This PDF file contains the front matter associated with SPIE Proceedings Volume 12259, including the Title Page, Copyright information and Table of Contents.

The numerical simulation of Puzhehei Lake water environment is of great significance for preventing Puzhehei Lake water pollution and protecting the water ecological environment in Puzhehei Lake basin. Based on the lack of hydrological and water quality data in Puzhehei Lake Basin, a large number of basic data were collected through pollution source investigation and water quality monitoring. On this basis, a two-dimensional hydrodynamic-water quality model of Puzhehei Lake was established by using MIKE21 model, which simulated the migration and diffusion of pollutants entering the lake, analyzed the current situation of pollution load entering the lake, and analyzed the water flow, hydrodynamic characteristics and migration and diffusion laws of pollutants entering the lake. The results show that: ① The annual load of COD, TN, TP and NH3-N in Puzhehei Lake in 2018 is 4090.0t, 401.3t, 34.4t and 122.6 t; ② Puzhehei Lake has obvious single flow direction and more circulation as a whole, but there is obvious backwater phenomenon in the lower reaches of Puzhehei Lake when the secondary dominant wind is downward.

Freak waves are both extremely large waves and highly transient time. Such a wave may lead to damage of ships to deaths. In this paper, to describe the connection between freak wave and wave essential factor, we use WAVEWATCHⅢ model simulating freak wave in the Japan Sea to explore freak wave，with the importing of ECMWF re-analysis wind field. By this way, we successfully simulate the formation of freak wave in the random wave. By analyzing the statistical elements of waves, it is found that the occurrence time of freak wave is in a medium sea state. It is unlikely to generate freak waves due to the nonlinear interaction of waves.By analyzing the wave spectrum, The main cause of the freak wave event is the interaction between current and swell.

The air quality near urban street is deteriorating due to more and more ultrafine particles emitted by vehicles. Therefore, the evaluation of exposure risks for pedestrians walking along the street is of significance. However, the pedestrians are usually ignored or regarded as motionless in previous investigations. These kinds of consumptions are different from the real scenario and tend to lead large errors. In order to mimic the real exposure risks of walking pedestrians, the dynamic mesh method combined with drift flux model was used to deal with human walking process and the dispersion of ultrafine particles. These results show that the moving pedestrians accelerate the air velocity nearby and the disturbance effect increases with the number of people. Besides, two vortices are generated along the pedestrians’ line. For the cases with lower wind speed, the more people there are, the higher the exposure concentration is. Yet this is not the case for scenarios with higher wind speed. Finally, the walking pedestrians have larger excess lung cancer risks and the people at the front and back of the line are more easily to expose to higher concentrations.

The natural disasters caused by extreme precipitations significantly have increased around the world. In the US, wild fires and flooding appear to increase year-by-year. The extreme precipitations are attributed to the climate change. Over recent years we have successfully used the random walk to simulate the global warming in many places around the world. This encourages us to use the random walk model to simulate the precipitations. In this investigation, we used the random walk model to simulate the precipitations in 50 US state capitals for the 20th century. The results show that the random walk can approximately simulate the precipitation in these cities in both 1/–1 and decimal forms. Thus the results suggest the random mechanism is one of causes for unusual precipitations over recent years.

Dominant seepage channels are formed after chemical flooding，lead to the low efficient and even non-efficient circulation of subsequent EOR methods，need quantitative identification. At present, dominant seepage channel identification methods are only judge whether there is dominant seepage channel in Wells, and cannot quantify the evolution process of dominant seepage channel between injection-production well pairs. In this paper, the streamline numerical simulation software is used to identify the dominant seepage channels quantitatively. Firstly, time-dependent and quantifiable fluid flow between wells, original permeability, water injection efficiency and water saturation were selected as the key parameters for characterization of dominant seepage channels. Secondly, the comprehensive identification mathematical model of dominant seepage channels is established and the weight of key parameters is given. Finally, the history of chemical flooding was accurately matched with the streamline numerical simulation software, and the key parameters are obtained. The distribution and evolution process of dominant seepage channels in chemical flooding process are given by comprehensive identification model. The results show that the calculated are high consistency with the injection profile of testing wells. This method can accurately identification the plugging layers of dominant seepage channels.

Numerical simulation is of great importance as implementation guides of chemical flooding projects. However, there are still significant difficulties remaining in the historical fitting process of chemical flooding simulation due to uncertainties of some related parameters. In order to enhance the accuracy of historical fitting, the numerical simulation parameters need to be calculated correctly. Based on laboratory experiments of viscosity and concentration curves of polymer solutions, rheological curve, competitive adsorption loss curve between surfactant and alkali, the least squares can be used to establish mathematical models for parameter calculation. On this basis, a software for calculation numerical simulation parameters is developed, and the interface of parameter calculation is realized. Through the application of field historical fitting, the results show that: the performance index calculated by numerical simulation is in very good agreement with the observation data, so a better historical fitting result has been obtained. The accuracy of parameter calculation is verified, at the same time, the time of historical fitting is shortened, which lays a good foundation for predicting chemical flooding performance.

The emerging business investment evaluation system is established based on fuzzy comprehensive evaluation. The subjective weight and objective weight of each index are determined by using G1-entropy weight synthesis method, combined to get the comprehensive weight of subjective and objective integration, and the comprehensive score of each business is calculated. Three key emerging businesses, namely smart grid and value-added services, integrated energy services and high-end equipment manufacturing, are selected for quantitative investment value evaluation algorithm validation to illustrate the effectiveness of the investment value evaluation model.

By collecting and sorting out the emergencies of major universities in China in recent years, this paper carries out specific cause analysis of emergencies and constructing probability prediction models, so as to achieve the purposeofeffectively predicting the probability of emergencies. The accuracy test of the probability prediction model of universityemergencies shows that the system prediction accuracy and result reliability are relatively high. The research results canbe used to predict the probability of emergencies in universities.

Pipe jacking engineering, as a non-open excavation construction method, is widely used in urban municipal engineering construction because of its small disturbance to the surrounding soil and no need to demolish existing buildings and underground structures. The pipe jacking construction of Hangzhou intake upward movement project ( Phase I ) needs to go through the gas station. In order to ensure that the construction process does not cause large deformation of the foundation soil and the oil storage tank of the gas station, the numerical simulation analysis of the disturbance response of the buried oil storage tank and the upper structure of the gas station during the pipe jacking construction and operation stage is carried out based on the finite element method. The simulation results show that: With the jacking of pipe jacking, the uplift of oil tank floor gradually increases. When DN3200 pipe jacking is under the oil tank foundation, the uplift increases greatly, and the maximum uneven settlement difference is 0.05 mm. When the pipe jacking is completed, the maximum uplift of the tank bottom plate is 0.14 mm, and no settlement occurs. The surface uplift at the business hall gradually decreases along the pipe jacking direction, and it is one side of settlement and one side of uplift. The maximum uneven settlement difference is 0.3 mm. When the pipe jacking is completed, the maximum settlement is 3.4 mm, and the maximum uplift is 0.15 mm. The normal operation stage of the water pipeline will not adversely affect the Zhipu Road Gas Station, but the fault state of the underground water pipeline (generally refers to the pipeline leakage) will cause stratum settlement and the risk of ground collapse.

The safety problems of petrochemical enterprises can not be collected and reflected in a short time, and there is a lack of effective risk evaluation system. Firstly, the weight calculation method is improved by interval type-2 fuzzy method, the internal relationship between influencing factors is considered, and the comprehensive weight of each factor is determined by combining subjective weight and objective weight; Then, the risk evaluation model of VIKOR method based on interval type-2 fuzzy improvement is established, the maximum benefit value and maximum regret degree of each scheme are analyzed, and the compromise risk value of the scheme is calculated; Finally, based on the production data of uncatalysed oxidation of cyclohexane, the risk assessment is carried out, the influencing factors such as system pressure and reaction temperature are analyzed, and the risk value of each scheme is calculated. The results show that the improved interval type-2 fuzzy risk evaluation model plays a key role in risk evaluation, and can accurately analyze the risk value of each scheme and prevent accidents.

Point cloud can represent 3D geometry conveniently, but its challenging for computers to process it. In this work, we design a transformer enhanced hierarchical neural network for accurate large scale point cloud semantic segmentation. We use semantic space's transformer block to learn global feature correlation. In this way, we can expand the receptive field of network to the whole input point cloud. Experimental results on S3DIS 3d semantic segmentation dataset show that, compared with the traditional hierarchical 3d semantic segmentation model, our transformer-enhanced hierarchical model achieved higher performance on overall accuracy and mIoU.

Analyzing the connectivity of satellite network and mining the important nodes are important research content to optimize the structure design of satellite network and analyze the characteristics of space targets. The spatiotemporal characteristics of large-scale and high dynamics are the most typical characteristics of satellite network. This paper proposes an analysis method for the spatiotemporal characteristics of satellite network, using spatiotemporal graph model to sample discrete in the time dimension and using complex network theory to structural modeling and characteristic analysis in the spatial dimension. Completes the experimental verification based on open-source satellite TLE files of the BDS constellation and the GPS constellation, analyzes the topology of 146 networks. Draw some conclusions including BDS satellite network has high connectivity, the satellites number 7,8,13 and 30 are important in GPS satellites network and others, our research provides a reliable method and technical reference for studying satellite network performance and the research on mining important nodes.

