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This paper aims to investigate new coincidence point theorems for self‐maps under an extended rational contraction. Our approach uses the p‐adic distance in partially ordered ultrametric spaces. Furthermore, to illustrate our major discoveries, we give a comprehensive numerical analysis. This study expands on prior research in partially ordered ultrametric spaces to provide a more comprehensive understanding of such spaces using rational contraction. [ABSTRACT FROM AUTHOR]

Building on previous work in fractional calculus, this paper introduces new definitions for the (ρ, k, φ)‐proportional integral and (ρ, k, φ)‐proportional H fractional derivative. This new approach retains the semigroup properties of traditional fractional integrals. A significant advantage of this fractional calculus is its compatibility with the majority of existing studies on fractional differential equations. Furthermore, we delve into the properties of the generalized fractional integrals and derivatives. We discuss, for instance, the mapping properties of the (ρ, k, φ)‐proportional integral. To elucidate these concepts, we introduce a set of new weighted spaces. Additionally, we explore the generalized Laplace transform of both the (ρ, k, φ)‐proportional integrals and (ρ, k, φ)‐proportional H fractional derivatives. Also, examples concerning the linear (ρ, k, φ)‐proportional H fractional equations are given to illustrate the main results. [ABSTRACT FROM AUTHOR]

Suppose that S T 1 is a class of close-to-star functions. In this paper, we investigated the estimate of Zalcman functional on the logarithmic coefficients and the third Hankel determinant for the class S T 1 with the determinant entry of logarithmic coefficients. Also, we obtained the sharp bounds of Zalcman functional J 2 , 4 f and J 3 , 3 f for the class S T 1 . [ABSTRACT FROM AUTHOR]

Purpose. As a scientific field, bioinformatics has drawn remarkable attention from various fields, such as information technology, mathematics, and modern biological sciences, in recent years. The topic models originating from the field of natural language processing have become the focus of attention with the rapid accumulation of biological datasets. Thus, this research is aimed at modeling the topic content of the bioinformatics literature presented by Iranian researchers in the Scopus Citation Database. Methodology. This research was a descriptive-exploratory study, and the studied population included 3899 papers indexed in the Scopus database, which had been indexed in this database until March 9, 2022. The topic modeling was then performed on the abstracts and titles of the papers. A combination of LDA and TF-IDF was utilized for topic modeling. Findings. The data analysis with topic modeling resulted in identifying seven main topics "Molecular Modeling," "Gene Expression," "Biomarker," "Coronavirus," "Immunoinformatics," "Cancer Bioinformatics," and "Systems Biology." Moreover, "Systems Biology" and "Coronavirus" had the largest and smallest clusters, respectively. Conclusion. The present investigation demonstrated an acceptable performance for the LDA algorithm in classifying the topics included in this field. The extracted topic clusters indicated excellent consistency and topic connection with each other. [ABSTRACT FROM AUTHOR]

Anemia is a global public health problem, especially common among children in developing countries, which affects their physical and mental health development. However, there is currently a lack of research on the relationship between anemia and academic performance. The objective of this study was to explore the association between anemia and academic performance, and the possible factors mediating this association among Chinese children. The data for this study came from the baseline survey of the Chinese Education Panel Survey Elementary School Cohort. The cohort was conducted from September 2018 to June 2019 in 160 elementary schools, covering 20 provinces and 40 counties/districts throughout China. Paper-based questionnaires were used, completed by 4th grade students, parents, head teachers, main teachers, and principals. The data used included questionnaire responses, physical measurements, and academic performance of 17,695 students. Based on students' hemoglobin levels and school altitude data, we grouped them into anemia and nonanemia categories using WHO criteria. The anemia group had 1,154 individuals, while the nonanemia group had 16,541 individuals. An ordinary least squares regression and mediation effect analysis were conducted. Our findings found the prevalence of anemia was 6.52% among Chinese Grade 4 students. Students without anemia had a higher average test score for three academic subjects than students with anemia (P < 0.001); their test scores for Chinese, Mathematics, and English were also higher (P < 0.05). Multivariate regression analysis showed a negative association between anemia and average test scores as well as individual test scores for the three subjects. Mediation analysis found that anemia affected academic performance directly (P < 0.05), and indirectly by decreasing the cognition score (P < 0.05). The indirect effect was 19.9% of the total effect. Findings highlighted anemia affected academic performance both directly and indirectly. Nutrition-related interventions should be implemented to prevent a decrease in academic performance among students with anemia. [ABSTRACT FROM AUTHOR]

This article investigates the construction of new traveling wave solutions for the conformable fractional Klein–Gordon equation, which is a well‐known mathematical and physical model that can be used to explain spinless pion and de Broglie waves. In order to accomplish this task, a classic and effective analysis method, namely, the extended tanh–coth method, was utilized. By introducing appropriate transformations, the conformable fractional Klein–Gordon equations are reduced to ordinary differential equations, and then the solutions with hyperbolic function form are obtained. In addition, the effect of fractional parameters on waveform is analyzed by drawing two‐ and three‐dimensional graphics. These results contribute to a deeper understanding of the dynamics of the conformable fractional Klein–Gordon equation. The research in this article also indicates that the extended tanh–coth method is a straightforward and concise technique that has the potential to be applicable to many other conformable fractional partial differential equations that appear in mathematical physics. [ABSTRACT FROM AUTHOR]

This research aims to improve the rationality and intelligence of AUTOMATICALLY HIGHER MATHEMATICALLY EXAM SYSTEM (AHMES) through some AI algorithms. AHMES is an intelligent and high-quality higher math examination solution for the Department of Computer Engineering at Pai Chai University. This research redesigned the difficulty system of AHMES and used some AI algorithms for initialization and continuous adjustment. This paper describes the multiple linear regression algorithm involved in this research and the AHMES learning (AL) algorithm improved by the Q-learning algorithm. The simulation test results of the upgraded AHMES show the effectiveness of these algorithms. [ABSTRACT FROM AUTHOR]

