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15 February 2021, Volume 42 Issue 2 Previous Issue    Next Issue
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Information & Control
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Information & Control

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Abnormal Condition Recognition Based on Improved Subjective Bayesian Method for Fused Magnesium Furnace YUAN Jie， WANG Shu， WANG Fu-li， SUN Xiao-hui 2021, 42 (2):  153-159.  DOI: 10.12068/j.issn.1005-3026.2021.02.001 Abstract ( 528 )   HTML ( 22)   PDF (776KB) ( 209 )   It is difficult for big data analysis to be applied to the smelting process of fused magnesium furnace because of a lot of uncertain information of the process. In order to identify abnormal conditions accurately， an online rule reasoning method based on improved subjective Bayesian is proposed. In view of the problem that the parameter value range of the traditional subjective Bayesian method is too wide， the mapping function is used to limit the value range to a finite interval， which improves the practicability of the method. In order to improve the robustness and accuracy of condition recognition， the fuzzy membership function is utilized to match the observation and evidence in the reasoning. Simulation results show that the method can effectively describe the uncertain information in the rules and accurately identify the abnormal conditions in the smelting process of fused magnesium furnace. References | Related Articles | Metrics

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H∞-Adaptive Variable Structure Control Based on Markov Jump Systems YANG Dong-mei， LU Di 2021, 42 (2):  160-165.  DOI: 10.12068/j.issn.1005-3026.2021.02.002 Abstract ( 752 )   HTML ( 12)   PDF (525KB) ( 261 )   The control problem for a class of nonlinear generalized delay Markov jump systems with generally uncertain transition rate is studied. First， a hybrid controller composed of a linear controller and an adaptive controller is designed for the unknown nonlinear parameters in the system， and a Lyapunov functional is constructed to make the trajectory of the system approach to the state space surface and the closed-loop system is admissible， satisfying H∞criteria γ. Furthermore， considering the characteristics of the generally uncertain transition rates matrices， a strict linear matrix inequality is constructed to make the conclusion more general. Finally， the effectiveness and feasibility of this control method are verified by numerical examples and image simulation. References | Related Articles | Metrics

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Capitalization and Trading System Design of Power Data Based on Blockchain WANG Ke-yuan， YU Lei， YAN Yong， SUN Yi 2021, 42 (2):  166-173.  DOI: 10.12068/j.issn.1005-3026.2021.02.003 Abstract ( 713 )   HTML ( 18)   PDF (902KB) ( 458 )   In the traditional centralized data trading system， sensitive data such as electric power data are easily abused due to duplicability. To address this， the blockchain-based power datas capitalization and trading system was proposed. Considering the trust in blockchain technology， a multi-party trusty network can be established between multiple parties in distributed ledger with cryptographic algorithms， multi-centralized architecture and distributed multi-party consensus protocol. The system was developed with Hyperledgers consortium blockchain framework Fabric， which made power data trading safe， transparent， traceable and immutable by means of the technical characteristics of the blockchain. In addition， a supervision mechanism was introduced. The system also provided Web service as application layer for ease of use. Finally， the system was tested by simulating multi-node deployment on a single device. And the results show that the system runs well in integrated test， meets the design requirements， and has low maintenance costs and enhances security. Compared with the traditional data trading system， the blockchain-based power datas capitalization and trading system demonstrates comprehensive functionality and security advantages. References | Related Articles | Metrics

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PV Power Forecasting with Univariate Input Based on mRMR-ESN HAN Peng， GUO Tian， WANG Jin-kuan， SHI Ze-wei 2021, 42 (2):  174-179.  DOI: 10.12068/j.issn.1005-3026.2021.02.004 Abstract ( 542 )   HTML ( 8)   PDF (1275KB) ( 250 )   Two kinds of prediction model are designed， ie， the traditional multivariable forecasting model using weather variables as input and the new univariate forecasting model using historical power data as input. The mRMR(minimum-redundancy and maximum-relevance)method is used to extract the features of the two models respectively， and ESN(echo state network)， which has advantages in time series prediction， is used to simulate and predict the photovoltaic (PV) power in the next 5minutes.The simulation results show that the mRMR method is used to extract the features of the historical PV power data， then， the feature subset that can make the prediction model reach the optimal effect is determined. The feature subset is used as the input of the univariate prediction model to obtain more accurate prediction effect. The new univariate prediction model can provide a new PV prediction idea for PV power station. References | Related Articles | Metrics

