This PDF file contains the front matter associated with SPIE Proceedings Volume 12725, including the Title Page, Copyright information, Table of Contents, and Conference Committee information.

In order to classify glass samples with known chemical composition, this paper adopts K-Means clustering analysis algorithm. By distinguishing the main element content of the two kinds of glass, we have made a subclassification under the major category. The high potassium glass is divided into high silica low potassium oxide group and low silica high potassium oxide group. Lead barium glass can be divided into low barium oxide low phosphorus pentoxide group and high barium oxide high phosphorus pentoxide group. Therefore, after the content of various elements of various glass is obtained, the grey correlation analysis model is used to make the data of each chemical component as the parent sequence and the other chemical components as the sub-sequence to solve the grey correlation coefficient of pair chemical components successively, so as to further analyze the correlation between their chemical components. Therefore, after the completion of the subclassification, it is helpful for archaeologists to distinguish the glass cultural relics after weathering. With the analysis of grey relational degree, the composition relationship of ancient glass relics can be further explored.

For the consideration of the differences in the influence of group pressure on individuals, based on the Hegselmann- Krause model, this paper introduces the concepts of group pressure, individual type and relationship degree. Based on the new individual interaction rules, the model is established to explore the influence of different factors in the model on the opinion evolution process. The model is built based on new individual interaction rules and explores the effect of group pressure and the proportion of different types of groups in the model on the opinion evolution process. The simulation results show that different network models affect the evolutionary process and the speed of convergence, but not the final evolutionary outcome.The proportion of non-conformity groups greatly affects the degree of consensus of the final opinion. True conformity groups contribute to group consensus, while equity conformity groups promote opinion diversity. The convergence time of group expressed opinions is generally shorter than that of private group opinions. The results of the study assist social managers in guiding the opinion dissemination process in a targeted manner according to the characteristics of different types of groups.

Liaoning Province, as a national traditional heavy industry area, contains 30 cities facing varying degrees of urban contraction. We classify these 30 cities by K-means clustering analysis. Then, the grey correlation model is established. By solving the grey correlation coefficient between the economic and social indicators and the total population of shrinking cities, the factors affecting the shrinking urban population are obtained. Finally, we establish a comprehensive evaluation system of shrinking cities with population, indicators and GDP as evaluation indicators. The entropy weight method model is established to determine the weight of each evaluation index in order to obtain the contraction comprehensive index of each city. The change rate of the comprehensive index of each city is calculated respectively, and then the development and evolution trend of each shrinking city is analyzed.

Through the construction of urban shrinkage evaluation indicators, we analyze 30 cities in Liaoning Province. We divide the degree of urban shrinkage according to the evaluation index system. Through the construction of population economic elasticity model, quantitative analysis is made on the impact of various factors in the economic society on the population change of the shrinking city. The results show that there are 5 prefecture-level cities and 13 county-level cities with moderate shrinkage, and 6 prefecture-level cities with severe shrinkage. Liaoning's economic growth of 1%, the population size will be reduced by 2%, indicating that most cities in Liaoning Province are smart shrinking cities. In addition, 12 typical shrinking cities are selected as the main research objects. After 12 time series pass the rank comparison test, a mathematical model is established based on GM (1,1) grey prediction model. Then we predict the urban comprehensive index and urban shrinkage of 12 prefecture level cities.

In this paper, according to the definition of carbon sinks, we established a carbon sequestration model by adding parameters, and calculated the carbon sinks of 10 main trees in the sixth and seventh inventory in the state-owned forest area of Heilongjiang Province. Subsequently, we analyzed the four first-level indicators that affect the effective area of the forest, and refined them into ten second-level indicators, and established a multi-index evaluation model based on the entropy weight method to comprehensively evaluate different forests. According to the evaluation results, we constructed the fitting relationship model between forest effective area and forest assessment results. Taking 9 kinds of effective forest area as an example, we get the comprehensive evaluation index corresponding to different forest effective area. Subsequently, we discussed the model of forest effective area based on the model of planting and cutting balanced forest management plan. Based on the previous evaluation model, taking the Saihanba forest as an example, combined with the specific situation of the effective area of the Saihanba forest, a goal programming model was established, to find the transition point of the effective area of the forest and formulate a suitable management plan for forest managers.