In this article, we present a new distribution, the so‐called heavy‐tailed Burr X (HTBX) distribution. It comes from the newly discovered heavy‐tailed (HT) family of distributions. A notable feature is that the associated probability density function can have a right‐skewed distribution that approximates symmetry, unimodality, and decreasing values, which makes it well suited for modeling various datasets. The mathematical properties of the new distribution are obtained by calculating the quantile function, ordinary moments, incomplete moments, moment generating function, conditional moment, mean deviation, Bonferroni curve, and Lorenz curve. Extensive simulation was performed to investigate the estimation of the model parameters using many established approaches, including maximum likelihood estimation, least squares estimation, weighted least squares estimation, Cramer–von Mises estimation, Anderson–Darling estimation, maximum product of spacing estimation, and percentile estimation. The simulation results showed the computational efficiency of these strategies and showed that the maximum likelihood strategy of estimation is the best strategy. The utility and importance of the newly proposed model are demonstrated by analyzing three real datasets. The HTBX distribution is compared to several well‐known extensions of the Burr distribution such as exponentiated Kavya‐Manoharan Burr X, Kavya‐Manoharan Burr X, Burr X, Kumaraswamy Rayleigh, Kumaraswamy Burr III, exponentiated Burr III, Burr III, Kumaraswamy Burr‐II, Rayleigh, and HT Rayleigh models by using different measures. The numerical results showed that the HTBX model fit the data better than the other competitive models. [ABSTRACT FROM AUTHOR]

The purpose of this study is to develop new iterative oscillation criteria for second‐order half‐linear advanced dynamic equations. These findings improve and extend recently established criteria for the same equation by several authors as well as encompass the existing classical criteria for associated ordinary dynamic equations. Some examples are given to show that the outcomes are accurate, practical, and adaptable. [ABSTRACT FROM AUTHOR]

The teaching characteristic of colleges and universities is determined by the teaching quality of teachers, but it is difficult to calculate with a linear mathematical explanation how to judge the teaching quality of teachers. In most colleges and universities, expert evaluations, supervision groups, peers listening to lectures in the classroom, and students' after-class evaluations are still used to determine the teaching ability of professors. It is undeniable that these judgment methods have certain practicality. Especially for new teachers, experts and peers can find problems in time and help new teachers quickly correct them, and they can also know how to better practice the "student-centered" teaching concept from the feedback of students after class. However, these judgment standards also have their limitations. For example, the classroom quality judgment standards for experts and peers are mostly set by some administrative departments according to social requirements, leadership requirements, and subjective cognition. Various institutions should have different weights for the same criterion, and if they all employ the same criteria, it will easily lead to imprecise conclusions. In addition, the expert group and students are also subjective and incomplete in the stage of teacher evaluation. Based on different nonquantitative factors, the evaluation standards for teachers in colleges and universities also need the scientific theoretical basis. Therefore, many scientists are considering whether to use a more intelligent and reasonable way to judge the quality of teaching. Nowadays, with the popularization of artificial intelligence (AI), the use of neural networks (NNs) is becoming more and more comprehensive. According to the characteristics of NNs, this paper uses the GA NNs algorithm to signify that this algorithm can be effectively used in the evaluation of teachers' teaching quality. In this paper, a large number of experimental results show that the use of GA NNs can be used to evaluate the quality of teaching, and the evaluation results can be obtained quantitatively in this way. For the assessment of teaching quality, quantitative results are also more powerful in teaching evaluation. [ABSTRACT FROM AUTHOR]

In order to solve the problems of uneven local educational resources, imperfect comprehensive practice systems, and insufficient teachers in rural schools, this paper proposes a research activity based on mobile information system. The research activities proposed in this paper take STEAM (the acronym of Science, Technology, Engineering, Art, and Mathematics) as the educational concept, carry out local research-based learning (research-based learning, hereinafter referred to as "research-based learning"), and create STEAM research activities suitable for local teaching in combination with the requirements of national education reform to improve students' scientific literacy such as innovation, scientific, and technological level, and independent practice and exploration. The results are as follows: 92% of the students in the experimental group think that STEAM research and learning activities are very interesting and recognize the research and learning process; STEAM research activities have a strong role in promoting the cultivation of students' three abilities and the training of core skills, and the scores are increased by about 50%; the excellent, good, qualified, and unqualified students in the experimental group accounted for 15%, 73%, 12%, and 0%, respectively, while the control group accounted for 6%, 55%, 32%, and 7%, respectively. Through the participation of STEAM research activities, the students' learning attitude has been greatly improved. The practice of STEAM research activities proposed in this paper in the research and implementation institute has achieved remarkable results, which provides experience for Western schools in the follow-up stage of compulsory education to carry out STEAM research activities. [ABSTRACT FROM AUTHOR]

Fractional variants of distance-based parameters have application in the fields of sensor networking, robot navigation, and integer programming problems. Complex networks are exceptional networks which exhibit significant topological features and have become quintessential research area in the field of computer science, biology, and mathematics. Owing to the possibility that many real-world systems can be intelligently modeled and represented as complex networks to examine, administer and comprehend the useful information from these real-world networks. In this paper, local fractional strong metric dimension of certain complex networks is computed. Building blocks of complex networks are considered as the symmetric networks such as cyclic networks C n , circulant networks C n 1,2 , mobious ladder networks M 2 n , and generalized prism networks G m n . In this regard, it is shown that LSFMD of C n n ≥ 3 and G m n n ≥ 6 is 1 when n is even and n / n − 1 when n is odd, whereas LSFMD of M 2 n is 1 when n is odd and n / n − 1 when n is even. Also, LSFMD of C n 1,2 is n / 2 ⌈ m + 1 / 2 ⌉ where n ≥ 6 and m = ⌈ n − 5 / 4 ⌉. [ABSTRACT FROM AUTHOR]