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Single Image Dehazing Based on Middle Channel Compensation YANG Ai-ping， XING Jin-na， LIU Jin， LI Xiao-xiao 2021, 42 (2):  180-188.  DOI: 10.12068/j.issn.1005-3026.2021.02.005 Abstract ( 501 )   HTML ( 10)   PDF (4186KB) ( 233 )   Focusing on foggy images with low contrast and blurry detail， this paper decomposes the images into texture layer and structural layer firstly. Then the structural layer containing most of the fog is dehazed， and the texture layer is enhanced. To avoid the effect of white objects in the scene on atmospheric light estimation， this paper proposes a kind of stereo decision map in RGB space， and designs an atmospheric light estimation method which can adaptively distinguish between sky and non-sky area based on a threshold constraining scheme. Due to the inefficiency of dark channel prior when dealing with large areas of sky and dense fog， a transmission estimation approach based on middle channel compensation is put forward， which can avoid color distortion of dehazed images. Furthermore， the transmission is refined by the guided filtering with side window， which can preserve image details. Extensive experimental results show that the proposed approach can realize haze removal thoroughly， and the dehazed image has natural colors and vivid details. References | Related Articles | Metrics

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Weak-Selection Backtracking Matching Pursuit Algorithm Based on Dice Coefficient JI Ce， WANG Jin-zhi， GENG Rong 2021, 42 (2):  189-195.  DOI: 10.12068/j.issn.1005-3026.2021.02.006 Abstract ( 577 )   HTML ( 15)   PDF (584KB) ( 224 )   In order to further improve the success rate and accuracy of reconstruction of the compressed sensing reconstruction algorithm， a weak-selection backtracking matching pursuit based on Dice coefficient(DWBMP) algorithm is proposed from the perspective of atomic matching criteria and pre-selection stage’s atom selection methods. First， the Dice coefficient matching criterion is used to measure the similarity between two vectors， and the best matching atom is selected to optimize the support set. Then， the backtracking idea is combined with weak-selection idea to eliminate the atoms with small similarity， thus completing the secondary selection of the atoms in the pre-selection stage. The MATLAB simulation results show that under the same conditions， the DWBMP algorithm has better success rate and accuracy of reconstruction than the classic compressed sensing reconstruction algorithm. References | Related Articles | Metrics

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Non-binary RC-LDPC Information Security Transmission Algorithm Based on Satellite Communication System LIU Jun ， ZHANG Li-li， JIANG Xiang-hong， ZHANG Yong-fang 2021, 42 (2):  196-200.  DOI: 10.12068/j.issn.1005-3026.2021.02.007 Abstract ( 536 )   HTML ( 9)   PDF (558KB) ( 173 )   It is easy for signal transmission based on satellite communication to be received illegally through wireless channels， leading to information leakage. Therefore， we propose a non-binary RC-LDPC(rate compatible low density parity check) encoding method for satellite channel based on the existing physical layer security research， and apply the method to the AMC system.The algorithm uses channel state information to secrete the private information in the deleted position. By narrowing the gap of safety， the proposed method elevates the drop rate of error curve of the legal receiver to ensure information security. The algorithm was simulated and analyzed based on NI USRP and LabVIEW. The simulation results show that the proposed algorithm can guarantee the receiver to receive correctly and the bit error rate of eavesdropper up to about 0.5， ensuring the safe transmission of information. References | Related Articles | Metrics

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Relationship Between the Number of Linear Regions and Expressive Power of Piecewise Linear Neural Networks MA Hai-tao， LU Jia-rui， YU Wen-xin， YU Chang-yong 2021, 42 (2):  201-207.  DOI: 10.12068/j.issn.1005-3026.2021.02.008 Abstract ( 664 )   HTML ( 6)   PDF (1249KB) ( 318 )   The neural network with piecewise linear activation function(PLNN) is extensively applied in machine learning. This paper gives a measure of the expressive power of PLNN model， i.e.， the number of linear regions， with the mathematical representation of linear regions presented. The relationship between linear regions is analyzed and the number of combined linear regions is calculated. A method for calculating the number of linear regions based on Z curve is developed. A case is given to calculate the number of linear regions of different network structures and the number of linear regions after merging， and the correlation between the number of linear regions and the accuracy of different network structures is analyzed. The results show that the number of linear regions can reflect the expressive power of PLNN model， which has great research significance for selecting network hyperparameters and explaining model boundaries. References | Related Articles | Metrics

