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With the development of computer operation technology and algorithms, the lumped dynamic model is more practical, and the development and application are more comprehensive. Among them, the direct coal liquefaction residual oil pyrolysis and coking technology, as a coal-to-liquid process, can increase the oil yield of the coal liquefaction process and reduce environmental pollution. The purpose of this paper is to study the experiment and algorithm of coal direct liquefaction residual oil pyrolysis and coking technology based on lumped kinetic engineering. Starting from the lumped kinetic engineering, this paper takes the direct coal liquefaction residual oil pyrolysis and coking technology as the research object. Based on the experiment of small- and medium-sized equipment, the residual oil pyrolysis and coking experiment is carried out. This paper further analyzes the components of the experimental products and explores the factors that affect the yield of residual pyrolysis oil based on the five lumped kinetic model of coking. Experimental data shows that when the pyrolysis temperature is 450°C, the content of liquefied heavy oil HS in the pyrolysis oil is 47.87%, the content of asphaltene A is 44.28%, and the content of preasphaltene PA is 7.85%; the pyrolysis temperature is 500 °C. At this time, the content of liquefied heavy oil HS in the pyrolysis oil is 54.97%, the content of asphaltene A is 40.23%, and the content of preasphaltene PA is 4.8%. It can be seen that, with the increase of pyrolysis temperature, the content of liquefied heavy oil HS increases, and the content of asphaltene A and preasphaltene PA decreases.

In this paper, we consider a natural convection flow of an incompressible viscous fluid subject to Newtonian heating and constant mass diffusion. The proposed model has been described by the Caputo fractional operator. The used derivative is compatible with physical initial and boundaries conditions. The exact analytical solutions of the proposed model have been provided using the Laplace transform method. The obtained solutions are expressed using some special functions as the Gaussian error function, Mittag–Leffler function, Wright function, and G -function. The influences of the order of the fractional operator, parameters used in modeling the considered fluid, Nusselt number, and Sherwood number have been analyzed and discussed. The physical interpretations of the influences of the parameters of our fluid model have been presented and analyzed as well. We use the graphical representations of the exact solutions of the model to support the findings of the paper.

Game theory has become an important tool to study the competition between oligopolistic enterprises. After combing the existing literature, it is found that there is no research combining two-stage game and nonlinear dynamics to analyze the competition between enterprises for advertising. Therefore, this paper establishes a two-stage game model to discuss the effect of the degree of firms’ advertising input on their profits. And the complexity of the system is analyzed using nonlinear dynamics. This paper analyzes and studies the dynamic game for two types of application network models: data transmission model and transportation network model. Under the time-gap ALOHA protocol, the noncooperative behavior of the insiders in the dynamic data transmission stochastic game is examined as well as the cooperative behavior. In this paper, the existence of Nash equilibrium and its solution algorithm are proved in the noncooperative case, and the “subgame consistency” of the cooperative solution (Shapley value) is discussed in the cooperative case, and the cooperative solution satisfying the subgame consistency is obtained by constructing the “allocation compensation procedure.” The cooperative solution is obtained by constructing the “allocation compensation procedure” to satisfy the subgame consistency. In this paper, we propose to classify the packets transmitted by the source nodes, and by changing the strategy of the source nodes at the states with different kinds of packets, we find that the equilibrium payment of the insider increases in the noncooperative game with the addition of the “wait” strategy. In the transportation dynamic network model, the problem of passenger flow distribution and the selection of service parameters of transportation companies are also studied, and a two-stage game theoretical model is proposed to solve the equilibrium price and optimal parameters under Wardrop’s criterion.

In economic growth, the gradual increase in the effect of information technology makes the enterprise economic information management increasingly important for the survival and development of the enterprises. This paper designs an enterprise economic information management system for the complex internal economic information management business and process of enterprises. It provides daily office, information access, document preview, and transmission. The proposed design (i) copes with the inconsistency and irregularity of enterprise economic information data, (ii) quickly obtains valuable information from these massive high-frequency data, and (iii) improves the economic benefits of data assets and data management efficiency. The printing function systematizes the information management for departments such as enterprise economic information, personnel, and production. The main focus of this research includes the mode, framework, and function of the whole system software. Moreover, it also comprises of the use of Internet platform big data technology to realize the practicality, stability, and security of the system database algorithm, which has been practically used by enterprises to improve office efficiency and meet the needs of daily management of enterprises. Based on the analysis of the current status of enterprise big data application, this paper constructs an enterprise economic informational management system based on big data and also describes in detail the key technologies of enterprise economic informational data management from three aspects: NoSQL-based big data storage management, Hadoop-based economic informational big data informational and economic informational big data analysis, and mining algorithm. Provide theoretical basis and basic technical support for online decision analysis.

The rapid development of artificial intelligence brings new development opportunities and challenges to English teaching university. This paper explores the concept of “smart education” and the path of building an ecological information-based teaching model of English college by interpreting the concepts of artificial intelligence, deep learning, ecological linguistics, and language education. Artificial intelligence, especially deep learning, will be promising in many aspects, such as the analysis of individual differences of language learners, customized learning content, diversified and three-dimensional teaching media, the role of teachers as smart classroom designers, and multidimensional and dynamic formative assessments. By relying on the data mining technology of deep learning to analyze learners’ characteristics, the smart classroom design, the promotion of language learners’ independent learning, and the establishment of dynamic and complete learner profiles, the language learning process is no longer a linear process but an evolving open loop, ultimately forming a harmonious development of various ecological niches in the language learning process. In this paper, we study and design a deep learning-based English informatics teaching system to develop a deep learning-based scoring prediction model. The model incorporates deep learning models based on word embedding and text convolutional networks, which can uncover the hidden interest features of academics for English. The experimental research results prove that the online e-learning service platform cannot only effectively meet the diverse and personalized English learning needs of university students, but also improve the learning efficiency of teachers and students.