In order to supplement and improve the landscape evaluation system of traditional villages and play a positive guiding role in the specific protection and development of village landscape, this paper proposes the ecological landscape environment evaluation of traditional villages in Guanzhong from the perspective of rural revitalization. First of all, the relevant national and provincial evaluation standards are deeply studied, and the comprehensive evaluation system of the traditional village landscape in the Guanzhong region is constructed by using expert scoring and an analytic hierarchy process, which includes 6 criteria and 25 indicators. Three typical villages of different types and different development stages, namely, village A, village B, and Village C, were selected for landscape investigation and comprehensive evaluation. The results show that the weight of village location and landscape pattern is the largest, that is, the most important. The second is architectural landscape, with a weight of 0.236, accounting for a high proportion. Then, it is the natural landscape and street landscape, with a weight of 0.1-0.2. Finally, it is the intangible cultural landscape and landscape style protection, with a weight of less than 0.1. The alpha value of the comprehensive evaluation questionnaire of the village A is 0.984. The alpha value of the comprehensive evaluation questionnaire of village B is 0.941. The alpha value of the comprehensive evaluation questionnaire for the landscape of village C is 0.986, which is greater than 0.8. Conclusion. This study makes a comprehensive evaluation of the landscape of typical traditional villages. [ABSTRACT FROM AUTHOR]

Educational data mining is becoming a more and more popular research field in recent years, mainly with the help of cross research conducted by various disciplines, so as to solve various difficult problems in the teaching and education process. In this paper, we proposed a hybrid approach for student performance prediction. We collected the dataset, including 15 characteristics of students from three categories (individual basic information, individual education information, and individual behavior information). Based on the random forest (RF) and simulated annealing (SA) algorithms, we binary encode the relevant parameters (number of features, tree size, and tree decision weights) as the target variables for algorithm optimization, use the out-of-bag error as the optimization objective function, and then propose the IRFC (improved random forest classifier) algorithm in this paper. Compared with other mainstream improved random forest algorithms, the research results demonstrate that the proposed algorithm in this paper has higher generalization ability and smaller OOB error. This study provides a methodological reference for the prediction of student achievement and also makes a marginal contribution to student management work. [ABSTRACT FROM AUTHOR]

With the development of computer technology, computers have become a part of people's lives and the Internet has connected the world's networks as a whole. Computer technology is changing people's study, life, and work. People's traditional education mode, thinking, content, method, and talent training program have a significant impact. The development from traditional to computer technology-based teaching methods has brought new developments and leaps in educational technology. This paper analyzes the research background, significance, and research status of the advanced mathematics auxiliary teaching system, introduces the related technologies and development modes used in the development of the system, and especially discusses the access database technology by ADO and the mathematical expression based on MathML language. Secondly, starting from the actual teaching, we analyze the functional requirements and performance requirements of the system in detail and make detailed planning and design for the system architecture, database selection, functional modules, etc. The design and implementation process of this teaching system are summarized. The teaching strategy inference engine is the key to the personalization and intelligence of the ICAI system. According to the learning models provided by different students, the system designs a corresponding teaching sequence for the learners by controlling the meta-knowledge of the domain knowledge base. The teaching strategy inference engine cuts the domain knowledge tree, selects the knowledge points suitable for the student, and sorts the selected knowledge points reasonably to generate an optimal teaching sequence. According to the students' learning situation, combined with the teaching rules in the teaching rule library, the students' grades are dynamically adjusted, so as to select new learning content for students and provide teaching suggestions in time. The student model is the premise of the ICAI system to achieve individualization and intelligence. The system makes a comprehensive evaluation and diagnosis of students through fuzzy comprehensive evaluation and fuzzy reasoning. On this basis, a cognitive student model is established, which is the teaching strategy that provided the basis for the formulation. [ABSTRACT FROM AUTHOR]

Deep learning is an important concept introduced into modern learning science. It is different from the surface learning of mechanically and passively acquiring knowledge and storing individual information but emphasizes learners' active and critical learning. It wants them to understand the full meaning of what they have learned. By establishing a link between existing knowledge and new knowledge, it transfers existing knowledge to a new environment, makes decisions, and solves problems. Deep learning plays an important role in students' learning. Deep learning ability is the key factor affecting the quality of learning and the development of students' academic ability. The quality of in-depth teaching is difficult to guarantee, which requires a complete, comprehensive, and evaluation system to evaluate it. This paper introduces the analytic hierarchy process to weight the indexes in mathematics deep learning and puts forward some suggestions on creating an environment for deep learning. The experimental results show that teachers' teaching accounts for the highest proportion of primary indicators, reaching 67%. Multimedia resources account for the highest proportion of secondary indicators, reaching 73.01%. This paper then puts forward some suggestions for indicators with large weights. [ABSTRACT FROM AUTHOR]

There is a huge amount of mathematical information in the world, and mathematics is everywhere and nowhere. Bayesian theory is based on a process of statistical inference that requires the calculation of general and prior information to obtain a posteriori information. Its main features are the use of probabilities to represent all forms of uncertainty and the use of probabilistic rules to enable learning and inference, estimating the probability of future occurrences by calculating the probability of a past time. In order to bring mathematics closer to life, this paper explores the teaching of mathematical applications in terms of material selection, teaching arrangement, and professional integration. At the same time, in order to better realize mathematics application teaching, effectively improve the classroom effect of mathematics application teaching, and make students better accept mathematical knowledge and apply it to practical applications, the design of mathematics application teaching in this paper is also based on Naive Bayes. [ABSTRACT FROM AUTHOR]

