This PDF file contains the front matter associated with SPIE Proceedings Volume 13219, including the Title Page, Copyright information, Table of Contents, and Conference Committee information.

In ecosystems, the extent to which plants benefit from biodiversity to adapt to drought is influenced by interactions between the environment and plant populations. In this paper, a plant community interaction model based on an improved LotkaVolterra competition model is established. The model analyzes various factors influencing plant drought tolerance from a community perspective, thereby further elucidating the importance of biodiversity. We initially construct a basic LotkaVolterra model using four plant species as subjects and run and validate the model. Then, trigonometric functions are introduced to explore variations in weather factors, synthesizing the impacts of environmental temperature and humidity through normalization indices. We also endeavor to handle more complex ecosystems by attempting to increase the number of species and alter species types. In addition, environmental influences on species, such as habitat reduction due to environmental pollution and human activities, are considered, introducing corresponding impact factors. Finally, our research indicates that the frequency and amplitude of drought events significantly affect the diversity and viability of plant communities. The degree of environmental pollution and habitat alterations also alter the stability and species diversity of plant communities. The improved Lotka-Volterra model can be used to explore plant relationships in complex arid environments.

Climate change has become a great challenge facing all mankind. Aiming at the problem of forest ecological environment protection, two mathematical models of forest carbon sequestration and forest management decision-making are established in this paper. Firstly, the carbon sequestration index of forest is evaluated by combining relevant indicators and a comprehensive evaluation method, which combines analytic hierarchy process and objective weight method. And the first-order exponential function is introduced to model the decay law of forest trees based on the IPCC theory, and the carbon sequestration model is established. In addition, based on the consideration of forest comprehensive benefits, a decision model based on multi-objective optimization is established for forest management, and the genetic algorithm is used to solve the optimal solution. Finally, we apply the model to Saihanba forest and the relevant parameters are analyzed. The results show that reasonable anthropogenic development, such as deforestation, does not affect forest, and can promote the carbon cycle process in forest.

In this paper, we show a two-stage estimation method to discuss the parameter estimation problem of the first-order generalized random coefficient autoregressive model (GRCA(1)). Firstly, we obtain the consistency and asymptotic normality of the covariance estimators by Hellinger minimum distance estimation methods and moment estimation methods respectively. Secondly, we obtain the estimators of parameters for the model by the weighted least squares method and prove the asymptotic properties of parameter estimators. Numerical simulations show that the two-stage estimation method in this paper has a smaller mean square error compared to the least squares method. Thus, Hellinger minimum distance method is better than the moment estimation method.

In this study, Total Volatile Basic Nitrogen (TVB-N) and Electrical Conductivity (EC) were used as key indicators to mathematically model the freshness of Siganus fuscessens. TVB-N is an important indicator used to measure the freshness of food products in the EU and China. This study considered exponential and modified exponential models for modeling the TVB-N formation. The modified exponential model showed the best fit in the model predicting TVB-N content of Siganus fuscessens at 25℃ and -18℃ storage conditions. It shows the best statistical parameters: 𝑅 ² (0.9965, 0.9194) 𝑅̅² (0.9956, 0.906), 𝑅𝑀𝑆𝐸 (1.652, 0.4331), 𝐴𝐼𝐶 (7.5921, -11.6904), 𝐴𝐼𝐶𝑐 (15.5921, -5.6904), 𝐵𝐼𝐶 (7.1757, - 11.5315), 𝑅𝑀𝑆𝐸_{𝐿𝑂𝑂𝐶𝑉}(3.1489, 0.4133), 𝑅𝑀𝑆𝐸_{Bootstrapping}(2.3468, 0.4069). On this basis, a prediction model for Siganus fuscessens TVB-N applicable to different temperatures was constructed using the Arrhenius equation to introduce the storage temperature 𝑇, which improved the generalizability of the model. Concurrently, an F-test was employed to verify the strong correlation between TVB-N and EC(𝑅 ² = 0.982 and 𝑅̅ ² = 0.978), and a linear model was derived using the least squares method. A quick measure of Siganus fuscessens's freshness can be obtained by measuring the EC since it is easier to measure than TVB-N. Based on the mathematical modeling between Siganus fuscessens freshness and TVB-N and EC indicators, this study provides reliable theoretical support and practical application value for the assessment of seafood freshness. It also provides new ideas and methods for research in the field of seafood storage and transportation.

There are many methods to describe the non-Gaussian statistical properties of electromagnetic scattering, and the beta distribution is proved to be correct. Traditional random electromagnetic fields assume that the number of steps is infinite, but in reality they are finite. In order to simplify the calculation, we ignore the step size N in our study, explore the random light field generated by the amplitude of the Beta distribution, and combine the obtained probability density function distribution to analyze the new statistical theory in depth.

Based on the aggregate smoothing of max(0,x), a smooth gradient descent method for unconstrained minimax problem is proposed. Firstly, the unconstrained minimax problem is transformed into an equivalent non-smooth problem containing max(0,x) function. The unconstrained smooth optimization problem is obtained by the aggregate smoothing approximation technique. Through the numerical experiments of three examples, compared with two typical algorithms, the proposed algorithm shows good competitiveness.

The variable sex ratio of sea lampreys will affect the interaction between the populations in the ecosystem. This paper establishes a statistical model of the change of sea lampreys’ sex ratio and a differential equation model of various population interactions to describe this effect, and analyzes it based on Lyapunov's qualitative theory. Based on an example in the Great Lakes region of North America, we verify the proposed mathematical model and analyze its sensitivity. The results showed that the sex ratio of the population can be increased by reducing the available resources of young lampreys, and it is feasible to control the number of lampreys in this way. Qualitative theory shows that the differential equation model has no stable equilibrium point, reflecting that the numbers of various populations will change dynamically when the sex ratio of lampreys changes. The mathematical model established by us also has good stability.

This article investigates the methodologies for calculating the caustics of plane curves, focusing on both parametric curves and algebraic curves defined by bivariate polynomials. We have derived the specific equations for caustics in these cases through theoretical analysis and validated them using the Python Sympy symbolic computation library. Additionally, simulation experiments were carried out using the POV-Ray renderer. Our research not only offers a combined theoretical and practical approach to study and compute caustics but also highlights the beauty of mathematics through specific examples, providing a new perspective for the mathematical modeling and simulation of optical phenomena.

In this article, a space-time finite element method (FEM) for time-fractional diffusion equations containing fractional derivatives of order ∝ ∈(0,1) with initial data and boundary value is given. We obtain an appropriate weak formula and a space-time finite element formula for this problem. Further we derive a posterior error estimator for space and time, and construct an adaptive algorithm according to these error estimators. Finally, the effectiveness of the adaptive algorithm is verified by numerical examples

This paper establishes a classification model of ancient glass artifacts based on the relevant data of ancient Chinese glass artifacts using logistic regression analysis. In order to study the compositional changes and identification of glass artifacts, firstly, the relationship between the surface characteristics of glass artifacts and weathering conditions is analyzed by using the chi-square test, and the data are visualized to illustrate the statistical laws; random sampling is used to eliminate the influence of unbalanced samples, and a univariate linear regression model is fitted to predict the content of the chemical compositions before weathering. Secondly, the changes in the average chemical content of the two glass surfaces under different weathering conditions were visualized and analyzed, and the pairwise test of the chemical composition data was carried out by the rank-sum test to classify the different samples based on the K-mean clustering, and the sensitivity of the classification was analyzed. Finally, grey correlation analysis was used to quantify the degree of correlation between different chemical compositions of the same type of glass, and the variation of the degree of correlation between different types of glass was visualized and analyzed.

C4 olefins find extensive applications in the fields of chemical engineering and pharmaceuticals, with ethanol being one of the primary raw materials for their production. However, the actual yield of C4 olefins tend to be low due to significant influences of production temperature and catalyst combination on the conversion rate of ethanol and the selectivity of C4 olefins produced. Thus, exploring optimal production conditions is important for C4 olefin production. Initially, we utilize a Spearman correlation coefficient model to analyze the relationship between ethanol conversion rate, C4 olefin selectivity, and temperature, revealing a strong correlation between the two and temperature. Subsequently, we use OLS linear regression analysis for ethanol conversion rate and C4 olefin selectivity under different catalyst combinations and temperatures. We conduct heteroscedasticity tests on the data to obtain optimal analysis results. The results indicate that ethanol concentration in the catalyst primarily affects ethanol conversion rate, decreasing by8.747units per unit increase, while cobalt loading in the catalyst primarily influences C4 olefin selectivity, decreasing by2.989units per unit increase. Finally, we innovatively propose a linear regression particle swarm optimization model comprising linear regression and particle swarm optimization modules, capable of finding the optimal strategy for catalyst combination and temperature from multiple variables, with a high fit of 0.959. Extensive experiments and comprehensive analysis have demonstrated the superiority of our proposed method.

Conspicuous brands have started to offer mass customization services, which enables consumers to customize their exclusive products by making aesthetic decisions such as color and fabric. However, less attention has been paid to the mass customization of conspicuous products, which could lead to unsuitable product decisions and pricing strategy, and then bring financial risks to the brand. Different from mainstream products, consumers of conspicuous products care not only about product quality, but also about its added value. Based on the conspicuous consumption behavior of consumers (exclusivity and conformity), this paper proposes a Hotelling model of conspicuous products’ mass customization using a rational expectation framework, and investigate different mass customization strategies in both monopoly and duopoly markets. The results show that the increase of conformity reduces the pricing of both the standard and mass-customized products, while the increase of exclusivity raises the pricing of the both products. By comparing equilibrium results in different market environments, we also find whether the mass customization strategy is profitable is related to product cost. This paper reveals how the introduction of mass customization affects brand decision-making in monopolistic and duopolistic markets and analyzes the importance of considering consumers’ conspicuous consumption behavior in pricing. The findings provide a theoretical basis and practical guidance for conspicuous brands to develop more suitable mass customization strategies.

The virtual element method has special advantage in grid construction. The interpolation functions on elements have no explicit expression, so the method is called "virtual". This leads to a series of problems in concrete calculation, and we need to map the solution function, trial function and load function to the polynomial space through the projection operator. Then, the projection functions were brought into the variational formulation to execute computation. In this paper, the virtual element method of the second-order elliptic problem is taken as an example, and the key steps such as the calculation of projection matrix and projection of functions mentioned above are discussed. In particular, we give the detailed implementation of these key steps. Finally, a numerical example is given, which verifies the correctness of the analysis results in this paper.

The study delves into the analysis of the popular Wordle puzzle game, leveraging data collected on Twitter to establish mathematical models. By examining Wordle players' behaviors, including strategy choices, word guessing frequency, and potential challenge modes, valuable insights are gained to optimize game design for an enhanced user experience. The research also explores the game's potential educational application, specifically as a tool for English vocabulary learning. Addressing the first question, an ARIMA time series model was employed to predict the number of reports on March 1, 2023. The model, refined by outlier removal and expert modeler matching, forecasts the final number of reports within the range of [11953, 17730], validated through residual ACF, PACF, and white noise tests. For the second question, word attributes were categorized into three indicators: part of speech, letter occurrence statistics, and the frequency of the five most common letters in the Oxford Dictionary. Pearson correlation coefficients revealed a general correlation between part of speech and difficulty mode (0.2774) and between high-frequency letter occurrence and difficulty mode (0.2093). These findings were further validated through a Pearson correlation coefficient hypothesis test. Future research will focus on optimizing ARIMA model parameters for increased accuracy, robustness, and generalization, while exploring additional word attributes to uncover more connections between game difficulty and word characteristics.

In this paper, a new parallel discretization scheme is proposed and applied to the radiation diffusion equation. The radiation diffusion equation is solved by differential operator splitting method, and the nonlinear diffusion equation is solved in the splitting step. The diffusion solution is predicted by a non-overlapping parallel discrete scheme, then a new conservationtype parallel scheme is used in the correction step. Typical numerical examples test the applicability of the algorithm, demonstrating good accuracy, stability and computational efficiency.

In this paper, based on Cauchy type integral formula of hypergenic functions in R ⁿ⁺¹ , an improved integral formula in the whole space for dual hypergenic functions is given by extending the corresponding integral representation of the dual hypermonogenic function.

Light pollution is a kind of physical pollution, mainly through visual damage to people's physical and mental health, the aggravation of light pollution, but also restrict the high-quality development of the city. Based on this, the modeling of this paper aims to study the risk level of light pollution and related intervention strategies. Firstly, find the data and preprocess the data. Then, the influencing factors affecting the risk level of light pollution in a location are established, which are divided into two levels of indicators. The first level of indicators is the amount and type of artificial light, the direction and intensity of light emission, the geographical location of the area under consideration, and the amount and type of natural light. The secondary index mainly considers 13 factors such as urban lighting conditions. Then, an improved evaluation model combining the entropy weight method and the gray correlation analysis method is applied to determine the risk level of light pollution in a location by bringing in relevant data. Finally, we indicate three possible measures for the government.

Riesz spaces, or vector lattices, are real vector spaces equipped with a lattice order ≤ that ensures compatibility with vector space operations. This paper explores the properties of lattice-ordered modules in the context of Riesz spaces and investigates their finite product. By utilizing category theory, a unifying mathematical framework, we gain valuable insights into the mappings and transformations of these structures. Riesz spaces have wide-ranging applications in mathematical analysis, optimization theory, economics, and other ields. By extending the concept of vector spaces to include left R-modules, this paper broadens the study of linear structures in a wider range of mathematical domains, enhancing their theoretical universality and application versatility. The development of Riesz spaces traces back to the convergence of functional analysis, algebra, and measure theory in the 1930s. This field is recognized as a distinct and mature area of study, with fundamental texts that establish a solid foundation. The theory of Riesz spaces also provides a convenient mathematical framework for studying and designing probabilistic logics. This paper contributes to a better understanding of the categorical structure of lattice-ordered modules and their applications in diverse mathematical domains.

