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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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

We discuss the approximation method of finding a common fixed point of two certain mappings defined on a Banach space. This paper deals with three modes of convergence, namely, weak, strong, and △-convergences in the presence of the uniform convexity of the norm. It is worth mentioning that the △-convergence which is closely connected with the weak convergence is discussed without assuming the Opial’s condition. Our results not only generalize the results recently announced by Garodia et al. but also rectify a gap in their paper. Finally, some concrete numerical examples are shown that our results are genuine generalizations of a number of results in the literature.

Tourism development can stimulate regional economic growth and improve living standards in economically underdeveloped regions. However, rapid tourism expansion may also negatively affect regional sustainability, particularly in eco-fragile areas. As a representative arid and semiarid region, Northwestern China provides a valuable case for analyzing the coupling coordination relationship within the tourism–economy–ecology (TEE) system. This analysis is crucial for promoting sustainable tourism development in eco-fragile areas. This paper utilizes the entropy weight method, coupling coordination degree (CCD), and obstacle degree models to assess the development level, coupling status, and related obstacles within the TEE system across the five northwestern provinces from 2011 to 2022. The results show the following. (1) While the northwest region has made significant strides in environmental management, most provinces have low comprehensive development status in tourism and economic subsystems, which lag behind the ecological system’s development. (2) The CCD level in each province improved continuously from 2011 to 2022. Provinces with lower coupling coordination in 2011 had higher improvement rates in the later period. (3) The obstacles to coordinated development shifted over time, ranging from low foreign exchange earnings from tourism and low international tourist arrivals in 2011 to low forest management areas in 2019 and a significant decline in foreign exchange earnings from tourism in 2022. (4) The impact of COVID-19 on the coordinated development of the TEE system has been relatively manageable. While most provinces in the northwest continue to see steady ecological improvement, the challenges of lagging tourism development and insufficient economic growth momentum remain significant. Based on this analysis, this paper offers four policy recommendations to support the sustainable development of arid and semiarid regions in Northwestern China. These recommendations provide valuable insights for achieving high-quality economic development in other eco-fragile areas.

The purpose of this paper is to discuss a nonlinear rational difference equation system with three variables. Firstly, by utilizing Jacobian theory, the stability of the system is obtained. Then, we explore the saddle point, nonhyperbolic point, and prime period-two solution and its boundedness. Finally, we verify the results obtained in the paper via computer numerical calculations.

In order to deal with the dependence of support vector machine (SVM) on kernel function and the limitation that the decision boundary formed by SVM is a hyperplane when dealing with nonlinear classification tasks, this paper combines the double-well potential function and the idea of fuzzy system and designs a novel SVM variant and a fourth-order fuzzy support vector machine based on class center (FOF-SVM). The FOF-SVM model eschews the use of traditional kernel functions and directly uses quartic hypersurfaces for data modeling. It achieves effective classification of nonlinear data without kernel tricks and reduces the adverse effects of outliers on the overall classification performance. In addition, the specific expression of the model is derived by solving the convex optimization problem. The experimental results on UCI benchmark datasets and artificial datasets demonstrate that compared with other classification models based on SVM, the model proposed in this paper can improve the classification accuracy by about 10%.

This paper offers an in-depth investigation into pure ideals within the Hurwitz series ring. Specifically, by focusing on the Hurwitz series ring, denoted as HR over a ring R, we present a comprehensive characterization of differential ideals. In this paper, we prove that these differential ideals can be expressed in the form HI, where I represents an ideal in the underlying ring R. Through this analysis, a comprehensive understanding of the structure and properties of pure ideals within the Hurwitz series ring is achieved.

Traditional short-term traffic volume forecasting approaches make it difficult to predict the highly spatiotemporally coupled short-time traffic. To tackle the problem, this paper first proposes a variational modal algorithm (GWO-VMD) based on the optimization of the gray wolf search algorithm. It aims to decompose and reduce the noise of short-time traffic flows. Meanwhile, it reduces the intricacy of data sequences and enhances the regularity pattern. To address the insufficient utilization of spatiotemporal features, this paper presents an innovative deep-learning traffic prediction framework based on the stacking of multiple temporal trend-aware graph attention (TGA) layers and gated temporal convolution (GTC) layers, which are called trend-aware temporal graph neural network (TTGAN). TGA dynamically models the space-time relationships of traffic data, and GTC models the temporal characteristics of traffic data. The experimental findings demonstrate that the MAPE model, as presented, achieves a reduction of 9% and 2% compared to the AGCRN and GWNET models, respectively, in the domain of deep spatiotemporal graph modeling. Data decomposition and noise reduction are necessary to achieve accurate results. This model has superior performance in terms of mean absolute error (MAE), coefficient of determination (R2), and explained variance score (EVAR).