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Coding Incentive Algorithm Based on PDChirp-Golay Signal BAO Xi-rong， GAO Hao-sen， LI Zheng-shuang， ZHANG Shi 2021, 42 (2):  208-212.  DOI: 10.12068/j.issn.1005-3026.2021.02.009 Abstract ( 584 )   HTML ( 6)   PDF (874KB) ( 214 )   To solve the problem of high sidelobe in ultrasonic imaging algorithms induced by LFM signal coding， a new method of PDChirp-Golay coding based on amplitude weighting is proposed. This method predistorts linear frequency modulation(LFM) signals， thus compensating the influence of ultrasonic probe on the emission signal， which makes the bandwidth of the echo signal increase， improves the axial resolution， and eliminates the Fresnel corrugation of the emission signal amplitude frequency characteristics at the same time， realizing sidelobe suppression. Then， the predistorted LFM signal is used to modulate Golay code. The range sidelobe level of Golay code is zero in theory， which makes the sidelobe further suppressed. The simulation results show that， compared with the single predistorted LFM signal and Golay code， Golay code modulated by the predistorted Chirp signal improves the axial resolution and contrast， and has a good anti-noise performance， which provides a theoretical basis for the realization of high-quality ultrasonic imaging system. References | Related Articles | Metrics

Resources & Civil Engineering

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Development and Application of a New Pre-stressed Expandable Pillar in Hard Rock Stope LI Kun-meng， LI Yuan-hui， WANG Zhe-chao， XIONG Zhi-peng 2021, 42 (2):  213-219.  DOI: 10.12068/j.issn.1005-3026.2021.02.010 Abstract ( 641 )   HTML ( 12)   PDF (1252KB) ( 227 )   In order to solve the problems of high loss rate of natural pillars and the inability of traditional artificial pillars to effectively contact roof in hard rock stope， a new pre-stressed expandable pillar was developed by using the volume increase characteristic of the self-developed expandable material after hydration reaction. Based on the laboratory and field industrial tests， the mechanical properties and load bearing mechanism were determined. The test results showed that with the increase of the amount of expandable material in the barrel-type expandable device under constrained conditions， its active support stress increased with a gradually increased increment， and it could reach 500kN under the conditions of full constraint and fully filled with expandable material. The pre-stressed expandable pillar had the advantages of short construction period(about 4h) and large active support stress(about 600kN). When recovering residual pillars in the room-and-pillar mining， the pre-stressed expandable pillars showed strain-hardening bearing characteristics， and the load on natural pillars was successfully transferred to the artificial expandable pillars. Under the conditions of ensuring the stope safety， economic benefit of the test stope increased by 1，700，000 CNY. References | Related Articles | Metrics

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Influence of Unidirectional Compressive Stress on the Crater Blasting of Sandstone ZHANG Feng-peng， YAN Guang-liang， HAO Qi-qi， GAO Ji-kai 2021, 42 (2):  220-225.  DOI: 10.12068/j.issn.1005-3026.2021.02.011 Abstract ( 498 )   HTML ( 6)   PDF (5031KB) ( 208 )   Considering the problems related to rock blasting under deep high in-situ stress， we conducted crater blasting tests on sandstone specimens under different unidirectional compressive stresses. The influence of static stress on the formation and propagation of crack network in the process of crater blasting was analyzed. The concept of failure zones formed in blasting crater， namely， block failure zone， transition zone and flaky spalling zone was put forward. The influence of static stress on the three failure zones in blasting crater and the characteristics of rock blasting failure under different static stress conditions were elucidated.The results show that static stress promotes the formation of cracks parallel to its own direction and inhibits the formation of cracks perpendicular to its own direction， thus changing the shape of the crack network. The static stress promotes the formation of blasting crater failure zone parallel to its own direction， and has the greatest influence on flaky spalling zone， followed by block failure zone and transition zone， and has little effect on the failure zone perpendicular to its own direction.When stress-strength ratio reaches 0.15， the influence of static stress on blasting effect needs to be considered. References | Related Articles | Metrics

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Effect of TX-100 on Flotation of Magnesite and Dolomite Using NaOL as Collector SUN Wen-han， LIU Wen-gang， YANG Ting， DAI Shu-juan 2021, 42 (2):  226-231.  DOI: 10.12068/j.issn.1005-3026.2021.02.012 Abstract ( 550 )   HTML ( 12)   PDF (1508KB) ( 132 )   Magnesite and dolomite are difficult to be separated by flotation because of their similar crystal structure， chemical composition， and dissolution characteristics. The effects of triton X-100(TX-100) on the flotation of magnesite and dolomite under sodium oleate system were studied by flotation tests， surface tension tests， FTIR tests and XPS tests. The results show that TX-100 can enhance the effect on the flotation separation of magnesite and dolomite by using NaOL. NaOL is chemically adsorbed on the surface of magnesite and dolomite， and may have competitive adsorption with TX-100 on the surface of dolomite. TX-100 reduces the surface tension of NaOL and promotes the dissolution and dispersion of NaOL. The concentration of Ca2+ needed to produce calcium oleate precipitation is increased by solubilization， which weakens the adsorption of sodium oleate on dolomite surface， thus selectively inhibiting the dolomite. References | Related Articles | Metrics