This study endeavors to establish an evolutionary game model to investigate the reverse logistics of construction waste and carry out simulation analysis. The model encompasses three primary actors: the government, construction companies, and the public, each with distinct strategy options and benefit matrices. Through the replication of dynamic equations, the temporal evolution of the system is simulated, and the equilibrium point's stability is scrutinized. The research outcomes reveal that, under particular circumstances, all three actors tend to adopt strategies favorable to the implementation of reverse logistics for construction waste. Additionally, it is observed that the system's initial conditions exert a notable influence on its progression towards a stable state. These insights offer theoretical underpinnings for refining the implementation of reverse logistics practices in the construction waste domain.

This study investigates the application of response surface methodology and Bayesian optimization in parameter tuning of genetic algorithms and their effectiveness. The research objective is to improve the performance of genetic algorithms in solving the traveler problem (TSP), including reducing the optimal path length and improving the convergence speed. We first detailed the mathematical principles and computational procedures of response surface methodology and Bayesian optimization. Subsequently, a hypothetical experiment is designed, which includes the implementation of the genetic algorithm, parameter settings, and the determination of evaluation criteria and performance metrics. The experimental results show that both response surface methodology and Bayesian optimization can effectively improve the performance of the genetic algorithm on the TSP problem. Bayesian optimization performs more significantly in terms of the reduction of optimal path length and the improvement of convergence speed, especially when dealing with complex parameter spaces. We provide a detailed comparison of the effectiveness of the two methods and analyze their characteristics and applicable scenarios. It is shown that these two parameter optimization techniques are of great significance in improving the performance of genetic algorithms and provide new perspectives for the theoretical development and practical application of genetic algorithms. Future research directions include exploring the application of these methods to other types of optimization problems and multi-objective optimization, as well as the possibility of combining adaptive parameter tuning and machine learning techniques.

Conventional data sets for solving infectious disease equations are mostly in unidirectional form, and the efficiency of solving application is low, which leads to the increase of the average relative error of the equations. Therefore, the application of exponential tight differential operator in solving infectious disease equations is proposed to be analyzed. According to the current test requirements, the design of high-precision compact differential format is carried out first, and the multi-objective approach is adopted to improve the efficiency of the overall solution application, the multiobjective public data set is established, and the stability analysis of differential solution is realized, based on which the model design of solving infectious disease equations with exponential-type compact differential operator is constructed, and the modification of the boundedness judgment is adopted to realize the solution application. The results show that the average relative errors of the final equations for the selected four test cycles are well controlled below 1.3, which indicates that the designed method for solving the infectious disease equation is more targeted and effective, and has practical application value.

This article introduced a method to optimize the time and energy consumption during riding. First, power curve can be derived to determine the relationship between the rider's position on the course and the force exerted to the rider in different conditions. Then, Markov process can be used to solve the optimization model based on dynamic programming model, and then the optimal strategy is obtained. Afterwards, the sensitivity of the model can be investigated by Functional Analysis. Finally, this paper gave the general process of using genetic algorithm to optimize this model.

Super-stationary structure is one of the very important structures in engineering design, and its internal force calculation is mostly done by force method equation, but the process is tedious and complicated. The current research on force method mostly starts from reducing the number of figure multiplication to simplify the calculation process, but the effect is very little. In this paper, we propose to use the "Hinging method" to select the basic structures of continuous beams and variable section beams, and we find that the "Hinging method" is more convenient, fast and practical in solving practical problems.

Aiming at the imperfection of the penetration performance evaluation system of inflammables and explosives, a quantitative study based on surface damage and penetration damage is proposed. The computational model under the terminal movement state is constructed, and the "damage degree" is innovatively proposed, which is used to investigate the influence of the detonation distance and the target thickness on the penetration performance. Based on the discrete event simulation, the simulation system is constructed, Based on different modules in discrete event simulation, the description and analysis of the terminal damage process of inflammables and explosivess can be achieved. By setting indicator parameters and automating simulation operation analysis, a large number of samples can be generated. Python programming is used to solve the model. The discrete event simulation results show that the penetration process of the inflammables and explosives can be quantified from the perspective of energy. The calculations show that the detonation distance and the target thickness have a greater impact on the surface damage and penetration performance, which lays a good foundation for the further study of the damage model of the inflammables and explosives on the equipment, which is beneficial for the safety of production and transportation.

As a traditional parameter estimation method, the least squares method is an important tool for studying the optimization of functions in an interval and for applying the optimal function to an unknown function, as well as a mathematical optimization method using the sum of squares of the errors to find the best-fitting function. When the error value between the estimated data and the actual data reaches the minimum, it means that the estimation model has a better fitting effect. The article derives the principle of the least squares method from a differential perspective and explains the origin of multivariate linear fitting. Curve fitting is described in detail, and the nonlinear fitting process is deduced on the basis of the polynomial fitting principle. In the article, in order to fit a three-dimensional sphere with the smallest possible error under the mean-square significance, the data of the three-dimensional sphere are nonlinearly fitted on the basis of utilizing the principle of the method of least squares, and Gaussian-distributed noises with zero mean are also added to compare with the original fitted sphere. On this basis, a weighted least squares is proposed using weight analysis thereby minimizing the error and finally fitting the optimal sphere.

This paper presents fast and accurate numerical methods for solving multi-dimensional fractional Helmholtz equation using spectral fractional Laplacian. By Dunford-Taylor integral representation of spectral fractional Laplacian, tensorial methods based on matrix transform technique can be used to discretize fractional Helmholtz equation. Our scheme can exactly solve system of equations using discrete sine transform, and it can significantly save computation cost and memory. To reveal the accuracy and efficiency of the suggested fast algorithms, two numerical tests are offered.

The sum limit is an important type of limit problem, but its forms are flexible and diverse, and there is usually no relatively fixed and simple solution. This article provides and proves a calculation formula for the limit of the sum formula in the form of

lim

n → ∞

n

∑

i = l

n k

ƒ

(

i q

n p

)

( p > q ≥ 0 )

. This formula has the advantages of simple calculation and wide applicability when solving such limits, and can be further applied to the calculation of product limits that can be transformed into such sum limits.

Limit is an important concept and basic operation in higher mathematics, and it is also the basis of calculus theory. Mastering the methods and skills of limit operation is the key to learn higher mathematics well. Mainly introduces six common methods for solving limit problems, two skills for solving limit problems and the idea of multiple solutions to one problem, and merges all kinds of methods of limit operation together.

Abstract: This article studies Bézier curves with shape parameters. Firstly, three of group of polynomial basis function with three shape parameters 𝛂, 𝛃, 𝛄 were presented. It is referred to as the second, third and fourth order αβγ-B basis functions. Then, the geometry meaning of the shape parameters are analyzed. Basis on the basis function three kinds of Bézier curves were constructed, which have the basic properties of Bézier curve. The shape of the curve has more flexible expression, and can be local or whole modified by the introduction of three shape parameters. And the composite curves which consist of the this curves can achieve 𝐆 ^𝟐 continuity when the control points of curves satisfy the 𝐆 ^𝟏 continuity conditions of Bézier curve. Finally, the practicability of the method is proved by the curve modeling design.

In this paper, we study the existence of positive solutions of the weighted fractional Laplace problem involving a singular term and a weighted critical Sobolev exponent. By using the idea of Nehari manifold methods and fibering maps, together with variational methods and the fractional Caffarelli-Kohn-Nirenberg inequality, we will prove that there exists at least two positive solutions when we have an appropriate choice of λ.

The semantic category involving the denotational semantics of computer functional programming languages should have pull-back properties. Functional programming languages are expected to be able to handle algebraic and lattice-ordered structures. An ideal semantic category involving a semantic model should have an algebraic and lattice-ordered structure, and the Riesz model domain is a category with an algebraic and lattice-ordered structure. Pull-back is also known as fibre product, is a important concepts in category theory, and is an abstraction of many concepts in mathematics, with rich connotations. Existence and uniqueness of pull-back is studied in the category of Riesz modules. The notion of pull-back is first introduced by constructing an object and a pair of morphisms that satisfy the notion of pull-back in the category of Riesz modules, and prove the existence and uniqueness of pull-back

Linear regressions are simple and convenient tools that are applicable in modeling the relationship of multiple variables; this regression can also extrapolate or interpolate based on given values to predict other values. To investigate how linear regressions, linear regressions with kernel trick, and linear regression with lasso and ridge regularizations are applicable in various real-life situations, this paper will discuss the distinctions between the regressions and assess each of their efficacy by implementing them in a couple of multi-variate datasets, one involving crime rates and Boston housing attributes, the other concerned with fuel efficiency and car features. We conclude that linear regression performs the best in MSE(40.316) and RMSE(6.349) metrics, while the Lasso regression performs best in MAE(2.804) and MAPE(19.689) metrics.

This study focuses on an in-depth investigation of centre of gravity rational interpolation as an important rational interpolation method. An important feature is that different interpolation weights can be used to derive different centre of gravity rational interpolation functions. By carefully choosing the interpolation weights, we can ensure that the centre of gravity rational interpolation does not produce poles or unreachable points, thus improving the numerical stability of the interpolation. However, when we try to approximate the interpolated function with oblique asymptotic properties, the traditional rational interpolation method may not be able to maintain the original oblique asymptotic properties. To cope with this problem, this paper proposes a novel centre of gravity rational interpolation method aimed at maintaining the oblique asymptote. First, we systematically investigate the conditions that the centre of gravity rational interpolation method needs to satisfy in order to ensure that the slant asymptote property is maintained. Then, we develop a complex optimisation model with the minimum value of Lebesgue's constant as the objective function, along with multiple constraints, including the rational interpolation of the centre of gravity not generating poles and unreachable points, the maintenance of the slanting asymptote property by the rational interpolation function of the centre of gravity, as well as the normalisation of the centre of gravity weights. By solving this model, we obtain the optimal values of the interpolation weights, which leads to the centre of gravity rational interpolation function possessing the slanting asymptote property. Through detailed numerical examples, we validate the effectiveness of this algorithm, demonstrating its excellent performance in approximating the interpolated function with oblique asymptotic properties. This research work not only provides new insights into theoretical mathematics, but also offers a more accurate and controllable interpolation method for engineering, science and data analysis, further promoting research and applications in related fields.

In the 18th century, mathematicians were quite interested in the factorial of the non-natural numbers such as 1.5 and 2.5, because when we plot the factorials of the positive integers on to the coordinate system, we can find that it seems like it has a smooth curve that can path through it. So we can find a general formula of the function of the factorials, which is the gamma function. In the year of 1729, Euler found this function(Beta function) when he was at the age of 22. 𝛣(𝑥) = ∫^+∞ ₀ 𝑒 ^−𝑡 𝑡 ^𝑥𝑑𝑡 . To make it easier for the application, we added 1 to the independent variable and the new function is the gamma function. 𝛤(𝑥) = 𝛣(𝑥) = ∫^+∞ ₀ 𝑒 ^−𝑡 𝑡 ^𝑥𝑑𝑡 After it is found out by Euler, it has been studied by the mathematicians from several aspects. And it has been applied to the different field of mathematics. In this paper, we are going to discuss about the identities and the applications of the gamma function. I hope it could be useful for the researchers after. In the chapter 1, we will introduce the background and list out the properties of the Gamma function and the functions that is related to it, and we will proof some of the theorems. In the chapter 2, we will discuss about the usage of the Gamma function in the field of integrals. In the chapter 3, we will discuss about the applications of the Gamma function in statistics. In the chapter4, we will introduce some other applications in mathematics. In the chapter5, we will conclude and make some expectations.

In this paper, we investigate the (3+1)-dimensional extended quantum Zakharov–Kuznetsov equation through the trial equation method and complete discrimination system. We successfully obtained 15 solutions including rational function solution, trigonometric function solution, hyperbolic function solution and elliptic cycle solution.

Implicit function theorem is one of the most classic and important results in modern mathematics[2]. It is used to describe whether one variable of a equation could be written as a function of the other variables, which also has a wide range of application[5]. For the proof of this theorem, one method is to discuss the properties of its partial derivatives in a certain field with the help of given conditions, in order to complete the continuity proof, and prove the differentiability of the function by using the differential mean value theorem. But obviously, such a proof is too complex. Therefore, in this paper, we will introduce some relevant contents of series, including the definition of series convergence and uniform convergence, the necessary conditions of convergent series, the continuity theorem of uniformly convergent function and Weierstrass discriminant, and take this as a starting point, construct a function sequence, and use the method of series to prove the implicit function theorem.

In natural and social phenomena, variables are usually random and independent, and most of them obey or approximately obey normal distribution. Student’s test scores are a typical example of this distribution. This work analyzes the examination scores by adopting a new normal distribution evaluation mechanism. First, on the basis of normal distribution, it introduces some novel features of density function by using double integral, polar coordinate transformation and squeeze theorem. Then, we proposed new statistical indicators and parameters to evaluate test paper quality and score distribution. Concrete examples proved that this mechanism has accurate judgment on the difficulty of examination papers and the distribution range of grades

In this paper, based on the function of multi-beam bathymetric system which can simultaneously send hundreds of beams to measure the depth of water at the same time, according to the real topographic characteristics of the seabed, the non parallel survey line design model based on beta is established. The overlap rate between adjacent coverage depth zones is constrained with the known measured sea area, and the whole sea area to be measured is guaranteed to be covered as much as possible. The coverage width of the survey line is calculated and the optimal survey line is designed under the condition of the slope of the seabed and the direction of the survey line.

A new definition of fractional derivative has recently been put forward, which solves many challenging problems in the field of fractional calculus. This derivative has no singular kernel named Caputo-Fabrizio time-fractional derivative (t-FD). Under this new definition, we investigate a class of boundary value problem (BVP) of fractional differential inclusions (FDI). By means of endpoint theory and Leary-Schauder alternative, the existence of solutions are generated. This is the first work dealing with BVP of FDI involving Caputo-Fabrizio (t-FD). Effectiveness of the obtained theoretical results is illustrated by several examples.