The compatibility law of prescriptions is the core link of TCM theory of “theory, method, prescription and medicine,” which is of great significance for guiding clinical practice, new drug development and revealing the scientific connotation of TCM theory, and is also one of the hot spots and difficulties of TCM modernization research. How to efficiently analyze the frequency of drug use, core combination, and association rules between drugs in prescription is a basic core problem in the study of prescription compatibility law. In this paper, a systematic study was made on the compatibility rules of traditional Chinese antiviral classical prescriptions and the mechanism of traditional Chinese medicine molecules. FP-growth algorithm was used to analyze association rules of 961 classical prescriptions collected and to explore the compatibility rules of traditional Chinese antiviral classical prescriptions. In terms of compatibility law of traditional Chinese antiviral prescriptions, this paper studied the compatibility law of traditional Chinese antiviral prescriptions based on the FP-growth algorithm and made exploratory research on the compatibility law information of 961 traditional classical antiviral prescriptions. Firstly, FP tree was constructed based on the classic recipe data set. Then, frequent item set rules were established, and association rules contained in FP tree were extracted. Finally, the frequency and association rules of antiviral TCM prescriptions were analyzed according to dosage forms (decoction, pill, paste, and ingot). The results show that the FP-growth algorithm adopted in this paper has excellent algorithm performance and strong generalization and robustness in the screening and mining of large-scale prescription data sets, which can provide important processing tools and technical methods for the study of the compatibility rule of traditional Chinese medicine prescriptions.

This paper uses the partial least squares method to construct the investor sentiment index in Chinese stock market. The Shanghai Stock Exchange 180 Index and the Shenzhen Stock Exchange 100 Index are used as samples. From the perspectives of holistic sentiment and heterogeneous sentiment, this paper studies the impact of investor sentiment on stock price crash risk. The results show that investor sentiment can significantly affect stock price crash risk in Shanghai and Shenzhen A-share markets, especially in the Shenzhen A-share market no matter from which perspective. And investor pessimism has a greater impact on stock price crash risk in the Shenzhen A-share market from the perspective of heterogeneous sentiment. Compared with the available researches, this paper makes two contributions: (i) the comparative analysis is adopted to discuss the differences between Shanghai and Shenzhen A-share markets, abandoning the research approach that takes the two markets as a whole in existing literature, and (ii) this paper not only studies the impact of investor holistic sentiment on stock price crash risk from a macro perspective, but also adds a more micro heterogeneous sentiment and conducts a comparative analysis.

In the process of global digital trade rules negotiation, game and cooperation coexist, and all parties are actively seeking cooperative relationship while negotiating game. Against this background, this paper provides a comprehensive overview of the negotiation process of global digital trade rules and analyzes the core issues of the negotiations and their implied political game. This paper firstly compares the core issues of global digital trade rules negotiations at multilateral and regional levels and quantitatively reflects the weighting relationship between core issues and keywords by means of a dynamic thematic model. In order to judge the potential partnership of each country, this paper constructs a theoretical model of partner selection for global digital trade rules negotiation from the perspective of political game and uses the data of 62 major digital trade countries for empirical testing. Compared with traditional trade agreements, the consensus reached in digital trade negotiations is less influenced by traditional economic geography factors and more influenced by the level of digital trade restrictions and political distance. When signing digital trade terms, a country tends to choose countries with similar levels of digital trade restrictions and high political similarity as partners. Financial restrictions and trade restrictions are the most important digital trade restriction factors that countries pay attention to when negotiating, and political stability is the most important political factor that countries pay attention to when negotiating. Compared with developed countries, developing countries pay more attention to market size, cultural differences, and digital infrastructure when negotiating. The formulation of global digital trade rules may follow a reconstructive path from bilateral to regional to multilateral, promoting regional digital trade rule systems at this stage and gradually expanding the scope of negotiations to the multilateral level.

All graphs under consideration are finite, simple, connected, and undirected. Adjacency matrix of a graph G is 0,1 matrix A = a i j = 0 , i f v i = v j o r d v i , v j ≥ 2 1 , i f d v i , v j = 1. . Here in this paper, we discussed new type of adjacency matrix known by 1-2 adjacency matrix defined as A 1,2 G = a i j = 0 , i f v i = v j o r d v i , v j ≥ 3 1 , i f d v i , v j = 2 , from eigenvalues of the graph, we mean eigenvalues of the 1-2 adjacency matrix. Let T n c be the set of the complement of trees of order n . In this paper, we characterized a unique graph whose least eigenvalue is minimal among all the graphs in T n c .

Based on the existing grey prediction model, this paper proposes a new grey prediction model (the fractional discrete grey model, FDGM (1, 1, t α )), introduces the modeling mechanism and characteristics of the FDGM (1, 1, t α ), and uses three groups of data to verify its effectiveness compared with that of other grey models. This paper forecasts the building energy consumption in China over the next five years based on the idea of metabolism. The results show that the FDGM (1, 1, t α ) can be transformed into other grey models through parameter setting changes, so the new model has strong adaptability. The FDGM (1, 1, t α ) is more reliable and effective than the other six compared grey models. From 2018 to 2022, the total energy consumption levels of civil buildings, urban civil buildings, and civil buildings specifically in Beijing will exhibit steady upward trends, with an average annual growth rate of 2.61%, 1.92%, and 0.78%, respectively.

The ℱ -coindex (forgotten topological coindex) for a simple connected graph G is defined as the sum of the terms ζ G 2 y + ζ G 2 x over all nonadjacent vertex pairs x , y of G , where ζ G y and ζ G x are the degrees of the vertices y and x in G , respectively. The ℱ -index of a graph is defined as the sum of cubes of the vertex degrees of the graph. This was introduced in 1972 in the same paper where the first and second Zagreb indices were introduced to study the structure dependency of total π -electron energy. Therefore, considering the importance of the ℱ -index and ℱ -coindex, in this paper, we study these indices, and we present new bounds for the ℱ -index and ℱ -coindex.