The random walk model is a well-known statistic model applied in a variety of fields. Contemporarily, a new diagnostic technique for identifying and exploiting patterns in financial products, e.g., the foreign exchange rate and stock price, has arisen. The random walk theory is still persuasive, prevailed dominated and admired by plenty of economists and statisticians. The aim of this paper is to examine the feasibility and application of random walk in finance with corresponding statistical analysis. It is started form performing a brief introduction on the research progress of random walk theory and principle of random walk model from a mathematical point of view. Subsequently, the performance of stock price and four structural exchange rates is investigated in this research where both univariate and multivariate tests are used in this model. According to the statistic tests, it is revealed that both stock price and foreign exchange rate follows a random walk pattern. Moreover, the price of one financial product is also independent of another product. Overall, these results shed light on rationality of random walk.

This paper constructs an extreme weather risk evaluation indicator system of different districts in Beijing from three dimensions: hazard, exposure, and vulnerability. On this basis, each indicator is quantified using the method of doublelayer indicators, and a risk evaluation is conducted considering extreme weather disasters, including extreme high temperature and extreme precipitation.

Probability theory, one of the most commonly used branches of mathematics, has been widely applied to various fields. The purpose of this paper is to make a comprehensive review of the probability theory. To carry out the general overview, this paper combines the key contents and proofs of random events of probability, random variables and distribution, and law of large number, successfully set up a brief summary of the achievements made in the above areas and prospect the future development of probability theory.

This paper analyzes the performance of Lasso, Ridge and Dropout Regression using different synthetic and real datasets covering classification and regression problems. The MNIST dataset displayed relatively satisfying results but little difference created by regularization. The Synthetic dataset displays a growing Mean Square Error(MSE) with greater signal to noise ratio as well as growing dimension of dataset. The comparison among the three regularizations reveals how Dropout regularization performs better with decreasing SNR, potentially related to the attribute of Dropout. However, the training model displayed mediocre results when tested upon real datasets and insignificant difference after the usage of regularizations, which could potentially be attributed to the depth of the training model being insufficient with the given data.

Select the floating population of ethnic minorities living in Tibet and Inner Mongolia as the research objects. Log-rank test and Breslow test compare the two autonomous regions in terms of years of residence with statistical differences ( P <0.01). The ethnic minority floating population lives in Inner Mongolia longer than Tibet. The results of multivariate Cox regression analysis showed that age, living in Inner Mongolia, poor health, and whether symptoms of a cold were the protective factors, and women and whether symptoms of jaundice were the risk factors. v

Probability theory is an area of mathematics that deals with the subject of likelihood. Probability theory is the mathematical cornerstone of statistical reasoning, and it is vital for data scientists to analyze data that are impacted by randomness. It is important in machine learning since the design of learning algorithms frequently relies on probabilistic data assumptions. Probability is a concept that is used to quantify the degree of uncertainty. The goal of probability theory is to express uncertain phenomena using a set of axioms. To cut a long tale short, when a system’s probable outcomes cannot be certain of, mathematicians try to depict the situation by calculating the probability of various events and scenarios. Random variables, independence, entropy and Chebyshev inequality will all be discussed in this paper. These mathematical concepts and theorems are essential and fundamental for future study in other scientific areas.

This paper focuses on the main factors affecting the number of COVID-19 deaths. By correlation analysis, the number of people vaccinated and the number of infection cases are the main factors of the number of deaths. A prediction model on the number of deaths using these factors and linear regression is therefore built. The model was next used to predict and compare the number of COVID-19 deaths with actual data in several countries. Additional influences were further analyzed for countries with poor fits.

This report is concerned with a random growth process with random stopping time. Such a process is widely used in the general setting of survival analysis where the stopping time is assumed to subtly depend on the growth process and the growth process is thought to reflect the accumulation of risk factors. Concrete applications of this type of stochastic processes can be found in the fields of health outcome researches, actuarial science, financial risk analysis and so on. In this report we focus on deriving an explicit formula that expresses the joint probability density function of the survival time and the cumulative risk factors at the time to die through two conditional expectations of the process. Such an explicit expression is crucial to many real applications.

In this paper, we prove that if G is a graph with maximum degree ∆ and without intersecting triangles embedded on a surface of Euler characteristic ε < 0 and Δ ≥√24-16ε+3, then χ _'list (G) = Δand 1)( χ list ′′ G +Δ=+1 .

The water resource value system is a gray system, which can be evaluated by using the method of gray comprehensive evaluation. The data of three water sources in Zichuan District are selected and processed according to the gray comprehensive evaluation model to obtain the reference value of water resource value, which provides reference for water resource pricing. The contradiction between supply and demand of water resources can be alleviated by reasonable pricing of water resources.

With the development of the Streaming media, the data transmission based network video is increasing. Moreover, the time-varying traffic volume of communication network leads to traffic congestion in the peak transmission period and under utilization of communication resources in the low peak transmission period. coded caching is a technology to solve the mismatch between data transmission services and communication resources. This technology can make use of the communication resources in the low peak period as much as possible to reduce the traffic congestion in the peak period, so as to improve the transmission efficiency of the communication system as a whole. For the centralized coded caching model, an array called placement delivery array (PDA) can describe the centralized coding cache scheme. Aiming at the centralized coded caching model, this paper constructs a class of PDA by using some methods based on combinatorial design.

With traffic congestion gradually becoming the heart problem of many cities, the traffic congestion phenomenon usually occurs at the intersection of large traffic flow. Traffic lights are the key to solving the problem of traffic congestion. To reasonably schedule traffic lights and alleviate traffic congestion at intersections, this paper first constructed a vehicle road traffic simulation system based on finite state machine, which can simulate and calculate the total score of vehicles under any scheduling scheme. Then, a genetic algorithm based on probability distribution is designed to optimize the scheduling scheme. Finally, the validity of the model and algorithm is verified by a case study. Compared with the traditional genetic algorithm, the genetic algorithm based on probability distribution can speed up the time more than 7 times and can calculate the convergence scheduling scheme more quickly. shorten the running time more than 7 times and has a faster convergence speed.

In this paper, we study the design of optimal furnace temperature curve for a kind of reflow furnace. First, a differential equation model describing the temperature variation of circuit board is established by using the differential element method. Then, according to the requirements of production process, the optimal furnace temperature curve model is constructed. Finally, discretization method and search algorithm are used to obtain the optimal furnace temperature curve.

Aiming at the characteristics of the local section of the pipe jacking construction of the Hangzhou water intake upmoving project (phase I) passing through the alternately distributed strata, from the perspective of pipe jacking machine selection, the influence of different cutter head cutting jacking rates on the vertical displacement and stress of the overlying rock soil layer is simulated and analyzed by controlling the excavation rate. The results show that the vertical displacement of the upper rock and soil of the pipe jacking machine is related to the jacking rate and the buried depth of the pipe jacking machine in the hard stratum. When the buried depth is deeper, the vertical displacement is larger, and the effect of jacking rate on vertical displacement is smaller. When the buried depth is less than 50 m, the vertical displacement of overlying rock mass decreases with the increase of the jacking rate. The circumferential and radial stresses of the monitored element at a depth of 60 m are consistent with the trend of elastic theoretical solutions. The research results can provide reference for the selection of pipe jacking machines with large cutter head or compound slurry balance pipe jacking head under different geological conditions.

Large-scale saddle-point linear systems appear in computational science and engineering fields such as fluid mechanics, image localization, parameter identification and constraint optimization. For a class of asymmetric saddle point problems, the defects of PSS-GSOR iteration are analyzed, and a modified iteration method is constructed. The main idea is to introduce new parameters to improve the sensitivity of iterative correlation coefficient matrix, and give a reasonable selection method of parameter positive definite matrix. According to the characteristics of the established iterative scheme, the convergence of the given iteration is proved by using the matrix eigenvalue theory, and the range of relevant parameters is obtained. Finally, through numerical experiments, the effectiveness of the modified PSS-GSOR method for solving saddle point problems is verified by comparison.

Polya’s Random Walk Theorem is a particularly classical and interesting result and also opens the door for many other discussions of probability and statistics problem. This paper aims to present readers with simple cases of Polya’s Random Walk and provide a proof of Random Walk Theorem in d_i (i=1,2,3) based on direct counting method, getting the result of it’s recurrent in d_i (i=1,2) and transient in d_3. This paper states the background of the theorem in a very clear way, which makes the paper more scientific and reliable. The paper also contains some of the literature reviews showing the rigorous attitude of the authors towards science. The main part of this paper consists of the proving process of the three individual dimensions of the Polya’s random walk theorem, in which the authors use precises formulas and calculations to prove the recurrence of Polya’s random walk theorem. At last, the authors present Law of Large Numbers, the first concept of limit theorem, and give the proof of Markov’s Law of Large Numbers, in order to prove the availability of the proving process of the three dimensions, which makes the paper more well-founded.

The study of gene helps people to better understand the patterns of human body. Nowadays Many diseases have been damaging people like Attention deficit/hyperactivity disorder or child psychiatry. Scientists have been trying to defect them by looking and the gene structure and organization of them. People tried to collecting data and do statistical research on it. Geno Statistics is a subject that focus on the mathematical way to study gene structure. It is widely used in the study research. It helps scientists to find a new way to analysis the mechanisms of the disease. Since this is a recent method more study is needed. Supervised Machine Learning is a very essential implement for the research of the genetics. We will explain the function of Supervised Machine Learning and then display some examples of the use of Supervised Machine Learning. We will also discuss the content of Precision Psychiatry in detail and show how it will help for the diagnose for the mental illness. In this article we will look at some practical application in these fields. Imagine genetics, child psychiatry, ADHD, Supervised Machine Learning and Precision Psychiatry.