With the change in global climate and the reduction of energy resources, people will focus on the use of renewable energy, wave energy is a kind of renewable energy with relatively rich reserves, the potential of marine renewable energy is huge and has a broad application prospect, the high efficiency and scale of wave energy devices have become the focus of the field. In this paper, for the design problem of the maximum output power of wave energy, according to the physical formulas and theorems such as force analysis and the law of conservation of energy, we describe the motion state of the float and the vibrator to establish a mathematical model and realize the solution to the maximum output power of the floattype wave energy converter. Using the relevant float dynamics to establish the relevant motion model, a one-dimensional y-axis coordinate system perpendicular to the horizontal plane is established, and the plane at the junction of the initial horizontal plane and the float is used as the coordinate origin to analyze the motion state of the float and the oscillator and solve the state equations by using the Runge-Kutta algorithm. Then the corresponding coordinate system is used to calculate the optimal value of the damping coefficient of the corresponding damper and the maximum output power of the corresponding PTO system in different cases. The equation is solved by Fourier fitting each variable for the time variable and transforming the equation into complex exponential form.

Marine clutter is the electromagnetic field of radar echoes, the current research mainly focuses on its scalar statistics, rather than the polarization characteristics. Based on the description of the polarization state by Stokes parameter, the paper analyzes the statistical polarization of electromagnetic wave following the Rayleigh distribution, and simulates the polarization electromagnetic wave based on zero-memory nonlinear transformation method.

In some applications, including but not limited to synthetic-aperture radar (SAR) imagery and wireless communication, the Weibull distribution is more flexible than the exponential distribution for these purposes because it fits particularly well at the heavy tail of the sea clutter. Accurate and efficient simulation of radar sea clutter is practically significant for radar signal processing and sea target detection. In this paper, we present an algorithm based on Zero Memory Nonlinear Transformation (ZMNL) to simulate the coherent correlated Weibull distribution, modeling random scalar fields with intensity following the Weibull distribution, and extend it to random vector fields. At last, we explored the application of time-domain fusion methods in sea clutter suppression.

In the ocean depth detection, the multi-beam detection technology is widely used. Compared with the traditional singlebeam sounding system, multi-beam detection can obtain the seabed depth value of multiple measurement points in a stripcovered area, thus improving the accuracy of ocean depth measurement. This paper mainly studies the beam coverage and measurement efficiency of multi-beam detection in the submarine slope, and solves the optimization work based on the sinusoidal theorem and trust domain solution method, which is helpful for multi-beam detection technology in submarine topographic survey, submarine geophysical exploration, submarine pipeline detection and other fields.

The tennis match is full of variables, and the outcome is affected by many factors, such as serving skills, physical strength and mental state. Good psychological quality is conducive to the stable performance of athletes. It is important to study these factors to improve the value of tennis matches. Firstly, this problem first selects indicators from the data set to establish a comprehensive evaluation system, including multiple indicators such as average serve speed and ACE number. Then the principal component analysis method is used to determine the number of retained principal components and calculate the weight. Then, according to the weight and index data of principal components, the comprehensive evaluation score of players in each round is calculated. Finally, through the calculation of the model, the performance of the players in each round can be quantitatively assessed and presented in a visual way. Secondly, we tested the scoring sequence of the two players in the first 10 matches through the Ljung-Box test, and the results showed that the score sequence of player 1 was autocorrelated in each match, while the score sequence of player 2 was random in only one match. Therefore, the performance of supporting players is affected by a variety of factors and is not random. Further analysis shows that the first two principal components of the players have a high correlation with the total score, while the third principal component has a low correlation. Thirdly, this question analyzes the performance of two tennis players in the match through the principal component comprehensive evaluation model, divides their performance into strengths and weaknesses, and adds corresponding labels to the data set. Then, a variety of machine learning classification models are used to dig and distinguish the player status. In the model evaluation, the random forest model performed the best, which could accurately identify the "momentum" change of players. Finally, by analyzing the characteristic importance of the model, some suggestions are put forward, such as improving ball speed, increasing service score and reducing unforced errors, so as to improve players' match performance. Fourthly, this question is tested in three randomly selected matches based on the trained random forest model. The results show that the prediction results of the model are highly correlated with the actual competition situation, which proves its accuracy. In addition, based on the research results, the model promotion process suitable for different competition types is provided. Based on the results of the analysis, this study provides suggestions to help coaches take advantage of the role of players' momentum in the game. At the same time, it puts forward the measures to deal with various events that affect the course of tennis match.

This research investigates the Bayesian integration of visual and auditory cues in a dynamic decision-making task. We introduce a volatile Posner dual-cueing task to simulate the volatility nature of sensory information and develop a Bayesian agent to model human behavior. The agent employs a hierarchical Bayesian model to estimate the validity of visual and auditory cues, which are assumed to follow a multivariate Bernoulli distribution with a time-varying coefficient of variation (CV). The agent's response model integrates the cues' attentional factors, weighted by their precisions, to predict reaction speed (RS). Through simulations, the agent demonstrates the ability to adapt to changes in cue validity and precision, reflecting the dynamic allocation of attention and the optimization of reaction speed. The results show that the agent's performance is consistent with theoretical predictions, suggesting that the model is promising to effectively captures the essence of human multimodal integration. The study paves the way for future work to validate the model with human behavioral data and enhance our understanding of cognitive processes underlying attention and decision-making.

Aiming at the Internet background where network rumor dissemination shows new characteristics, the study of network rumor dissemination law in Internet media has become the key to network rumor governance. Based on the K-means clustering algorithm, this paper proposes an online rumor propagation model considering the dual influence of neighbors and associations. CA-Markov Based on the clustering algorithm, this paper proposes a model of online rumor propagation considering the dual influence of neighbors and associations, and through the model, we study the dynamic change of individuals' viewpoints on online rumors, so as to judge the overall trend of rumor propagation. Through simulation experiments, it is found that the higher the knowledge level of individuals and the more they stick to their own viewpoints can effectively reduce the scale of rumor spreading and the duration of rumor spreading; moreover, the more the number of associations participating in rumor discussion, the scale and duration of rumor spreading will also increase accordingly. This paper considers a two-factor model of Internet rumor propagation with the influence of neighbors and associations, and quantifies the dynamic change of individuals' attitudes towards rumors, but due to the fact that there may be different channels for individuals to propagate Internet rumors, this paper does not take into account the possibility that different channels may affect the propagation of Internet rumors.

In the process of ethylene production, the operating data of ethylene cracking furnace not only has the problems of time variability, non-gauss, strong noise, and outlier influence but also the collected data is incomplete, presenting the problem of scarce data with labels and abundant data without labels. To solve the above problems, this paper proposes a soft measurement model based on a semi-supervised Bayesian T-distribution mixture for the coking diagnosis of ethylene cracking furnaces. The model adopts a semi-supervised structure to solve the problem of the small number of data labels, adopts a T-distribution model to ensure the robustness of the model to strong noise and outliers under the Bayesian framework, and solves the solid variation of process data through the mixed model—complexity, non-Gaussian, and nonlinear problems. Finally, the experiment was carried out on the coking data of an ethylene cracking furnace in a petrochemical plant to verify the feasibility and prediction accuracy of the model under the condition of limited label data, and also to verify the robustness of the model to outliers.

Purpose: To systematically explore the research pulse and hotspots of clustering algorithms in pharmaceutical intellectual property rights in China, and to provide reference for researchers to comprehensively and objectively grasp the research trend in this field. Methods: Adopting clustering algorithms such as co-occurrence analysis, LLR algorithm, EM algorithm and mutual information algorithm, and using CNKI database as the data source, we searched and summarized the literature collected since the establishment of the database up to 2023, and drew the knowledge map and carried out the visualization analysis. Results: the research on pharmaceutical intellectual property rights in China started late and the awareness of intellectual property rights is weak; the cooperation between Chen Feng, Zhang Jing and Yang Jun is closer, and more work has been done in the research of pharmaceutical intellectual property rights. Keywords co-occurrence analysis found that the research hotspots are the object, law, system, measures and role of pharmaceutical intellectual property rights; cluster analysis found that the research focuses on the strategic research on intellectual property rights protection in the pharmaceutical industry; time series mapping shows that my current pharmaceutical intellectual property rights in China are in the stage of high-quality development. Conclusion: China's pharmaceutical intellectual property research needs to strengthen international cooperation and exchange, and continuously improve the traditional pharmaceutical intellectual property protection system and pharmaceutical intellectual property-related laws and regulations

The aim of this paper is to investigate the effects of light pollution on the environment and human health, proposing effective intervention measures. A widely applicable metric is developed to determine light pollution risk levels in different regions, forming the basis for a reliable assessment model. This model, integrating Analytic Hierarchy Process (AHP), Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) model, and multiple regression analysis (MRA), offers a comprehensive understanding of light pollution risk by considering regional development, light usage, and geographical factors. The assessment model demonstrates high accuracy and reliability in measuring light pollution risk, providing valuable insights into the interaction between factors such as light intensity, biodiversity loss, GDP, and population. Empirical analysis reveals regional disparities in light pollution risk levels, underscoring the need for targeted interventions to mitigate its adverse impacts. Overall, the developed light pollution risk assessment model serves as a valuable tool for policymakers, facilitating informed decision-making and effective intervention strategies.

The Spotted Lanternfly(SLF) originates from Asia and spread to the United States about a decade ago, where it has since proliferated and inflicted significant damage on a variety of agricultural industries. Therefore, investigating the transmission behavior of SLF and devising strategies to suppress its spread is a worthwhile topic to study. In this study, we selected SLF monitoring data from four vineyards in New York State in 2022, established a population life model based on the life history and annual population dynamics of SLF, and combined it with the natural environment of New York State, autonomous dispersal behavior of SLF, reproductive behavior, human intervention, and other factors to construct a multi-level state transition network aimed at simulating the spatial-temporal distribution of the pest in New York State. In addition, we designed a cost-allocation strategy based on a greedy algorithm and a simulated annealing algorithm to evaluate the effectiveness of the three interventions and to predict the population of SLF in these four vineyards for the next five years after the intervention. The final results showed that the strategy was effective in suppressing the spread and growth of SLF in the vineyards with sustained impacts.

In view of the traditional concrete weir blocking river longitudinal connectivity, affect the problem of river habitat. According to the existing river scattered grain permeable low weir structure, we proposed Y1, Y2, Y3, Y4 four permeable ecological weir form. Using numerical simulation technology of the flow field characteristics, analyze the section flow rate, along the flow rate and stability. According to the analysis results, Y1 weir is simpler than Y2 of the flow field with less circulation, and the damage of the weir is less and conducive to the passage of aquatic organisms. For the channel permeable weir, the flow rate of Y4 is less than that of Y3, which is conducive to the stability of the weir, and the flow rate of Y4 in the weir channel is less than that of Y3, which is more conducive to the passage of aquatic organisms. The backwater capacity of slope permeable ecological weir is stronger, which is suitable for the mountain river channel with small flow during the dry season; the channel permeable ecological weir is stronger for the plain river channel with abundant water supply.

The conventional method of seabed terrain matching is limited by its underlying principle and practical constraints, resulting in inadequate positioning accuracy and efficiency. To overcome this problem, this study proposes a novel approach to achieve precise distribution of survey lines for multibeam surveys. The approach utilizes an enhanced genetic algorithm of Adaptive Large Neighborhood Search Algorithm (ALNS). This method is of great importance for ensuring the safety of maritime navigation and improving the production of nautical charts. The study begins by establishing a mathematical model for measuring multibeam lines and simulating water depth data. Subsequently, bathymetric data is matched through adaptive selection, and the results are analyzed and calculated using various selection operators. The optimal selection operator is then employed for the final calculation. Finally, the integration of ALNS with the genetic algorithm leads to the optimal scheme for survey line distribution. Experimental findings demonstrate that this optimization method effectively improves measurement accuracy and coverage for multibeam surveys. It offers a viable solution for optimizing seabed topography measurements.

Addressing the challenge of monitoring profiles in the context of the phase I linear quantile mixed model, this paper assumes that binary profiles obtained from fixed samples collected over time adhere to a normal distribution. We then introduce a control chart grounded in the linear quantile mixed model, aimed at tracking changes in regression coefficients and exploring the robustness of the F-test estimation coefficient. Simulation results demonstrate that the proposed control chart offers a robust tool for statistical process control.

Nowadays, most of the 10 kV distribution network cable lines are laid underground in the form of direct burial or casing, and the cable is cut off by the construction machinery, resulting in the accident of line tripping. In the construction of urban construction, third-party external forces such as manual excavation, mechanical excavation and illegal invasion will cause serious damage to underground cables. Therefore, it is of great engineering application value to develop cable marking piles with sound source localization function and find the location of damage points in time. In order to improve the accuracy and effectiveness of positioning, but also to achieve rapid positioning of the source of damage, this paper is based on the sound sensor, using its flexibility, efficiency and timeliness, by controlling the number and location of the sound sensor, combined with the sound intensity to locate the sound source. At the same time, the sound sensor is connected with the number and position of the marking pile, and the traditional cable marking pile is improved to accurately locate the damage source in time.

In recent years, applications ranging from underwater navigation and construction to environmental monitoring and marine resource management have driven an escalating need for accurate and comprehensive bathymetric mapping of the marine environment. However, the complexity of the marine environment requires sound mathematical modeling of survey lines to ensure comprehensive coverage, optimal resource utilization, and high-quality data collection. This work outlines a mathematical model based on geometric and projection relationships in three-dimensional space to simulate a scenario in a designated sea area for bathymetric surveying. By knowing the slope angle of the seabed, assuming a planar seabed and considering the ship's position along a survey line, a model is developed to determine the coverage width of multibeam sonar beams on the seabed. The model involves calculating the water depth at different points along the survey line using the tangent of the slope angle, and then employing trigonometric functions and equations to establish a relationship for the coverage width, which is equal to the length of the segment intersected by the sonar beams on the seabed line. Further, the model accounts for the overlap ratio between adjacent survey stripes to optimize survey line planning for complete area coverage while minimizing resources and time. Additionally, a visualization of the seabed depth variation is suggested through plotting, simplifying the calculation by projecting the varying slope onto a horizontal plane. This approach facilitates the design of survey lines across the sea area, ensuring efficient and comprehensive bathymetric mapping.