The existing Z -test for correlated proportions under classical statistics is applied when observations in the data are exact and precise. In the current paper, Z -test for correlated proportions is proposed to deal with the data having indeterminate observations. The statistic of Z -test for correlated proportions under neutrosophy is introduced in the paper. The testing procedure of the proposed test is given. The application of the proposed test is given using the price of oil data. From the application, it is clear that the proposed test outperforms the existing Z -test for correlated proportions under classical statistics in terms of flexibility, adequacy, and information. The simulation study also shows the effect of indeterminacy on the statistic of the proposed test.

The purpose of this paper is to introduce the notation of single-valued neutrosophic hyper BCK-subalgebras and a novel concept of neutro hyper BCK-algebras as a generalization and alternative of hyper BCK-algebras, that have a larger applicable field. In order to realize the article’s goals, we construct single-valued neutrosophic hyper BCK-subalgebras and neutro hyper BCK-algebras on a given nonempty set. The result of the research is the generalization of single-valued neutrosophic BCK-subalgebras and neutro BCK-algebras to single-valued neutrosophic hyper BCK-subalgebras and neutro hyper BCK-algebras, respectively. Also, some results are obtained between extended (extendable) single-valued neutrosophic BCK-subalgebras and single-valued neutrosophic hyper BCK-subalgebras via fundamental relation. The paper includes implications for the development of single-valued neutrosophic BCK-subalgebras and neutro BCK-algebras and for modelling the uncertainty problems by single-valued neutrosophic hyper BCK-subalgebras and neutro hyper BCK-algebras. The new conception of single-valued neutrosophic hyper BCK-subalgebras and neutro hyper BCK-algebras was given for the first time in this paper. We find a method that can apply these concepts in some complex networks.

In today's global competition environment with rapid changes in market and technology, it is more and more difficult for enterprises to fully grasp the latest knowledge and learn all the technologies by relying on their own strength. It is particularly important for enterprises to establish a network relationship of a certain intensity with other external entities (upstream and downstream enterprises, peer enterprises, scientific research institutions, government departments, financial institutions, and other organizations) for their technological learning and improvement of technological innovation performance. From different perspectives, the academic circles have confirmed that the strength of network relationship does have an impact on the technological innovation performance of enterprises. This paper will explore the measurement scale of technology learning cost, and from the basic perspective of technology learning cost, deeply explore and analyze how enterprise technology innovation performance is affected by the strength of enterprise network relationship. This paper argues that the strength of network relationship can affect the cost of technology learning and therefore the performance of technology innovation. The main contents of this study include the following. (1) Through the collation and review of the related theories of network relationship strength, technological learning cost and technological innovation performance, and the existing research results, the theoretical model of this study is established, and the theoretical assumptions of this study are put forward. (2) A presurvey is carried out first, and the data collected from the presurvey are used to test the reliability and validity of the scale of this study, and the appropriate measurement scales for the strength of network relationship, technology learning cost, and technology innovation performance are determined. (3) Adopt the method of regression analysis combined with the SME method, to verify this paper builds the theoretical model, and further clarify the network relation intensity, technology acquisition cost, and cost of technological learning all dimensions and performance of technological innovation and network strength, technological learning mechanism between cost, and performance of technological innovation.

Based on information asymmetry theory, principal-agent theory, and risk management theory, this paper analyzes the mechanism of the impact of big data on financial decision-making, analyzing four dimensions: how big data enhances the information base for forecasting, how big data improves the relevance of decision-making, how big data builds new competitive advantages, and how big data promotes dynamic decision-making. Secondly, through the analysis of specific implementation cases of enterprise big data in financial decision-making, we focus on the real problems faced in management and the effect of solving problems through big data platform. The enterprise realizing the integration of business and finance not only can better lead business expansion, but also can improve the management level within the enterprise, which is conducive to the improvement of core competitiveness. The integration of industry and finance is essentially achieved through the application of various financial management modules to the business operations of enterprises, including budget management, capital management, fixed asset management, and financial accounting. If we want to implement the whole process of financial integration, it is impossible to achieve this manually, and we must first build a powerful information system as a guarantee. Under the guidance of theories of information asymmetry, stakeholders, and management information systems, Internet finance enterprises should build their own integrated business finance system based on the demand for business finance integration in the Internet finance industry, to enhance the matching of business finance data of Internet finance enterprises, improve the efficiency of enterprise management, and realize business finance integration. Finally, through the research of this paper, we hope to provide reference for other similar enterprises to apply big data for financial decision-making. Through the application of big data, higher economic benefits are achieved in procurement management, production control, capital budget, and investment decision compared with the previous ones. It is concluded that in the era of big data, massive data can be used to serve enterprise decision-making in depth, which can break the business and financial barriers, improve the efficiency and quality of decision-making, optimize the organizational structure and personnel, and enhance the prediction and early warning capability. The application of big data tools has become the key to assisting financial decision-making and enhancing enterprise value.

The relationship between financial system and economic development is not a simple linear relationship. In some cases, the development of finance may not improve the economic development level. This paper studies the influence of the financial system on the high-quality economic development, constructs the comprehensive index of the financial system by the factor analysis method, and calculates the green total factor productivity as the index of high-quality economic development by the CRS multiplier model. Empirically, this paper takes the panel data of 30 provinces, municipalities, and autonomous regions in China from 2005 to 2018 as samples, constructs the panel threshold model, and applies the financial system, economic development level, infrastructure, and industrial structure as threshold variables to study the nonlinear relationship between the financial system and high-quality economic development. The results demonstrate that the impact of the financial system on the high-quality economy presents an inverted U-shaped relationship when the financial system and industrial structure are the threshold variables, indicating that there is an optimal interval, that is, when the financial system threshold is between 0.1355 and 0.1377 and the industrial structure threshold is between 0.1364 and 0.1408, the financial system plays a greater role in the allocation of funds and has the most obvious positive impact on high-quality economic development. Meanwhile, the impact of the financial system on the high-quality shows a marginal decreasing trend when the economic development level and infrastructure are the threshold variables; when the economic development threshold is less than 0.1409 and the basic setting threshold is less than 0.1167, the financial system has the greatest effect on promoting high-quality economic development. Based on the research results, targeted policy suggestions are put forward.