The article starts with the convergence of the Fourier series, discusses point-wise convergence, convergence almost everywhere, convergence in the L^p space, and transitions to Riemann-Lebesgue Lemma. Then the article starts from the summability in norms of Fourier series, then introduces three important kernels in Fourier analysis: Dirichlet kernel, Fejér kernel, and Poisson kernel, and explores whether they are Summability kernels. Closely related, the article explores Several properties of convolution. The last part of the article discusses some important inequalities in the L^p space and uses non-classical methods called the tensor power trick to prove some interpolation theorems, such as the Riesz-Thorin Interpolation theorem and the Hausdorff-Young Inequality.

Nowadays, the study of carbon sequestration in forests is a good way of weighing up the relationship between man and nature, so it is necessary to optimise carbon sequestration models and improve forest management plans. We have therefore evaluated carbon sequestration indicators in forests through a variety of factors in order to develop a grey correlation analysis model to analyse the effects of population, temperature and gross forestry product on the amount of carbon sequestered. We then used the variables identified in the analysis to build grey models for different regions and tree species in order to find the predicted amount of CO2. In addition to this, we also used principal component analysis to find that in addition to carbon sequestration, average annual temperature, gross national product and annual precipitation are the factors that have a greater impact on forest efficiency. This analysis allows a good treatment of forest carbon sequestration, and then a linear regression model is used to model the amount of money invested in forests in the gross national product. The study can predict the value of carbon sequestration and also balance the relationship between nature and humans, and thus determine forest management plans measured in time, which is a hot topic of research in this field.

Based on the remote sensing image data of 2015 and 2018, supported by GIS software platform and spatial transfer matrix analysis, this paper makes statistics on the land use type transfer and change characteristics of Nanjing City from 2015 to 2018, and then estimates the value of land resources assets under the influence of Land-Use and Land-Cover Change(LUCC) in the past 3 years. The results are as follows: ① In the past 3 years, the regional land use structure has changed significantly that woodland and water have decreased significantly and the proportion of construction land has increased year by year. ② Land resource assets in Nanjing showed an upward trend, mainly in terms of economic and social values.③The expansion of new construction land led to over-consumption of land resources liabilities and a decrease in net land resources assets in 2018 compared to 2015. The results of the study are important scientific guidance for regional land resource use planning and sustainable environmental development.

Concrete face rockfill dam is one of the most competitive dam types. Compared with traditional earth-rockfill dams, concrete face rockfill dams have low cost, short construction period, and better adaptability to geological conditions. Taking an actual dam project as an example, a three-dimensional model is established to calculate and analyze the seepage of fractures under various conditions such as different damage locations and different water pressures, and then obtain the law of each seepage factor. The analysis results show that the damage near the bottom of the panel poses a greater threat to the seepage safety of the dam, and more attention needs to be paid to the monitoring and protection of the bottom of the panel. With the increase of water pressure, the seepage head in the dam increases. The upstream water level has the most obvious impact on the seepage in the early stage of the dam. When the water level just begins to rise, attention should be paid to the safety and protection of the dam. There is no obvious influence between the location of the fracture and the action of the reservoir water level.

Based on the relevant parameters and engineering geological conditions of pipe jacking construction of Hangzhou water intake upward moving project (phase I), the influence of explosion impact of buried oil storage tank in gas station on pipe jacking structure is numerically simulated based on finite element method. According to the conversion formula of TNT equivalent method, the gasoline explosion is converted into the corresponding TNT equivalent explosion for analysis, and the explosion shock wave over-pressure is 0.485 MPa by using empirical formula. The simulation results show that the maximum principal stress of the western pipeline decreases gradually from the near explosion source to the far end due to the explosion shock of the oil tank, but the influence of the explosion shock on the shear strain of the pipeline is not obvious. The axial force Fy, shear force Fx and Fz of the pipeline change periodically along the axis of the pipeline, and the plane bending moment Mx of the yz of the pipeline fluctuates greatly, and the fluctuation range is ± 40KN·m. The maximum vibration velocity of the water pipeline caused by the oil tank explosion is about 6.54 cm / s, the maximum principal strain is 225×10⁻⁶, and the maximum principal stress is 47.43 MPa, which is far less than the allowable value of the corresponding pipeline. When the oil tank explodes unexpectedly, the water pipeline will not be damaged, but when there are construction personnel working in the water pipeline, most of the personnel will die or the internal organs will be seriously damaged.

The problem of hypoxia at high altitude is particularly prominent, which has caused great difficulties in the development of mineral resources in high altitude areas. Artificial oxygenation is one of the most effective technologies to solve hypoxia at high altitude at present, so it is urgent of setting oxygen supply and ventilation parameters and studying the law of oxygen diffusion.This paper adopts the method of combining field experiment and simulation research to study the law of oxygen diffusion, and to carry out the optimization of local artificial oxygenation technology in metal mine.The results show that when the particle size of the smoke sample is smaller, the effective diffusion coefficient at the initial time is larger, which has higher precision and efficiency under the same pressure.

In a closed system, there is an infectious disease that can spread from person to person multiple times and can be transmitted during the incubation period. There is only one infected person in the system at the beginning, with temporary immunity. In this paper, the state of the initial infected person is divided into three stages. In each stage, we establish SI model, SIR model and SIRS model to list ordinary differential equations, and discuss the changes in the number of patients in the closed system when the initial latent person is a public place worker or other personnel. In addition, we establish SEIRS model to analyze the protective effects of different protective measures taken by staff in closed systems.The research shows that the best effect is to do a good job of protection before infection and timely isolation after infection.

The article focuses on introducing some properties of representative special functions with basic steps as the clue to follow the logic of each property. It is a review paper, so no results come out from it, but it will be a good paper for beginners to take a closer look at special functions. It also includes some extra stuff like Gamma Function and Applications of Orthogonal Polynomials.

Pearl River is one of the most important rivers in water resource system of South China. East River, West River and North River conflux at Pearl River estuary with eight bayous flowing into South China Sea. The characteristics of flow and tide in this sea area are in complex condition. Based on systematic analysis on historical research achievements for Pearl River Estuary, a 2-D mathematics model for large scale area including shallow sea area of eight bayous was approached to execute hydraulic numerical simulations under different hydrographic conditions separately. Approaching from analysis on the calculation results of flow vector field, potential lines and coastal current distribution, the movement features and regularities for tide current at Pearl River estuary were studied with emphasis in this paper.

In this paper, different integral methods for the finite element calculation of nodal force in the equation of motion are studied. The single point quadrature method has high calculation efficiency, but the calculation accuracy is low. In order to control the hourglass deformation, the anti-hourglass node force must also be introduced. Using multi-point Gaussian quadrature can avoid hourglass deformation and obtain high calculation accuracy at the cost of increasing part of the calculation. The simulation results show that the eight point Gaussian quadrature is closer to the theoretical value than the single point quadrature, and can well control the hourglass deformation. Obviously, the calculation result of the eight point Gaussian quadrature is obviously better than the single point quadrature. The calculation results also show the rationality and effectiveness of the method and program described in this paper. It provides a practical and effective means for the numerical analysis of penetration process.

In today’s society, mathematical modeling has attracted more and more attention due to its wide application, and optimization model is one of the most commonly used models. In this paper, linear programming, integer programming and nonlinear programming in the optimization model are taken as examples, combined with the three problems in the national college students ' mathematical modeling competition, the application of three optimization methods in mathematical modeling is briefly analyzed. Finally, the methods of solving optimization problems are summarized.

The calculation of serious technique index and using historical data is an important cornerstone for back test of trading strategy. It is a critical step that how to complete this calculation and test in determine the ultimate success of quantitative analysis. On the basis of python multiprocessing library, this paper proposes and implements a multi-process parallel computing model which is light-weight and easy-using. This model abstracts the multi-process concurrent computing as a base class which is used for all kinds of index calculation and history back tests to be independent operated. It could reduce the coupling between various strategies calculation and make full use of the CPU resources that effectively improve the computing speed of back testing strategy as well as provide a reliable guarantee for quantitative analysis.

In this paper, we study the general coupled nonlinear Schrödinger system (GCNLSS) which describes propagation of femtosecond pulse in birefringent fiber. By using direct integral method and the complete polynomial discriminant system method, we get different kinds of solutions including singular solutions, solitary wave solutions and elliptic function double periodic solutions.

Group theory, as a part of abstract algebra, was originated from 19th century and keep reaching its peak since around 50 years ago. The important results were collaborative efforts from various mathematicians including Cauchy’s Theorem, Sylow’s Theorem and Lagrange’s Theorem, and these results put group theory in a significant place of algebra.This paper talks about both finite group actions and infinite group actions with definition and accessible examples. The paper then gives definition and explanation on stabilisers and orbits, also with their corresponding examples in order to provide the demonstration of the statement of Orbit-Stabiliser Theorem, after that, its proof follows. In the last part of this paper, we finally introduce the statement of Cauchy’s Theorem and present its proofs as understandable as possible.

Trees are connected graphs without cycles, which are widely used in different fields. One of the hot topics in graph theory is the eigenvalue of graph's adjacency matrix, also known as graph's adjacency spectrum, which is an important research field of graph theory and has a wide range of practical applications. In this paper, we prove that the spectral radius of the adjacency matrix of the complete binary tree is 2√2 when the number of nodes tends to infinity by the eigenvalue of the adjacency matrix of the complete binary tree.