This study introduces Geometric Sound as a subfield of spatial sound featuring audio stimuli which are sonic holograms of mathematically defined 3D shapes. The effects of Geometric Sound on human physiology were investigated through EEG, heart rate, blood pressure, and a combination of questionnaires monitoring 50 healthy participants in two separate experiments. The impact of Geometric Sound on Faraday wave pattern morphology was further studied. The shapes examined, pyramid, cube, and sphere, exhibited varying significant effects on autonomic nervous system markers, brainwave power amplitude, topology, and connectivity patterns, in comparison to both the control (traditional stereo), and recorded baseline where no sound was presented. Brain activity in the Alpha band exhibited the most significant results, additional noteworthy results were observed across analysis paradigms in all frequency bands. Geometric Sound was found to significantly reduce heart rate and blood pressure and enhance relaxation and general well-being. Changes in EEG, heart rate, and blood pressure were primarily shape-dependent, and to a lesser extent sex-dependent. Pyramid Geometric Sound yielded the most significant results in most analysis paradigms. Faraday Waves patterns morphology analysis indicated that identical frequencies result in patterns that correlate with the excitation Geometric Sound shape. We suggest that Geometric Sound shows promise as a noninvasive therapeutic approach for physical and psychological conditions, stress-related disorders, depression, anxiety, and neurotrauma. Further research is warranted to elucidate underlying mechanisms and expand its applications. [ABSTRACT FROM AUTHOR]

With the rapid development of artificial intelligence (AI) concept technology, it promotes the innovation of educational concept. Mostly for the education information analysis in the class of mathematics in the university, it should be based on a big data-driven system to promote the quality of teaching in the classroom. In the method of teaching math in university, teachers should take full advantage of the benefits of a big data-driven system powered by AI, grow a good teaching model for students, promote education through big data, progressively teach students according to their aptitude, develop in a tailored direction, increase teaching quality and effectiveness, and finally create more great talents for our country. For the sake of improving the resource sharing and the management level of the curriculum which teaches advanced knowledge about mathematics teaching, based on a particle swarm optimization algorithm, an advanced math teaching system is proposed in this paper. The fusion model that can be used in the teaching process of math in university is constructed, the adaptive scheduling of the curriculum which teaches advanced knowledge about mathematics auxiliary teaching resources is realized by an optimization algorithm used for fusion particle swarm, the autocorrelation feature of the curriculum which teaches advanced knowledge about mathematics auxiliary teaching resources is extracted, and the adaptive optimization of the curriculum which teaches advanced knowledge about mathematics auxiliary teaching resource fusion is realized by fuzzy correlation feature matching and statistical analysis. In the process of particle swarm optimization, the combination of statistical features is studied and managed, the resource scheduling and information fusion are realized, and the management capability of the curriculum which teaches advanced knowledge about mathematics auxiliary teaching is promoted, and the experimental results demonstrate that the designed system has a high integration of teaching information resources and strong information scheduling ability and improved the management level of the curriculum which teaches advanced knowledge about mathematics complementary teaching. [ABSTRACT FROM AUTHOR]

Mathematics courses in higher education (advanced mathematics, linear algebra, etc.) are characterized by abstract concepts, many easily confused concepts, many nature theorems, and large amount of calculation of many difficulties. In most cases, due to the knowledge level, knowledge structure, and requirements of the teaching process, the traditional mathematics teaching adopts the straight-to-point approach to the introduction of mathematical concepts, and the explanation of property theorems mostly adopts the method of giving the theorems first and then analyzing and proving them for the calculation problems are mostly manual calculation. Educators are mainly concerned with how to organize teaching so that the trainees can acquire more knowledge, while ignoring the subject status of the trainees, and it is often related to the talents of higher education. The training goals are consistent. The traditional mathematics teaching only reflects a function of knowledge inheritance, but lacks the function of knowledge innovation. The lack of concept generation process in teaching makes the abstraction stronger; the lack of case analysis process makes the applicability weaken; and the serious separation of engineering problem solving and computer operation makes it lack of practicability. The current mathematics knowledge and curriculum make students in a passive position in the process of mastering basic knowledge. From the study about the present condition of the math education and the real requirement, the thesis will talk about content, characteristics, and the relationships for the practical education along with interactive teaching process. What is more, the ways of education and online education is able to be presented. At the same time, this paper also obtains the maximum weight value of each teaching quality evaluation index through analytic hierarchy process, introduces the quadratic fuzzy comprehensive calculation method of fuzzy operator, and determines the maximum component of the evaluation level as the final evaluation level according to the most subordinate degree criterion of fuzzy comprehensive evaluation. Especially in the formulation of teaching quality evaluation model in China, the qualitative description is processed quantitatively by the method of fuzzy mathematics and statistics, so that the qualitative index and the quantitative index are organically combined. [ABSTRACT FROM AUTHOR]

The rapid development of artificial intelligence, "Internet +," big data, 5G, and other technologies in the twenty-first century has not only brought great changes to the field of education but also brought unprecedented opportunities and challenges to the reform and innovation of mathematics teaching. The use of intelligent technology to carry out the reform of college mathematics teaching in depth and effectively improve the quality of teaching has become a hot topic discussed by the majority of mathematics teachers. This paper carefully analyzes and sorts out the problems existing in the current intelligent college mathematics teaching and systematically studies the related theories and design principles of the blended teaching mode. The ideas and approaches of the reform of college mathematics blended teaching supported by intelligent technology are deeply discussed from the aspects of improving the level of teachers, setting up a blended teaching team supported by intelligent technology, optimizing the informatization construction of teaching environment and establishing rich teaching resources, building an online and offline classroom teaching system, personalized learning under the background of microclass and cloud class, cross-university blended learning in the network environment, and mathematics precision teaching evaluation and optimization using big data. [ABSTRACT FROM AUTHOR]

The regression model is generally utilized in several fields of study because of its applications. Regression is an extremely incredible approach; it builds up a connection between dependent and independent variables. We have addressed a powerful computational model by utilizing dengue information joined with fuzzy multiple linear regression. Information is accumulated on dengue fever through the survey. This paper is centered on the comparison of the crisp method with fuzzy multiple linear regression, and then, the utilization of a fuzzy multiple regression method is explained after the comparison. We have used multiple regression and then converted the said technique into three fuzzy cases. The effectiveness of the fuzzy multiple regression model is measured by numerical computation and comparison of both techniques. 2020 Mathematics Subject Classification. Primary 30C45; 30C50; 30C80; Secondary 11B65, 47B38. [ABSTRACT FROM AUTHOR]