In this paper, the eigenvalue inverse problem for generalized Jacobi matrices with period plus edges is studied, and such problems have some applications in research in the fields of mathematics, engineering, quantum mechanics, and other disciplines. A row-by-row inversion of the nonzero elements of the matrix is carried out with the given two eigenpairs, and several lemmas are formed by discussing the cases during the inversion process, which in turn gives the solution of this inverse problem, and the corresponding existence uniqueness theorem of the solution is obtained. And two numerical examples are used for checking and achieving the expected results.

Global warming has become an urgent issue in the world today, therefore, developing carbon sink models based on forest systems is crucial. Firstly, the stock conversion method is established by combining the growth characteristics of the forest system with the control equation of a discrete-time economic system. This results in the regression equation for accounting the forest carbon sink. Secondly, establish a linear programming model with the goal of minimizing carbon consumption during forest harvesting. Finally, we have calculated that China's forest carbon storage will reach 22.12 billion tons by 2025, therefore, we need to maintain an annual logging volume of 423 million cubic meters. Using logging volume as a control variable, minimize the carbon consumption generated by China's forests due to economic development. In addition, we have considered the carbon sequestration benefits and socio-economic benefits of forests. Firstly, the Net Primary Productivity (NPP) of vegetation is used as a forest carbon sink indicator, and the CASA model based on remote sensing data is used for calculation to estimate the forest carbon sequestration capacity. Secondly, using geographic detectors to identify the dominant factors affecting vegetation NPP. Research has shown that vegetation cover directly affects vegetation NPP and thus indirectly affects the value of forest ecological services. Then, using NPP data to calculate the value of forest ecosystem services, the relationship between GDP and the value of forest ecosystem services is further explored. The results indicate that GDP growth comes at the cost of sacrificing ecological benefits, and increasing vegetation coverage can effectively improve "green GDP".

Sex ratios of sea lampreys vary in response to the external environment. In order to analyze sex ratio and its dependence on local conditions, we need to develop models that reflect the relationship between sex ratio and resource availability. In this paper, we establish a link between individual sex and the availability of larval food resources. Then, we extend the object of study from individuals to populations and express the dynamics of the sex ratio as a differential equation. We introduce other factors affecting the sex ratio to refine the relationship between reproductive rates and sex ratios. To better model the growth of the lamprey population, we developed a Gompertz model that initially approximates the growth rate of the exponential function. And the introduction of the Allee effect provides a more comprehensive view of population growth.

The in-depth understanding of the topography and geomorphologic features of the seabed constitutes the basis for human to fully understand the ocean, effectively explore the ocean and scientifically and rationally utilize the ocean. Our focus is on the optimization of line layout of multi-beam sounding technology in seafloor topographic mapping, aiming to explore the reasonable layout strategy under the dual objectives of ensuring comprehensive coverage and efficient measurement[1]. As a key tool to obtain basic spatial geographic information of water area, multi-beam sounding system has a direct influence on the selection of direction and location of survey lines, especially in the face of complex seabed topography, the change of strip coverage between adjacent survey lines may lead to regional missing survey phenomenon. Aiming at the overlapping rate control problem in the layout of survey lines, our research uses the sine theorem and other geometric principles to establish the coverage width and overlapping rate model under the specific situation that the survey line is along the isobath direction, and reveals the law that the coverage width of the multi-beam sounding system is positively correlated with the water depth under the condition of fixed survey line interval, and gives specific numerical results through empirical data. The paper further discusses the layout scheme of survey lines with optimal measurement efficiency, defines the area coverage index per unit slope length, and constructs the corresponding layout models for the two special terrain types projected as isosceles trapezoid and rectangular parallel to the isodepth line. Through the stepwise optimization calculation, it is found that the layout scheme based on trapezoidal projection cannot reach the effective solution when the overlap rate is set to 20% while meeting the requirement of full coverage. Under the condition of rectangular projection, if the overlap rate is set to 10%, the optimal solution is obtained: the shortest 70 measuring lines need to be laid, and the total length of the measuring lines is 259280 meters. Moreover, the test results after a small adjustment of the overlap rate show that the solution has certain convergence, thus enhancing its possibility as the optimal solution. The research results of this paper not only deepen the understanding of the theory of line layout of multi-beam sounding system, but also provide an optimization method in practical operation, which is of great significance for improving the accuracy of ocean surveying and mapping, working efficiency and reducing resource waste.

This paper focuses on word difficulty prediction and classification on the basis of capturing a year's word game data. Although Wordle was all the rage, recent tracking data shows that the Wordle popularity appears to be declining gradually, and the number of players has a downward trend. To promote the healthy development of Wordle and assist game developers in adjusting their game strategies in time, this paper establishes a word difficulty prediction model. Before Wordle difficulty prediction model is established, we preprocessed the data, rasterizing the area to be studied. In phase I, we introduced a PSO-LSTM prediction model and performed specific training, achieving an accuracy rate of over 85%. After coding the letters in “EERIE”, we successfully obtained the percentage of word “EERIE” on March 1,2023 will appear. The second phase uses hierarchical clustering analysis to subcategorize words by difficulty. The difficulty of words is then divided into five levels based on the folded graph of clustering coefficients derived from the elbow rule. Finally, this paper presents a model accuracy test and suggests the idea that this model can predict the data of serial relationship within the existence time and can be extended to the evaluation and weighted ranking under the influence of other factors.

To better understand the significance of lampreys in the ecosystem, we developed a model of the lamprey-trout ecosystem based on Lake Superior. We introduced sex ratio and growth potential based on the physiological characteristics of lampreys, and improved the traditional Lotka-Volterra model by considering climate change, species migration, and disease transmission. Simulating the above model in a diverse ecosystem, it was found that lampreys with sex ratio can survive better in the ecosystem and bring greater resistance stability as well as resilience stability to the external environment after a disaster occurs, and once it is lost, its reproduction rate and predatory activities will be affected. The population size of the ecosystem will be drastically reduced, which will also lead to a decrease in the stability of the ecosystem.

We construct a positive-preserving nonlinear scheme to solve the the pressure equation of two phase flow model with tensor permeability in porous media on general quadrilateral grid, and a traditional upwind finite volume method to solve the saturation equation. We prove the pressure is positive if only injection well present with 0 value boundary condition. Numerical experiments show that the the numerical pressure and the saturation are positive and without nonphysical oscillation with tensor permeability on general quadrilateral grid.

Continued outbreaks of infectious diseases have underscored the urgency of devising and implementing effective control measures to mitigate infection rates. Among the strategies employed, the isolation of communities harboring potential infection vectors stands out as a key method to curtail the spread of such diseases. In this vein, this study introduces a refined SEAIR (Susceptible, Exposed, Asymptomatic, Infectious, and Recovered) transmission model that integrates contact patterns determined by inter-community population movements. The robustness of the model is evidenced by its strong fit with empirical infection data. The results underscore a pronounced degree of interaction within individual neighborhoods, underscoring the critical role of targeted local public health strategies and interventions. The model predicts that heightened isolation measures within communities experiencing infections can effectively control the spread of infectious diseases within three weeks. This finding accentuates the pivotal role of isolation at the community level as a viable public health response to infectious disease outbreaks.

The mechanism of viscoelastic polymer solution flooding is very complicated. In order to further improve the flooding effect and improve the flooding mechanism, the flow characteristics of viscoelastic polymer solution under different models were developed. In order to study the microscopic flow characteristics of polymer solution, this paper studies the typical reservoir porous model-sudden shrinkage channel model. Phan-thine-tanner (PTT) model, Upper-Convected Maxwell constitutive model, Oldroyd-B model are selected to establish a two-dimensional, steady and isothermal mathematical model of fluid flow. The finite difference numerical method is applied to solve the mathematical model, the stream function contours, velocity contours are drawn. The effect of the parameters of viscoelastic polymer solution on the flow characteristics was studied, and the effect of viscoelasticity on the microcosmic sweep efficiency was analyzed.

The restoration of Chinese variant characters refers to the process of converting variant characters in a text to the standard form of Chinese characters. Existing methods mainly treat the variant character restoration as a text error correction or machine translation task. Due to the diversity of variant character forms and the fact that many Chinese characters are visually or phonetically similar but have distinct meanings, Chinese variant character restoration presents challenges. However, traditional text correction models are used to handle aligned sequences, which cannot be directly applied to the variant character restoration. Moreover, using machine translation models for restoration results in low efficiency of restoration and restoration errors. To address these issues, the variant-T model based on multi-dimensional features and local attention is proposed in this paper. The multidimensional word embedding based on the RoCBERT is used to extract multi-dimensional features of text. Further, a model based on local attention is employed, and a local masking mechanism is proposed, which effectively the problem of incorrect restoration. Experimental results show that the word error rates are reduced to 0.51% and 0.62%, and the F1 scores reach 85.2% and 85.7% on the SIGHAN14 and SIGHAN15 datasets. Furthermore, the word error rate is reduced to 0.2% on the variant SMS datasets, which outperforms other models.

As one of the four ancient civilizations, China annually excavates a significant number of glass artifacts, making it imperative to investigate their composition and associated factors for the preservation of cultural heritage linked to glass products. This study meticulously classifies glass artifacts by employing methods such as categorical variable correlation, systematic hierarchical clustering, and correlation coefficients based on data provided by Chinese archaeologists. The research explores the factors influencing surface weathering of these artifacts while establishing a model using distance-based classification approach to determine artifact typology based on their composition. These findings contribute to an in-depth understanding of Chinese glass artifacts and provide crucial insights for conserving glass cultural relics

This paper presents an obstacle-informed A* algorithm that incorporates obstacle positioning to optimize path planning, diverging from traditional A* and Dijkstra algorithms that focus solely on distance. The proposed method integrates a novel penalty function, dependent on a cost factor B, to reduce node traversal by avoiding areas dense with obstacles. Although less effective in complex terrains due to B settings, a methodology for B determination is provided. Simulation tests on grid maps with varied obstacles validate the algorithm's effectiveness.

With the ongoing development of the techniques in the new eras, multi-beam line measurement for the assessment of water depth has become a significant research topic. In this paper, we developed a model for multi-beam bathymetric coverage width, taking into account several factors, such as the propagation velocity and propagation time index of sound waves in seawater. Additionally, we considered the correlation between coverage width, line spacing, and overlap rate. The geometric algorithm and triangulation principle were applied for the improvement of multi-beam bathymetric lines. Based on the investigation result of the sounding of each angle route, the shortest route path of sounding suitable for different sea terrains is determined.

Let 𝑯̇ is a star graph of order 𝒔 + 𝟏, 𝓑̇ ≜ 𝓑̇ _{𝑯̇ ,𝝁} denote an arbitrary signed bipartite graph with 𝑯̇ as a star complement for a non-main eigenvalue 𝝁. In this paper, it is proved that 𝓑̇ exists if and only if 𝝁 is an integer such that 𝝁 ∉ {−𝟏, 𝟎, ±√𝒔} and 𝒔 − 𝝁 ^𝟐 is divisible by (𝝁 + 𝟏) ^𝟐 . The spectrum of 𝓑̇ is given and the maximum order of 𝓑̇ is 𝟐𝒔 . It is proved that if 𝝁 is positive and the maximal signed graph 𝓑̇ has adjacent vertices 𝒗_𝟏, 𝒗_𝟐 with the net-degree 𝒔, then 𝓑̇ − 𝒗_𝟏 − 𝒗_𝟐 is net-regular. Furthermore, extremal signed graphs 𝓑̇ are characterized in the case of 𝝁 = 𝟏, 𝒔 = 𝟓 and 𝝁 = 𝟐, 𝒔 = 𝟏𝟑.

In order to scientifically and reasonably evaluate green suppliers, a multi-attribute decision-making method based on a probability language terminology set is proposed. Firstly, considering the characteristics of green suppliers, a green supplier evaluation index system is constructed from four dimensions: quality, logistics cost, delivery stability, and green indicators. Secondly, to address the issues of fuzziness in evaluation information and insufficient consideration of interrelationships between attributes, a probability language DEMATEL model is developed to determine weights, and a probability language scoring function is used to rank alternative suppliers. Finally, the feasibility and effectiveness of the proposed method are validated through case analysis and comparative analysis.

This article deals with the mixed local and nonlocal equation with critical Sobolev exponent. By using the fibering map and Nehari manifold techniques, together with variational methods, we establish the existence results of a nontrivial solution under certain suitable hypotheses on the parameter λ and the weighted functions 𝑝(𝑥) and 𝑞(𝑥) .

Semantic categories involving the semantics of computer functional programming languages should have Cartesian closure. Functional programming languages are expected to be able to handle algebraic and lattice-ordered structures. The ideal semantic category involving semantic models should be the category of Riesz modules with algebraic and lattice-ordered structures. According to the above requirements, we based on the category of Riesz module, Study the exponential object in the category of Riesz modules, and proves that the category is cartesian closed.

Nonlinear evolution equations have always been the most important and difficult points of research in various disciplines. In this paper, the generalized equation based on the Hirota-Satsuma coupled equation describing the interaction of two long waves with different dispersion relations is studied. We obtain the integrable form of this equation through travelling wave exchange and surface kinetics behavior, and obtain three types solutions of this equation through the complete discrimination system for polynomials, including singular solutions, solitary wave solutions, and double periodic solutions. We take out particular value for each parameter and draw images of solutions to understand the existence of the solutions.

Superconducting critical temperature has great significance in superconducting applications. Traditional critical temperature prediction using experimental and computational physics methods, there are problems such as high experimental cost and long calculation time. Machine learning model has the advantages of fast prediction speed and low threshold of use. At present, traditional machine learning algorithms use more superconducting property characteristic parameters, resulting in large calculations, over-fitting, and other problems. In this paper, aiming at the situation of excessive features in the prediction algorithm, the method based on superconducting microscopic theory combined with the analysis of physical and chemical properties of materials is adopted to select the feature parameters and use them for machine learning model training and prediction, which can improve the prediction accuracy, effectively prevent over-fitting. For example, reduce RMSE from 8.4K to 2.7K through mutual information screening features, improving the prediction accuracy by 68%.