Group theory as a major category in abstract mathematic, it combines number theory, algebraic equations and geometry. Their new perspectives of group theory made contemporary math its unparalleled status in applied science, and it has evolved into multiple threads to calculate or explain different aspect in specific field of studies. And in the mid and late 20th century, mathematicians start to focus on finite group, a thread which can be more useful and easier to visualise.

Fungi, as decomposers in the ecosystem, play an important role in the decomposition of lignocellulose and promote the carbon cycle in the ecosystem. In this paper, the decomposition of fungi was simulated by establishing a mathematical model, and the effects of humidity and temperature on the decomposition rate of fungi were analyzed by linear regression model without considering the interaction between fungi. Combined with differential equations and metacellular automata model, the interaction between fungi was considered to describe how different populations of fungi interact in a given environment.

The Schwarz lemma plays an important role in the theory of geometric functions in complex variable. This article extends the classical Schwarz lemma to non-commutative and non-associative spaces. Using Cauchy integral formula and the relationship between Cauchy kernel and Poisson kernel, we obtain the Schwarz lemma with sharp constant in octonionic analysis.

The purpose of this paper is to use the wavelet transform context structures based on Granger causality analysis to investigate the correlation between housing prices and inflations in first-tier cities, namely Beijing, Shanghai, Guangzhou and Shenzhen. Wavelet analysis can be used for filtering, noise removal, multi-resolution time-frequency analysis, and other functions, especially for analyzing non-stationary signals. Results indicate that the relationship is generally positive but changes over time, displaying low to high-frequency cycles. Moreover, most of the situations that show a correlation between housing prices and inflations are that housing prices led inflations, which illustrate that housing prices are crucial to the economy.

This paper is in the field of constructive mathematics, mainly discussing the existence of algorithmic functions between left and right numbers. A L (Left) number is any strictly increasing algorithmically given sequence of rational numbers bounded above by a bounding element θ ,which is a rational number. Two such numbers can be added in a natural way, but not be subtracted. One can also add a rational number and subtract a rational number from it. We can also assume that each rational number is naturally presented by some L number given as a geometric progression of rational numbers; R numbers are defined similarly. We showed there is no algorithmic map that maps a L number to an equivalent R number.

In the book “Proofs that Really Count”, A. T. Benjamin and J. J. Quinn provided several identities involving Fibonacci numbers and left some unproved ones. Krzywkowski found that coverings in an area with dimension 2n can be enumerated by Fibonacci numbers. In this paper, by applying the combinatorial interpretation provided by Krzywkowski, we give combinatorial proofs of three unproved identities in the book “Proofs that Really Count”

Group theory is one of the most important aspects in modern science, mathematics, statistics, and computer technology. It was discovered in the nineteenth century in the context of delivering algebraic expression solutions. The group was defined precisely as the set of all permutations of an algebraic statement's roots that satisfy the condition that any two of these permutations belong to the set. This paper defines finite group actions as well as infinite group actions and provides examples. We reviewed some essential features of group action in this study. A comprehensive demonstration of the Cauchy theorem was also provided as an application of group action theory. Cauchy's theorem is a theoretic statement that claims that elements of all conceivable prime orders exist in a finite group.

The residue formula has a crucial influence on the field of complex functions. This paper overviews the residue formula and its proof. Afterward, this paper introduces Cauchy theorem, Cauchy formula, and higher order derivative theorem, which can be proved by residue formula. Subsequently, we find that the last three formulas are essentially the extension of the residue formula in different situations, and they can be used to effectively solve specific integral problems. We end this paper by applying these four formulas to solve a certain type of integral.

Residue theorem is a powerful tool in complex analysis to compute difficult real definite integrals. In this paper, with the help of special auxiliary functions, we’re going to use residue theorem to transform the calculation of real integrals into the calculation of residue. Moreover, we obtain a rather universal approach to solve this kind of problem. Finally, we apply this approach to reckon some specific infinite integrals and derive a special condition for a class of real integrals to be zero.

Conformal mapping is an important branch of complex analysis, which studies complex functions from a geometric point of view by mapping one region to another through an angle-preserved analytic function. It can simplify complex problems by mapping an irregular or complex domain to a regular or easier region. In this paper, we overview the definition of conformal mapping, the definition of linear fractional transformation, three well known automorphisms with conformal mapping and the history of Riemann mapping theorem. Besides, based on the Riemann mapping theorem, we study the Schwarz-Christoffel mapping from polygonal domains to the upper half plane or to the unit disk by giving the explicit construction of the conformal mapping. In addition, we also study the applications of conformal mapping on simplifying the Dirichlet problem by transforming Dirichlet problem in complex domains to Dirichlet problem in the unit disk, in which case the solution can be given by Poisson integral formula.

Dimitriadis and Bayer (2019) proposed a new regression framework which simultaneously models the quantile and the Expected Shortfall (ES) of a response variable given a set of covariates. This framework allows the use of different covariate vectors to make combined predictions of the models. Combined forecasting methods often provide a more practical way to synthesize the information provided by individual forecasting methods. Expected loss ES as a risk measure that satisfies subadditivity, especially since the Basel Committee recommended it as an alternative risk measure in 2016, has received more attention. In this paper, under the regression framework of Dimitriadis and Bayer (2019), different quantile covariates are used to study the advantages and disadvantages of different risk prediction models for combined prediction. CAViaR-SAV-VaR quantile prediction method by introducing AR(1)-GARCH model and quantile regression. A series of combinations of each prediction model are performed to explore the optimal combination of prediction models. In this paper, a series of independent forecasting models and combinations of models are used to empirically analyze the daily logarithmic return data of my country's Shanghai Composite Index. The results show that the forecasting effect of the combined model based on CAViaR-SAV-VaR and RM is better than other model combinations.

This paper discusses some basic properties of an algebra structure -- group in six sections. The content starts with basic operations of elements in a set and continues with an introduction of group concepts in sections 1 and 2. The review of basic operation in a set prepares important concepts that will be used later in group theory. Subgroups and cyclic groups are reviewed in Sections 3 and 4 to complete the introduction of one single group’s property. Concrete examples and geometry visualizations are included to deepen the understanding of the abstract concept and to offer a direct intuition. Subgroup and cyclic groups are also related to basic number theory which is also discussed in the content. Homomorphism and Isomorphism are discussed in sections 5 and 6. These two concepts relate to two and more groups together, giving a mapping with a good property among two and more groups.

The Monte Carlo Simulation is a widely adopted measure to solve for complicated results using repeated simulations. Its application has extended to a plethora of subjects and different variants of the method have been created. This article elaborates the key principles of Monte Carlo simulation and consults extensive sources to present some of its latest applications across scientific fields. Based on systematically reviewing previous scholars’ works, it is concluded that Monte Carlo simulation is efficient in simulation, estimation, and optimization but still has noticeable drawbacks like low speed of execution. These results shed light on tutorial of the Monte Carlo method as well as paving a path for future development.

Given the precondition that the probability of moving in each direction is identical, the properties (recurrent or transient) of random walks in dimension 1, 2 and 3 are discussed. Random walks in dimension 1 and 2 are verified recurrent while in dimension 3, they are proved transient. Afterward, random walks’ applications in different scientific fields are demonstrated and listed. In finance and biology areas, random walk hypothesis (the fluctuation of stock prices follows random walks and is unpredictable) and Lévy walks (a special class of random walks with move steps follow a power-law distribution) are introduced separately. In addition, their applications in physics (simulating the movement route of a molecule in a liquid or gas) and computer science (network embedding, semi-supervised learning and computer vision) are mentioned briefly. Finally, the current limitations and future development of random walks are considered. These results shed light on the importance of random walks in modern science and pave a path for future implementation of it in multiple fields.

This article concentrates on the application of Cauchy residue theorem in different fields and the links between the work of Cauchy, who developed his theory of residue in one variable, and other contributing mathematicians, such as Laurent and Sokhostkii. Laurent introduced Laurent series and developed Laurent theorem based on the work of Cauchy. Sokhostki studied the properties of residue. We will overview the work of these three mathematicians and mention the application of Cauchy residue theorem in integration and series summation. When calculating the integral of a real function, we transform the problem into calculating the integral of a complex function along a chosen contour, and then use the residue theorem to get the answer. When computing the sum of a series, we transform the problem into summing the residues of a function on specific points, and then use the residue theorem to transform the latter problem into computing the integral of the function along a contour.

The normal distribution has many important properties and has a wide range of important applications in practice. This paper generalizes the related properties of one-dimensional and two-dimensional normal distributions to the related properties of n-dimensional normal distribution, and makes a summary and gives a more some detailed proof.

Multi-robot coordination demonstrates outstanding performance in exploring and tracking targets in unknown environments, especially in complex terrain or disaster environments. In these cases, the distribution of the search area is changeable and irregular, and the exploration target may also move in an unknown environment. To quickly determine the location of these exploration targets, we propose a distributed control strategy in the article, which applies Bernoulli Thompson sampling to solve the multi-armed bandit problem to allow multiple robots to share information and efficiently search targets. This algorithm significantly speeds up the robot's search for targets, especially when most targets are concentrated in certain fixed areas of the environment.

