation

Under the background of digital transformation,the reform of the higher vocational mathematics curriculum faces urgent challenges and opportunities.This article explores the impact of digital transformation on the reform of higher vocational mathematics curriculum and emphasizes the importance of improving teaching methods centered on learners.The article proposes specific reform methods and discusses the practical application of digital technology in the reform process.By combining digital technology with specific reform methods,further conducting innovative practice research,and continuously exploring the path of reform,we can effectively improve the quality of higher vocational mathematics classroom teaching and provide strong support for the cultivation of comprehensive qualities and employment abilities.

Measurement Analysis and Evaluation of Twenty-Five Years of Mathematics Education Research in China:Visual Econometric Analysis Based on CiteSpace Knowledge Mapping(1999-2024)

Since the new century,China’s mathematics curriculum reform in basic education has continued to move forward in attempts and explorations,presenting many new changes,trends,movements,and developments.Sorting out,analyzing,and summarizing the achievements,experiences,problems,and challenges in this journey are conducive to providing insights for the reform and development of the Chinese basic education mathematics curriculum in the new era.This paper analyses the research on mathematics education in China(1999-2024)using the visual measurement of CiteSpace knowledge mapping,hoping to provide directions for the future of mathematics education in China.

A Study on the Application of Task-Driven Teaching Method in High School Mathematics Teaching: Taking “The Determination of Vertical Line and Plane” as an Example

The“Ordinary High School Mathematics Curriculum Standards(2017 Edition,2020 Revision)”clearly stated in“Teaching Suggestions”that“teaching activities based on the core literacy of mathematics should grasp the essence of mathematics,create appropriate teaching situations,put forward appropriate mathematical questions,stimulate students to think and communicate,and form and develop the core literacy of mathematics.”The task-driven teaching model is a new type of teaching method that takes tasks as the main line,teachers as the guide,and students as the main body,which can enable students to engage deeply in classroom discussions and think actively.Based on the characteristics and principles of the task-driven teaching method,this paper designs a high school mathematics classroom teaching based on the task-driven teaching method,hoping to provide a reference for the majority of front-line teachers.

The Integration Strategy of Class Teacher Management and Mathematics Teaching

The professional and moral education of high school mathematics teachers will make classroom management work better,but their work pressure will also lead to classroom management problems.To do a good job in high school class teacher management and organically integrate it with mathematics teaching,we need to start from two aspects:mathematics teaching class teachers and class teacher work teaching,and penetrate mathematical thinking into daily classroom management,moral education,and classroom culture construction.Based on the attributes of the subject,we guide high school students to reflect after class to stimulate their self-management initiative through the cultivation of qualified class representatives.In addition,it is necessary to skillfully resolve classroom generative problems,change the roles of teachers and students,and integrate classroom management with mathematics teaching.

A Study on High School Mathematics Teaching Design Based on Teaching for Robust Understanding: Taking the Cosine Theorem as an Example

Teachers’teaching behavior plays a crucial role in students’development,and there are problems in the current teaching behavior of mathematics teachers such as ignoring students’cognitive needs,lack of equal opportunities for students’classroom performance as well as lack of formative evaluation of students.In order to solve the phenomenon,this paper analyzes and explains how to promote teaching based on the Teaching for Robust Understanding(TRU)evaluation framework with the goal of focusing on the development of all students,taking the teaching design of The Cosine Theorem as an example,and provides ideas and methods for first-line high school mathematics teachers.

Effects of QD2R Numeracy Enhancement Strategy on the Mathematics Performance of Grade 10 Students

Learning mathematics requires an effective and strategic teaching approach.This study aimed to assess the mathematics performance of the learners with the implementation of the numeracy enhancement strategy QD2R(Questions,Drills,Repetition,and Recitation)and to propose a strategy implementation plan to elevate their performances.This study employed the use of a quasi-experimental research design,purposive sampling with 70 Grade 10 students of Lian National High School who were distributed equally to control and treatment groups.The pre-test and post-test results were statistically analyzed using independent and paired sample t-tests,and a survey questionnaire was examined by getting the mean and standard deviation.The results indicated that better performance was achieved by the students from the treatment group compared to the students from the control group,as revealed by the Mean Percentage Score(MPS)results,mean scores,and P values of their pre-test and post-test scores.The learners’perception of the implementation of this strategy was to a great extent,wherein it was perceived to be more helpful in concepts related to understanding the lesson compared to concepts related to developing their attitude and skills.Moreover,the proposed implementation plan of numeracy enhancement strategy QD2R had three expected outcomes:elevated understanding and performance in mathematics lessons;modified strategy to focus on the development of attitude and skills towards mathematics;and refined and well-implemented QD2R strategy in teaching mathematics.Relative to these expected outcomes,appropriate measures,timeframe,and resources of each were comprehensively formulated.

Discussion on the Skillful Use of Mind Maps in High School Mathematics Teaching

With the continuous development of China’s education,the social requirements for high school teaching are constantly improving.The teaching of high school mathematics is a key point in the high school curriculum,but also a major difficulty.Due to the strong logic and abstraction of the content of high school mathematics,some students find it very difficult to learn.In order to solve this problem,high school mathematics teachers can make use of mind maps to teach,so that students can exercise their thinking ability,and realize the improvement of comprehensive ability in mathematics.This paper analyzes the shortcomings of high school mathematics classrooms under the background of new curriculum reform and discusses the significance and methods of applying mind maps in high school mathematics classrooms,so as to put forward reasonable suggestions for realizing the efficient teaching of high school mathematics.