Considering that the embedding theorem is the key to studying the regularity of partial differential equations, in this paper, we established a compact embedding for fractional spaces HW ^s,p in bounded domains on the Heisenberg group.

In recent years, among the causes of death that are relatively easy to induce, the death rate of cardiovascular disease consistently ranks the first place and continues to rise year by year. The calcium signal involved in calcium ions is the main cause of cardiovascular disease at the microscopic level. Calcium wave is one of the representative calcium signals, so it is important to understand its mechanism. The diffusion and mechanism of calcium waves in the sarcoplasmic reticulum of cardiomyocytes were studied in this paper. Based on the spatial diffusion mechanism of calcium waves in the sarcoplasmic reticulum, a numerical calculation model of calcium waves in the sarcoplasmic reticulum was established by considering the physical spatial structure of calcium waves, the dissociation reaction between calcium ions and other substances, and the transport of calcium ions by calcium pumps. The computer program was used to simulate the calcium waves in the sarcoplasmic reticulum. The model in this paper simulated the triggering and propagating process of the calcium waves in the local myocardium.

Air pollution poses significant risks to human health, ecosystems, and socio-economic stability. Accurately predicting PM2.5 concentration and Air Quality Index (AQI) is crucial for understanding pollution factors and devising effective control measures. This paper addresses Question C of the 2023 Huazhong Cup, focusing on predicting air quality using a multivariate hybrid prediction model, Prophet-XGBoost, which combines the Prophet time series decomposition algorithm and the XGBoost machine learning model. To address problem 1, this study performed KNN interpolation and IQR outlier removal on the data in Annex 1 and Annex 2 to eliminate missing and outliers in the meteorological data, and then standardised the data. Then, Random Forest Regression (RFR) was used to filter out the features related to the changes of PM2.5 concentration. Firstly, the Random Forest model was trained to determine the decision tree and the optimal number of leaves of the model, and then regression analysis was performed to find out the importance of these features to PM2.5 concentration, and the three main features screened out were PM10, the average temperature and CO, with the scores of 0.7742, 0.1075 and 0.0910, respectively. Comparison with the multiple linear regression model in the model evaluation demonstrated the accuracy of the model, and the calculation of Pearson's correlation coefficient confirmed the reasonableness of the model. In order to solve problems 2 and 3, when constructing the multi-step model, this study divides the training set and test set according to the ratio of 8:2, and firstly trains the prediction results of the known data based on the Prophet timedecomposition algorithm and the XGBoost machine learning model respectively. The results show that the two models have their own advantages and disadvantages, in order to obtain the prediction results that can meet the cyclical and seasonal changes of meteorological features, as well as its unstable and nonlinear characteristics, this study combines the two models together and adopts the Prophet-XGBoost combined prediction model model. The indexes of the combined model are greatly improved compared with the single model, which proves the reasonableness of the hybrid model prediction. Finally, the Prophet-XGBoost model was used to predict the PM2.5 concentration and AQI at the given times in Annex 3, and the air quality warning levels were determined based on the prediction results, which provided a useful reference for the formulation of more effective air quality management strategies.[1]

In view of the problem of multibeam survey line in the 2023 Higher Education Cup China Undergraduate Mathematical Contest in Modeling, this paper proposes an optimal survey line method for multibeam planning based on the geometric shortest path model. Through this method, the coverage width of multibeam survey line and the overlap rate of adjacent two survey lines are calculated, and the multibeam survey line planning is carried out for sea areas with different depths, so as to achieve the shortest path survey line coverage in the range of 10%-20%overlap rate and achieve the optimal detection effect. Through the model solving and verification results, this method can be widely used in the survey problem of the seabed slope area with inclination, so as to improve the efficiency and accuracy of the survey ship in the seabed survey task.

Additive manufacturing technology, with its characteristics of no mold and short production cycle, provides a new scheme for the machining and manufacturing of high performance and difficult material parts. However, the forming process of additive manufacturing is non-equilibrium solidification, which is easy to form uneven microstructure and reduce the mechanical properties of the parts. Special energy field assisted forming technology has great potential in improving the manufacturing problems of high-strength difficult-to-process materials. In recent years, it has been continuously applied to additive manufacturing to improve the microstructure and properties of parts. Ultrasonic assistant is an important method to reduce the residual stress in the additive manufacturing process, and its scientific principle is still a frontier scientific issue. Therefore, this paper uses molecular dynamics (MD) method to study the influence of ultrasonic assistance on residual stress in additive manufacturing process. In this paper, the process of ultrasound-assisted 3D printing of graphene reinforced aluminum (Al) matrix composites was simulated by MD method. The effects of ultrasonic aid on grain size, orientation and dislocation in the composites were analyzed, and the mechanism of ultrasonic aid reduction of residual stress was revealed, which provided theoretical guidance for ultrasonic aid additive manufacturing process.

Grey wolf optimization (GWO) algorithm, when applied to multidimensional and nonlinear optimization problems, often encounters the problems of getting stuck into local optimums and slow rate of convergence. Aiming at above two problems, we propose the grey wolf optimization algorithm on the basis of dynamic weights (DGWO) in this paper. This strategy can dynamically adjust the position updates of other individuals depending on the three best search agents' own locations, thus improving the search precision and speed of GWO. Additionally, to validate the usefulness of our proposed algorithm in treating multidimensional and nonlinear optimization projects, six classical benchmark functions are selected as test targets and some classical algorithms are compared with them in this paper. The results of simulation experiments indicate that DGWO exhibits superior optimization search performance compared with other competing algorithms.

Forest ecosystem management is facing increasing problems due to global climate change. Precise simulation and monitoring of forest biomass is a crucial method to elucidate the effects of climate change, understand the growth dynamics of forests, and promote the sustainable management of forests. This paper presents the optimization of the 3-PG stand growth process model using Morris sensitivity analysis and Bayesian parameter optimization algorithm, based on data from the Huitong Long-term Ecological Research Station for Chinese Fir Plantations. Additionally, a web-based fir biomass simulation and visualization system was developed using the optimized model. The results demonstrate that the optimized model has greatly enhanced the precision of the simulation in comparison to the default 3-PG model, achieving an average accuracy of 99.4%. This improvement is particularly relevant for simulating fir biomass. The biomass data for roots, stems, and foliage output by the model can be utilized for biomass visualization by considering the 5% quartile, median, and 95% quartile values to show the range of uncertainty in the model's predictions while highlighting the central tendency of the data. Through the system, users could easily access and analyze the biomass trends of various components of fir. By inputting fundamental information such as climate data and stand characteristics, users could obtain intuitive simulation results for fir biomass. This work involved the optimization of the 3-PG growth process model and the development of a fir growth simulation system using this model. The purpose of this system is to give data and technical assistance for the management of fir resources and the sustainable management of forest ecosystems. At the same time, in order to expand the application scope of the model, the system provides an interface for users to input data for model optimization by themselves, which realizes the simulation of the biomass of different tree species and responds to the dynamic changes of the forest ecosystem in a more comprehensive way

Due to the complexity of hydrological characteristics in lake systems and their susceptibility to environmental changes, water level control in lake systems has always been a highly challenging issue. This paper proposes a water level equilibrium control scheme for lake systems based on an intelligent anti-interference architecture using neural networks. By analyzing the spatial distribution structure and historical hydrological data of the Great Lakes system, a mathematical model for water level equilibrium control is established. Subsequently, an intelligent controller structure based on neural networks is proposed. This controller can real-time perceive changes in lake system water levels and automatically adjust control strategies to maintain water levels fluctuating within appropriate ranges. Finally, the proposed method is applied to a simulator of the Great Lakes system in North America. The results indicate that the proposed method can achieve stable control of lake water levels under different environmental conditions, demonstrating good stability and robustness.

This study addresses the critical issue of order cancellation in China's competitive online takeout service market, with a particular focus on Meituan. It explores the relationship between service response times, specifically waiting times, and the rate of order cancellations, aiming to develop predictive models to identify and intervene in high-risk orders proactively. The research methodology integrates logistic regression, propensity score matching (PSM), and back propagation neural networks to analyze data from a leading Indian takeout service, Swiggy, highlighting the study's international applicability. Initial findings suggest that extended waiting times significantly enhance the probability of order cancellations, impacting customer loyalty and satisfaction negatively. Through empirical analysis, logistic regression identified specific waiting time stages that critically influence cancellation probabilities. PSM was employed to examine the effects of reassignment on order cancellations, showing that strategic order reassignment could mitigate cancellation risks. Lastly, a back propagation model demonstrated high accuracy in predicting cancellations, suggesting potential for early intervention. This study not only provides a robust statistical framework for understanding and reducing order cancellations but also offers actionable insights for improving operational efficiency and customer retention in the fast-paced takeout industry.

The intact rate of product storage is an important indicator requirement for warehouse management. To ensure the intact rate of product storage, maintenance work needs to be carried out. This article conducts research on the optimization of joint maintenance plans for multiple independent products. We have constructed a multi class independent product joint maintenance plan optimization with cost as the goal, storage integrity requirements, and batch maintenance management mode as constraints. Design a heuristic algorithm suitable for the model to solve the problem of independent and unified testing of different types of products in the same batch. The application examples show that the model and algorithm proposed in this article are very effective for optimizing maintenance plans.

In the process of implementing multi-target interception by the air defense system of systems (SoS), the deployment position, interception range, and weapon speed of each fire unit in the air defense SoS vary due to the different characteristics of the various incoming air targets, the direction of attack, and the interception value, among other factors. Facing many different incoming targets, recommending the most suitable air defense unit to intercept in the Air Defense System of Systems (SoS) is a typical decision problem. This paper presents a novel model for utilizing interception suitability to support situation-driven shooter recommendations in air defense systems. To account for typical situational factors such as target threats, shooter deployment, and remaining firepower, the interception suitability computational model is designed to incorporate each of these variables. This model determines the level of suitability of an interception solution for a given context. To operationalize this concept, a behavior tree was developed to outline the decision-making process for recommending shooter intercept strategies based on the level of interception suitability presented by a given scenario. The model was then tested through simulation experiments conducted by a behavior-tree agent in typical task scenarios, showcasing its effectiveness in enhancing the overall interception efficiency of air defense systems.

Targeting unexpected scenarios such as crowd congestion and road congestion, this paper presents an emergency evacuation path planning model based on an enhanced ant colony algorithm. The heuristic function and pheromone concentration update strategy were enhanced, leading to the optimization of the evacuation path. A grid map model was constructed to simulate emergency evacuations under both congested and non-congested conditions in a real-world scenario. It is demonstrated that the enhanced ant colony algorithm exhibits superior convergence speed and global search capability, enabling the generation of safer evacuation routes considering both crowd congestion and road congestion.

With the continuous development of society, the distribution of cultural and educational resources has become a concern, which is related to the quality of local cultural heritage and education popularization. Traditional resource allocation methods usually have some problems, such as low efficiency, obvious inequality and difficulty in dealing with uncertainty. In order to meet these challenges, this study introduces an improved Particle Swarm Optimization(PSO) algorithm, and constructs an intelligent allocation model of local cultural and educational resources based on adaptive PSO to optimize the allocation of cultural and educational resources. Through the simulation experiment based on real data, this study verifies the effectiveness of the improved PSO algorithm in the allocation of local cultural and educational resources. The results show that the improved PSO algorithm not only improves the efficiency of resource utilization, but also optimizes the resource allocation strategy and reduces the occurrence of inequality. The algorithm also responds to the uncertainty well, which is expected to provide strong support for the intelligent allocation of local cultural and educational resources.

A modified Grey Wolf Optimization (CGWO) algorithm is introduced, employing a cosine improvement factor strategy to address the challenges of slow convergence speed and low optimization accuracy encountered in the initial Grey Wolf Optimization (GWO) algorithm. This approach aims to enhance the efficiency of the GWO algorithm by integrating a cosine function-based improvement factor strategy. The optimization performance of CGWO is compared with that of several classic swarm intelligence algorithms across four typical test functions. The results of experiments indicate that CGWO shows superior convergence speed, optimization accuracy, and stability when compared to three other classics warm intelligence algorithms.

Each year, a significant number of rare, protected, or endangered wildlife are illegally captured and trafficked, forming a vast illicit trade network that poses a serious threat to wildlife survival, potentially leading to species extinction and ecological imbalance. In response to this issue, we have launched a five-year project based on data analysis^[1] aimed at reducing the scale and impact of illegal wildlife trade. The project will develop strategies through identifying target stakeholders, forecasting potential impacts, and evaluating the likelihood of project success. We collected and analyzed illegal wildlife trade data from 2003 to 2021. The results indicate that China is one of the world's largest importers of illegal wildlife trade, thus selecting the Chinese government as the optimal target client. Concurrently, literature and data analysis underscore the impacts of illegal trade on natural environments and biodiversity, emphasizing the necessity for enhancing legal frameworks, strengthening enforcement, raising public awareness, and fostering international cooperation. We employed a system dynamics model^[2] to simulate the impact of project implementation on illegal wildlife trade, and established a logistic regression model^[3] to analyze the likelihood of project success. Model predictions demonstrate a relatively high probability of success for the project. Additionally, sensitivity analysis was conducted, considering the influence of changes in factors such as public awareness and enforcement intensity on success probability, along with the potential impacts of external factors such as international cooperation and economic conditions. In conclusion, this paper aims to assist in understanding and evaluating strategies to reduce illegal wildlife trade, providing a comprehensive framework based on empirical analysis. We selected the Chinese government as the optimal target client, believing in its significant role in global wildlife conservation and effective reduction of illegal wildlife trade through this project.