The curvature of the level set of elliptic partial differential equation solutions is always an important content in the study of convexity. Curvature is an important invariant of surface, which characterizes the degree of curve bending, is the important basis of differential geometry. Curvature is widely used in machining. In this paper, we study the completely nonlinear elliptic Monge-Ampère equation det D²u = e^u with 0 boundary value Dirichlet condition in four-dimensional Euclidean space. It is proved that the auxiliary function obtains the maximum value at the boundary, and then the mean curvature and Gauss curvature of the level sets of the solutions of the equation are estimated quantitatively.

By researching the theory of polynomial in the higher algebra and the divisibility of integer in the elementary number theory, we reach a conclusion that it’s advantageous to combine them together in the elementary education professional. Taking some similar definitions, theorems, conclusions and proof method of theorems for example, we prove this method proposed in this paper is effective to avoid repeated learning and improve the learning efficiency. Hence students could realize the internal relations between different knowledge and digest them. So it has instructive significance to the mathematics teaching of the elementary school.

Under the context of the rapid development of artificial intelligence, the introduction of causal inference will improve the accuracy of machine analysis of data. This work aims to introduce three methods of calculating causal effect, linear regression, propensity score matching and causal forest, illuminate some about the combination of causal inference and matching-learning. Here, we substitute the dataset National Supported Work experiment by Lalonde (1986) into three methods and compare the results. We show experimentally that causal forest Causal forests can minimize data bias and obtain more accurate estimates of causal effects.

Linear programming is an important branch of operations research and a mathematical method to assist people in scientific management. In this paper, linear programming is mainly used to obtain the optimal solution to a real transportation problem. In this problem, we added a lot of restrictions to the destination and transportation to simulate the most realistic scenario. In addition, we have tested multiple sets of data and come to some regular conclusions. This research can well control the cost of transporting goods, so as to obtain more benefits, and it has reference value in practical application.

Wasserstein distances in optimal transport provides a mathematical tool to measure distances between functions or more general objects. By Wasserstein distances, we define a distance on the moduli space of a class of statistical manifolds. We construct a Riemannian metric of this space and verify that the defined distance can be regarded as the induced distance of the metric.

For this paper, we mainly consider a class of Kirchhoff-type fractional Laplace equation with singular term. By using the variational way and other analysis measures, we get an important result, which is uniqueness of positive solutions for a kind of Kirchhoff type equations with weak singular term.

A class of the strong singular Kirchhoff-type fractional Laplace problem with Hardy term is considered in a bounded domain Ω ⊂ R^N . A uniqueness of positive result is obtained by variational methods. A novelty is that the Kirchhoff coefficient a,b may vanish at zero, that is, considering the Kirchhoff-type problem in the degenerate cases.

It has been shown that ∫^∞_n(𝐥𝐨𝐠 𝒙)^𝟐/𝟏+𝒙^𝟐 𝒅𝒙 = 𝝅^𝟑/𝟖, and 𝐥𝐨𝐠 𝒛 has been chosen to be a branch of the logarithm function in this paper. Meanwhile, logz is holomorphic in the domain: {𝒛: 𝑰𝒎𝒛 ≥ 𝟎 𝒂𝒏𝒅 𝒛 ≠ 𝟎}. Then this study calculates how to express residue of f as 𝟏 + 𝐳^𝟐 = (𝐳 − 𝐢) ∙ (𝐳 + 𝐢), and there are two solutions of 𝟏 + 𝐳^𝟐 = 𝟎: 𝒛_𝟏 = 𝒊 𝒂𝒏𝒅 𝒛_𝟐 = −𝒊. The function has only one pole occurs at 𝐳 = 𝐢. This result applies to more calculation of integral along curves.