This paper is about the equilibrium point of fuzzy difference system. First, using fuzzy cut-set theory, the fuzzy difference system is transformed into a system of rational difference equations. Second, the existence and uniqueness of the solutions of rational difference system are achieved by iterative method, inequality property and mathematical induction method, and then the solution of fuzzy difference system is obtained. Finally, the two equilibrium points of the rational difference system are discussed by using the linearization theory, and then the sufficient conditions for the instability of the zero equilibrium point of the nonlinear fuzzy difference system are obtained.

In this paper, a generalized (1+1)-dimensional equation is studied based on Bell polynomials. In special cases, mKdV equation and nonlinear Schroሷdingerequation can be returned. Firstly, we use the relation between the Bell polynomial and the Hirota bilinear to derive the bilinear form of the equation. And then the soliton solutions of the equation are obtained. Finally, two examples are given for analysis.

In this paper, we will give a summary of 𝑝𝑝-group, Sylow 𝑝𝑝-subgroup and Sylow theorems, and we will introduce similar properties of Hall ππ-subgroup, which is generalized case of Sylow 𝑝𝑝-subgroup. And then we will give a strict proof of Sylow theorems. At the same time, we also use this theorem to prove a series of useful theorems.

Contemporarily, the random walk is widely applied in the field of finance, suggests that the history stock price has no relation or impact on the stock price tomorrow, i.e., the direction the of stock price is entirely random and unpredictable. This paper investigates random walk simulation in Finance based on the information retrieval and literature review. According to the analysis, if one holds the strong belief in the random walk theory, well-perform ETH or portfolio strongly relevant to core Index (e.g., S and P 500, Nasdaq) will be a proper choice for investors. Otherwise, if one holds that the price movements are inherit connected instead of random variation, statistic evaluation (also known as technical analysis) can be applied to earn with extra returns via time-selection trading actively and positively. Based on enough trials, this paper will try to explore the nature and patterns of random process, which sheds light on future stock price prediction and explanation.

Hepatitis B virus (HBV) is a global health threat, with around 800,000 HBV-related deaths each year. Vaccination is currently available, and it is recommended to all newborns by the WHO. However, there is a possibility that the vaccination-induced protection might not be lifelong as antibody levels do wane over time. This paper builds upon a susceptible-infectious-recovered (SIR)-type HBV transmission model, adding the effects of waning of the immunity. The mathematical model is then simulated through Matlab. Both steady state solution and computer simulation show that a shorter duration of vaccination-induced protection could lead to a significantly higher prevalence of susceptible, specifically from 15.00% for lifelong protection to 82.16% for 20-year protection. A larger susceptible population, in turn, will result in a higher number of acute cases and new chronic cases. Furthermore, the analysis of booster shot effects on the number of newly infected suggests that implementing a boosting strategy could be beneficial.

This paper presents the recurrence formula of a specific kind of improper integral with the bounds of 0 and positive infinity, involving a certain power of the natural logarithm of z, divided by the sum of one and a certain power of z, with respect to z. We use two integer variables as the power of the natural logarithm and the power of z in the denominator of the integrand to parameterize this integral. Moreover, we present some discoveries for particular integral among this integral type as well. To compute the integral, we get inspiration from the residue theorem to construct a contour as the new integration path. Besides, we cope with the redundant paths via integral transformations as well as mathematical induction. After computing it, we conclude a recurrence formula and try different values of the parameters for some observations. To prove the observations, we apply some properties of the infinity, the series, and the Euler numbers. This recurrence formula makes this integral easier for us to calculate, and these observations reveal more beautiful properties of this integral category.

We use the Newton–Maclaurin inequality to explore the problems related to the viscosity solutions for parabolic Hessianequations, in which the existence and uniqueness are studied, the equations is − y_t + S_k(D ²y) = g.

Helmholtz equation is widely used in physics and engineering. We present the sixth-order fast algorithm of the threedimensional Helmholtz equation with large wave numbers. For the difference scheme of the equation, a three-diagonal structure is generated by the fast Fourier transform which transforms the original problem into an independent small system. The novel feature of the high-order algorithm lies in its accurate numerical solution and shorter computation time. The method makes it possible to solve the Helmholtz equation with large wave numbers. Finally, the feasibility and accuracy of the proposed algorithm are verified by several numerical experiments.

The Burgers equation is transformed into a second-order linear partial differential equation by Hopf-Cole transform. Then the time variables are discretized by weighted implicit scheme, the spatial variables are discretized by cosine DQ method, and the Lagrange interpolation function is selected as the basis function, finally the implicit DQ discretization scheme for the initial boundary value problem of Burgers equation is established. The scheme has the advantages of simple mathematical principle, convenient use and less calculation and memory requirements. Numerical example shows that it has high calculation accuracy and can effectively capture physical phenomena such as shock waves. It is a competitive numerical calculation method.

We frequently use condition number ( ) to judge the collinearity of a linear regression model. If the is large, we tend to believe the result of the least square estimate (LSE) is unreliable. However, in this article, we will give an example to show that is not a perfect indicator to reflect the influence of collinearity. In some cases, a model with high collinearity is quite likely to give an ideal LSE. Therefore, we put forward relative mean squared error ( ) to judge whether the collinearity significantly influences the LSE. Though is not theoretically perfect now, it indeed does better than when tested by the data we generate.

Ecological and environment conservation is a comprehensive issue for world to persist and require associated efforts from individuals and governments especially in aspect of stable sand preservation. Especially in the evaluation of established environmental protection area. Our main contributions can be described as assessing and comparing restoration situation of Saihanba, evaluating sand prevention levels, simulating and determining environment protection locations and extending model to environment preserving. we establish press-state-response (PSR) model to evaluate ecological environment through collecting related indicators and selecting primary indicators by principal components analysis (PCA). The model performance is compared with the data of before and after restoration of Saihanba and the model evaluation results are basically compliant with real curves. we collect the amount of clean water, sum of released oxygen and count of carbon sequestration to behave as aim lay in established multi-level hierarchical process (MLHP) model. We utilize entropy weight method (EWM) to assign diverse weights for collected third layer data aspects including the quantity and quality of Saihanba tree farm, economic effect of tree farm and Saihanba tree resource effectiveness. We also predict the future twenty years trend of sandstorms after utilizing the proposed prevention methods.

At present, many places have issued related policies of photovoltaic building integration, which will affect the development of listed companies related to photovoltaic building integration. This paper will be based on the effective market hypothesis, Markowitz portfolio theory, capital asset pricing model such as the classic model, combined with GARCH model to 37 photovoltaic building integrated related enterprises in Shanghai and shenzhen stock market volatility of the stock data of yield of modeling, using the normal distribution method of value at risk under different confidence level to calculate, Based on the value at risk and volatility of individual stocks, A reasonable quantitative evaluation ranking of financial risks is carried out, and the performance evaluation of individual stocks in photovoltaic building integration board is carried out through improved and indicators. Five stocks, including Longji Stock, Shenzhen Energy, Haida Stock, Qingyuan Stock and Southern Glass A, are selected as high-quality stocks. Combined with national policy background knowledge and risk analysis results, for the future development trend of photovoltaic building integrated plate summary report.

Using Bayes Theorem and the conditional probability knowledge, this paper provides a method to predict a student’s GRE Score range based on his/her TOEFL Score. To locate the specific GRE range, a data set of 500 undergraduate students who have taken GRE and TOEFL exams is used as the statistics. This paper also borrows the statistics from the official website as the prior probabilities. The result shows that not only is there a positive relationship between the scores of the two exams, polarization also occurs regarding the two standardized exams scores. However, since the data set is retrieved from only one single spot, the reliability and universality are yet to be tested. A combination of more data sets obtained from different sites may help improve the prediction accuracy.

The application field of big data technology is very wide. In any industry, data and information can be analyzed through big data, and the results of these analysis are of high practical value. However, with the advent of the Internet era today, various fields are constantly developing, including the education circle. Using network education to carry out a series of teaching activities, can comprehensively improve the effectiveness of education. In the current COVID-19 epidemic, many schools and many industries have adopted computer technology and big data technologies, such as web conferencing, online classroom, remote conferencing, remote video and other teaching and production activities. This paper focuses on the role and value of computer data analysis in applied mathematics. The research shows that cloud data analysis has super high application value in applied mathematics.

This paper is aimed to discuss the importance of Cauchy residue theorem through different aspects. Firstly, we will overview Cauchy residue theorem and its proof. Then the application of Cauchy residue theorem to calculate a complicated integral of a real-valued function will be investigated. Finally, we will explore to compute the 1D Green’s function for the Helmholtz equation by Cauchy residue theorem.

Cauchy’s residue theorem is a significant theorem in complex number analysis. Motivated by the residue theorem built by Cauchy, numerous researchers have studied and tried to apply this theorem in different academic fields. In this paper, we are going to generalize Cauchy’s residue theorem in multiple fields. Firstly, we will review the residue theorem and some theorems developed from the residue theorem. Then a definite integral of function will be calculated as an example to show the application of residue theorem in real number calculation. Next, we discuss the theorems of logarithmic residue which is discovered by utilizing residue theorem, and a short proof will be used to illustrate the connection between different logarithmic residue theorems. Finally, based on Jacobi’s residue theorem, we will have a brief synopsis of the application of residue theorem in combinatorics. By these generalizations, we find that the residue theorem can be widely applied in different academic aspects.

