Table of Content

15 June 2023, Volume 8 Issue 6

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Independent Number and Independent Polynomial of Complete Product of Graph

Yang Limin

2023, 8(6):  1-8. 

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In graph theory， independent number and independent polynomial are NP-hard problems. They are very difficult problems， however， by transforming the problem， an effective method to solve independent number and independent polynomial can be found. By transforming the stable set problem of radix k into a k-order complete subgraph problem， the calculation method of independent polynomial is obtained. Anology， by transforming the size of the maximum stable set into the size of the maximum complete graph， the calculation method of the independent number is obtained. Using combinatorial calculations， explicit formulas for the independent number and independent polynomial of many graph's complete product are given. Furthermore， using the generating function， the Merrifield-Simmons index of the graph is derived. It is proved that some coefficient sequences of independent polynomials are unimodal and some are not， and the conjecture that the coefficient sequences of the independent polynomial of trees are unimodal is denied， which is of great value and significance to combinatorial mathematics and graph theory.

Studying the 3X+1 Conjecture by Quaternary Numeral System

Wu Wenliang, Jiang Na, He Jiaying, Zhou Yangchuan

2023, 8(6):  9-13. 

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In this paper， we explore the 3X+1 conjecture by using quaternary numeral system and obtain some interesting results. The quaternary representation of an odd number that can be compressed and iterated into 1 through a finite number of 3X+1 conjectures， consisting of a root， prefix， and suffix. The quaternary representation of lower iteration numbers determines the root， prefix， and suffix of higher iteration numbers.

Research on the Solution of Pure Integer Programming Problem Based on Number Theory

Zhou Bin

2023, 8(6):  14-19. 

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In order to avoid the need to consider the relaxation linear programming problem in solving pure integer programming problem， an efficient new solution method for pure integer programming problem is proposed by using the indefinite equation theory in number theory and the estimation method for solving inequality equations. Through the derivation of two theorems， it is proved that the new solution method is feasible to solve pure integer programming problems. Taking the pure integer programming problem as an example， the cutting-plane method， the branch-and-bound method and the new solution method proposed are used to solve it respectively. The results show that compared with the cutting-plane method and branch-and-bound method， the new method is simpler for solving simple pure integer programming problems.

The High-Precision Runge-Kutta Method for Solving Two-Dimensional Acoustic Wave Equation

Chen Li, Zhu Xingwen, Zhang Chaoyuan

2023, 8(6):  20-23. 

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Based on the two-dimensional acoustic wave equation， the eighth-order NAD-RK algorithm is developed by combining the higher order partial derivative of the discrete space of the eighth-order NAD operator and the discrete time derivative of the third-order Runge-Kutta method. The theoretical and numerical errors of the eighth-order NAD-RK algorithm are analyzed， and its stability conditions are derived in detail. The results show that compared with the eighth-order Lax-Wendroff scheme and the eighth-order staggered grid scheme， the eighth-order NAD-RK algorithm has the smallest numerical error.

MV-Raft： A New Consensus Algorithm forAllianceChain Based on Multidimensional Vectors

Wu Guifeng, Hu Fa, Zeng Xin, Yang Dengqi, Li Xiaowei

2023, 8(6):  24-32. 

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The default algorithm of Raft for existing alliance chains uses a random mechanism for node crashes， without considering that different node weights may result in longer consensus times and greater log synchronization pressures on leader nodes. To address this issue， a Raft algorithm based on multidimensional vectors is proposed， called MV-Raft. The algorithm first constructs an eigenvalue vector according to factors that affect the efficiency of reaching a consensus， and then broadcasts the above eigenvalue vector to the whole network when the distributed system is started or a single node is newly added to the system. The similarity between nodes is calculated based on the eigenvalue vector， and the n nodes with the highest similarity are cached within each node for prioritized operation during the election and synchronization process. The simulation results show that MV-Raft algorithm can reduce the time consumption of the whole process by 16%， and reduce the pressure of a single leader node by 73% at most.