In order to reasonably evaluate the shrinkage degree of 30 cities in Liaoning Province, this paper proposes an Entropy Weight TOPSIS-Grey Correlation Analysis method. Based on the Entropy Weight TOPSIS method and Grey Correlation Degree, the evaluation model of shrinkage degree of 30 cities in Liaoning Province is constructed. Based on the data, we determine six indicators to construct an evaluation model of urban shrinkage, including population growth rate, GDP growth rate, per capita GDP, secondary and tertiary industry employment population growth rate, per capita total social consumption and per capita public budget expenditure. According to the results, the cities are classified into severe shrinkage cities, moderate shrinkage cities, mild shrinkage cities, slight shrinkage cities, and critical or growth cities. In addition, the Grey Correlation Analysis method is used to further quantitatively analyze the impact of various indicators on the shrinkage of urban population changes. We find that the total social consumption per capita and GDP per capita are highly correlated, and except for the growth rate of the employed population in the secondary and tertiary industries, the remaining four indicators are positively correlated with the population growth rate as a whole.

Nowadays, the data generated by expressway operation is large in scale and various in types. When analyzing expressway safety risk, the traditional methods are easily subject to the subjective limitations of analysts, as well as the limitations of experience or knowledge, making it impossible to accurately predict traffic risk, and the traditional attribution theory model cannot simultaneously process and analyze multiple heterogeneous data. The data warehouse and data mining technology based on big data drive can analyze the operation data of different ranges and regions in a unified way, mine the spatio-temporal distribution characteristics, improve the scientific utilization efficiency of traffic data resources, and improve the information service level for traffic safety and early warning. This paper starts with the characteristics of road traffic accident information collection data and the key problems of data analysis and application in China point, reduce the occurrence of road traffic accidents through multi angle and all-round grey clustering evaluation method analysis.

In recent years, the application of game theory in guidance field has attracted widespread attention. In this paper, we design a guidance law combining game theory in the context of the interception problem, and verify its superiority of the guidance performance through simulation.

Due to the rise of modern technology and industry, the handicraft industry inevitably fell into decline, although many of them has been passed on for hundreds of years. Some of them have become intangible cultural heritage but are still on the verge of being lost. In this paper, we separate the population into susceptible person, the exposed, propagandist and silencer to predict potential future of the intangible cultural heritage based on SIR model but with adaptations. Besides, by finding out different disease-free equilibrium under different situations using calculation, hopefully these results could make efforts to protect the traditional culture.

With the rapid development of computer and Internet technology, digital information has shown an explosive growth. Traditional text clustering models suffer from high data dimensionality, sparse data and lack of semantic understanding. This paper uses CiteSpace bibliometric analysis and LDA model hierarchical clustering method to visualise and analyse the evolution process and research frontiers of the green port knowledge domain, which has certain practical significance for the in-depth promotion of green port practices in China.

Building a service-oriented police organ that people trust and satisfy is the goal of China's police reform. Police trust is the public's dynamic psychological judgment on the possibility of the police serving the public and enhancing the public's interests. The existing studies mostly discuss the direct influencing factors of public satisfaction. This paper aims to explore the mechanism of the influence of police trust on public satisfaction. According to the theory of self determination, the hypothesis model is constructed, and then the empirical data is used for EFA and CFA verification. First, the research found that police trust has a positive impact on public satisfaction. Second, it is found that police efficacy plays an intermediary role between police trust and public satisfaction. Third, it is found that police reputation plays a moderating role between police trust and public satisfaction. This paper verifies the positive influence of police trust on public satisfaction and its mechanism, constructs the SEM of people's subjective attitude, enriches the antecedent research of public satisfaction, and the conclusion provides some practical enlightenment for improving public satisfaction.

With the development of technology, internet technology is becoming more and more mature, so that users can choose different categories of information according to their needs and suitable for their own characteristics and preferences when surfing the internet, instead of having to passively obtain it. Therefore, when browsing information, users will choose websites that interest them or suit their characteristics and interests according to their own needs, and search engines will calculate the corresponding ranking according to the user's browsing information, and finally recommend the website to the target user. The application of recommendation technology in the field of information retrieval not only helps users to obtain useful content from the huge amount of data, but also improves the effect of search engine optimization. This paper introduces a recommendation model based on mathematical expressions and focuses on its role in modelling user behaviour, while the algorithmic process is also described in this paper.