Solving the Diophantine equation has fascinated mathematicians from various civilizations. In this paper, we propose the resolution of quadratic Diophantine equations with integer coefficients. Our contribution consists of generalizing certain results which have already been developed in the literature. This paper also proposes the criterion on the solvability of the quadratic Diophantine equation here studied.

The collaborative R&D of new products between enterprises is prone to the “free-rider effect” due to knowledge spillover. To avoid that, this paper establishes a three-stage dynamic game to explore the collaborative R&D co-competition behavior between asymmetric horizontal supplier enterprises. In this paper, we incorporate the uncertainty of R&D success probability into the model and reverse induction is applied to solve it. In the model, two asymmetric enterprises play dynamic games under three modes: complete noncooperation, semicooperation, and complete cooperation. We discuss the sensitivity of various asymmetric factors to the R&D investment level and profit of enterprises. The results indicate that the R&D investment level of supplier enterprises is positively correlated with the absorptive capacity, technology spillover, and R&D success probability, and negatively correlated with the initial R&D investment and innovation efficiency under the three co-competition modes. Especially, when the absorptive capacity of the enterprise or the degree of technological spillover of the other party exceeds a certain value, the profits of the enterprise in the mode of complete noncooperation and semicooperation will intersect, which can easily lead to “free-riding” behavior. It provides a decision-making basis for the direction and extent of enterprises’ R&D efforts. In addition, some methods are proposed to improve the level of R&D investment and increase the income of enterprises under three modes.

The action of any group on itself by conjugation and the corresponding conjugacy relation plays an important role in group theory. Generalizing the group theoretic notion of conjugacy to semigroups is one of the interesting problems, and semigroup theorists had produced substantial amount of research in this direction. The challenge to introduce a new notion of conjugacy in semigroups is to choose the suitable set of conjugating elements. A semigroup may contain a zero, and if zero lies in the conjugating set, then the relation reduces to the universal relation as can be seen in the notions ∼l, ∼p, and ∼o. To avoid this problem, various innovative notions of conjugacy in semigroups have been considered so far, and ∼n is one of these notions. ∼n is an equivalence relation in any semigroup, coincides with the usual group theoretic notion if the underlying semigroup is a group, and does not reduce to a universal relation even if S contains a zero. In this paper, we study ∼n notion of conjugacy in some classes of epigroups. Since epigroups are generalizations of groups, our results of this paper are innovative and generalize the existing results on other notions. After proving some fundamental results, we compare our results with existing ones and prove that they are worth contribution in the study of conjugacy in epigroups.

This paper investigates the existence of positive solutions for an iterative system of nonlinear two-point tempered fractional boundary value problem. Utilizing Krasnoselskii’s fixed point theorem in a cone, we establish criteria for the existence of positive solutions. The proofs involve transforming the problem into an equivalent Fredholm integral equation of the second kind. We further explore solution uniqueness using Rus’s theorem and examine Hyers–Ulam stability, particularly for the case when only a single fractional differential equation is considered, m=1. Our study represents a significant departure from previous works by including Riemann–Liouville tempered fractional derivative operators and an iterative equation. This research sheds light on the diverse applications of iterative functional differential equations, extending beyond noniterative counterparts. Throughout the paper, presumptive conditions are applied, and the results are validated through illustrative examples.

In this paper, by using Poisson distribution probability, some characteristics of analytic multivalent q-symmetric starlike and q-symmetric convex functions of order η are examined. Then, by utilizing the Poisson distribution and the concept of the q-analogue Salagean integral operator, the p-valent convergence polynomial was introduced. Furthermore, a number of subclasses of analytic symmetric p-valent functions linked to novel polynomials are also deduced. After that, specific coefficient constraints are determined and symmetric δ,q-neighborhoods for p-valent functions are defined. In relation to symmetric δ,q-neighborhoods of q-symmetric p-valent functions formed by Poisson distributions, this paper presents new inclusion results. In addition, a detailed discussion of certain q-symmetric inequalities of analytic functions with negative coefficients is also provided.