Group is the earliest developed, the most extensive and the most fully used part of abstract algebra, which is the basis of establishing other algebraic structures. The study of group theory originated from the study of permutation groups. Then it is found that the most important problem is not the permutation itself, but the properties of sets under algebraic operations. Therefore, the concept of general group is put forward, which expands the research object and application of group and enriches the research methods of group theory. Group theory has important applications in natural sciences including computer science. Such as the combination technology, coding theory, information security and other fields.

Modern algebra is importance for advanced math. It includes group theory, ring theory, and field theory. For the first course of Modern algebra, group theory, is not easy to think. Furthermore, group theorem is also a study of algebraic structure. We will focus set theorem and modular arithmetic a little bit. We also need to know something about functions (injection, surjection, and bijection). We also involve some basic method of proving problem, such as induction. Meanwhile, we summarize fundamental theory for finite groups and some infinite group cases. First, we introduce some basic definitions. Next, we summary some basic types of subgroups. Finally, we prove an Orbit- Stabilizer Theorem.

Residue theorem is an important theorem in complex analysis. In this paper, we revisit this theorem and present several of its applications. The first application we discuss is to calculate definite integrals whose anti-derivatives are unknown or difficult to find. Then Fresnel integral is proved by residue theorem. In addition, this theorem provides other approaches in proving Jordan normal form theorem and the fundamental theorem of algebra. Finally, it also serves as a handy tool for calculating ζ(2) and generalizing ζ(2k) using Bernoulli numbers.

Recent years, to facilitate the flow and transport of hydrocarbons to wells, the hydraulic fracturing technology is widely used in unconventional geological resources with extreme low in-situ permeability to increase formation permeability. However, it’s found that, fracture permeability decreases sharply during the development of reservoirs caused by the increase of effective stress. Specifically, due to effective stress, proppant embedment and compaction occurs in the fractures, leading to the decrease of fracture permeability. In this paper, we focus on developing a reasonable theoretical model to determine the essential controls on proppant embedment and compaction. In addition, we will study the stress dependent permeability of fractures. Results suggest that the predictions from our developed model agree well with the available experimental data presented in the literature. In addition, proppant embedment and compaction will be affected by effective stress, rock lithology parameters, proppant size as well as proppant lithology parameters, etc. Our proposed model can reveal the mechanisms that affect proppant embedment-compaction in hydraulic fractures.

Nozzles, which are widely used in turbojet engines, can determine the state of the final discharged air flow with their shapes and structures. Research on nozzles has a long tradition and computational fluid dynamics (CFD) have played an important role in it. The influence of the inlet Mach number and size of its throat on the symmetrical nozzle flow are studied by getting streamlines’ data. To that end, the small disturbance equation (SDE) method is used with the full potential equation and the wave equation for subsonic and supersonic flows, respectively. The SDE method has a great ability to converge. Subsonic and supersonic cases have different trends passing through the nozzle. Flow’s horizontal velocity can be adjusted by changing nozzle’s shapes and sizes. This paper provides a reference for nozzle parameters’ selection.

Cables have been widely used in long-span bridges as the main bearing structures. The safety of cables has great importance, and thus identification of the tension as accurately as possible is vital to reflect its bearing conditions and performance degradation of cables. To address this issue, this paper proposes an Implicit Function Method (IFM) to investigate the tension of cables using vibration-based methods. The method introduces three non-dimensional parameters to describe the relationship between tension and vibration frequency. Both inclined angle, sag, and bending stiffness are considered to create the frequency characteristic equation and the trust-region dogleg method is used to find the solution of implicit functions. The efficacy of the method is demonstrated by a field experiment in bridge engineering, and the results show that the proposed method improves on the string theory method with higher identification precision.

Biot-Savard Law is an important law for calculating magnetic induction intensity. The formula is summarized and generalized by a large amount of experimental data, so the form is complicated, and the solution process is tedious. In this paper, the magnetic field of a long straight wire carrying current is solved by Brio-Savard Law as an example, and the shortest form of the formula is obtained by selecting the appropriate integration variables and giving the key points of application, so as to simplify the calculation process and improve the calculation efficiency.

This paper mainly proves that the elliptic curve 𝑦² = 3mx(𝑥²−8) only have integer point (𝑥, 𝑦) = (0,0) with the help of elementary method such as the properties of congruence and Legendre symbol.

The acceleration of the urbanization process puts a higher demand on traffic management. In the last few years, ITS(intelligent transportation systems) have played a significant role, and traffic prediction is an important content among them. In fact, traffic forecasting is very challenging, mainly due to the temporal-spatial nature of the related traffic data. For this article, we propose an optimization method of graph convolutional neural network with Bi-GRU to optimize traffic prediction. Experiments show that our model has achieved good results and provides a new perspective for studying such problems.

Predicting the change trend of water quality is an important evidence to maintain and govern the current water quality. The Grey Markov SC GM（1,1）model was used to forecast the index of permanganate in water source. The result shows the Grey Markov SC GM (1,1) model can not only reveal the overall change trend of water quality of the water source, but also overcome the error arising from the random fluctuation. As a result it is a feasible and practical method.

The multi-dimensional grey prediction model can analyze the relationship between multiple driving factors and the explained variables. Aiming at the operation status of Hainan regional economic system, based on the previous research results, this paper selects 8 driving factors related to the operation status of Hainan regional economic system, and carries out the weighted grey correlation analysis to quantify the influence of each driving factor. Then a multi-dimensional grey prediction model is further established. The results show that GM (1,2) has high accuracy and is suitable for the research model of Hainan regional economic system.

With the increasing attention to environmental issues, sustainable waste management (SWM) has become a serious challenge for Beijing. Beijing municipal authorities implemented the pilot project of waste classification in 2008 to promote sustainable waste management, but it did not meet expectations due to various restrictions. Therefore, this study focuses on identifying a comprehensive and detailed list of barriers for the successful implementation of sustainable waste management (SWM) in Beijing. Through an extensive literature review, 12 barriers are identified. Using an integrated approach including the Maximum Mean De-entropy Algorithm (MMDE), Interpretive Structural Modeling (ISM) and Cross-Impact Matrix Multiplication Applied to Classification (MICMAC), a hierarchical model of SWM implementation barriers is constructed. Finally, the dominant barriers hindering the implementation of MSW management in Beijing are prioritized to provide insights for industrial decision-makers and policymakers. The results indicate that the 12 barriers can be divided into five categories, among which the barriers from the government and resident have effectively delayed the process of Beijing SWM implementation. The government and the participants in the waste recycling industry have an effective framework to guide the management and recycling of solid waste and how to effectively reduce participation risks in the waste recycling market.

In order to ensure the safety of long distance pipeline and prevent the occurrence of pipeline failure accidents, the minimum deviation Kent method is used to establish the risk analysis model of long-distance pipeline,and the three pipelines of central Sichuan oil and gas mine are used as examples for application. Firstly, the IAHP model is established by FTA- AHP for qualitative identification and quantitative calculation of pipeline risk factors. The entropy weight method is introduced to calculate the weight of each factor, and the minimum deviation model based on Structural Importance-EW is constructed to calculate the combined weight. Finally, based on the weight calculation results, the improved Kent method is used for risk assessment,the risk levels are all in the medium risk area.The research results show that the evaluation results are basically consistent with the actual situation, and can be applied to the risk assessment of other long-distance pipelines, which can lay the foundation for the implementation of daily safety management of long-distance pipelines.

As one of the biggest threats to coastal cities, typhoons (hurricanes) cause huge economic losses every single year. How to effectively reduce the loss of typhoons in these areas is a permanent topic for human beings. The main body of this article is divided into two parts. The first part will take Hurricane Katrina as an entry point to assess its impact on coastal cities in the southern United States based on the Hazus model, an American standardized risk modeling methodology. A series of assessments on the demographic model and the degree of damage to buildings is conducted. As a multifunctional model, Hazus can be used to assess the damage caused by typhoons and in combination with The American Society of Civil Engineers’ standards to propose some practical methods to improve urban resilience. These methods mainly include but are not limited to suggestions for house structure, which will be fully discussed in the following chapters.

Electric vehicles (EV) are a crucial technology to tackle environmental issues like air pollution and energy depletion. In this paper, we use a static computable equilibrium model to estimate the effects of two different policies: the subsidy and the credit regulation. The results show that both policies have negligible effects on the macro economy. The subsidy on EV creates more emissions as the substitution between conventional vehicles and EV isn’t very effective, leading to more production. The credit regulation, otherwise, suppresses the production of conventional vehicles while encouraging the production of EV, thus, emissions of CO₂, NO_x, Dust, COD are largely reduced. And the combination of the two policies has a mixed effect. However, the emissions of SO₂ and NH₃-N increase no matter which policy is implemented, suggesting that different sectors perform diversely under the stimulus. Policy-maker needs to make a trade-off between the benefits and risks of certain policies.

The reform of transmission and distribution prices requires grid companies to strengthen input and output efficiency and optimize resource allocation. This paper establishes a mathematical model that controls the upper limit of the investment scale based on the transmission and distribution price, and calculates the investment capacity of the power grid based on the asset-liability ratio target. Case verification shows that using this model, power grid companies can objectively evaluate their own maximum investment capabilities, and provide a scientific basis for power grid companies to formulate reasonable investment plans, at the same time, it also provides a reference for other companies to calculate their investment capacity under the limitation of debt ratio.

The construction of migrant workers professionalize-tion is the inevitable trend of the current construction industry development, by collating and analyzing the related literature at home and abroad, the article puts forward the theory model of the development of the construction workers professional and 10 factors affecting the development of construction workers professional, and using the Logistic regression model analysis that it is concluded that the six key factors: Age, education level, vocational skills training, labor contract signing, social security participation and full-time degree, finally puts forward targeted development countermeasures and suggestions to enhance the attraction of the construction industry, popularize the formal employment mode, improve the technical training system.