Stability of non-autonomous system is in general difficult to analyze and the frozen in time assumption is known to break down in high dimensional system. This work proposes another criterion to analyze the stability of non-autonomous system by obtaining its upper bound on the energy growth. The computation of upper bound is then formulated as a convex optimization problem based on linear matrix inequality. We also perform pendulum experiments with a linear varying or oscillating length to analyze its stability. The experimental results demonstrate that the time-varying length of pendulum will lead to a growing oscillation amplitude of pendulum and the associated growth rate also agree well with the upper bound prediction based on the linear matrix inequality. This work provides a new analysis framework to analyze stability of non-autonomous system.

Let G be a finite directed graph with no loop and no heavy edges, or an undirected graph with no loops and no edges. 𝑁 is a given natural number. This paper proves that the existence problem of two paths with length 𝑁 in G (referred to as 𝑁-path) is completely equivalent to the solutions of a multivariate of polynomial 𝑁 the range of {0,1} or {0,1, −1}. Therefore, the Gröbner bases method can be used to give an effective discrimination of the existence of the solution. This result can be applied to solve the problems of cutting edge judgment, tree and forest judgment in G.

In the article, at the first, the new notion of LP well-posedness has been generalized in the paper. the LP well-posedness is related to a approximate function ℎ₁(𝜀, 𝑢) and ℎ₂(𝜀, 𝑢) rather than simple parameter 𝜀. And so as to to discuss the LP well-posedness, then some different metric characterizations of LP well-posedness was established and approximating solution set was constructed. In the end some equivalence results of strong LP well-posedness (resp., in the generalized sense) is proved.

In this work, we come up with a continuous-time second order inertial augmented Lagrangian dynamical system with damping function for solving convex optimization problems with affine equality constraints with three variables. The constrained optimization problem can be transformed into unconstrained optimization problem by using the augmented Lagrange function method. By using Lyapunov analysis method, the asymptotic properties of the dynamic system at t → ∞ is studied and the convergence rates are established when the damping coefficients are different situations.

As one of the forms of semiparametric model, the variable coefficient regression model increases the flexibility and adaptability of the model by assuming that the regression coefficient in the linear regression model is the unknown of other independent variables, overcomes the "dimensional disaster" in the high-dimensional data model, and embeds the geographically and temporally weighted variable coefficient regression model (GTWRM). Based on the basic theory of wavelet estimation, this paper proposes a wavelet kernel coefficient estimation method for the model, and uses the wavelet kernel function to obtain the coefficient estimation.

In this study, the chemical composition data of ancient glass were sorted out and analyzed. Based on the training principle of BP neural network, BP neural network was established to solve the problem. After several iterations, 14 input layers, 5 neurons and the training method of radial basis function were finally determined. The data before weathering of weathered relics were finally obtained, so as to predict and restore the missing value of ancient glass chemical elements. In order to verify the rationality and sensitivity of the results, certain parameters were determined to process the data, and cluster analysis was performed again. By comparing the two results, we found that the difference between the two results was small, which verified the rationality and stability of the classification results. Then, through k-means algorithm, the types of glass were subclassified based on the different chemical composition content. For example, high-potassium glass was divided into high-potassium high-calcium glass and high-potassium low-calcium glass, and lead-barium glass was divided into lead-barium high-calcium glass and lead-barium low-calcium glass.

In the processes of industrial defects detections, deep neural networks have received much favor for its high efficiency and low labor cost. As is known, a big amount of dataset is the precondition to train any network. However, the datasets of industrial defects tended to be small and hard to obtain. To solve the problem above, we raise a thought of simulation based on MCMC aiming to sample from the posterior distribution of the defect’s images, which is viewed as the limit distribution of certain Markov Chain. Once we capture the posterior distribution, the law of the defects is revealed. 1Therefore, generating pseudo samples by the law is quite reasonable. It has been proved that the algorithm is practicable by advanced devices and economical in the long term. The significance of this work is to raise a practicable thought towards the problem of mini-batch industrial datasets. Code is available at https://github.com/MrSmallWang/solutions-tosmall- datasets.