The study of accounting profitability was initiated by the famous American scholars Ball and Brown in the 1960s. In recent years, with the continuous development of market economy, the continuous improvement of the accounting legal system and accounting standards for enterprises has promoted the research on accounting profit in capital market in China. Due to the restriction of some objective conditions, there are not many valuable research results on the relationship between accounting earnings and stock price changes, and the research methods suitable for the study of accounting earnings still need to be explored and summarized. The China Securities Regulatory Commission (CSRC) has required listed companies to publish quarterly financial and accounting reports since 2002, and the condition of using the regression analysis method to study the accounting profit of listed companies is available. In this context, this paper designs a vector autoregressive model to study the correlation between stock price and accounting profit. First, combining the literature and the research results of accounting profit at home and abroad, this paper expounds the statistical analysis of accounting profit. Then, this paper analyzes the accounting profitability of listed companies in China from static and dynamic perspectives. Finally, according to the accounting profit status and profitability statistical analysis of accounting information, accounting profit and growth relationship, and accounting profit information and the relationship between stock prices, this paper is concluded. Also, this paper shows how to improve the profitability of listed companies and how can investors effectively use the accounting earnings information of listed companies for stock investment and put forward corresponding policy suggestions.

Fuzzy mathematics has been used more and more extensively and deeply in various fields since its emergence, and it has been more and more recognized. However, there is less research on fuzzy mathematics in the field of economic management. This paper attempts to introduce fuzzy theories and methods into economic management. On the premise of introducing fuzzy decision-making theories and methods, several fuzzy theories and methods that are commonly used in economic management are given. The fuzzy correlation method of economic phenomena is proposed, and the method is used to study the correlation between economic phenomena. Besides, this paper also uses fuzzy methods to analyze the relationship between economic phenomena—fuzzy relevance, and uses fuzzy two-way decision-making methods to carry out economic management and decision-making so that the decision-making results are more reasonable, scientific, and operability. In addition, this paper rationally explains the phenomena and laws existing in economic activities from a fuzzy perspective and gives models for fuzzy inference, diagnosis, and production decision-making, which have important meaning and profound theoretical value and practical value.

The Jordan–Hölder theorem is proved by using Zassenhaus lemma which is a generalization of the Second Isomorphism Theorem for groups. Goursat’s lemma is a generalization of Zassenhaus lemma, it is an algebraic theorem for characterizing subgroups of the direct product of two groups G 1 × G 2 , and it involves isomorphisms between quotient groups of subgroups of G 1 and G 2 . In this paper, we first extend Goursat’s lemma to R -algebras, i.e., give the version of Goursat’s lemma for algebras, and then generalize Zassenhaus lemma to rings, R -modules, and R -algebras by using the corresponding Goursat’s lemma, i.e., give the versions of Zassenhaus lemma for rings, R -modules, and R -algebras, respectively.

Based on the theory of atmospheric refraction, combined with the atmospheric parameter data of NCEP (National Centers for environmental prediction), the Fourier interpolation fitting algorithm is used to model and analyze the parameters affecting atmospheric refraction on a global scale. The atmospheric temperature and density model with space-time variation is constructed. The spacecraft state equation and the measurement equation with the starlight apparent height as the observation quantity are established. Moreover, the Unscented Kalman filter is applied to the indirect sensitive horizon autonomous astronomical navigation of starlight refraction. The relative error of fitting the measured data with the spatiotemporal atmospheric temperature model established in this paper is less than 2%. The position estimation error of the navigation system is 94 m, and the velocity estimation error is 0.16 m/s. Compared with the traditional model, the navigation and positioning considering complex atmospheric changes are more accurate.

In this paper, we study the notion of approximate biprojectivity and left φ -biprojectivity of some Banach algebras, where φ is a character. Indeed, we show that approximate biprojectivity of the hypergroup algebra L 1 K implies that K is compact. Moreover, we investigate left φ -biprojectivity of certain hypergroup algebras, namely, abstract Segal algebras. As a main result, we conclude that (with some mild conditions) the abstract Segal algebra B is left φ -biprojective if and only if K is compact, where K is a hypergroup. We also study the approximate biflatness and left φ -biflatness of hypergroup algebras in terms of amenability of their related hypergroups.

In this paper, we study algebraic properties of lattice points of the arc on the conics x 2 − d y 2 = N especially for d = 1 , which is the Fermat factorization equation that is the main idea of many important factorization methods like the quadratic field sieve, using arithmetical results of a particular hyperbola parametrization. As a result, we present a generalization of the forms, the cardinal, and the distribution of its lattice points over the integers. In particular, we prove that if N − 6 ≡ 0 mod 4 , Fermat’s method fails. Otherwise, in terms of cardinality, it has, respectively, 4, 8, 2 α + 1 , 1 − δ 2 p i 2 n + 1 , and 2 ∏ i = 1 n α i + 1 lattice pointts if N is an odd prime, N = N a × N b with N a and N b being odd primes, N = N a α with N a being prime, N = ∏ i = 1 n p i with p i being distinct primes, and N = ∏ i = 1 n N i α i with N i being odd primes. These results are important since they provide further arithmetical understanding and information on the integer solutions revealing factors of N . These results could be particularly investigated for the purpose of improving the underlying integer factorization methods.