This paper mainly deals on the issue of a chaotic synchronization of a master and slave systems. It is generally the requirement of the synchronization that someone needs at least one to one master and slave systems. In the current study, the authors introduce the concept of a synchronization in which there is no need of slave/response system externally. Furthermore, the synchronization has been demonstrated here within a system among the subsystems of different orders. In addition, adaptive control is chosen for the synchronization among various combinations in multiswitching manner. For demonstration purpose, Lorenz Six Dimensional Hyper Chaotic System (L6DHCS) is chosen. There are three different kinds of possible switches presented by the authors formed within the considered system. The numerical simulations are carried out to validate the effectiveness of the analytical technique using Mathematica. [ABSTRACT FROM AUTHOR]

THz time-domain spectroscopy has evolved as a noncontact, safe, and efficient technique for paper characterization. Our previous work adopted peak amplitude and delay time as features to determine paper basis weight using terahertz time-domain spectroscopy. However, peak amplitude and delay time tend to suffer from noises, resulting in degradation of accuracy and robustness. This paper proposes a noise-robust phase-shift based method to enhance measurements of paper basis weight. Based on Fresnel Formulae, the physical relationship between phase shift and paper basis weight is formulated theoretically neglecting multiple reflections in the case of normal incidence. The established formulation indicates that phase shift correlates linearly with paper basis weight intrinsically. Subsequently, paper sheets were stacked to fabricate the samples with different basis weights, and experimental results verified the developed mathematical formulation. Moreover, a comparison was made between phase shift, peak amplitude, and delay time with respect to linearity, accuracy, and noise robustness. The results show that phase shift is superior to the others. [ABSTRACT FROM AUTHOR]

Expanding the analytical aspect of mathematics enables researchers to study more cosmic phenomena, especially with regard to the applied sciences related to fractional calculus. In the present paper, we establish some Chebyshev-type inequalities in the case synchronous functions. In order to achieve our goals, we use k , ψ -proportional fractional integral operators. Moreover, we present some special cases. [ABSTRACT FROM AUTHOR]

This study proposed an evaluation model of mathematics teaching quality under recurrent neural network for the sake of making the evaluation model of mathematics teaching quality have good fault tolerance. This model decomposes the initial data sequence of mathematics teaching quality evaluation into high- and low-frequency sequence by wavelet analysis and reconstructs it by using phase space. After introducing the recurrent neural network model, the data is reconstructed after model training, and the data mining is carried out for the evaluation of mathematics teaching quality. In the process of constructing the evaluation model, the evaluation index system should be constructed based on three dimensions firstly, and the evaluation index of association rules should be defined, so as to realize deep dig of data and obtain the phase space distribution of data and then carry out the constraint test of parameters to evaluate the mathematics teaching quality scientifically and accurately. After verification, it is known that the average values of training error and test error of the model proposed in this paper are 3.02% and 2.61%, and the average values of absolute error and relative error are 0.58 and 3.82%. This model can retain the valid data information in the initial sequence, and the evaluation results of mathematics teaching quality are relatively ideal, which greatly improves the efficiency and level of mathematics teaching. [ABSTRACT FROM AUTHOR]

In this paper, we consider the three-dimensional Cauchy problem of the nonisentropic compressible Euler equations with relaxation. Following the method of Wu et al. (2021, Adv. Math. Phys. Art. ID 5512285, pp. 1–13), we show the existence and uniqueness of the global small H k k ⩾ 3 solution only under the condition of smallness of the H 3 norm of the initial data. Moreover, we use a pure energy method with a time-weighted argument to prove the optimal L p – L q 1 ⩽ p ⩽ 2 , 2 ⩽ q ⩽ ∞ -type decay rates of the solution and its higher-order derivatives. [ABSTRACT FROM AUTHOR]

Some examples of dialectics philosophy in higher mathematics are illustrated in this paper. Firstly, the principle of interconversion between quality and quantity in dialectics philosophy is quantified by the mathematical definition of the limit theory. Secondly, some natural and social phenomena imply the definition of continuous function in incremental form and it is a new explanation for the Zeno paradox. Finally, the dialectics relationship between the local change and the whole change of some variables is discussed in the differential median theorems. [ABSTRACT FROM AUTHOR]

Malignant melanoma is one of the most threatening cancers to human health. Only 14% of patients with malignant melanoma have a remaining life span of 5 years. At present, there have been some studies looking for potential prognostic indicators of esophageal cancer from the level of genes and infiltrating immune cells, but there are still some problems that need to be resolved urgently. This paper proposes IGHG3 as the immune infiltration of malignant melanoma, which takes into account the computational mathematics. It aims to deduce the characteristics of immune cell infiltration in malignant melanoma and study the relationship between different immune cell infiltration characteristics and prognosis. The method in this article is to establish a computational mathematical model for the immunotherapy of melanoma, then study the method of identification of the affinity of the IGHG3 reagent, and finally obtain the gene expression of immune infiltration. The functions of these methods are, respectively, to predict the dynamic behavior of T cells with two different specificities through mathematical models and to test the matching degree of different concentrations of IGHG3 reagent with the human body. Then use the ssGSEA algorithm to obtain immune infiltration related data and calculate the difference between the weighted empirical cumulative distribution function of all genes in the effect of IGHG3 on melanoma that was carried out. The experimental results showed the computational mathematical method genome and all the remaining genes. In this study, a computational mathematical method to detect the IGHG3 gene expression had a significant inhibitory effect on A375 cells in the experimental group, and the knockdown efficiency reached 85.6%. [ABSTRACT FROM AUTHOR]