Backtracking Algorithms for Solving Set Subsets Based on Binary Tree and Variable Length Sub-Ｔree

Zhao Qinyi, Zhao Yuqin

2023, 8(6):  33-37. 

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The backtracking algorithm adopts the depth-first search strategy， and prunes when constraint condition dissatisfied， which is suitable for solving problems with large combinations. Two backtracking algorithms based on binary tree and variable length sub-tree are proposed to solve the set subsets， and the design of two algorithms uses compatibility technology， and pruning is not required in the search process. All set subsets can be solved. The time complexity of the two algorithms is ideal， and the operation efficiency of the algorithms is high. The complexity of the backtracking algorithm for solving set subsets based on variable length sub-tree is O （2n） ，and the algorithm efficiency is higher when the scale of problem solving increases.

Numerical Simulation of Two Wooden Frame Structures of the Bai Dwellings in Dali

Zhao Jing, Li Yan

2023, 8(6):  38-43. 

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This study focuses on the overall performance of traditional wooden dwellings in Dali Bai area. Two commonly used wooden frame structures in Dali Bai dwellings were selected as research objects， and the ANSYS finite element numerical simulation method was used to establish a structural overall model. The deformation and stress characteristics of two wooden frame structures under static load were analyzed， and the displacement and acceleration responses of the two wooden frame structures under earthquake loads were obtained through time history analysis. The results showed that under load， the peak deformation of the two wooden frames was within the allowable range，and the compressive， bending and shear bearing capacities of the components all met the requirements. According to the modal analysis， the longitudinal stiffness of the wooden frame was weak， and the transverse stiffness was slightly greater than the longitudinal stiffness， which conformed to the general vibration sequence of the structure. On the basis of modal analysis， the dynamic response analysis of wooden frame was carried out， obtained a comparison between two types of wooden frames， the dynamic amplification factors of each node of the two wooden frames did not show significant differences. The peak displacement and acceleration response did not appear at the same time， and there was a certain phase difference. In conclusion， the two types of Dali Bai traditional wooden frame structures are basically intact and currently in a safe state.

Dali Climate Prediction Based on Long Short-Term Memory Network Model

Yuan Jincheng, Li Zhongmu

2023, 8(6):  44-51. 

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Based on the Keras framework， a long short-term memory network （LSTM） model is constructed for climate prediction in Dali. The experimental results showed that the model could accurately predict the temperature， precipitation， humidity， and sunshine hours from June 2016 to May 2021， with root mean square error（RMSE） of 1.544 ℃， 2.720 mm， 6.521% rh， and 1.990 h， and mean absolute percentage error（MAPE） of0.087 ℃， 4.025 mm， 0.085% rh， and 0.462 h. The model performs well in predicting temperature and humidity， but the prediction error is relatively large for precipitation and sunshine hours due to their large fluctuations and extreme values. The RMSE and MAPE obtained by the experiment are lower than those obtained by traditional models such as recurrent neural network  （RNN）， support vector machine （SVM）， and K-nearest neighbor （KNN）. Therefore， the LSTM model can produce higher prediction accuracy for climate prediction in Dali.

Analysis of Spatiotemporal Variation Characteristics of Extreme Climate Index in Yunnan Province from 1959 to 2015

Zhu Zhanpeng, Li Zhongmu

2023, 8(6):  52-60. 