A supply chain network design (SCND) problem with fuzzy dual objective integer programming is proposed for stochastic transportation lead time. The conflict objectives considered in this paper are to maximize the total net profit associated with the supply chain network design and to minimize the delay probabilities associated with the transportation lead time between the production plant and the distribution center and the distribution center and the customer. It is assumed that the possible risks associated with transport lead times follow a normal distribution with defined mean and standard deviation. The model is tested with different levels of risk to achieve maximum satisfaction in the network. By considering acceptable levels of satisfaction, the results of the analysis of the proposed model will provide different scenarios, which will help decision makers better understand the supply chain network required for the design. LINGO software programming solution, and case analysis. The results show that the lower the risk level, the higher the probability of product delivery to customers ahead of time, and the lower the profit.

Chaohu area is a more economically developed area in Anhui Province, so protecting and improving the ecological environment of Chaohu area has become a significant task for the national and Anhui provincial governments’ environmental protection work. According to the specific conditions of the Chaohu Lake are, this paper calculates the ecological carrying capacity index of the Chaohu area by constructing a factor analysis model. The grey relation analysis model analyzes factors affecting the ecological carrying capacity index. According to the empirical results, the ecological carrying capacity index is generally on the rise, which indicates that the ecological carrying capacity of the Chaohu area is rising. Greening coverage area and Agricultural acreage exert the most significant impact on the ecological carrying capacity index. Based on the empirical results, this paper proposes a further work.

According to the HIV and AIDS infection and incidence data of Guangdong residents from 2011 to 2020, the GM (1,1) model of metabolism was established based on the grey system theory, and the results were calculated by Matlab: Q=0.0089≤0.01, mean square error ratio C=0.2765≤0.35, −= < a 0.0035 0.3 . The test accuracy of this model is level 1. The GM (1,1) metabolic model is used to predict the number of HIV and AIDS cases in Guangdong province in the next five years. The data results show that the number of HIV will decrease in the next five years and the overall level of ADIS will increase Using grey Verhulst model analysis AIDS deaths each year, the data is not saturated state, it is on the rise Reflect the Guangdong province AIDS prevention and control work in the future a long way to go Through the model analysis to predict the trend of disease and death, HIV/AIDS prevention and control management measures for developing the Guangdong provides a reliable basis.

In order to effectively improve the consumption level of distributed energy and promote the healthy development of the electricity market, an efficient and reliable energy trading mechanism needs to be proposed urgently. This paper takes the micro-energy grid system as the research object, and comprehensively considers the user’s energy demand changes, market energy management, and transaction mechanisms, combined with Electricity spot market, and designs a distributed energy trading model oriented to the spot market. Optimal output, to solve the economic benefits of the unit and the economic benefits of the region. The study of distributed energy trading mechanisms in this article provides a reference for future electricity market transactions in micro-grids and also provides an important basis for the promotion of green certificate transactions.

Fire is an important disturbance in earth’s system. In the arctic region, fire can release huge amount of carbon as the arctic peatland stored almost one third of carbon storage in the earth’s soil. The gaseous carbon compounds are usually greenhouse gases, which can enhance the greenhouse effect, and warm the arctic region. Fire risk in the arctic region is positively correlated to the warmer climate. There is a potential positive feedback between the climate and the carbon loss from wildfire in the arctic region, but the relation between fire carbon emission and climate change in the arctic largely remains unknow. This study aimed to analyse the correlation between the climate factors and the fire carbon emission. This study used Multiple Linear Regression and ANCOVA to analyse the correlation of the carbon emission from 2001 to 2018 in Alaska. The findings indicated that the fire carbon emission in Alaska fluctuated significantly within those years, and the high carbon emission was associated with the large fire events, which burned massive amounts of areas. The carbon emission was mostly affected by the temperature and humidity, but the correlation was negative. As the fire carbon emission was not covaried with the warming climate, the future fire carbon emission might be depending on the interactions among various climate factors.

With the continuous development of aerospace technology, people's obsession with outer space resources is getting deeper and deeper. At 1:30 a.m. Beijing time on April 25, a start-up company called Planetary Resources was founded and boldly announced its plan to mine planetary resources, a move that shocked many media. However, is the exploitation of space resources as good as everyone imagines, and what impact will outer space resources have on the global capital market and people's lives after they enter the global capital market? These questions have not been scientifically analyzed and studied so far. In this paper, we will take the example of mining the mineral resources of the planet Kepler 452b, through consulting relevant literature; three factors that can most affect asteroid mining are selected: economic strength, military capability, and technological level. We set the weight initialization of economic strength to 24 %, the weight initialization of science and technology level to 45 %, and the weight initialization of military capability to 31 %. The principal component analysis comprehensive evaluation model is used to analyze the impact of asteroid mining conditions on global equity. Through analysis, we find that the change of weight value will affect the scale of planetary mining, and then cause fluctuations in the global nickel, gold, platinum, and other precious metal markets, which has a negative impact on global equity to some extent. Reflected in the Gini coefficient, it is the dynamic change of the Gini coefficient value that first increases and then decreases.

A rigid-flexible coupling positioning stage (RFCPS) is proposed in this study for long-stoke-high-precision (LSHP) positioning, and its dynamic model is established. The structure of the RFCPS contains three parts: the working stage, the frame and the flexure hinge group. The flexure hinges can provide micro deformation to compensate the positioning error cause by the friction of the mechanical bearing. In order to consider the deformation of the flexure hinges, the flexible multi-body system dynamic analysis method is adopted to establish the dynamic model of the RFCPS. The investigation of the principle model demonstrates that the floating frame of reference formulation (FFRF) has higher accuracy than the absolute nodal coordinate formulation (ANCF) for the deformation analysis of the RFCPS. Sequentially, a finite element based model (FE model) is established by using the FFRF. Numerical simulation results shown that the results of the FE model is consistent to the analytical solution, and the deformation of the flexure hinges is effectively obtained. The establishment of the dynamic model lays the foundation for structural optimization and control system design of the RFCPS.

With the help of "Shanghai-Hong Kong Stock Connect" to implement quasi-natural experiment, this paper adopts the data of southbound capital and Hong Kong stocks from 2010 to 2020, and constructs PSM+DID model to compare and analyze the impact of the southbound capital on the volatility of Hong Kong stock prices after entering the Hong Kong stock market. The results show that southbound Capital can stabilize the volatility of Hong Kong stock prices by leveraging its information advantages to hold Chinese concept stocks investment. The paper also provides suggestions for the future development of China’s capital market.

In view of the actual needs and problems of weapon R&D project budget performance evaluation, a performance evaluation index system covering the whole process of weapon R&D projects is designed from three aspects: project decision-making, implementation process and project output. In order to avoid information distortion and loss in the evaluation process, the cloud model is combined with traditional matter-element-extension model. A cloud matterelement model is constructed to comprehensively evaluate the budget performance of weapon R&D projects, and the effectiveness and feasibility of the evaluation model are verified by an example.

As it is reported, the detailed COVID-19 cases have exceeded 400 million worldwide. And there is another outbreak of the COVID-19 infection in England due to the emergence of a new variant: Omicron. Through implementing distinctive control measures, most vaccination has been accomplished to an expansive levels in this country and is as of now in advance. Due to the popularity of vaccines and the success of anti-epidemic measures, the English government decide to announce the last legal restrictions being lifted by February 24, which means that English will be the first country to declare victory over COVID-19. To judge whether the decision is correct or not, we estimate confirmed cases, death, daily new confirmed cases and trend through modeling and simulating method. Considering the effectiveness of vaccines, we raise a new epidemic model named SEIR-V. Our results appear that if transmission rate increases by 15% compared to the current rate due to unwinding of social distancing conditions, the daily new cases can crest to 200k per day around April 1, 2022. The combination of vaccination and controlled legal restrictions is the key to tackling the emergency of the new variant Omicron epidemic. Considering that the new variant strains increase transmissibility and have high resistance to vaccines, the English government should continue the current epidemic prevention measures to avoid the emergence of a second wave of the epidemic.

According to the idea of life cycle assessment, taking the floor of a building as the object, this paper uses BIM technology and tools to build a multi-dimensional information model of the construction project, further defines the relationship between BIM model elements and building materials, and quantifies the environmental impact of building materials. Through the classification, characterization, standardization and weighted evaluation of the results generated by the BIM-LCA function module (Tally), the impact potential of different environmental impact types in each stage and the environmental impact size of the same environmental impact type in different stages are obtained. The analytic hierarchy process is used to establish the environmental impact assessment index database of construction projects in order to measure the feasibility of construction projects.

Forest products can sequester carbon as well as living plants. Therefore, we can maximize carbon sequestration by appropriately cutting trees and it is quite necessary to study the optimal forest management plan. Firstly, this paper studies how to determine the amount of carbon dioxide that forest and its products can sequester through mathematical analysis, which contributes to making a forest management plan with the aim of maximizing carbon sequestration. Nevertheless, we propose a comprehensive evaluation model. We establish indicators form from multiple aspects and then employ the entropy weight method(EWM) and the coefficient of variation method to calculate the weights of the first-level and second-level indicators respectively.