Fuzzy linear programming has a wide range of applications in agricultural economic management. In this paper, the mathematical model of fuzzy linear programming was studied in detail, and then under the restriction of elastic constraints, the f(ti) and g (t0) function expressions and their optimal solutions were obtained. Subsequently, the fuzzy linear programming was applied to the agricultural economic management of the five urban areas of Zhengzhou, and its applicability was studied. The results showed that the f(ti) and g (t0) function expressions obtained by different stretch degrees were not the same, and both had a unique optimal solution. In addition, the mathematical model based on fuzzy linear programming could well predict the pull force in agricultural economic management, so as to provide theoretical support for the application of fuzzy linear programming.

With the frequent occurrence of emergency events, decision-making (DM) plays an increasingly significant role in coping with them and has become an important and the challenging research focus recently. It is critical for decision makers to make accurate and reasonable emergency judgments in a short period as poor decisions can result in enormous economic losses and an unstable social order. As a consequence, this work offers a new DM approach based on novel distance and similarity measures using q-rung linear Diophantine fuzzy (q-RLDF) information to assure that DM problems may be addressed successfully and fast. One of the useful methods for determining the degree of similarity between the objects is the similarity measure. In this paper, we propose some new q-rung linear Diophantine fuzzy (q-ROLDF) distances and similarity measures. The Jaccard similarity measure, exponential similarity measure, and cosine and cotangent function-based similarity measures are proposed for q-LDFSs. The defined similarity measures are applied to the logistics and supply chain management problem, and the results are discussed. A comparison of new similarity measures is developed, and the proposed work’s advantages are discussed.

The tourism industry is contributing to the rise in the national economy because of its outstanding advantages in increasing employment and winning regional economic vitality. But, there is no study to systematically evaluate the performance of China’s tourism economy. Therefore, this paper adopts a multilevel gray model and scientifically constructs a tourism economic performance evaluation index system. It is found that China’s tourism economic performance has the advantages of excellent development infrastructure conditions and abundant tourism resources but still has deficiencies in the aspects of social environment support, international market demand, and tourism environment support. The sustainable development potential of China’s tourism industry needs to be strengthened in three aspects in the future, namely, strengthening the government’s macroguidance, expanding the tourism high-quality talent pool, and enhancing the construction of tourism infrastructure and service facilities.

The first general Zagreb index M γ G or zeroth-order general Randić index of a graph G is defined as M γ G = ∑ v ∈ V d v γ where γ is any nonzero real number, d v is the degree of the vertex v and γ = 2 gives the classical first Zagreb index. The researchers investigated some sharp upper and lower bounds on zeroth-order general Randić index (for γ < 0 ) in terms of connectivity, minimum degree, and independent number. In this paper, we put sharp upper bounds on the first general Zagreb index in terms of independent number, minimum degree, and connectivity for γ . Furthermore, extremal graphs are also investigated which attained the upper bounds.

A proper cluster is usually defined as maximally coherent groups from a set of objects using pairwise or more complicated similarities. In general hypergraphs, clustering problem refers to extraction of subhypergraphs with a higher internal density, for instance, maximal cliques in hypergraphs. The determination of clustering structure within hypergraphs is a significant problem in the area of data mining. Various works of detecting clusters on graphs and uniform hypergraphs have been published in the past decades. Recently, it has been shown that the maximum 1,2 -clique size in 1,2 -hypergraphs is related to the global maxima of a certain quadratic program based on the structure of the given nonuniform hypergraphs. In this paper, we first extend this result to relate strict local maxima of this program to certain maximal cliques including 2-cliques or 1,2 -cliques. We also explore the connection between edge-weighted clusters and strictly local optimum solutions of a class of polynomials resulting from nonuniform 1,2 -hypergraphs.

Aiming at the problems of low image data retrieval accuracy and slow retrieval speed in the existing image database retrieval algorithms, this paper designs a clothing image database retrieval algorithm based on wavelet transform. Firstly, it represents the color consistency vector of clothing image, reflects the composition and distribution of image color through color histogram, quantifies the visual features of clothing image, aggregates them into a fixed size representation vector, and uses the Fair Value (FV) model to complete the collection of clothing image data. Then, the size of the clothing image is adjusted by using the size transformation technology, and the clothing pattern is divided into four moments with the same size. On this basis, the clothing image is discretized with the help of Hu invariant moment to complete the preprocessing of clothing image data. Finally, the generating function of wavelet transform is determined, and a cluster of functions is obtained through translation and expansion. The wavelet filter is decomposed into basic modules, and then, the wavelet transform is studied step by step. The clothing image data are regarded as a signal, split, predicted, and updated and input into the wavelet model, and the retrieval research of clothing image database is completed. The experimental results show that the design of the retrieval algorithm is reasonable, the retrieval data accuracy is high, and the retrieval speed is fast.

In today’s society, calligraphy, which reflects one’s basic writing skills, is becoming more and more important to people. People are influenced by calligraphy in their studies, work, etc. Improving calligraphy writing skills has become one of the key directions for developing one’s abilities at this stage. As an important means of improving writing skills, calligraphy practice products are attracting more and more attention and purchases. In particular, in recent years, as the market economy has developed in a deeper direction, people’s demand for calligraphy practice products has diversified and calligraphy practice product companies have launched a variety of products to meet the public’s calligraphy practice needs in order to adapt to the reality of consumer demand. However, with the development of the Internet culture industry and influenced by objective factors such as school holidays and seasons, the current market demand for calligraphy practice products is rapidly and dynamically changing, making market changes difficult to grasp and leading to poor sales, which directly affects the profits of calligraphy practice product-related companies. The artificial intelligence neural network method realizes the nonlinear relationship between the input and output of sample data through the self-learning ability of each neuron and has a certain nonlinear mapping ability in prediction, which plays a great role in the market demand prediction of many commercial products. Based on this, this paper proposes a recursive neural network-based algorithm to predict the future demand and development trend of calligraphy practice products through extensive and in-depth research, so as to provide positive and beneficial guidance for enterprises’ future production and sales.