This paper describes a novel perspective on the foundations of mathematics: how mathematics may be seen to be largely about "information compression (IC) via the matching and unification of patterns" (ICMUP). That is itself a novel approach to IC, couched in terms of nonmathematical primitives, as is necessary in any investigation of the foundations of mathematics. This new perspective on the foundations of mathematics reflects the facts that mathematics is almost exclusively the product of human brains, and has been developed, as an aid to human thinking, mathematics is likely to be consonant with much evidence for the importance of IC in human learning, perception, and cognition. This perspective on the foundations of mathematics has grown out of a long-term programme of research developing the SP Theory of Intelligence and its realization in the SP Computer Model, a system in which a generalised version of ICMUP—the powerful concept of SP-multiple-alignment—plays a central role. This paper shows with an example how mathematics, without any special provision, may achieve compression of information. Then, it describes examples showing how variants of ICMUP may be seen in widely used structures and operations in mathematics. Examples are also given to show how several aspects of the mathematics-related disciplines of logic and computing may be understood as ICMUP. Also discussed is the intimate relation between IC and concepts of probability, with arguments that there are advantages in approaching AI, cognitive science, and concepts of probability via ICMUP. Also discussed is how the close relation between IC and concepts of probability relates to the established view that some parts of mathematics are intrinsically probabilistic, and how that latter view may be reconciled with the all-or-nothing, "exact," forms of calculation or inference that are familiar in mathematics and logic. There are many potential benefits and applications of the mathematics-as-IC perspective. [ABSTRACT FROM AUTHOR]

In this paper, the theory of viscoelastic material relaxation modulus testing, testing method, and material relaxation modulus parameter solution method is studied. Based on the IoT sensor test devices and the Hertzian mathematics theory, the relationship between the compression amount, pressure, and relaxation modulus of a rigid spherical indenter pressed into a flat viscoelastic material is studied. In combination with the Boltzmann superposition principle, the relaxation modulus test method and theory for viscoelastic materials are proposed. A good fitting curve was obtained to solve the relaxation modulus parameters of various materials under the three-element Maxwell model. The experimental setup and the results of the parameter fitting were analyzed to verify the feasibility and accuracy of the results. [ABSTRACT FROM AUTHOR]

In order to improve the effect of classroom teaching and realize the improvement of mathematics teaching quality, this article combines data-driven decision-making technology to design a mathematics teaching plan system and applies data-driven decision-making technology to the design of mathematics teaching plan by improving the big data algorithm. In addition, this paper designs a mathematics teaching plan design system based on data-driven decision-making technology. The system learning module displays the knowledge points in a chapter-sequential navigation mode and stores data or information in the nodes, which are connected to form a network structure through chains. Finally, this paper verifies the designed system with experiments. From the results of the experimental research data, it can be seen that the mathematical teaching plan design system based on the data-driven decision-making technology constructed in this article has good practical effects. On this basis, the system constructed in this article can be verified through further practice. [ABSTRACT FROM AUTHOR]

With the increasing importance of mathematics in basic education, how to evaluate and analyze the intelligent effect of mathematics teaching classroom through scientific methods has become one of the indicators to evaluate the intelligent classroom. This paper studies the design and application of mathematics teaching intelligent classroom based on the PCA-NN (principal component analysis-neural network) algorithm. Firstly, this paper briefly describes the current research status of mathematics teaching intelligent classroom design and PCA-NN algorithm. Secondly, combined with the key factors of mathematics teaching, it formulates specific standards and puts forward an adaptive strategy of intelligent and personalized intelligent mathematics teaching classroom. Finally, the algorithm is verified by experiments. The results show that, for students with different mathematics basic levels, the mathematics teaching intelligent classroom based on the PCA-NN algorithm can effectively improve the quality of mathematics classroom teaching. Through the research on the factors such as teaching quality, effect, and interaction mode involved in the process of mathematics teaching classroom design, the intelligent classroom design factors affecting teaching quality are determined. This paper analyzes and studies the system from different angles. The research results provide some help for the current quality evaluation of classroom teaching and use the PCA-NN algorithm to make quantitative analysis and multivariate verification of mathematics classroom teaching effect. [ABSTRACT FROM AUTHOR]

Nowadays, building intelligent systems for science, technology, engineering, and math (STEM) education is necessary to support the studying of learners. Intelligent problem solver (IPS) is a system that can be able to solve or tutor how to solve the problems automatically. Learners only declare hypothesis and goal of problems based on a sufficient specification language. They can request the program to solve it automatically or to give instructions that help them to solve it themselves. Knowledge representation plays a vital role in these kinds of intelligent systems. There are various methods for knowledge representation; however, they do not meet the requirements of an IPS in STEM education. In this paper, we propose the criteria of a knowledge model for an IPS in education. These criteria orient to develop a method for knowledge representation to meet actual requirements in practice, especially pedagogical requirements. For proving the effectiveness of these criteria, a knowledge model is also constructed. This model can satisfy these criteria and be applied to build IPS for courses, such as mathematics and physics. [ABSTRACT FROM AUTHOR]

Convex functions play an important role in many areas of mathematics. They are especially important in the study of optimization problems where they are distinguished by a number of convenient properties. In this paper, firstly we introduce the notion of h -exponential convex functions. This notion can be considered as generalizations of many existing definitions of convex functions. Then, we establish some well-known inequalities for the proposed notion via incomplete gamma functions. Precisely speaking, we established trapezoidal, midpoint, and He's inequalities for h -exponential and harmonically exponential convex functions via incomplete gamma functions. Moreover, we gave several remarks to prove that our results are more generalized than the existing results in the literature. [ABSTRACT FROM AUTHOR]