In this paper, a CUSUM (Cumulative Sum) statistic containing two parameters is firstly proposed to estimate the location of the mean change-point, and the collinearity of the estimated quantity is proved. Secondly, the numerical simulation study presents satisfied result for the estimation of the mean change-point. Finally, by comparing with the other statistics, it is found that the two-parameter CUSUM statistic is more stable and the estimation of the mean change-point using this statistic is more accurate.

Structure of telescopic boom is becoming increasingly complicated, since truck crane with excellent performance, larger-ton as well as intelligence has dominated the tendency of development, enterprises home and abroad attach importance to the investigation of telescopic boom and some achievements have been obtained. So far, structure of telescopic boom with single cylinder and pinning system equipped with high intelligence and reliable performance represents the newest technology. Targeted with telescopic boom with single cylinder and pinning system, the paper builds the model of the whole telescopic boom. Secondly, the paper investigates the statics of telescopic boom, which provides strong proof for the optimization design of telescopic boom, more specifically, at the background of crane with lifting competence 25 ton(rating load), contour plot of press and displacement for each boom in all-extended condition are also studied, which contributes to strengthening design of slide-pad attached to moving boom and also confirms location of regional stress concentration for each boom. Finally, the cross-section size for the first telescopic boom is optimized by using optimization toolbox provided by MATLAB software which brings about the reducing gross weight of the whole system.

In order to solve the problem of low reliability parameter estimation accuracy of relay protection devices in intelligent substations under the condition of small samples, a parameter estimation method of three-parameter Weibull distribution based on GM-SVR is proposed. First of all, in view of the high reliability of the protection device at the initial stage of operation, a three-parameter Weibull distribution model is introduced. Secondly, the SVR is introduced on the basis of the GM(1,1) model, and a high-precision parameter estimation model of GM-SVR Weibull distribution is established by making use of the high reliability of the GM(1,1) model for position parameter estimation under the condition of small samples and the advantage of SVR method in small sample data processing. In order to solve the problem that the traditional model ignores the influence of equipment aging and maintenance, the equivalent fallback time and maintenance improvement coefficient are introduced to improve the time-varying model. Through the calculation of an example and comparison with other methods, it is proved that the GM-SVR method has higher accuracy of model parameter estimation, and the model considering the influence of maintenance can more effectively study the reliability of relay protection devices.

In Game Theory, the computation and counting of equilibrium and the structural features of equilibrium are major research topics. The existence of equilibrium naturally forms a decision problem. The Nash equilibrium composed of mixed strategies always exists in the matrix and double matrix games. Therefore, calculating Nash equilibrium is the main task in the matrix and double matrix games. For the double matrix game, the measure of its Nash equilibrium can be based on the stability implied in the Nash equilibrium definition. Besides, a propositional formula can construct a two-player game given as a bi-matrix by specifying a proper finite set of strategies and adding a transformation. In this study, we investigate the development of Nash equilibriums by analyzing the structure-property of bi-matrix. We examine the characterization of Nash equilibrium creation and the relationship between satisfiable assignments of formula and Nash equilibriums of generated Game based on the characterization of bi-matrix formation and the stability principle of Nash equilibriums. The method from analysis and logic helps examine some relationships between combination optimization issues in graph theory and game systems by examining the structure of bi-matrix and combining the stability principle of Nash equilibriums to research the characterization of Nash equilibriums.

In this paper, we focus on the Cauchy problem for the modified Camassa-Holm-Novikov equation with an additional weakly dissipative term. We will investigate 3 aspects. First, we present some key facts about local well-posedness and blow-up criteria. Second, the wave-breaking phenomenon will be ensured by displaying some conditions related to the initial data. Then we present some results about the wave breaking criteria. We finally explore the global existence problem.

In recent years, epidemics, earthquakes, forest fires, floods, and other public health emergencies and natural disasters have occurred frequently, and the role of emergency logistics has become more and more prominent. In this paper, on the basis of sorting out the current situation of emergency logistics guarantee in China, we use hierarchical analysis and fuzzy evaluation methods to calculate the weight of each index factor and guarantee the effectiveness of emergency logistics, respectively. The study gives examples to analyze and calculate the guarantee effectiveness of emergency logistics so as to draw the influence of emergency logistics. The key factors of emergency logistics can provide decision guidance for strengthening the construction of the emergency logistics system and improving the level of emergency logistics guarantee.