Aiming to address the shortcomings of Dung Beetle Optimizer (DBO) in the areas of accuracy and convergence speed in dealing with cloud computing task scheduling issues, this paper suggests an advanced Dung Beetle Optimizer (DGTDBO)- based cloud computing task scheduling method by combining the differential strategy and the perturbation strategy. Among them, the differential strategy strengthens the global exploration performance of the method, while the perturbation strategy improves the capability of the algorithm to escape from the local optimal trap. Through validation on different sizes of cloud computing systems, it is confirmed that the suggested DGTDBO can enhance the solution accuracy and speed of the algorithm effectively. It is considered as a promising cloud scheduling method.

Tennis, more than any other sport, is a game of Momentum. The absence of a clock to do the dirty work of finishing off an opponent, and a scoring system based on units used, makes the flow of the match much more important than any lead that has been established. In this study, we have developed Markov Chain model to predict the flow of play, Random Forest model to assess the impact of momentum changes on match outcomes. By comparison with XG-Boost, and LGBM, which achieves the accuracy of 0.6231 and 0.7061, we find that Random Forest achieves the highest accuracy of 0.8572 and passes the Monte Carlo test with a p-value of 0.048, rejecting the null hypothesis that momentum is unrelated to match outcomes.

In recent years, the growth of the overall economy and the improvement of residents' consumption levels have led to rapid growth in demand for air passenger transport. Specially, large hub airports generate enormous passenger traffic, and the mobility of people exhibits traits of high dynamics, high density, varying time distribution, and significant service pressure. To address the issue of whether taxi drivers wait for passengers and return to the airport or not, the taxi passenger data observed by the taxi management of Beijing Capital International Airport is modelled and analyzed. Given the fluctuation in airport passenger numbers and taxi driver profit conditions, it is feasible to construct a hierarchical model through the implementation of the hierarchical analysis technique. This model will comprise a decision-making model that ensures the selection of the appropriate taxi drivers at the airport that predicts the profits of both long and short distance drivers, alongside simulation. Subsequently, and feasibility analyses are then conducted to refine decision making practices. The correlation between key factors, such as the taxi driver's duration of stay at the airport, is then analyzed to compare profits from both Options so that the driver can ultimately make the decision. Ultimately, this profit-driven system enhances profitability and labor efficiency, facilitating optimal decision-making for taxi drivers.

Traditional GDP accounting only pursues the development of economic aggregate, ignoring the loss of energy resources and the destruction of natural environment, thus triggering a new upsurge of green GDP research in the theoretical circle. Compared with traditional GDP, green GDP is a more sustainable economic evaluation index, considering resource cost and environmental cost when calculating national economy. Based on the internationally accepted green Gross Domestic Product (GGDP) calculation method and scholars' research, a new GGDP calculation model is proposed in this paper, which is mainly divided into two parts: natural resource loss and environmental pollution loss, which are respectively divided into two primary factors. The portfolio of sub-criteria reflecting sustainable development capacity was reduced to 13 factors. Principal component analysis was used to find out the representative principal factors. On this basis, the relationship between the main factors, gdp and global mean temperature, and the influence of each factor on the temperature forecast in 2020-2040 are analyzed. Based on IESI and BP neural network model, a global temperature mitigation prediction model considering the sea temperature and land temperature of each climate country is established. The results show that there is a 74% probability that the GGDP growth rate is positively correlated with temperature change over 50 years. Using the computational model GGDP, the differences between development patterns and global GDP and green GDP are analyzed, and the relationship between environmental efficiency and global mean temperature is examined. All factors are proportional to global temperature, indicating that natural resource utilization and pollution emissions have significant effects on economic growth and temperature rise. Finally, it evaluates the global sustainable development level from the perspective of economy and environment, and establishes the sustainable development evaluation method.

In order to deal with transportation emergencies and improve emergency management capability, it is of great significance to scientifically evaluate emergency management capability for transportation emergencies. Game theory and fuzzy theory are introduced to construct a fuzzy comprehensive evaluation model of emergency management capability for transportation emergencies. Combination weight is calculated based on game theory, and membership degree is calculated using the whitening weight function. Case study is also conducted. The results show that emergency management capability of the city is generally average, and emergency legal system, emergency equipment, and emergency information platform have an impact on emergency management capability. Case study shows that the model is feasible and applicable in transportation emergency management capability evaluation, which provides support for improving transportation emergency management capability.

This work investigates an adaptively updating rule of the penalty in alternating direction method (ADM) for 𝑙1 problem. The adjusting criterion is motivated by the iterative behaviors of the objective and residue of constraint. The main algorithm is focused on the ADM framework of the dual problem. By studying the iterative behaviors, the dynamically updating scheme is developed with default values of startup, frequency and scaling. Numerical experiments show that the novel algorithm can not only speed up the classic ADM, but also make the choice of initial penalty parameter more flexible.

Fuzzy comprehensive evaluation is a method based on fuzzy mathematics that applies the principle of fuzzy relationship synthesis to quantitatively assess factors with unclear boundaries and difficult quantification through comprehensive evaluation. As this method gradually improves and becomes more widely applied, it becomes capable of handling problems involving a large number of complex phenomena and interactions among various factors, yielding satisfactory results. To demonstrate the practical feasibility of this method, we applied it to a specific problem concerning lamprey, resulting in conclusions consistent with natural phenomena, thus validating the rationality of fuzzy comprehensive evaluation. Furthermore, based on our conclusion, feasible solutions are provided to address the problem of lampreys in the five major lakes.

The paper introduces a factory-specific SLAM algorithm that seamlessly integrates deep learning with feature point filtering to address challenges associated with inaccurate and biased positioning data in industrial environments. By carefully considering the distinct characteristics of factory settings, particularly those where AGV robots operate, our approach effectively distinguishes between dynamic and static entities commonly encountered in such environments. To achieve this, we employ a deep learning-based dynamic object detection mechanism along with a refined feature point filtering process. Initially, deep learning algorithms are utilized to identify potential dynamic objects in the scene, providing valuable prior information. Subsequently, a feature point filtering algorithm is meticulously crafted to eliminate feature points that may introduce interference. This refinement ensures a more rational removal of dynamic feature points, thereby improving the positioning precision and robustness of the visual SLAM system in dynamic factory environments. Extensive experimental results demonstrate that, when compared to ORB-SLAM2 and DS-SLAM, the proposed algorithm achieves superior positioning and mapping accuracy in factory settings. This advancement not only addresses a longstanding challenge in robotics but also represents a significant stride towards enhancing the autonomy and reliability of AGV robots in industrial applications.

Quantile regression is a technique used to estimate the conditional quantile of the response variable. Unlike the classical least squares method, it doesn't assume any specific error distribution and offers a more comprehensive assessment of the impact of independent variables on the conditional distribution of the response variable. Consequently, quantile regression boasts unique advantages in practical applications. In this study, we employ the quantile regression method to determine coefficients in the time series model. By processing time series data using quantile regression and monitoring it alongside control charts, we aim to validate the approach using real-world examples of population and birth rate data in our country.

This study proposes entropy weight-fuzzy evaluation and stacking model to quantify and predict momentum in sports competitions. While many traditional studies have explained the existence of momentum from psychological and statistical perspectives, this study focuses on analyzing momentum in sports based on mathematical model and machine learning. Taking 2023 Wimbledon Men’s Singles Final as an example, this study conducted corresponding data processing. Next, the study employed the entropy-weighted fuzzy evaluation model to quantify momentum and utilized stacking models to predict momentum fluctuations with high precision, aiding coaches in providing targeted guidance for athletes to enhance performance and strategic planning. Furthermore, this study also conducted a generalizability test on the model, applying it to various sports events including other matches in the Wimbledon tennis championship and the Olympic badminton finals. The results show that the model can effectively capture the momentum of athletes and predict fluctuations in moments in matches across different sports events.

The lamprey is an ancient fish species with a unique life history. They spawn in the ocean, their young grow in freshwater, and adults return to the sea to reproduce. The gender ratio of lampreys is influenced by environmental factors and has significant impacts on the ecosystem. In this paper, our team has constructed a mathematical model to explore the series of impacts caused by changes in the gender ratio of lampreys in the ecosystem due to resource availability. To understand the impact of changes in the gender ratio of lampreys on the ecosystem, we establish a Lamprey-Ecosystem Model. Before constructing this model, we first develop a lamprey Gender Ratio Model and a Population Dynamics Model based on the Logistic Function Model to prepare for subsequent modeling. Then, starting with the construction of a Food Web Model, we determine that the main interaction between lampreys and other species is predation, leading us to establish a Lotka-Volterra Model. Combining the premise, we derive a Resource Competition Model from the Food Web Model. Subsequently, we introduce the Gompertz Model from the Niche Model to study the differences in ecological niches.

The objective of this work is to analyze the isolated calmness of the mapping of semidefinite programming problem Karush-Kuhn-Tucker solution. We give the equivalence between the dual/primal strict Robinson constraint qualification and the primal/dual second order sufficient condition of the semidefinite programming. Based on the results, we get the equivalent conditions of the isolated calmness of the Karush-Kuhn-Tucker solution mapping.

China's road network construction is expanding on a large scale, leading to a complex and intricate network connection. As the economy grows, there is a rise in people's travel demand, resulting in frequent road congestion and diverse user travel preferences. This paper examines the challenge of path planning in a large-scale road network under a situation where users have multiple preferences. A path planning model is developed to accommodate the user's preferences for traveling distance, time, and vehicle fuel consumption. Improved contraction hierarchies are suggested to enhance fast path planning in large road networks based on these preferences. The suggested approach is tested using numerical simulation on the road network data in Hubei Province and compared with Dijkstra's algorithm, BiDijkstra's algorithm, and A* algorithm. The test findings confirm that enhanced contraction hierarchies can efficiently determine superior path planning strategies in various preference circumstances across diverse scales.

The kernel function is introduced by the Kernel Extreme Learning Machine on the basis of the original Extreme Learning Machine, which effectively improves the capability of prediction of the Extreme Learning Machine, but the hyperparameters of it still affect the model performance to a large extent. As an effective metaheuristic algorithm, the Arithmetic Optimization Algorithm is frequently utilized to address optimization problems. This work introduces the Kernel Extreme Learning Machine optimized by the Arithmetic Optimization Algorithm (AOA-KELM) in an effort to significantly improve the efficiency of the Kernel Extreme Learning Machine. Regularization coefficients and Kernel parameters are the hyperparameters under optimization. On the UCI dataset, the performance of the proposed algorithm is verified through comparison with the Extreme Learning Machine–Grey Wolf Optimizer, Deep Extreme Learning Machine, Backpropagation Algorithm, and Support Vector Machine. The results obtained from the numerical analysis validate the superiority of the proposed method, since the proposed algorithm significantly outperforms its competitors.

In the context of coping with the leakage problems of water supply systems brought about by urbanization and population growth, this study employs DBSCAN density clustering analysis, truncated mean analysis, and descriptive statistics to construct a generalized mathematical model for the detection and identification of outlier points in water supply flow data. By applying these methods, we integrated the distribution characteristics of the data, the outlier identification of the truncated mean method and the noise point detection of the density clustering algorithm. The experimental results show that the model performs well in terms of rationality and sensitivity, providing strong support for improving the efficiency and sustainability of flow anomaly identification in smart water systems. This research provides innovative and practical solutions to practical problems in urban water supply systems.

The site selection of cultural and tourism projects is a complex process that is influenced by multiple factors such as geographical location, natural resources, regional economy, and operational capabilities. This paper proposes an improved K-means clustering algorithm to address the issue of site selection for cultural and tourism projects mentioned above. Points that are far apart from each other are selected as initial clustering centers, and the factor for measuring distance between data points is redefined. The shortest path is used as a similarity measure to establish a multi region cultural and tourism project site selection model. Finally, through the specific example of Qin Opera Town, the site selection process of cultural and tourism project centers in 100 data points is analyzed, and the minimum total distance between cultural and tourism centers and residential areas is taken as the evaluation goal. By comparing the results with traditional K-means clustering and enumeration methods, it is shown that the improved algorithm has better results and lower time complexity. It can play a positive role in the site selection of multi regional cultural and tourism projects, improve visiting efficiency, and create economic benefits.

Energy disaggregation is a pivotal technique employed in Non-Intrusive Load Monitoring (NILM) to accurately estimate the power consumption of individual appliances in households. Recent advancements in trasformer models, particularly in domains like Natural Language Processing (NLP), have underscored their potential for enhancing classification performance. In this paper, we propose a novel algorithm for energy decomposition using an adapted transformer-based architecture. Our approach integrates the rapid Fourier transform with a multi-head attention mechanism to efficiently transform time-series feature data into frequency domain features, followed by noise reduction achieved by multiplying the data with a trainable matrix. The DFT-NILM model, also known as the denoising Fourier transformer, has been evaluated on publicly available electrical data. The evaluation shows that the DFT-NILM model outperforms existing state-of-the-art methods in terms of performance.

The characterization of the correlation of quantum States plays a key role in the study of quantum information theory. Classical correlation is a quantum state that remains unchanged under local orthogonal projection, and it is not affected by decoherence. The entangled quantum state must be quantum correlation, and there is also quantum correlation in the separable quantum state. Relevance is a common phenomenon in nature. From the perspective of information theory, classical relevance can be described under Shannon's information theory. Therefore, it is necessary to explore the relationship among classical correlation, quantum correlation and quantum nonlocality. For the two-body quantum system, this paper gives the corresponding definitions of classical correlation state, left classical associated state and right classical associated state from the perspective of probability density, especially the definition of classical independent associated state. Different from the definition of local orthogonal projection measurement, it is easier to construct classical correlation state and quantum correlation state from the perspective of probability distribution, and further analyze the characteristics of eigenvalues and their corresponding eigenvectors. The selection of standard orthogonal basis, the corresponding relationship between separable ground state and classical correlation, entangled ground state and quantum correlation in two-body quantum system are studied. The corresponding characteristics of left classical correlation state and right classical correlation state are explored, and the relationship between separability and correlation, the relationship between convex combination and correlation of quantum States, and the left classical correlation state and right classical correlation state may also be quantum correlation States are illustrated by examples, and the definition of independent classical correlation state and its relationship with edge distribution are further obtained.