This paper studies the location-routing problem of emergency facilities with time window under demand uncertainty. We propose a robust mathematical model in which uncertain requirements are represented by two forms: the support set defined by cardinal constraint set. When the demand value of rescue point changes in a given definition set, the model can ensure the feasibility of each line. We propose a branch and price cutting algorithm, whose pricing problem is a robust resource-constrained shortest path problem. In addition, we take the Wenchuan Earthquake as an example to verify the practicability of the method. The robust model is simulated under different uncertainty levels and distributions and compared with the scheme obtained by the deterministic problem. The results show that the robust model can run successfully and maintain its robustness, and the robust model provides better protection against demand uncertainty. In addition, we find that cost is more sensitive to uncertainty level than protection level, and our proposed model also allows controlling the robustness level of the solution by adjusting the protection level. In all experiments, the cost of robustness is that the routing cost increases by an average of 13.87%.

As the mixed education model gradually becomes widespread in various universities in Japan, the evaluation of the quality of IT English mixed education has become a very important issue, and it is worth considering the corresponding evaluation method. In this paper, we use a data mining algorithm to implement an evaluation method for the interconversion of quantitative data and qualitative concepts and use the IT English mixed teaching model to evaluate and analyze the teaching quality of the course. The evaluation method is feasible and provides a mixing method. Evaluation of the quality of education. Reference method.

A modular irregular graph is a graph that admits a modular irregular labeling. A modular irregular labeling of a graph G of order n is a mapping of the set of edges of the graph to 1,2 , … , k such that the weights of all vertices are different. The vertex weight is the sum of its incident edge labels, and all vertex weights are calculated with the sum modulo n . The modular irregularity strength is the minimum largest edge label such that a modular irregular labeling can be done. In this paper, we construct a modular irregular labeling of two classes of graphs that are biregular; in this case, the regular double-star graph and friendship graph classes are chosen. Since the modular irregularity strength of the friendship graph also holds the minimal irregularity strength, then the labeling is also an irregular labeling with the same strength as the modular case.

The low-rank representation (LRR) method has recently gained enormous popularity due to its robust approach in solving the subspace segmentation problem, particularly those concerning corrupted data. In this paper, the recursive sample scaling low-rank representation (RSS-LRR) method is proposed. The advantage of RSS-LRR over traditional LRR is that a cosine scaling factor is further introduced, which imposes a penalty on each sample to minimize noise and outlier influence better. Specifically, the cosine scaling factor is a similarity measure learned to extract each sample’s relationship with the low-rank representation’s principal components in the feature space. In order words, the smaller the angle between an individual data sample and the low-rank representation’s principal components, the more likely it is that the data sample is clean. Thus, the proposed method can then effectively obtain a good low-rank representation influenced mainly by clean data. Several experiments are performed with varying levels of corruption on ORL, CMU PIE, COIL20, COIL100, and LFW in order to evaluate RSS-LRR’s effectiveness over state-of-the-art low-rank methods. The experimental results show that RSS-LRR consistently performs better than the compared methods in image clustering and classification tasks.

The physical and structural properties of molecular structure or graph such as boiling point, melting point, surface tension, or solubility are studied using topological index (TI). Topological index is a mathematical formula that can be applied to any graph which models some molecular structures. The various operations play an important role in graph theory such as joining, union, intersection, products, and subdivision. In this paper, we computed the bounds for general Randic coindex of F -sum graphs such as ( S -sum, R -sum, Q -sum, and T -sum) in the form of their factor graphs. At the end, results are illustrated by numerical table for the particular F -sum graphs.

The field of graph theory is broadly growing and playing a remarkable role in cheminformatics, mainly in chemistry and mathematics in developing different chemical structures and their physicochemical properties. Mathematical chemistry provides a platform to study these physicochemical properties with the help of topological indices (TIs). A topological index (TI) is a function that connects a numeric number to each molecular graph. Zagreb indices (ZIs) are the most studied TIs. In this paper, we establish general expressions to calculate the connection-based multiplicative ZIs, namely, first multiplicative ZIs, second multiplicative ZIs, third multiplicative ZIs, and fourth multiplicative ZIs, of two renowned dendrimer nanostars. The defined expressions just depend on the step of growth of these dendrimers. Moreover, we have compared our calculated for both type of dendrimers with each other.

A stable and holomorphic implementation of complex functions in ℂ plane making use of a unit circle-based transform is presented in this paper. In this method, any complex number or function can be represented as an infinite series sum of progressive products of a base complex unit and its conjugate only, where both are defined inside the unit circle. With each term in the infinite progression lying inside the unit circle, the sum ultimately converges to the complex function under consideration. Since infinitely large number of terms are present in the progression, the first element of which may be deemed as the base unit of the given complex number, it is addressed as complex baselet so that the complex number or function is termed as the complex baselet transform. Using this approach, various fundamental operations applied on the original complex number in ℂ are mapped to equivalent operations on the complex baselet inside the unit circle, and results are presented. This implementation has unique properties due to the fact that the constituent elements are all lying inside the unit circle. Out of numerous applications, two cases are presented: one of a stable implementation of an otherwise unstable system and the second case of functions not satisfying Cauchy–Riemann equations thereby not holomorphic in ℂ plane, which are made complex differentiable using the proposed transform-based implementation. Various lemmas and theorems related to this approach are also included with proofs.

This paper investigates the risk contribution of 29 industrial sectors to the China stock market by using one-factor with Durante generator copulas (FDG) and component expected shortfall (CES) analyses. Risk contagion between the systemically most important sector and other sectors is examined using a copula-based ∆CoVaR approach. The data cover the 2008 global financial crisis and the beginning of the COVID-19 pandemic. The empirical results show that the banking sector contributed most to systemic risk before and during the global financial crisis. Nonbank finance became equally important in 2020, and the COVID-19 pandemic promoted the position of the computer and pharmaceuticals sectors. The spillover effect diminishes over time, but there remains risk contagion between sectors. The risk spillover trend is consistent with that of systemic risk.