The mixed rationality phenomenon on complete rationality of traffic managers and limited rationality of route selection of drivers, exacerbated by the complexity of urban transport path-guidance behavior. First, analyze finite route choosing behavior by evolutionary game topologically, and then facing the urban road network system, the route guidance simple evolutionary game model was put through, based on the three choice behaviors of the driving experience, guidance information, and combination with guidance information, and the evolutionary game theory of black box. Finally, select such as the route travel time, the average travel speed of path, the route load degree and congestion index, and take central zone of Baoshan for example, whose result indicate: it is a relatively reliable route selection method for combination with guidance information and driving experience, especially the most outstanding in the rush hour, and helpful to optimize the overall route networks.

In this paper, we study a predator-prey model with Beddington-DeAngelis functional response and two delays. In this model, selective harvesting of predator species is discussed and two delays describe the time that juveniles take to mature. We have analyzed the effects of delay and harvesting on the model dynamics. First, the existence, uniqueness of positive equilibrium are discussed. Then, by analyzing the associated characteristic equation, stability of positive equilibrium and some sufficient conditions for the existence of Hopf bifurcation are given. Finally, the theoretical prediction is proved by matlab numerical simulation results.

Fuzzy neural network system is composed of fuzzy system and neural network system. In fuzzy the neural network system, the fuzzy logic system and the neural network system can play their respective advantages to achieve functional complementarity. In this paper, a fuzzy system based on semi-tensor product is proposed. Then fuzzy system and neural network are designed for hybrid control. Finally, the corresponding algorithm is proposed. The simulation results show that this method can shorten the control time of the system and improve the control effect.

H. Steinhaus proposed a conjecture about irrational numbers, called the Steinhaus conjecture. Sós et al. proved it, and the results of the study are referred to as the “Three Gap Theorem.” In this paper, we promote the Steinhaus conjecture and prove the generalization of the Three Gap Theorem, in which the definition domain of independent variables is extended from natural number sets to integer sets, and an application of the extended conclusion in the field of music art is illustrated.

To solve the problem of wind noise and structural resistance caused by vehicle external structural parameters, this paper carried out multi-objective optimization for the tail multi-parameters. Based on the selected four parameters of C-Pillar angle, trunk angle, rear box length and boat tail angle of Ahmed model, the central combination test design of response surface Box-Benhnken was carried out in the selected range. The sampled data sets were numerically simulated in star-ccm+, and the surface sound pressure level and drag coefficient of the model were obtained. The optimal Latin hypercube sampling data sets were used to verify the accuracy. Finally, the response surface model was established, and the optimal front window surface SPL was 65.11dB with an error of 1.36%, and the optimal drag coefficient was 0.1210 with an error of 1.68%, taking Curle SPL and drag coefficient as the optimization objective.

In this paper, we construct a prediction and classification model based on neural network and K-means clustering algorithm to complete the prediction of glass composition before weathering and the classification of unknown glass. In the process of studying glass relics, we discussed the important chemical components and analyzed their influence on the properties of glass. At the same time, through the collected data, the neural network algorithm is used to train and test the data to analyze the composition content of glass before and after weathering. Then, the classification simulation of the data is carried out according to the K-means clustering algorithm. Finally, the classification results of glass relics with different chemical composition in the classification model are analyzed. We conclude that there are six classification systems for high-potassium glass and lead-barium glass. Effective classification can not only reduce the difficulty of scholars' archaeological classification, but also effectively improve the research value of glass relics.

Commonly, it is assumed that the carrying capacity is constant in the conventional predator-prey model. In contrast, we investigate a predator-prey scenario which have a common prey in this work, the carrying capacity of the predator and the prey are variables changing with the amount of common prey which consumed by both predator and prey. We were able to establish the necessary requirements in favor of asymptotic stability globally and uniqueness of periodic solutions.