High-quality grass-roots statistics are an important guarantee to objectively reflect the development of grass-roots social and economic operations and provide strong data support for government decision-making. A combined empowerment cloud model is constructed to evaluate the quality of grass-roots statistics. Firstly, the index system for evaluating the quality of grassroots statistics is proposed based on GB/T 36344-2018 national standard framework; secondly, to calculate the weights of subjective and objective indicators, AHP-CRITIC is used in combination with game theory to estimate combination weights; then, the cloud model is constructed to evaluate the quality of grassroots statistics; finally, the proposed method is proved to be reasonable and effective through example analysis, and the cloud The model takes into account the randomness and fuzziness of some indicators and can provide a scientific and reliable decision basis for the evaluation of the quality of grass-roots statistics.

The shortest path problem has always been the most fundamental but extremely important problem in operations research and optimization research. Given a weighted graph (directed or undirected) 𝐺 = (𝑉, 𝐸, 𝜔) , |𝑉| = 𝑛, |𝐸| = 𝑚, and the two points s and t in G are the starting and ending points, respectively. The single source and single endpoint shortest path problem aims to find the shortest s-t path. The main contributions of this article are as follows: (1) Based on the cycle-reducing algorithm, algorithm, a hierarchical single-source single-sink shortest path algorithm is obtained. The advantage of this algorithm is that it runs faster and avoids accessing all vertices in the graph to save time and storage space. (2) Based on the 𝐴∗ algorithm, a new lower bound distance estimation function is proposed to solve the single source and single endpoint problem. (3) Propose a dynamic simulation-based method for solving the shortest path problem: embed a nonnegative weighted graph into Euclidean space and use dynamic simulation software to solve the shortest s-t path. The advantage of this method is that it is very accurate and can solve all the shortest s-t paths without visiting too many keyless points.

Rigid body to any point of momentum moment theorem is a rigid body rotation in the important content, with the rapid development of industrial technology, more and more fields require understanding of rigid body system relative to any point of momentum moment change law. And calculate the momentum moment of rigid body system for fixed point, moving point, center of mass and axis, due to the form of similar easy to cause confusion. In this paper, the momentum moment theorem is discussed from the general situation when the center of moment is different situations, and the inner connection between various forms is revealed. The application of the Moment of Moment Theorem to several special "centers of moments" is illustrated by examples.

In this paper we consider sublinear Schrödinger-Poisson equations. Suppose some suitable conditions hold, the problem has at least one least energy solution by using variational method.

With the continuous advancement of China's strategy of building a transportation power. Factors such as running environment and train marshalling length require higher and higher dynamic performance of coupler/draft gear systems of heavy-haul locomotives, such as the complexity of running lines, the limitation of heavy-haul train formation and so on. Improving the pressure stability of the coupler/draft gear device, studying the structural characteristics of the coupler/draft gear device, the design and modeling of the coupler/draft gear device, and carrying out dynamic simulation research are necessary and effective means to solve the above problems and improve the innovation level of the coupler/draft gear systems of heavy- haul locomotives. For this reason, with the help of modeling software (Universal Mechanism,UM), the coupler/draft gear systems model of heavy-haul locomotives is established, and the dynamic performance of 2 HXD1 locomotives + 43 C70 gondola locomotives running on complex lines is studied. The effects of line curve radius and downhill slope on dynamic parameters such as coupler force and wheel-rail lateral force of heavy-haul locomotives are analyzed. It has important guiding significance for improving the operation security of heavy-haul locomotives on complex lines.

Crowd evacuation stands as a critical subject in urban planning and emergency management. However, owing to the intricate and unpredictable nature of crowd behavior, coupled with the diverse urban environments, achieving effective crowd evacuation remains a formidable challenge. To delve into the nuanced variations during crowd evacuation, we introduce a mesoscopic evacuation model based on adaptive grids partitioning. This model involves performing adaptive grids partitioning according to crowd density within the designated grid density analysis range in the evacuation scenario. In this approach, we conduct evacuation simulation experiments by simulating pedestrian flow through density flow between grids. The experimental results demonstrate that adaptive grids partitioning aptly responds to microscopic changes in the crowd evacuation process. The mesoscopic evacuation model proposed in this paper notably enhances the utilization rate of evacuation exits. The comparative visualization simulation experiments using Pathfinder software attests to the smoothness and reliability of the model.

In this paper, we generalize the block splitting preconditioner presented by Cao to a two-parameter preconditioner for solving generalized saddle point linear systems and prove that the eigenvalues of the corresponding preconditioned matrix are only clustered at two points when the iteration parameters approach zero. Numerical experiments have verified the effectiveness of the theoretical results.

This study aims to explore a class of computational solutions to semilinear hyperbolic equations. The nonlinear terms in the equation, including the dissipation term and the external source term, make the nonlinear characteristics of the equation more complex. Nevertheless, the influence of these nonlinear features on discretization is still significant and cannot be ignored. Therefore, this study concentrates on how to construct an effective discretization method to ensure the accuracy of nonlinear terms in discrete formats. According to this, two kinds of effective schemes are designed by using the idea of transforming nonlinearity into linearity and iteration theory, they are finite difference scheme and multiple integral finite volume scheme respectively. And then we gave numerical examples for the above two schemes. Comparing with the existing reliable numerical results, it is demonstrated that these formats are effective and feasible.

This paper investigates the inverse problem of using geomagnetic monitoring to identify magnetization anomalies with varying magnetic permeability. Suppose that there is a set of magnetization anomalies which are increasing or decreasing with time in the Earth's crust. This change process interferes with the normal geomagnetic field, which leads to changes in its magnetic permeability. Without considering the rate of change parameter, we not only uniquely recover its position and magnetic permeability, but also establish a unique recovery result for the number of magnetization anomalies.

In this article, we think about a unique recovery result for piecewise constant conductivity in n-layer media conductivity problem in R ^d for the case of multiple magnetization anomalous objects without overlap. Firstly, solution of the problem is obtained by layer potential theory, the extension theorem of the harmonic function and the continuous transmission condition. Secondly, equations related to the layer potential are transformed into conductivity equations using the jump formula, based on the Calderón equation and the property of the self-adjoint operator. Finally, we obtain a unique recovery result for the piecewise constant conductivity in n-layer media.

This paper aims to explore human-robot collaborative assembly systems that enable efficient assembly operations through coexistence, interaction, cooperation, and collaboration between humans and robots. First, the paper defines the concept of human-computer interaction and makes clear that the research focus includes the relationship between human and robot, path planning, safety design and task assignment. By studying these key issues, the advantages and challenges of human-robot collaborative assembly systems can be revealed. The research results show that the human-robot collaborative assembly system has significant advantages. First, through cooperation and collaboration between humans and robots, the efficiency and quality of assembly operations can be improved. Secondly, the optimization of path planning and task allocation can reduce the waste of time and resources in the assembly process. In addition, the consideration of safety design can ensure the operation safety of man-machine collaborative assembly system. However, human-robot collaborative assembly systems also face some challenges. It includes optimizing task allocation and scheduling, communication and collaboration between workers and robots. In order to overcome these challenges, this paper discusses the future development direction of human-robot collaborative assembly systems.

Biological experiments are an important means of studying calcium transients in myocardial cells, but it is difficult to conduct simultaneous interactions between various components within the cell. This article constructs a geometric model of the occurrence space of atrial sarcoplasmic reticulum calcium transient, and constructs a dynamic model based on the physiological mechanism of sarcoplasmic reticulum calcium transient. By using the constructed dynamic model for the numerical calculation of sarcoplasmic reticulum calcium transient in atrial muscle, most of the results are in line with biological experimental results. In addition, this numerical model can also simulate the morphology of various sarcoplasmic reticulum calcium transients in myocardial cells by optimizing the dynamic model of sarcoplasmic reticulum calcium transients and adjusting parameters.

Soliton theory and integrable system have important applications in the fields of mathematics and physics, and their research is of great significance to our understanding of nature, the search for new integrable systems has been the focus of integrable theory. Due to its complexity, little is known about the high-order and high-dimensional eigenvalue problems.In this paper, based on the nonlinear method of eigenvalue problem, we discuss a non-self-adjoint fourth-order eigenvalue problem, by using the relation between the potential function and the characteristic function, the Bargmann constrained system is obtained. Secondly, a set of suitable Jacobi-ostrograndsky coordinate systems is constructed, in which Lax pairs of the evolution equations corresponding to the fourth-order eigenvalue problem are nonlinear, the exact integrable Hamiltonian canonical systems on symplectic manifolds are obtained. Finally, the involution representation of the solutions of the corresponding evolution equations on the finite dimensional subspace is obtained. The solutions of the nonlinear evolution equations are constructed by using the solutions of the classical systems. The problem of high order and high dimension eigenvalue problem is solved.

Optimizing the key parameters of the range extender has an important impact on improving the fuel economy and reducing the emissions of the range extender electric vehicle. Firstly, GT-Power is used to establish a one-dimensional performance simulation model of the engine, and the working conditions of the engine are determined according to the ISG motor, which is combined with the study of the effect of the compression ratio on the likelihood of detonation to improve the thermal efficiency of the engine by increasing the compression ratio. Through the joint simulation of Isight and GT-Power, the NSGA-II genetic algorithm was applied to optimize the ignition advance angle and air-fuel ratio corresponding to the optimized compression ratio, with fuel consumption rate and emission minimization as the optimization objectives.

As awareness of protection and the energy structure deepen, new energy vehicles (NEVs) are gradually emerging in the Chinese market. This paper employs a mathematical model to forecast the future of China's NEV industry. Firstly, the upper, middle and lower reaches of the NEV industry are considered, and a subjective and objective weighting method combining a hierarchical method and an entropy weight method is employed to preprocess the relevant data. According to the weight of each index, the number of power batteries, the scale of new energy vehicle enterprises and the number of public charging piles are the three main factors affecting NEVs. A grey prediction model is established for data processing and quasi-exponential law testing. At the same time, a polynomial model is introduced to predict the future new energy automobile industry. This has important reference value for formulating the future new energy automobile policy and enterprise strategy.

In recent years, the rapid development of electric vehicles has led to a greater demand for electric vehicles. Due to the lack of range of electric vehicles, the imperfect function of stations and pilesand the limitations of charging facilities, long-distance travelers have developed "mileage anxiety", which greatly affects the development of electric vehicles. The existing literature mainly considers the shortest time or the shortest distance for electric vehicle path selection and does not fully consider the cost of charging stations. In this paper, we propose an optimization model of charging path for electric vehicle urban cluster traffic based on comprehensive objective function. Firstly, the comprehensive objective function about time, distance and cost is constructed by linear weighting method. Secondly, an iterative algorithm is used to calculate the values of all paths, and then the optimal path is confirmed. Finally, a simulation method is used to verify the effectiveness of the method proposed in this paper. The results show that the optimization model proposed in this paper has better results compared with the three single-element objective functions.

This study analyzes the impact of psychological momentum (PM) on score fluctuations in male tennis players. t employs Principal Component Analysis (PCA) to create a Real-Time Momentum Evaluation Model, comprising three principal components: "Offense," "Stability," and "Defense." Meanwhile, changes in momentum are plotted to reflect player performance throughout the game. A Randomized Testing model is developed to assess momentum randomness. It reveals a significant correlation (96%) between maximum momentum scores and game winners. This study introduces a randomized permutation test, indicating that momentum is unlikely to be random, further supporting these findings. A Turning Point Prediction Model is introduced to forecast game fluctuations, defining turning points as instances where the momentum difference exceeds a threshold. By analyzing the importance ranking of determining factors, this study identifies the top three main influencing factors as the number of games played, break points won, and player scores.

In recent years, with the rise of blockchain technology, smart contracts have also rapidly developed and applied in various industries. However, vulnerabilities in smart contracts can lead to serious consequences. When using current fuzz testing tools for vulnerability detection, a large number of test inputs are randomly generated, resulting in low code coverage due to high randomness. To address this issue, we propose a new adaptive genetic algorithm that combines the fuzzy testing process to generate a large number of test cases. We designed a fitness function for evaluating individual strengths and weaknesses in the adaptive genetic algorithm based on branch coverage and data dependency during the detection process. Based on the diversity and effectiveness of the current generated test cases, we dynamically adjusted the crossover and mutation probabilities during the algorithm execution process, gradually optimizing the quality of test cases in multiple testing iterations. According to the experimental results, the method proposed in this article has higher code coverage and vulnerability detection accuracy compared to other tools for detecting contract vulnerabilities.

In the field of metrology, the general instrument installed in enterprises and institutions is often accompanied by the mandatory verification of the established period, but its working health is unknown. This paper carries out the health status research of general instrument based on the common two-norm form in engineering applied mathematics, uses the unilateral construction test algorithm to analyze the data samples of typical equipment pressure gauge and verify the algorithm ability, and provides a complete implementation method for the health status evaluation of general instrument in service.

For the cooperative searching problem of UAV swarm in unknown environment without prior information, an area covering search method inspired by swarm intelligence is proposed. First, the grid method is used to model the search environment discretely, and the UAV swarm cooperative covering search optimization model is established. Second, the creating and updating method for UAV search map is designed based on the scouting behavior of wolf pack. Third, considering the search reward and cost, the UAV cooperative search efficiency function and the search path decision method are constructed. The simulation results show that the proposed method can effectively improve the covering rate, and the search efficiency is significantly higher than that of random search method.

Based on data modeling and analytical techniques, this paper aims to establish a data-driven model for analyzing global temperature variations by examining the relationships between global temperatures, time, geographical locations, and regional disaster indices. The DBSCAN clustering method is employed to identify reference cities, and their temperature data are utilized to calculate the global average temperature. Future temperature projections are made using the Exponential Smoothing Time Series model and Grey Prediction Model. Subsequently, heatmaps and curves are drawn employing statistical data to elucidate the interplay between temperature, location, and time. This research provides objective and effective methods and measures for interpreting and responding to changes in global temperatures.