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With the increase in greenhouse gas concentrations， extreme climate events have become increasingly prominent. Plateau and mountainous areas are sensitive and fragile regions affected by climate change. Based on the daily temperature and precipitation data of 116 meteorological stations in Yunnan Province， the Mann-Kendall test and Sen slope estimation were used to analyze the spatiotemporal variation characteristics of extreme climate indexes in Yunnan Province from 1959 to 2015. The results showed that all nine extreme temperature indexes had significantly changed， with extreme warm indexes showing a significant increase and extreme cold indexes showing a significant decrease. The decline rate of frost days （FD） in northwest and central Yunnan was significantly higher than other areas， and multiple extreme temperature indexes in the central part of Honghe Prefecture and the western part of Pu'er City showed a higher rate of change than other areas. Only the consecutive wet days （CWD） index among the eight extreme precipitation indexes passed the significance test at the level of 0.05， and the changes in the other indexes were not significant. The total annual precipitation decreased， while the amount of intense precipitation （R95pTOT） and extremely intense precipitation （R99pTOT） increased， indicating a trend towards more concentrated and intense precipitation. There was low consistency in spatial variation， and most stations did not show significant trends. Multiple extreme precipitation indexes in the central part of Honghe Prefecture， the western part of Pu'er City， and the southwestern part of Dehong Prefecture showed significant decrease， indicating a trend toward drought in these regions.

Diversity and Faunal Characteristics of Amphibians and Reptiles in Lanping Yunling Provincial Nature Reserve

Cui Maohuan, Rao Dingqi

2023, 8(6):  61-68. 

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The amphibians and reptiles in Lanping Yunling Provincial Nature Reserve were investigated by field investigation and visiting investigation. The results showed that 49 species of amphibians and reptiles were recorded in Lanping Yunling Provincial Nature Reserve， belonging to 3 orders and 13 families. Of these， there were 22 species from 18 genera and 8 families of amphibians and 27 species from 17 genera and 5 families of reptiles. All 49 species belonged to the Oriental region，with 41 species（83.7%） found in the Southwest area and 8 species（16.3%） found distributed over a wider area. The amphibians were mainly terrestrial and adapted to higher elevations and drought， while the reptiles were characterized by high activity and strong adaptability. Some species were distributed on the periphery. One species was listed as a national second-class protected animal， one as a Yunnan provincial protected animal， ten as threatened species in the China Vertebrate Red List， one as an Appendix Ⅱ of the Convention on International Trade in Endangered Species of Wild Fauna and Flora， and 41 as"Terrestrial wildlife species that are beneficial or of significant economic or scientific research value and are under national protection". Based on the characteristics of amphibian and reptile diversity and threats in the reserve， suggestions for protection and management were proposed.

A Dynamic Study on Students' Physical Fitness inDaliUniversity

Li Jia, Yang Yingfei

2023, 8(6):  69-74. 

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In order to understand the development trend of the physical fitness of students in Dali University， the data of the physical fitness survey of students in Dali University in 2015 and 2021 were compared. The results showed that compared with 2015， the height， body weight， and body mass index （BMI） of Dali University students in 2021 showed an increasing trend in body shape. In terms of physical function， the vital capacity and weight index of male and female students showed a overall decreasing trend in2021. Interms of physical quality， the speed， flexibility and endurance of male students showed an increasing trend， while the upper limb strength and lower limb explosive power showed a decreasing trend. The flexibility， endurance and waist and abdominal strength of female students showed an increasing trend， while the lower limb explosive power showed a decreasing trend and the speed quality remained stable. The study results suggested that the physical fitness of Dali University students was mixed， with an increasing trend observed in body shape， a decreasing trend in physical function， and an unbalanced development in physical quality. Therefore， scientific and effective intervention measures should be taken to address the problems existing in the development of students' physical fitness to improve their physical health level.

Observation and Evaluation of the Effect of Exercise Prescription Intervention on College Students' Neck-Shoulder Syndrome under the Integration of Sports and Medicine

Zou Weimin, Qi Daoyu, Xue Wenbiao, Li Hua

2023, 8(6):  75-78. 