One of the major shortcomings of Hopfield neural network (HNN) is that the network may not always converge to a fixed point. HNN, predominantly, is limited to local optimization during training to achieve network stability. In this paper, the convergence problem is addressed using two approaches: (a) by sequencing the activation of a continuous modified HNN (MHNN) based on the geometric correlation of features within various image hyperplanes via pixel gradient vectors and (b) by regulating geometric pixel gradient vectors. These are achieved by regularizing proposed MHNNs under cohomology, which enables them to act as an unconventional filter for pixel spectral sequences. It shifts the focus to both local and global optimizations in order to strengthen feature correlations within each image subspace. As a result, it enhances edges, information content, contrast, and resolution. The proposed algorithm was tested on fifteen different medical images, where evaluations were made based on entropy, visual information fidelity (VIF), weighted peak signal-to-noise ratio (WPSNR), contrast, and homogeneity. Our results confirmed superiority as compared to four existing benchmark enhancement methods. [ABSTRACT FROM AUTHOR]

This paper draws on data from a quantitative study of upper secondary students' general mathematical self-efficacy, anxiety towards mathematics, and their relationship to achievement in mathematics. The main objective of this article is to discuss the type of information that may be lost if potential problems of validity and extreme multicollinearity in exploratory factor analysis would be solved by only removing variables without doing a profound analysis. We also describe a method that treats Likert items in the questionnaire as ordinal variables that may represent the underlying continuous variable. Our study shows, for example, that removal of problematic variables without a profound analysis leads to a loss of significant information about test anxiety. Our qualitative analysis of problematic variables also led to an unexpected finding regarding the relationship between general mathematical self-efficacy and motivational values in mathematics. [ABSTRACT FROM AUTHOR]

Generating relations involving the special functions have already proved their important role in mathematics and other fields of sciences. In this paper, we aim to provide some presumably new generating relations in connection with the generalized multi-index Bessel–Maitland function J ν j m , q λ j m , γ . . The main results presented here, being very general, can yield a number of particular or equivalent identities, some of which are explicitly demonstrated. [ABSTRACT FROM AUTHOR]

In this paper, an algorithm is introduced to solve the global optimization problem for melanoma skin cancer segmentation. The algorithm is based on the smoothing of an auxiliary function that is constructed using a known local minimizer and smoothed by utilising Bezier curves. This function achieves all filled function properties. The proposed optimization method is applied to find the threshold values in melanoma skin cancer images. The proposed algorithm is implemented on PH2, ISBI2016 challenge, and ISBI 2017 challenge datasets for melanoma segmentation. The results show that the proposed algorithm exhibits high accuracy, sensitivity, and specificity compared with other methods. [ABSTRACT FROM AUTHOR]

The poor comprehensiveness of the evaluation indexes of quality evaluation methods for the traditional college mathematics teaching model reform results in low accuracy of the evaluation outcomes. In this paper, aiming at this problem, a quality evaluation method for the college mathematics teaching model reform, based on the genetic algorithm, is proposed. The simulated annealing algorithm uses the weighted comprehensive objective evaluation multiobjective optimization effect that can effectively improve the accuracy of the evaluation results. In the training process, the gradient descent back-propagation training method is used to obtain new weights for the quality evaluation of college mathematics teaching mode reforms and to score various indicators and evaluate the indicators. The mean value of the outcomes is the result of mathematics teaching quality evaluation. The experimental results show that the training error of the convolutional network of the proposed method is significantly small. Based on the genetic algorithm that improves the convolutional network training process, the obtained quality evaluation outcomes are higher in accuracy, better in goodness of fitness function, and considerably lower than other state-of-the-art methods. We observed that the improved genetic algorithm has a more than 90% goodness of fit and the error is significantly lower, that is, 0.01 to 0.04, than the classical genetic algorithm. [ABSTRACT FROM AUTHOR]

The article discusses various reports published within the issue including one by Li on the fractal time series from the point of view of systems of fractional order, article by Liu on the chaotic time series and an article by Cattani on the fractal shapes and the symmetries of DNA from a view of fractal time series.

J wave is the bulge generated in the descending slope of the terminal portion of the QRS complex in the electrocardiogram. The presence of J wave may lead to sudden death. However, the diagnosis of J wave variation only depends on doctor’s clinical experiences at present and missed diagnosis is easy to occur. In this paper, a new method is proposed to realize the automatic detection of J wave. First, the synchrosqueezed wavelet transform is used to obtain the precise time-frequency information of the ECG. Then, the inverse transformation of SST is computed to get the intrinsic mode function of the ECG. At last, the time-frequency features and SST-based and the entropy features based on modes are fed to Random forest to realize the automatic detection of J wave. As the experimental results shown, the proposed method has achieved the highest accuracy, sensitivity, and specificity compared with existing techniques. [ABSTRACT FROM AUTHOR]

Quasi-cyclic (QC) LDPC codes play an important role in 5G communications and have been chosen as the standard codes for 5G enhanced mobile broadband (eMBB) data channel. In this paper, we study the construction of QC LDPC codes based on an arbitrary given expansion factor (or lifting degree). First, we analyze the cycle structure of QC LDPC codes and give the necessary and sufficient condition for the existence of short cycles. Based on the fundamental theorem of arithmetic in number theory, we divide the integer factorization into three cases and present three classes of QC LDPC codes accordingly. Furthermore, a general construction method of QC LDPC codes with girth of at least 6 is proposed. Numerical results show that the constructed QC LDPC codes perform well over the AWGN channel when decoded with the iterative algorithms. [ABSTRACT FROM AUTHOR]

This study explored the effectiveness of learning mathematics according to the STEM approach in developing mathematical proficiency with its five components (conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition) in some mathematical concepts among second graders of intermediate school. The quasi-experimental method with the experimental and control group design was used. The participants were 40 second graders of the intermediate school in the second semester of the school year 2021-22. The experimental group (N = 20) was taught according to the STEM approach, while the control group (N = 20) was taught according to the conventional approach. Data were collected by a researcher-developed mathematical proficiency test measuring conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. Results of the t-test revealed significant differences in mathematical proficiency between the post-test mean scores for the experimental and control groups in favor of the experimental group. Implications drawn from the results are offered. [ABSTRACT FROM AUTHOR]