The world economy is affected by fluctuations in the price of crude oil, making precise and effective forecasting of crude oil prices essential. In this study, we propose a combined forecasting scheme, which combines a quadratic decomposition and optimized support vector regression (SVR). In the decomposition part, the original crude oil price series are first decomposed using empirical modal decomposition (CEEMDAN), and then the residuals of the first decomposition (RES) are decomposed using variational modal decomposition (VMD). Additionally, this work proposes to optimize the support vector regression model (SVR) by the seagull optimization algorithm (SOA). Ultimately, the empirical investigation created the feature-variable system and predicted the filtered features. By computing evaluation indices like MAE, MSE, R2, and MAPE and validating using Brent and WTI crude oil spot, the prediction errors of the CEEMDAN -RES.-VMD -SOA-SVR combination prediction model presented in this paper are assessed and compared with those of the other twelve comparative models. The empirical evidence shows that the combination model being proposed in this paper outperforms the other related comparative models and improves the accuracy of the crude oil price forecasting model.

Background. Coal washing is a complicated process and difficult to control, which has many controlling parameters with strong coupling relationship. It is still a challenge to realize the self-perception, self-adjustment, and self-evaluation of coal washing machine, improve the quality of coal washing, ensure production safety, and reduce labor cost. Methods. Through the intelligent transformation of jig, this paper proposes an intelligent washing method with cooperated deep reinforcement learning and evolutionary computation. First, it designs a fault warning method based on statistical analysis, helping to recover the normal running state of jig with manual maintenance. Then, it constructs a regulation strategy generation method with deep reinforcement learning supported by the fusion of artificial experience and historical data. Last, for the lack of monitoring data caused by poor communication quality and environment, the regulation strategy prediction method with evolutionary computation and surrogate model is proposed. Results. In practice, this method shows accurate fault warning accuracy and rapid cleaned coal ash adjustment response ability. Conclusions. This shows that the method proposed in this paper is of great significance for intelligent washing and can better cope with the special situation when the washing equipment sensing data are missing.

This paper is an attempt to establish the existence and multiplicity results of nontrivial solutions to singular systems with sign-changing weight, nonlinear singularities, and critical exponent. By using variational methods, the Nehari manifold, and under sufficient conditions on the parameter η which represent some physical meanings, we prove some existing results by researching the critical points as the minimizers of the energy functional associated with the proposed problem (2) on the constraint defined by the Nehari manifold, which are solutions of our system, under some sufficient conditions on the parameters α, β, μ, and η. To the best of our knowledge, this paper is one of the first contributions to the study of singular systems with sign-changing weight, nonlinear singularities, and critical exponent.

In this paper, we study some generalized contraction conditions for three self-mappings on generalized b-metric spaces to prove the existence of some unique common fixed-point results. To unify our results, we establish a supportive example for three self-mappings to show the uniqueness of a common fixed point for a generalized contraction in the said space. In addition, we present a supportive application of nonlinear integral equations for the validation of our work. The concept presented in this paper will play an important role in the theory of fixed points in the context of generalized metric spaces with applications.

This paper concerns the universality of the two-layer neural network with the k-rectified linear unit activation function with k=1,2,… with a suitable norm without any restriction on the shape of the domain in the real line. This type of result is called global universality, which extends the previous result for k=1 by the present authors. This paper covers k-sigmoidal functions as an application of the fundamental result on k-rectified linear unit functions.

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]

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]

In this paper, we consider a portfolio optimization problem where the wealth consists of investing into a risky asset with a slow mean-reverting volatility and receiving an uncontrollable stochastic cash flow under the exponential utility. The Hamilton–Jacobi–Bellman equation formulated from the optimal investment problem is a high-dimensional nonlinear partial differential equation and difficult to find its analytical or numerical solutions. The paper provides a tractable asymptotic approach which treats the initial problem as a perturbation around the constant volatility problem. In this paper, we present a formal derivation of asymptotic approximation and prove the accuracy of the value function. Moreover, an illustrative example is provided to assess our approximate strategy and value function.

This paper proposes an improved whale optimization algorithm with chaotic mapping and adaptive iteration strategy (CMAIS-WOA). This algorithm addresses the issues of the WOA algorithm that is prone to local optimal solutions with low stability. CMAIS-WOA utilizes chaotic mapping to enhance the diversity and coverage of the initial population. Also, it adaptively adjusts the weight values based on the current distribution of whale populations and the fitness of search agents. In addition, CMAIS-WOA uses an improved nonlinear convergence factor to adjust the breadth-first and depth-first search during the optimization process. The performance of the proposed CMAIS-WOA is evaluated by using 13 classical benchmark functions and IEEE CEC2014 test suite. The experimental results show that CMAIS-WOA effectively improves the stability of the optimal solution and helps the algorithm to approach the global optimal solution. The method proposed in this paper contributes to the field of optimization which solves problems more powerfully and efficiently.