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In order to explore the effect of exercise prescription intervention on college students' neck-shoulder syndrome under the integration of sports and medicine， 120 college students suffering from neck-shoulder syndrome from September 2021 to June 2022 were selected and divided into observation group and control group according to random number table method， with 60 students in each group. The control group received non-regular exercise intervention only， while the observation group received exercise prescription intervention （badminton exercise， resistance exercise）， and the improvement of neck-shoulder syndrome in both groups was observed. The results showed that after the intervention， the ranges of motion on the left lateral flexion， right lateral flexion， forward bend， backward stretch， left rotation， and right rotation of the observation group were significantly higher than those of the control group， and the differences between the groups were statistically significant（P<0.05）. The physiological curvature of the cervical spine of the observation group was lower than that of the control group， and the VAS score and cervical spine dysfunction index were lower than those of the control group. The differences were statistically significant（P<0.05）. It is suggested that under the background of integration of sports and medicine， exercise prescription can effectively relieve the clinical symptoms of neck-shoulder syndrome in college students， improve their cervical spine function， and have good application effect， which is worthy of application and promotion.

Executive Political Connections， Changes in Environmental Regulatory Modes， and Corporate

Environmental Investment

Tang Liang, Lu Jingnan, Jiang Haifeng, Xue Jiuyang

2023, 8(6):  79-87. 

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aking the heavily polluting companies listed in China's A-share market from 2008 to 2020 as the research sample， this study empirically tests the specific effect of executive political connections on corporate environmental investment， and discusses the moderating role of changes in environmental regulatory modes on executive political connections and corporate environmental investment. The results show that there is a positive correlation between executive political connections and corporate environmental investment， while changes in environmental regulatory modes are positively related to corporate environmental investments. Furthermore， changes in environmental regulatory modes can inhibit the positive correlation between executive political connections and corporate environmental investments. These findings further confirm the promoting effect of executive political connections on corporate environmental investments and enrich the research on factors influencing such investments.

Analysis of Yield and Agronomic Traits of Maize Hybrids Bred from Inbred Line 2408

Ma Chenyu, Liu Chaorui, Lü Jianguo, Zhou Dongyan, Ye Zhilan

2023, 8(6):  88-94. 

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Superior maize in bred lines are the basis of selecting superior hybrids， analysis of yield and related agronomic traits of hybrid maize is beneficial to accelerate the process of breeding. In this study， maize inbred line 2408 and other 106 inbred lines were used as materials， then 2408 was tested and matched with 106 inbred lines， respectively， then their agronomic traits of the yield and yield components of the test combination were analyzed. The results showed that the yields of crosses 2635， 2709 and 2674 were relatively high. The correlation degrees between the yield of cross combinations and related agronomic traits were shown as follows： plant height > ear diameter > kernel percentage > water content >rows per ear > kernels per rows > ear length> ear height> 5 ears dry weight > 5 ears grain weight > hundred-grain weight > tassel branch number > length of bare tip. The correlative degree between 5 ears grain weight and 5 ears dry weight was the highest， the relationship among plant height， ear diameter， kernel percentage， water content and rows per ear was relatively close， and the contribution of bare tip length to each character was the least. Therefore， in the subsequent breeding work， the three traits of plant height， ear diameter and kernel percentage can be used to select new hybrid maize varieties with high yield and good quality and corresponding excellent inbred lines， so as to further lay the foundation for the breeding and promotion of plateau maize varieties in Yunnan Province.

Analysis and Research on the Mathematics Test Papers of Yunnan Province Academic Test for the Junior High School Students in Recent Years

Shen Fanqi, Liang Xiyao, Qian Yuchen, He Ke, Zhang Chaoyuan

2023, 8(6):  95-100. 

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In 2022， Yunnan Province implemented the new reform of the academic test for the junior high school students （referred to as the "middle school entrance examination"）. Compared with previous years， the number of questions， the proportion of score and the structure of the examination paper have changed greatly. This research compares the mathematics test papers of the middle school entrance examination in Yunnan Province from 2015 to 2022， and makes a comparative analysis of the difficulty level， the amount of questions， and the penetration of core competencies， so as to provide a reference for junior high school mathematics teachers' teaching and candidates' review.