Over the years, a dedicated study has been conducted on models of robotic swimmers with a low Reynolds number. The extensive scope ranges from microswimmer fundamentals to potential applications of nanorobotic auto-operators in medical operations. This article examines a collection of papers that investigate the appropriateness and accuracy of models for assessing the hydrodynamics of microswimmers. In addition, microorganisms have a range of swimming patterns and morphologies, but the emphasis of this article is the helical flagellum. By reviewing relevant research, we provide a variety of application examples based on these methodologies.

Combining nonlinear programming and least squares method, this paper proposes a two-stage mixed fuzzy linear regression model based on distance criterion. In order to ensure that the error of fuzzy estimated value and fuzzy observation value can be reduced when the explanatory variable is a clear number, the fuzzy regression model has a fuzzy adjustment term in addition to the clear regression coefficient. Firstly, based on the distance criterion, a nonlinear programming model is established to obtain the regression coefficient of the explanatory variables, and the fuzzy adjustment term is obtained based on the distance criterion and the least square method. Compared with the existing methods that cannot determine the sign of the coefficient, the method can accurately determine the sign of the regression coefficient. Finally, it is verified that the model has smaller mean square error and higher reliability than other models through a large number of numerical experiments and practical examples.

Shale gas is regard as a clean, low-carbon and green energy, and the utilization and efficient development of shale gas is of great significance for achieving the dual carbon goals. Horizontal well hydraulic fracturing is an important way to develop shale gas resources. Predicting the production of shale gas under different engineering or geological conditions of shale reservoirs is crucial to the optimal fracturing design of shale gas development. This study proposes a LSTMbased intelligent model to predict the gas production of shale, and this novel smart model predicts gas production quickly and accurately. We comprehensively evaluate and compare the performance of the AI network, and the results of test show that the LSTM-based AI model can output gas production data by inputting reservoir and engineering parameters. The mean value of relative error of the LSTM-based AI model is 5.32%, which is reliably for the prediction of gas production. The peak of relative errors of this AI model in this study on day 100, 300, and 500 are 4.67%, 6.53%, and 8.23%, respectively. This study can provide an effective and quick method for shale gas prediction and improve the intelligence level of energy development.

This paper mainly introduces several kinds of global conformal parameterization theories and algorithms, which can deal with complex surfaces under different genus. Pure first-order differential algorithm and pure second-order differential algorithm are based on the contents of global differential geometry, whose core ideas come from Riemann’s single-valued theorem and Teichmuller theory. Ricci flow algorithm and quasi-conformal mapping algorithm are based on the contents of the field of geometric partial differential equations, which can be optimized by minimizing energy to get results. The optimal transport algorithm is based on convex differential geometry and geometric variational principle, which can be transformed into computational geometry algorithm to find the solution.

Muddy children puzzle is a well-spread mathematical puzzle. It can be solved by two ways, which are Kripke Structure and true and false statement. The model checking problem is solved by searching the state space of the system. Ideally, the verification is completely automatic. The main challenge is the state explosion problem. The problem occurs in systems with many components that can interact with each other, so that the number of global states can be enormous. This paper observes that any propositional planning problem can be modeled as an LTL model checking problem as any propositional goal g can be expressed in the form of a counterexample to the temporal formula in LTL. If the problem is solvable, the LTL model checker will return a counterexample, which manifests a solution for the planning problem. This paper shows that the puzzle is solvable for any number of agents if and only if the quantifier in the announcement is positively active (satisfies a form of variety).

China is the world's largest consumer of tobacco and the world's largest victim of tobacco, so I hope to solve the problem of smoking transmission, which is important to control the scale of its transmission and reduce the harm to public health and socioeconomic development. In this paper, we use the infectious disease dynamics model (SIR) to solve the problem of smoking transmission. This paper introduces the SIR model as the basis and then establishes three new models to analyze the spread of smoking, and then calculates the Basic reproduction number according to the disease free equilibrium of the three models. Finally, the conclusions of the three models are used to propose corresponding countermeasures and suggestions, so as to analyze and solve the problem of the spread of smoking and provide a reference. The three models are used to calculate the Basic reproduction number.