In this paper, we are dealing with the ill-posed Cauchy problem for an elliptic operator. This is a follow-up to a previous paper on the same subject. Indeed, in an earlier publication, we introduced a regularization method, called the controllability method, which allowed us to propose, on the one hand, a characterization of the existence of a regular solution to the ill-posed Cauchy problem. On the other hand, we have also succeeded in proposing, via a strong singular optimality system, a characterization of the optimal solution to the considered control problem, and this, without resorting to the Slater-type assumption, an assumption to which many analyses had to resort. On occasion, we have dealt with the control problem, with state boundary observation, the problem initially analyzed by J. L. Lions. The proposed point of view, consisting of the interpretation of the Cauchy system as a system of two inverse problems, then called naturally for conjectures in favor of which the present manuscript wants to constitute an argument. Indeed, we conjectured, in view of the first results obtained, that the proposed method could be improved from the point of view of the initial interpretation that we had made of the problem. In this sense, we analyze here two other variants (observation of the flow, then distributed observation) of the problem, the results of which confirm the intuition announced in the previous publication mentioned above. Those results, it seems to us, are of significant relevance in the analysis of the controllability method previously introduced.

Innovation ecosystem management is now a new paradigm in innovation management research. Innovation ecosystems are dynamic innovation alliances based on noncontractual governance. In this paper, a traditional cooperative innovation game model and a cooperative innovation game model with noncontractual mechanism are developed and compared. The results show that the cooperation formed only by contractual mechanisms’ model is unstable and the system is likely to collapse. The noncontractual mechanism can be used as a supplement to the contractual mechanism to make the game develop towards a stable “cooperation-cooperation” state. The research conclusion of this paper will make the core companies in the innovation ecosystem realize the important role of noncontractual mechanism and help them make decisions.

The algebra of split quaternions is a recently increasing topic in the study of theory and numerical computation in split quaternionic mechanics. This paper, by means of a real representation of a split quaternion matrix, studies the problem of canonical forms of a split quaternion matrix and derives algebraic techniques for finding the canonical forms of a split quaternion matrix. This paper also gives two applications for the right eigenvalue and diagonalization in split quaternionic mechanics.

Low energy consumption and green transformation of automobile product portfolio is the trend of the times. Automotive manufacturers make product portfolio decisions by setting multiple criteria such as fuel consumption, sales, and volume. It is also important to take into account the symbiotic interaction effects between automotive products. In order to achieve the above research objectives, this paper constructs the Lotka–Volterra MCGP model to make multicriteria decisions on automobile product portfolio design from the perspective of energy sustainability with BMW Brilliance is taken as an example to illustrate the process of using the multicriteria model. The empirical analysis successively measures product growth using the logistic model, analyzes the symbiotic relationship of product portfolios using the Lotka–Volterra model, and finally performs multicriteria evaluation using the MCGP model. In order to verify the reliability of the model, this paper verifies the robustness of the model from the perspectives of parameter dynamics, system boundaries, and model scalability. The results of empirical analysis and robustness analysis show that the Lotka–Volterra MCGP model proposed in this paper is applicable to the multicriteria decision-making of automobile product portfolio design from the perspective of energy sustainability.

In the operation of service-sharing platforms, online review information is crucial to attracting consumers. Considering consumers’ preference for online review information, this paper discusses the pricing policy selection for a service-sharing platform providing vertically differentiated services in sharing economy, which is worth studying. In this paper, a platform service supply chain composed of a high-quality service provider, a low-quality service provider, and a service-sharing platform is considered. For the two pricing policies of a platform: service provider pricing and platform pricing, the profit-maximizing models are constructed, and the optimal high-quality and the low-quality service prices are obtained. This paper also analyzes the effects of online review information on the profits of service providers, platform profits, consumer surplus, and social welfare under the two policies. The results show that under the platform pricing policy, the platform can gain more profits, while the surplus of consumers and service providers may decrease. When the online review information exceeds a threshold, the high-quality service provider profit under the service provider pricing policy is larger than that under the platform pricing policy. Under the platform pricing policy, the low-quality service provider can earn more profit. We also find that the low-quality service provider is more motivated to encourage consumers to provide online reviews regardless of the pricing policy.