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Influencing Factors on Backfill Strength and a Combined Strength Prediction Model ZHANG Peng， GAO Qian， WEN Zhen-jiang， ZHANG Tao 2021, 42 (2):  232-241.  DOI: 10.12068/j.issn.1005-3026.2021.02.013 Abstract ( 619 )   HTML ( 8)   PDF (1102KB) ( 394 )   The water-cement ratio， packing density and specific surface area are important factors that influence backfill strength. However， few studies have investigated the significance of these influencing factors. Hence， uniaxial compressive strength tests were carried out on test blocks aged 3d， 7d and 28d using a 3-factor 5-level orthogonal design. A variance analysis was performed on the experimental results. The results from this statistical analysis indicated the following F-value ratios for the three factors(water-cement ratio∶packing density∶specific surface area) at different ages: 3d(698.404∶26.148∶0.910)， 7d(862.626∶35.465∶1.286) and 28d(1585.404∶31.695∶1.338). According to the analysis results， the influencing factors had the following order of significance: water-cement ratio > specific surface area > packing density. Due to the small F-values of the specific surface area and packing density， these variables were not considered as factors affecting strength when establishing a strength prediction model. To obtain a backfill with the maximum strength， the optimal mixture had a 1.2 water-cement ratio， a specific surface area of 410m2/kg， and a packing density of 0.6%. To study the relationship between the water-cement ratio and strength， the water-cement ratio in the optimal mixture was varied， and 30 groups of strength tests were performed with samples containing different water-cement ratios after ageing for 3d， 7d and 28d. Based on the experimental results， a combined model was established for predicting strength at 3d， 7d and 28d with a combination of grey theory， fuzzy set theory and Markov theory. The measured values were plotted on the same scatter diagram as the values predicted with the GM(1，2) model， the regression analysis model and the combined model. A subsequent analysis verified that the combined model had higher accuracy and robustness than other models. References | Related Articles | Metrics

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Water Control Optimization Method of Foundation Pit with Suspended Waterproof Curtain ZHANG Zhi-hong， QIN Wen-long， ZHANG Qin-xi， GUO Yan-chen 2021, 42 (2):  242-251.  DOI: 10.12068/j.issn.1005-3026.2021.02.014 Abstract ( 774 )   HTML ( 11)   PDF (2314KB) ( 407 )   The calculation formulas for water inflow of a circular foundation pit with different insertion depths of waterproof curtain are proposed based on the principle of seepage continuity of groundwater and Darcy’s law. The analytical solution of ground subsidence outside the foundation pit with different insertion depths of waterproof curtain is proposed according to the method of resistance coefficient widely used in ship engineering in China. Finally， an applicable procedure of dewatering of foundation pit with waterproof curtain partially penetrating aquifers was developed， in which water control cost is set as the target， and ground subsidence and groundwater inflow are set as the constraints conditions considering both safety and economy of foundation pit design. The proposed optimization method for water control was applied in a project site in Tongzhou district， Beijing. References | Related Articles | Metrics

Materials & Metallurgy

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Occurrence State and Distribution Regularity of Niobium in a Beneficiation Product of Bayan Obo SUN Lin-quan， YU Hong-dong， WANG Li-na， QI Tao 2021, 42 (2):  252-259.  DOI: 10.12068/j.issn.1005-3026.2021.02.015 Abstract ( 712 )   HTML ( 8)   PDF (1623KB) ( 286 )   The chemical composition， mineral composition， occurrence state of niobium and niobium minerals’ dissemination characteristics of Nb-bearing mineral raw materials of Bayan Obo were investigated by means of mineral liberation analyzer(MLA)， X-ray diffraction， scanning electron microscope， energy disperse spectroscopy and chemical analysis. The research results show that the chemical and mineral composition of the raw materials are complex， of which the grade of niobium and the total mass fraction of rare earth oxide are 1.10% and 1.37%， respectively. The main niobium minerals are nioboaeschynite， ilmenorutile， pyrochlore， dingdaohengite， mangancolumbite， niobite， baotite， and fergusonite， in which the highest mass fraction of nioboaeschynite， the highest mass fraction of niobium in mangancolumbite， and the highest metal distribution rate of niobium in nioboaeschynite are 1.84%， 54.34%， and 44.85%， respectively. The particle size of niobium minerals is relatively fine. Except nioboaeschynite， the liberation degrees of the rest niobium minerals are relatively low， which are mainly attached with riebeckite and iron oxide. From the perspective of process mineralogy， only by solving the problems of efficient enrichment of micro fine-grained niobium minerals and separation of Nb/Ti in raw niobium-bearing mineral materials could the goal of efficient and comprehensive utilization of Bayan Obo niobium mineral resources be achieved. References | Related Articles | Metrics