Research on the Teaching Design of Advanced Mathematics Courses Based on Outcome-Based Education Concept

This paper first analyzes the characteristics and current situation of the Advanced Mathematics course;secondly,it proposes a teaching model that integrates the outcome-based education(OBE)philosophy and blended teaching method,reorganizing the teaching objectives,teaching content,and assessment evaluation process of the Advanced Mathematics course;lastly,through practice,it is proved that this approach can effectively improve students’mastery of course content,enhance students’ability to apply mathematical knowledge,and strengthen teaching effectiveness.

Enhancing Proficiency in Quadratic Equations and Functions Through the MILAPlus Strategy

This study investigates the efficacy of the Mathematics Independent Learning Activity Practice and Play Unite Scheme(MILAPlus)as an instructional strategy to improve the proficiency levels of Grade 9 students in quadratic equations and functions through a study carried out at Quezon National High School.The research involved 116 Grade 9 students and utilized a quantitative approach,incorporating both pre-assessment and post-assessment measures.The research utilizes a quasi-experimental design,examining the academic performance of students before and after the introduction of MILAPlus.The pre-assessment establishes a baseline,and the subsequent post-assessment measures the impact of the instructional strategy.Statistical analyses,including t-tests,assess the significance of differences in mean scores and mean percentage scores,providing quantitative insights into the effectiveness of MILAPlus.Findings from the study revealed a statistically significant improvement in both mean scores and mean percentage scores after the utilization of MILAPlus,indicating enhanced proficiency in quadratic equations and functions.The Mean Proficiency Scores(MPS)also showed a substantial increase,demonstrating a marked improvement in overall proficiency levels among Grade 9 students.In light of the results,recommendations were given including the continued utilization of MILAPlus as an instructional strategy and aligning its development with prescribed learning competencies.Emphasizing the consistent adherence to policies and guidelines for MILAPlus implementation is suggested for sustaining positive effects on students’long-term performance in mathematics.This research contributes valuable insights into the practical application and effectiveness of MILAPlus within the context of Grade 9 mathematics education at Quezon National High School.

Instructions for contributions

Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,ChinaSociety for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal withthe first issue published in 1993.It is not a translation of Applied Mathematics-A Journal of ChineseUniversities,Series A,which is in Chinese.The primary goal of this journal is to publish innovativeand original research papers in applied mathematics,including applications of theoretical results inpractical fields.

An activated variable parameter gradient‐based neural network for time‐variant constrained quadratic programming and its applications

This study proposes a novel gradient‐based neural network model with an activated variable parameter,named as the activated variable parameter gradient‐based neural network(AVPGNN)model,to solve time‐varying constrained quadratic programming(TVCQP)problems.Compared with the existing models,the AVPGNN model has the following advantages:(1)avoids the matrix inverse,which can significantly reduce the computing complexity;(2)introduces the time‐derivative of the time‐varying param-eters in the TVCQP problem by adding an activated variable parameter,enabling the AVPGNN model to achieve a predictive calculation that achieves zero residual error in theory;(3)adopts the activation function to accelerate the convergence rate.To solve the TVCQP problem with the AVPGNN model,the TVCQP problem is transformed into a non‐linear equation with a non‐linear compensation problem function based on the Karush Kuhn Tucker conditions.Then,a variable parameter with an activation function is employed to design the AVPGNN model.The accuracy and convergence rate of the AVPGNN model are rigorously analysed in theory.Furthermore,numerical experiments are also executed to demonstrate the effectiveness and superiority of the proposed model.Moreover,to explore the feasibility of the AVPGNN model,appli-cations to the motion planning of a robotic manipulator and the portfolio selection of marketed securities are illustrated.

Multi-dimensional size effects and representative elements for nonpersistent fractured rock masses: A perspective of geometric parameter distribution

This study takes a fractured rock mass in the Datengxia Hydropower Station,China as an example to analyze the size effects and determine the representative elementary sizes.A novel method considering geometric parameter distributions is proposed in this work.The proposed method can quickly and simply determine the size effects and representative elementary sizes.Specifically,geometric parameter distributions,including fracture frequency,size and orientation,are generated on the basis of the Bernoulli trial and Monte Carlo simulation.The distributions are assessed using the coefficient of variation(CV),and the acceptable variations for CV(5%,10%and 20%)are used to determine representative elementary sizes.Generally,the representative element of rock masses is the representative elementary volume(REV).The present study extends the representative element to other dimensions,i.e.representative elementary length(REL)and representative elementary area(REA)for one and two dimensions,respectively.REL and REA are useful in studying the size effects of one-(1D)and twodimensional(2D)characteristics of rock masses.The relationships among multi-dimensional representative elementary sizes are established.The representative elementary sizes reduce with the increase in the dimensions,and REA and REV can be deduced by REL.Therefore,the proposed method can quickly and simply determine REL and further estimate REA and REV,which considerably improves the efficiency of rock mass analysis.

Research on the Teaching Reform of Medical Higher Mathematics with BOPPPS Teaching Module

Using BOPPPS teaching module combined with the present situation of medical higher mathematics teaching in Guangxi University of Chinese Medicine, this paper introduces the application of this teaching method in medical higher mathematics teaching, and explores the thinking of teaching reform of medical higher mathematics in Guangxi University of Chinese Medicine, so as to improve classroom teaching efficiency.

A Key to Solving the Angle Trisection Problem

This paper describes the methodology (or approach) that was key to the solution of the angle trisection problem published earlier in article entitled, “A Procedure For Trisecting An Acute Angle.” It was an approach that required first, designing a working model of a trisector mechanism, second, studying the motion of key elements of the mechanism and third, applying the fundamental principles of kinematics to arrive at the desired results. In presenting these results, since there was no requirement to provide a detailed analysis of the final construction, this information was not included. However, now that the publication is out, it is considered appropriate as well as instructive to explain more fully the mechanism analysis of the trisector in graphical detail, as covered in Section 3 of this paper, that formed the basis of the long sought solution to the age-old Angle Trisection Problem.