With the continuous development of human society, the global warming caused by greenhouse gas emissions is becoming more and more serious. In order to better cope with global warming, this paper uses the SARIMA model to predict global temperature. Then, SARIMA (1,1,1) (1,1,1) model is established to forecast the temperature. It is found that the temperature in 2050 and 2100 will not reach 20℃, and the global average temperature is expected to reach 20℃ in about 2180. Through model evaluation, it is found that the R-square of SARIMA model is 0.87.

The design extreme rainstorm in the region where the city is located has a non-negligible impact on the city’s flood control and water drainage. Taking the Taihu Basin as an example, the joint distribution is constructed based on the Archimedean Copula function combining the city and the region on the basis of measured precipitation data from the basin’s representative gauges. The risks of extreme rainstorms encountering between regions and cities with different durations are quantitatively calculated and analyzed. Results show that with the increase of the return period, the risk of extreme rainstorms in the city and the region is decreasing; when the extreme rainfall of the region occurs at the return period of 50 years or 100 years, the risks of extreme rainfall of urban areas encountering are basically around 10%, and the risk value never exceeds 20%, which is relatively safe for the flood control and drainage system to work in the urban area; the Copula function is easy to solve with strong adaptability, and can be used to quantify the encountering risk between the design rainfall of city and region.

With the increasing popularity of electric vehicles (EVs), the location of charging stations has gained significant attention in the auto industry. However, unreasonable locations can lead to reduced return on investment, land resource wastage, and user attrition. Therefore, this study fully considered the interests of investors and user requirements in determining EV charging station locations. An improved non-dominated sorting genetic algorithm II (INSGAII) was developed, incorporating a double-layer coding strategy and hierarchical elite individual selection. Moreover, a multi-objective optimization model was proposed, considering investment costs and user comprehensive costs, along with constraints such as charging pile numbers, service range, and charging uniqueness. Performance validation against traditional nondominated sorting genetic algorithm II (NSGAII) and multi-objective particle swarm optimization algorithm (MOPSO) using the same dataset, alongside verification with actual test case data, confirmed the effectiveness and practicality of INSGAII in determining optimal EV charging station locations.

This study analyzes and optimizes the key structural components of a handling manipulator based on fatigue simulation and finite element simulation methods. Taking the handling manipulator as the research object, the structural design scheme of the manipulator is optimized based on the morphological matrix method. The key structural components of the handling manipulator are analyzed by fatigue simulation and finite element simulation methods to verify the accuracy of the theoretical derivation. The results show that the computer-controlled flatbed manipulator is the best design scheme, and the fatigue value of the gear transmission method is smaller, the stress value of the clamping claw mechanism is smaller, and the stress distribution is more uniform, with a maximum stress of 47.5 N/mm2.The proposed manipulator can effectively prolong its working life, and lays a theoretical foundation for the optimization of the manipulator's structural design and mechanical properties.

Extreme weather events in today's world are causing significant damage to people's property and affecting the decisions of insurance companies. We develop and optimize Insurance Risk Assessment Model (IRAM) and Community Building Preservation Model (CBPM) models to quantify the risk of increasing insurance policies and provide recommendations for insurers and real estate companies to make decisions. We collect data from two countries, then select indicators and use the AHP-EWM approaches and Topsis method to derive the weights of each indicator and calculate the composite score, then we use a gray prediction model to predict the Insurance risk comprehensive score (IRC) of the future direction and set up a benchmark to predict the suitability of increasing the number of contracted policies. To solve the problem of whether and how to establish a real estate project, we construct an objective function and formulate restrictive conditions, and use Particle Swarm Optimization to find the optimal approach to establish the real estate project. Moreover, we select specific historic building indicators and combine them with IRC to train a machine classification model by using the XGBoost method, which can label specific neighborhood buildings as deserving of additional policy protection. Finally, we select Himeji Castle as historic building and evaluate it using IRAM and CBPM respectively, the result of IRAM shows that the region where Himeji Castle is located is not suitable for increasing contracted policies, and the result of CBPM shows that Himeji Castle is unsuitable for continuing to add policies to be protected. Our model IRAM and CBPM pass the sensitivity analysis, and final prediction results show that the accuracy rate and recall rate of the classification model are 0.91 and 0.88, which has the best performance in terms of each metric used for comparison.

Objective: To explore the effects of residents' social support and network information anxiety on loneliness and their influencing factors under public health emergencies. Methods: CART decision tree and logistic regression were applied to construct a risk prediction model, and the area under the ROC curve (AUC) was used to evaluate the model performance and compare the predictive ability of the two models. Factor analysis was used to explore the types of loneliness, and ordered multicategorical logistic regression was used to analyze its influencing factors. Results: The AUC value of the logistic regression prediction model was higher than that of the decision tree, and logistic regression was chosen to construct the prediction model. The model reflected three variables such as social support, online information anxiety, and gender as the influencing factors of loneliness. Based on the survey, five types of loneliness were derived, which were named as personal existence loneliness, personal emotional loneliness, information query loneliness, information use loneliness, and subjective support loneliness. Necessary social support, authenticity of online information, and anxiety level were statistically related to loneliness (all P < 0.05). The results of ordered multicategorical logistic regression showed that the existence of personal loneliness was negatively correlated with the authenticity of online information (P=0.016, OR=0.584, 95% CI:0.389-0.908), positively correlated with frequent anxiety (P<0.001, OR=3.108, 95% CI:1.988-4.860), and negatively correlated with the necessary social support into a negative correlation (P=0.013, OR=0.628, 95%CI:0.435 to 0.908); personal emotional loneliness was positively correlated with frequent anxiety (P=0.023, OR=1.647, 95%CI:1.070 to 2.537); and information-seeking loneliness was negatively correlated with the truthfulness of online information (P=0.003, OR=0.547 , 95% CI:0.351 to 0.852) and positively correlated with anxiety level (P=0.008, OR=1.925, 95% CI:1.246 to 2.974). Conclusion: Residents' loneliness can be affected by necessary social support, authenticity of online information, anxiety level and ot

Firefighting and rescue operations are crucial for ensuring the safety of lives and properties of every individual. In this study, we employed the SARIMA model and multiple function fitting methods to fit and forecast firefighting events of various magnitudes. Taking fifteen regions as examples and considering their geographical information, population density, and dispatch data, we predicted future dispatch counts and losses, and developed a shortest rescue indicator for interregional rescue operations. This research provides valuable insights and references for predicting and responding to firefighting incidents.

This paper proposes a metaheuristic optimization algorithm called Cooperative Learning Optimization algorithm (CLO). The algorithm simulates human cooperative behaviors, including imitative learning, creative learning, random learning, and selective learning, to establish a mathematical model for searching optimal solutions. The CLO algorithm is compared with other algorithms in 30-dimensional, and 500-dimensional optimization problems, demonstrating its robustness and ability to solve high-dimensional optimization problems. Finally, Friedman and Wilcoxon tests are conducted, showing significant differences between the CLO and the compared algorithms, highlighting the effectiveness of the CLO in optimization. The advantages of this algorithm lie in its simplicity, ease of operation, and good convergence performance.

Through the coordinated control of the main and pre-signal, the contraflow left-turn lane intersection dynamically transforms the opposing exit lane into the entrance left-turn lane. This transformation has improved the capacity of leftturning vehicles. However, during vehicle operation at the intersection, traffic conflicts can easily occur for vehicles making left turns. This safety issue should not be underestimated. Data collection in this study was conducted using drones and camera equipment. This study focuses on left-turning vehicles with different entrance lanes appearing at the intersection at the same time. Characteristic variables affecting the safe operation of vehicles were extracted. The traffic conflict indicators PET, forward conflicts, and rear-end conflicts are used as conflict evaluation criteria. Logistic regression was used to analyze significance and to exclude irrelevant factors. With the utilization of random forest (RF), support vector machine (SVM), extreme gradient boosting (XGBoost), and multilayer perceptron (MLP) methods, an optimal binary classification model was trained and the relationship between traffic characteristic variables and traffic conflict is established. The results show that the random forest model can effectively predict the occurrence of traffic conflicts based on the characteristic variables collected by the 10-second time unit, and the overall accuracy is 81.8%.

This study proposes a practical train manning problem (TMP) for a bi-directional massive rapid transit (MRT) line with a certain number of crew points. The TMP aims to determine a set of manning duties for each rover to man the daily train services subjected to practical constraints by minimizing the total idle time of rovers. It is crucial for the MRT operators to solve the TMP because rovers are able to handle possible train faults and/or emergencies through their fast responses. In this paper, we build a binary nonlinear and nonconvex programming model with explicit constraints for the proposed TMP, by considering three possible train manning scenarios with different idle times. Moreover, we conduct a case study of the Singapore circle line and perform necessary sensitivity analysis of various parameters involved in the TMP. Results indicate that our model can solve the TMP problem effectively and the solutions help to improve the manning duties assignment.

In this study, a catastrophe risk assessment system is established, which includes a catastrophe risk assessment model and an ARIMA risk prediction model. Taking Fukuoka as the study area, the risk factors are calculated for the region from 1950 to 2022. On this basis, a risk factor prediction model is constructed to dynamically transform the risk factors. The risk factors of the area from 2023 to 2029 are predicted, and the preliminary analysis of the catastrophe risk assessment is realized. Secondly, since the ARIMA risk factor prediction model only analyzes risk factors and time series, it is difficult for the model to feedback the catastrophe risk factors implied by the natural geographical environment and economic conditions of a certain place at a certain time. Therefore, this study constructs a multi-factor risk factor decision tree regression model based on physical geographic data and socio-economic data, further improves the policy risk assessment system. Finally, we predict the risk factors in Texas and provide a decision-making basis for catastrophe risk assessment.

The rise of the two major industries of new energy and new energy vehicles has created prerequisites for achieving carbon emission reduction. The Yangtze River Delta is the largest carbon emission economic zone in China, so it is urgent to reduce carbon emissions. By analyzing the development of new energy vehicles in the Yangtze River Delta, this paper constructs the index system affecting carbon emission, establishes the carbon emission prediction model based on genetic algorithm parameter optimization of extreme learning machine, predicts the carbon emission trend, and provides an effective plan for the development and emission reduction of new energy vehicles in the Yangtze River Delta. After analysis and validation, the model in this paper can comprehensively analyze the development of new energy vehicles in the Yangtze River Delta (YRD) and the country as a whole, explore the relationship between the development of new energy vehicles and the goal of carbon neutrality, predict the time of carbon peak and carbon neutrality in the YRD region, and provide a theoretical basis for the implementation of relevant policies.

Corrosive gases like CO₂, H₂S, and O₂ are commonly present in natural gas collection and transmission pipelines, leading to significant corrosion issues within the infrastructure. While the addition of quantitative corrosion inhibitors has traditionally helped slow down pipeline corrosion, instances of pipe perforation still occur. Currently, existing corrosion rate prediction models do not account for the effectiveness of protective measures, making it challenging to accurately calculate the remaining life of pipelines. Consequently, a novel approach has been developed to estimate the remaining life of gathering pipelines in the presence of CO₂, H₂S, and O₂. The novel approach is rooted in a corrosion rate prediction model that incorporates factors such as chloride ion concentration, dissolved oxygen levels, pipeline routing, and the efficiency of corrosion inhibition in influencing the corrosion rate. This approach involves segmenting the natural gas gathering and transportation pipeline into multiple time nodes spanning from production to evaluation. By calculating the corrosion rate at each node and determining the accumulated wall thickness value of the pipeline, it becomes possible to assess the remaining life of the pipeline. In contrast to current technologies, the discrepancy between the wall thickness loss value predicted by this new method and actual internal inspections is less than 10%. This enhanced accuracy significantly improves the prediction of remaining pipeline life, offering a reliable basis for decision-making regarding pipeline inspection and maintenance schedules.

This study introduces a holistic approach to outcome prediction using multiple indicators. We develop an innovative methodology that combines factor analysis for weight determination of variables, facilitating dimension reduction, with Long Short-Term Memory (LSTM) neural networks for comprehensive evaluation and precise forecasts. To assess the efficacy of our proposed technique, we undertook empirical research in the domain of weather-related risk—a field of growing importance that demands further investigation. The findings indicate that our predictive model, which merges factor analysis with LSTM, excels in multivariate forecasting, yielding relatively consistent results. Moreover, it underscores the projection that the impact of weather-related disasters is likely to escalate in tandem with population and economic growth.

To solve the problem of formation and cooperative obstacle avoidance of multi-wheeled robots in the environment with obstacles, an algorithm combining the leader-follower and improved potential field with rapidly exploring random trees(IPFRRT) is proposed in this paper. The kinematic model of multiple robots is established, and the control rate of the path following of the following robots is designed by the backsteeping according to the error differential equation, and the stable formation of the robots is realized. At the same time, the IPFRRT is used as the path planning method for the leader, and the improved artificial potential field method is used as the local obstacle avoidance algorithm for the followers in the formation, so that the multi-robot system can simultaneously avoid obstacles in the formation. The Matlab simulation experiment shows that the robot system can quickly form and maintain formation, continue to recover formation after avoiding obstacles, and make the following error tend to 0 after avoiding obstacles, which verifies the feasibility of the formation control method.

This paper proposes an improved safe adaptive ant colony algorithm for underground parking lot path planning problems. Firstly, by enhancing the heuristic function and introducing the distance to the target node and the adaptive enhancement coefficient, ants are inclined to move towards the target node to avoid falling into local optima. Secondly, the adoption of Gaussian distribution for initializing pheromones and a limited pheromone update strategy enhances the search efficiency of the algorithm. Finally, a comprehensive scoring strategy is designed to select the optimal path. Simulation results from three different scale environment maps demonstrate that this algorithm outperforms traditional A star algorithm in target orientation and surpasses traditional and improved ant colony algorithms in terms of turning times and time. With efficiency and practicality, it can be effectively applied to the problem of underground parking lot path planning, providing an effective solution to improve urban traffic efficiency and alleviate parking difficulties