In order to promote the teaching reform, deepen the professional construction, innovate the talent training mode and course teaching mode, improve teachers' advanced vocational education teaching design ability and teaching level, and promote the connotation construction of higher vocational colleges, an evaluation method of higher mathematics teaching reform effect based on big data analysis technology is proposed. In the research, the teaching status of advanced mathematics courses and the problems existing in teaching are firstly analyzed and studied. Then, on the basis of comprehensive analysis of various influencing factors of course teaching effect evaluation, a set of two-level index system with a total of 25 indicators is established. The results verify the rationality of these indicator settings. Finally, combined with the real historical data of the teaching evaluation effect of a private college, the validity of the proposed model is verified. The experimental results show that the 530 sample data of the course are submitted to the RBF network for the training, and the network converges after 3385 iterations. Among all 100 test samples, the maximum test error is 0.0513, of which 92 samples are judged correct, 7 samples are judged as excellent, and 3 samples are judged as medium. Therefore, the evaluation accuracy rate of the RBF network is as high as 92%. It is concluded that this method provides a new way to evaluate the teaching effect of the course objectively and impartially. [ABSTRACT FROM AUTHOR]

Huxley's model of simple allometry provides a parsimonious scheme for examining scaling relationships in scientific research, resource management, and species conservation endeavors. Factors including biological error, analysis method, sample size, and overall data quality can undermine the reliability of a fit of Huxley's model. Customary amendments enhance the complexity of the power function-conveyed systematic term while keeping the usual normality-borne error structure. The resulting protocols bear multiple-parameter complex allometry forms that could pose interpretative shortcomings and parameter estimation difficulties, and even being empirically pertinent, they could potentially bear overfitting. A subsequent heavy-tailed Q-Q normal spread often remains undetected since the adequacy of a normally distributed error term remains unexplored. Previously, we promoted the advantages of keeping Huxley's model-driven systematic part while switching to a logistically distributed error term to improve fit quality. Here, we analyzed eelgrass leaf biomass and area data exhibiting a marked size-related heterogeneity, perhaps explaining a lack of systematization at data gathering. Overdispersion precluded adequacy of the logistically adapted protocol, thereby suggesting processing data through a median absolute deviation scheme aimed to remove unduly replicates. Nevertheless, achieving regularity to Huxley's power function-like trend required the removal of many replicates, thereby questioning the integrity of a data cleaning approach. But, we managed to adapt the complexity of the error term to reliably identify Huxley's model-like systematic part masked by variability in data. Achieving this relied on an error term conforming to a normal mixture distribution which successfully managed overdispersion in data. Compared to normal-complex allometry and data cleaning composites present arrangement delivered a coherent Q-Q normal mixture spread and a remarkable reproducibility strength of derived proxies. By keeping the analysis within Huxley's original theory, the present approach enables substantiating nondestructive allometric proxies aimed at eelgrass conservation. The viewpoint endorsed here could also make data cleaning unnecessary. [ABSTRACT FROM AUTHOR]

There has been several Lagrange and Hermite type interpolations of entire functions whose linear canonical transforms have compact supports in ℝ. There interpolation representations are called sampling theorems for band-limited signals in signal analysis. The truncation, amplitude, and jitter errors associated with the Lagrange type interpolations are investigated rigorously. Nevertheless, the amplitude and jitter errors arising from perturbing samples and nodes are not studied before. The aim of this work is to establish rigorous analysis of their types of perturbation errors, which is important from both practical and theoretical points of view. We derive precise estimates for both types of errors and expose various numerical examples. [ABSTRACT FROM AUTHOR]

Multiple anthropometric equations have been developed aiming to provide accurate and affordable assessment of body fat composition in male athletes. This study examined correlations of values obtained from seventeen different anthropometric equations to DXA as well as BIA and DXA values. Male athletes (n = 101) from three different combat sports, wrestling (n = 33), judo (n = 35), and kickboxing (n = 33), with an average age of 20.9 ± 4.2 were included. Body fat percentage was estimated using anthropometry, BIA, and DXA. Correlations between anthropometric methods and DXA, as well as BIA and DXA, were determined using Spearman's rank correlation. Sixteen out of seventeen estimates of body fat percentages using existing anthropometric equations showed strong positive correlation with the values derived from DXA measurements (r = 0.569 − 0.909). The highest correlation was observed using the equation derived by Yuhasz, r = 0.909 , followed by the equations from Oliver et al., Evans et al., Faulkner, and Thorland et al. (r ≈ 0.9). Statistical analysis of body fat percentages from DXA and BIA measurements also showed high positive correlation (r = 0.710). Correlation of seventeen anthropometric equations with BIA and DXA methods revealed that equations by Yuhasz, Oliver et al., Evans et al., Faulkner, and Thorland et al. are suitable alternative for assessing body fat percentage among male athletes from combat sports, showing even stronger correlation than BIA method. [ABSTRACT FROM AUTHOR]

The aim of this study is to predict the COVID-19 infection fifth wave in South Africa using the Gaussian mixture model for the available data of the early four waves for March 18, 2020-April 13, 2022. The quantification data is considered, and the time unit is used in days. We give the modeling of COVID-19 in South Africa and predict the future fifth wave in the country. Initially, we use the Gaussian mixture model to characterize the coronavirus infection to fit the early reported cases of four waves and then to predict the future wave. Actual data and the statistical analysis using the Gaussian mixture model are performed which give close agreement with each other, and one can able to predict the future wave. After that, we fit and predict the fifth wave in the country and it is predicted to be started in the last week of May 2022 and end in the last week of September 2022. It is predicted that the peak may occur on the third week of July 2022 with a high number of 19383 cases. The prediction of the fifth wave can be useful for the health authorities in order to prepare themselves for medical setup and other necessary measures. Further, we use the result obtained from the Gaussian mixture model in the new model formulated in terms of differential equations. The differential equations model is simulated for various values of the model parameters in order to determine the disease's possible eliminations. [ABSTRACT FROM AUTHOR]