A damage simulation software of armor piercing projectile and high-explosive anti-tank is introduced in this paper. The software is composed of four parts: armor piercing projectile and HEAT power simulation module, target protection simulation module, damage simulation module and damage assessment basic database. The software has the functions of damage element parametric modeling, target similarity parametric modeling, target vulnerability analysis and damage effectiveness evaluation of armor piercing projectile. The software provides a variety of damage evaluation demonstration cases.

Based on the finite element analysis software, numerical simulations are carried out for the heat pipe embedded in the enclosure. Firstly, a CFD model is developed for a two-phase heat siphon heat pipe with unidirectional heat transfer function, and the experimental condition of liquid filling rate of 0.6 is used to obtain the internal phase distribution clouds of the heat pipe under four different heat flow density conditions The simulation of the evaporative section is consistent with the visualization experiment, and the VOF model is able to describe the gas-liquid separation and bubble aggregation phenomena realistically and accurately. Finally, the practical application prospects of the enclosure structure and the shortcomings of the research are pointed out.

Since the spread of the COVID-19 virus among people all around the world, authorities have adopted various policies against it. Effective policies are usually based on strong academic support. Scholars have done a lot of research on the development of the virus and the epidemic. Compartmental models are widely used to solve infectious diseases related problems. Based on the extensive research on the COVID-19 virus by previous scholars, it is verified that there is a significant latency period when susceptible are transferred into exposed. Hence, the SEIR model is widely used to model the COVID-19 epidemic. And in this paper, we use a revised SEIR model to highlight the significance of the limitation term, analyzing the trend of the epidemic under the different methods of isolations. The research data is based on the outbreak of the epidemic in Nanjing in July 2021. The paper examines that isolation is one of the most effective measures to cut off the transmission route of COVID-19.

The maintenance and support capability of the army's equipment is an important factor in maintaining and restoring equipment performance and ensuring the continuous generation of combat effectiveness. Through literature review and expert consultation, the influencing factors of maintenance capability are identified, and on this basis, a model of influencing factors of equipment maintenance support capability based on decision-making experiment and evaluation laboratory method(DEMATEL) and the interpretation structure model method(ISM) is constructed. Using the cause-effect diagram and the multi-level hierarchical structure model to study the correlation between the influencing factors, and put forward relevant suggestions, it has certain guiding significance for the construction of the military equipment maintenance support capability.

The traditional grey target decision-making model comprehensively compares the Euclidean distance between the index value and the bull's-eye, to judge the pros and cons of the decision-making scheme. The power operation is easily affected by the extreme index value, which has the amplification or reduction effect on the calculation of the target center distance, thus affecting the rationality of the scheme selection. The grey target decision-making model based on cobweb area weakens the influence of extreme value on target center distance, but increases the interaction between adjacent indexes. If the indexes are out of place, it may produce reverse order phenomenon. In view of the shortcomings of the above model, it is proposed to use the triangle area to represent the gap, between the decision-making plan and the bull's-eye, that is, the distance formula in the traditional grey target decision-making model is replaced by the comprehensive area, which is applied to the decision-making problem of interval grey number, and a grey target decision-making model based on triangle area is constructed. The model not only avoids the influence of extreme index values, but also avoids the reverse order problem caused by ectopic indexes. An example is given to verify the effectiveness of the method, and the results of several models are compared to illustrate the effectiveness and practicability of the method.

Heart disease has become a global trend illness, with high mortality and death toll. Based on the accumulated case data, data analysis can be used to predict potential heart disease patients more accurately and optimize the treatment. Comparing with other research, this study uses the most basic algorithm in the tree-based methods to predict the data. In the research, some exploratory analysis on the heart disease data set is done firstly. By analyzing the relationship between each variable, the symptom factors related to heart disease are obtained preliminarily. Then this study develops two heart disease prediction models using two kinds of tree methods and compares the error of the two models. It turns out that the random forest model fits better than the decision tree model which can predict the data much more accurate. This can help medical professionals predict heart disease status based on a patient's clinical data and improve patient treatment efficiency. Also, the study gives hints about the causes of the heart diseases, which will be useful in preventing these fatal illnesses.

Forest fires have a tremendous negative impact on the global ecology and the national economy. Advances in information machine technology have paved the way for the use of Unmanned Aerial Vehicles (UAVs) to fight forest fires, including monitoring fires and expanding signal propagation. However, in practical applications, we must consider the characteristics of UAVs such as monitoring range and the difficulties in balancing safety and economics. We take the 2019-2020 bushfires in Victoria and New South Wales as a case study and explore how best to combine two types of UAVs, SSA drones and radio repeater drones, to balance safety and cost-effectiveness. In this paper, we first employ the particle swarm algorithm to reasonably schedule the minimum number of SSA drones patrolling the sky while maximizing their surveillance area for the fire area. Then, we propose a Topology Spanning Tree (TST) algorithm to determine the locations of Emergency Operations Centers (EOCs) and Radio Repeater drones and the minimum number required. Then, we use the Ant Colony Algorithm to find the shortest path of the drones from the EOCs to the designated patrol location to reduce the loss of their flight power. Finally, we set up a multiple regression equation to find the minimum cost using the size and frequency of fire events as parameters.

In this paper, a predator-prey model with nonlinear harvesting of prey is studied, and the impact of harvesting rate on the ecosystem is evaluated. By selecting harvesting rate as a control parameter, the optimal control model of harvesting rate is established. Moreover, using the Pontryagin maximum principle to transform the optimal control problem into a Hamiltonian system, analytical expression of the optimal harvesting rate is obtained. Numerical simulation is performed by using the pseudo-spectral method, and results show that a reasonable harvesting rate can achieve a win-win scenario both economically and ecologically.

The ideal paraboloid is the basis for the adjustment of fast reflection panel. Through the ideal paraboloids in different directions of celestial bodies, select the main cable nodes to participate in the adjustment, and establish the corresponding model to calculate the expansion and contraction of the actuator corresponding to the main cable nodes, so as to make the reflection panel close to the ideal paraboloid as much as possible. In this paper, two methods are used to establish the ideal paraboloid model. Model 1: Based on the geometric characteristics of parabola, the results are displayed by MATLAB software; Model 2: Based on the ideal paraboloid solved by the ideal paraboloid and the proof results, the three-dimensional coordinate equation of the ideal paraboloid in any direction of the celestial body is calculated by using the coordinate axis rotation method. At the same time, the main cable point screening model and the calculation model of the adjustment expansion of the main cable point actuator are established. The adjustment parameters of the reflection panel under the celestial orientation are obtained, and the adjusted receiving ratio is 67%; The receiving ratio of the reference sphere is 20%, and the difference between them is 3 times, which proves the effectiveness of adjusting the reflection panel close to the ideal parabola.

This paper focuses on the quantitative assessment of inhabitants' health in Fujian Province from 2008 to 2020 in terms of living, environment, medical and health, culture, and sports. First, important indicator data are gathered using statistical sources such as the Fujian Statistical Yearbook, the China Health Statistical Yearbook, and the Fujian Provincial Bulletin on the Status of the Ecological Environment. The ideal weight is then determined by integrating the analytical hierarchy process (AHP) and the entropy weighting method (EWM) with the additive integrated weighting approach, resulting in the establishment of a fuzzy complete assessment model. The findings demonstrate that, during the last 10 years, the health of citizens in Fujian Province has showed an overall higher trend, with a favorable overall growth.

The competing interests of the Colorado River between areas and fields have been controversial problems since the last century, especially during continuous drought conditions. This study presents a novel solution balancing general usage with electricity generation, and efficiency with equity. We first model the reservoirs in a widely used method in geology to establish the relationship between water level and water volume, then establish a multi-objective model with a criterion in the form of objective functions. We finally use the Genetic Algorithm (GA) to evaluate the optimized plan, which turns out to be consistent with intuitive cognition, showing that the proposed model should be effective to be used in various regions with different water circumstances. The code for the model can be found in this Github repository: https://github.com/Violet24K/Water-Allocation-Model.git

For scenes with high complexity and deep control depth, the traditional 3D digital twin model can no longer play a guiding role. This paper adopts the embedded Cyber-Physical Fusion System (CPS) for seamless integration and synchronization, and uses the twin support vector machine algorithm to design a multi-mode intelligent storage and retrieval system in automated three-dimensional warehouses. The experimental research proves that the paper proposes an intelligent storage and retrieval system for logistics automatic warehousing, and combines the experiments to prove the feasibility of the system.

The development of the Industrial Internet has promoted the progress of social productivity, but it also faces attacks from abnormal network traffic. Network intrusion detection systems (NIDSs) ensure the safe and reliable operation of networks by monitoring the network traffic status and detecting abnormal traffic and attacks in a timely manner. To detect network intrusions in real time and efficiently, we propose a hierarchical intrusion detection model CNNTransformer NIDS with traffic spatio-temporal feature fusion, combined with soft feature selection based on attention mechanism. The model is used for multi-attack detection on the UNSW-NB15 dataset. The comparative experimental results show that: i) spatial features can effectively describe the normal and abnormal states of traffic; ii) temporal features can help the model to better distinguish different types of attacks; iii) the fusion of the spatio-temporal features can comprehensively improve the detection performance of the model. The results of the ablation experiments verify that the attention-based soft feature selection enables the model to effectively focus on the differences between normal and abnormal traffic and between different kinds of attacks, resulting in a 0.32% reduction in the missed detection rate, a 1.36% reduction in the false detection rate, and a 1.68% improvement in the detection rate of NIDS.