There are many reasons for escalator reversal failure, and the reasons are distributed in different locations. It is difficult to locate the specific location of the fault in the actual fault troubleshooting. At the same time, the information related to the failure is not used in the troubleshooting, so there is a problem of inefficient troubleshooting. To this end, this paper proposes a multiattribute decision-making method that integrates dynamic information and gives the optimal troubleshooting order to improve the efficiency of the troubleshooting. First of all, according to the structure of the escalator components, the escalator reversal fault tree is established. Secondly, a static decision matrix is established by comprehensively considering the failure probability, search cost, and influence degree of the bottom event of the fault tree. Finally, the influence matrix of information on each attribute is given by the dynamic information obtained in troubleshooting, the static decision fusion influence matrix determines the dynamic decision matrix, the dynamic decision matrix is weighted and normalized, and the Technique for Order Preference by Similarity to Ideal Solution is used to determine the optimal troubleshooting order. Taking the reversal failure of a certain type of escalators as an example, the method of multiattribute decision-making of fusion dynamic information is used to shorten the troubleshooting time, improve the efficiency of troubleshooting, and verify the effectiveness of this method.

In the field of subdivision, the smoothness increases as the arity of schemes increases. The family of high arity schemes gives high smoothness comparative to low arity schemes. In this paper, we propose a simple and generalized formula for a family of multiparameter quaternary subdivision schemes. The conditions for convergence of subdivision schemes are also presented. Moreover, we derive subdivision schemes after substituting the different values of parameters. We also analyzed the important properties of the proposed family of subdivision schemes. After comparison with existing schemes, we analyze that the proposed family of subdivision schemes gives better smoothness and approximation compared with the existing subdivision schemes.

The Jacobi–Davidson iteration method is very efficient in solving Hermitian eigenvalue problems. If the correction equation involved in the Jacobi–Davidson iteration is solved accurately, the simplified Jacobi–Davidson iteration is equivalent to the Rayleigh quotient iteration which achieves cubic convergence rate locally. When the involved linear system is solved by an iteration method, these two methods are also equivalent. In this paper, we present the convergence analysis of the simplified Jacobi–Davidson method and present the estimate of iteration numbers of the inner correction equation. Furthermore, based on the convergence factor, we can see how the accuracy of the inner iteration controls the outer iteration.

At this stage, broadening the consumer market, upgrading the consumption system and gradually establishing a consumption-led development concept are key factors in promoting high-quality economic development. At the same time, China's macro economy is also experiencing another test. The rapid development of China's real estate market in recent years has attracted a large number of investors, and real estate prices have produced irrational and substantial increases. Behind the boom of the real estate market is a social system crisis driven by profiteering and the growing seriousness of real estate financial bubble. So exploring the mechanism of the influence of real estate prices on the upgrading of residents' consumption is important for the current stage of China. Therefore, it is important to investigate the mechanism of real estate price impact on consumer upgrading for the coordinated development of real estate industry and national economy. In this paper, we analyze and examine the theory on the consumption improvement by the literature survey method. We also summarize the present research on the correlation and the influence mechanism of the real estate price and the consumption improvement and choose the index which reflects the present state of the real estate industry and the consumption of the inhabitant. Besides the input indicators that qualitatively manage the impact of housing prices on the improvement of residents' consumption, we first use the descriptive statistics method to understand the level of the Chinese real estate market and improve consumer spending. Based on this, the descriptive statistical method is applied to define the current state of China's real estate market and the level of improvement in consumption, and to define the standard for improving consumption in China. On the other hand, based on the spatial and spatial spillover points of view, we use spatial analysis framework combined with exploratory spatial data analysis and GIS to investigate spatial correlation between consumption structure and housing price, and accurately reflect the spatial clustering status of the index by drawing. Moran dispersion plot and Lisa cluster plot, then the spatial Darwinian model, are used to investigate the impact of real estate prices on the increase in occupant consumption from a macro perspective.

In this paper, the interest is in estimating the Weibull products when the available data is obtained via generalized progressive hybrid censoring. The testing scheme conducts products of interest under a more flexible way and allows collecting failure data in efficient and adaptable experimental scenarios than traditional lifetime testing. When the latent lifetime of products follows Weibull distribution, classical and Bayesian inferences are considered for unknown parameters. The existence and uniqueness of maximum likelihood estimates are established, and approximate confidence intervals are also constructed via asymptotic theory. Bayes point estimates as well as the credible intervals of the parameters are obtained, and correspondingly, Monte Carlo sampling technique is also provided for complex posterior computation. Extensive numerical analysis is carried out, and the results show that the generalized progressive hybrid censoring is an adaptive procedure in practical lifetime experiment, both proposed classical and Bayesian inferential approaches perform satisfactorily, and the Bayesian results are superior to conventional likelihood estimates.

The problem of increasing farmers’ income has been a hot issue of social concern. Understanding the farmers’ income and the overall development trend is conducive to the rational layout of the social economy and promotes the steady development of a well-off society. Based on this, the paper selects the per capita disposable income (PCDI) of farmers’ households from 2012 to 2019 in 11 cities of Hebei Province as the research object and applies the fractional grey model (FGM (1,1)) to predict farmers’ income from 2020 to 2024. The results show that the farmers’ income will increase in the next five years. However, the growth rate of farmers’ income is slow in the areas with a large base of farmers’ income and strong in the areas with a small base of farmers’ income. The area with the highest trend in the growth rate of farmers’ income is Zhangjiakou and the lowest place is Handan. Only Shijiazhuang’s income growth rate is on the rise. Finally, suggestions are given to promote farmers’ income in Hebei Province.

With the increasing load and speed of trains, the problems caused by various random excitations (such as safety and passenger comfort) have become more prominent and thus arises the necessity to analyze stochastic dynamical systems, which is important in both academic and engineering circles. The existing analysis methods are inadequate in terms of computational accuracy, computational efficiency, and applicability in solving complex problems. For that, a new efficient and accurate method is used in this paper, suitable for linear and nonlinear random vibration analysis of large structures as well as static and dynamic reliability assessment. It is the direct probability integration method, which is extended and applied to the random vibration reliability analysis of dynamical systems. Dynamical models of the dynamic system and coupled system “three-car vehicle-rail-bridge” are established, the time-varying differential equations of motion are derived in detail, and the dynamic response of the system is calculated using the explicit Newmark algorithm. The simulation results show the influence of the number of representative points on the smoothness of the image of the probability density function and the accuracy of the calculation results.

Many problems in real life exist that are full of confusion, vagueness, and ambiguity. The quantification of such issues in a scientific way is the need of time. The negative binomial distribution is an important discrete probability distribution from the account of classical probability distribution theory. The distribution was used to study the chance of kth success in n trials before n − 1 failures for crisp data. The literature lacks in dealing with the situations for interval-valued data under negative binomial distribution. In this research, the neutrosophic negative binomial distribution is proposed to generalize the classical negative binomial distribution. The generalized proposed distribution considers the indeterminacy and crisp form from interval-valued. Several properties of the proposed distribution, such as moment generating function, characteristic function, and probability generating function, are also derived. Furthermore, the derivation of reliability analysis properties such as survival, hazard rate, reversed hazard rate, cumulative hazard rate, mills ratio, and odds ratio are also presented. In addition, order statistics for the proposed distribution, including w th , joint, median, minimum, and maximum order statistics are part of the paper. The proposed distribution is discussed from the real data applications perspective by considering the different case studies. This research opens the way to deal with the problems that follow conventional conveyances and include nonprecisely determined details simultaneously.

Talents are the key of rural revitalization. Under the background of Beijing-Tianjin-Hebei Coordinated Development, Hebei Province has always put talent revitalization at the core of rural revitalization. In order to promote the process of rural revitalization in Hebei Province, it is very important to understand the scale of rural talents. Firstly, the GM (1,1) model was used to predict the scale of rural talents in Hebei Province from 2020 to 2025. The prediction results showed that, in the rural development of Hebei Province in the next few years, the scale of production-oriented talents would gradually decline, while the scale of service-oriented, business-oriented, management-oriented, and skilled talents would show varying degrees of growth. Secondly, the grey relational analysis was used to analyze the importance of different factors for rural talents. Through the grey relational analysis, it was found that the infrastructure had the greatest impact on production-oriented talents, the agricultural industrialization operating rate had the strongest impact on service-oriented talents, and the urban-rural income level had the greatest impact on business-oriented talents, management-oriented talents, and skilled talents. Finally, according to the results of the GM (1,1) model and grey relational analysis, aiming at different types of rural talents, this paper puts forward countermeasures and suggestions from the aspects of strengthening rural infrastructure construction, improving rural medical and health conditions and improving income distribution pattern.

Multigranulation rough set theory is an important tool to deal with the problem of multicriteria information system. The notion of fuzzy β -neighborhood has been used to construct some covering-based multigranulation fuzzy rough set (CMFRS) models through multigranulation fuzzy measure. But the β -neighborhood has not been used in these models, which can be seen as the bridge of fuzzy covering-based rough sets and covering-based rough sets. In this paper, the new concept of multigranulation fuzzy neighborhood measure and some types of covering-based multigranulation fuzzy rough set (CMFRS) models based on it are proposed. They can be seen as the further combination of fuzzy sets: covering-based rough sets and multigranulation rough sets. Moreover, they are used to solve the problem of multicriteria decision making. Firstly, the definition of multigranulation fuzzy neighborhood measure is given based on the concept of β -neighborhood. Moreover, four types of CMFRS models are constructed, as well as their characteristics and relationships. Then, novel matrix representations of them are investigated, which can satisfy the need of knowledge discovery from large-scale covering information systems. The matrix representations can be more easily implemented than set representations by computers. Finally, we apply them to manage the problem of multicriteria group decision making (MCGDM) and compare them with other methods.

In this paper, we proposed an improved family of estimators for finite population mean under stratified random sampling, which needed a helping variable on the sample mean and rank of the auxiliary variable. The expression of the bias and mean square error of the proposed and existing estimators are computed up to the first-order approximation. The estimators proposed in different situations were investigated and provided a minimum mean square error relative to all other estimators considered. Four actual data sets and simulation studies are carried out to observe the performance of the estimators. For simulation study, R software is used. The mean square errors of all four data sets are minimum and percent relative efficiencies are more than a hundred percent higher than the other existing estimators, which indicated the importance of the newly proposed family of estimators. From the simulation study, it is concluded that the suggested family of estimators achieved better results. We demonstrate theoretically and numerically that the proposed estimator produces efficient results compared to all other contend estimators in entire situations. Overall, we conclude that the performance of the family of suggested estimators is better than all existing estimators.

In this paper, the convergence to minimizers of a convex function of a modified proximal point algorithm involving a single-valued nonexpansive mapping and a multivalued nonexpansive mapping in CAT(0) spaces is studied and a numerical example is given to support our main results.

We introduce a new method for estimating the nonparametric regression curve for longitudinal data. This method combines two estimators: truncated spline and Fourier series. This estimation is completed by minimizing the penalized weighted least squares and weighted least squares. This paper also provides the properties of the new mixed estimator, which are biased and linear in the observations. The best model is selected using the smallest value of generalized cross-validation. The performance of the new method is demonstrated by a simulation study with a variety of time points. Then, the proposed approach is applied to a stroke patient dataset. The results show that simulated data and real data yield consistent findings.