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Effects of Hydrogen-Based Gas Injection on the Release of Typical Pollutants in the Sintering Process ZHOU Hao-yu， FAN Xiao-hui， LI Qian， GAN Min 2021, 42 (2):  260-267.  DOI: 10.12068/j.issn.1005-3026.2021.02.016 Abstract ( 555 )   HTML ( 8)   PDF (1226KB) ( 212 )   Coke oven gas and steam were used as the hydrogen-based injection media to analyze the effects of injection media， injection mode and the amount of gas injection on the release of typical pollutants in the sintering process. The results show that the temperature distribution of the sintering layer has obviously improved， with the high temperature range of 1200-1300℃ widened evidently， after the hydrogen-containing gas is injected. After the coke oven gas(0.6%Vol.) was injected on the sintering material surface， the peak concentration of NO○x in flue gas is reduced by about 100mg/m3， and the average concentration is reduced by 21.1%. This is mainly because the gas injection broadens the high temperature range of the material layer and the injection of steam on the sintering material surface has a significant effect on the reduction of CO emissions. After the steam is sprayed， the CO in the sintering flue gas is reduced from 11690mg/m3 to 9918mg/m3， a decrease of 29.4%. This is mainly because water vapor reacts with the carbon in the sintering raw material to produce water gas. The simultaneous injection of coke oven gas and water vapor on the sintering material surface can achieve a comprehensive reduction of NO○x and CO emissions. References | Related Articles | Metrics

Mechanical Engineering

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Design Method of Excavator Operation Interface Based on Task-Structure-Iteration Fusion REN Jia-jun， WANG Ya-kun， LI Juan-li， LI Ai-feng 2021, 42 (2):  267-275.  DOI: 10.12068/j.issn.1005-3026.2021.02.017 Abstract ( 434 )   HTML ( 5)   PDF (2010KB) ( 158 )   A task-structure-iteration fusion design method is proposed to improve the experience of operator manipulating mining excavator and the operation interface design. Questionnaire， field investigation and literature analysis are carried out to investigate the operator perceptive status to environment and information in the task and to find out the shortcomings of the existing operation interface， and the design points aiming at the defects are obtained. The mapping between modules and the design points is established by dividing the layout of operation interface into several modules with a structure split method. The arrangement methods of the console， control panel and control components are developed， with shading and anti-misoperation considered. The engineering software Jack is used to iteratively evaluate the visibility， accessibility and comfortability of mining excavator operation interface. The results show that the rationality of the operation interface is improved by the task-structure-iteration fusion method. References | Related Articles | Metrics

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Rapid Detection of Cold Heavy Rail Surface Defects of Production Line Based on One-Dimensional Convolution Network ZHANG De-fu， SONG Ke-chen， NIU Meng-hui， YAN Yun-hui 2021, 42 (2):  276-281.  DOI: 10.12068/j.issn.1005-3026.2021.02.018 Abstract ( 528 )   HTML ( 7)   PDF (1491KB) ( 239 )   An intuitive and efficient method based on machine vision was applied to the automatic detection of cold heavy rail surface defects of production line. Color binocular linear scan camera gathered the depth information and RGB information. Depth information was employed for the rapid detection of defects， and for defect segmentation combined with RGB information. Then a deep learning network was proposed for the rapid detection of defects. The network mainly includes a feature extractor based on one-dimensional convolution network， a classifier composed of full connection layers and dropout layers， and a filter with size prior. Finally， a data acquisition platform was setup and the data of heavy rail samples were collected for the verification of network performance. The results show that the network proposed performs well. The defect-level detection rate is 100% and the false detection rate is 35% on the collected data， which is better than that of the compared networks. References | Related Articles | Metrics

Management Science

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Three-Tier Supply Chain Coordination Based on the Differentiated Channels Under the Risk Aversion of Retailers YU Li-ping， LI Li-jie 2021, 42 (2):  282-289.  DOI: 10.12068/j.issn.1005-3026.2021.02.019 Abstract ( 540 )   HTML ( 7)   PDF (595KB) ( 371 )   Considering the risk aversion of retailers in the face of uncertain market demands， in the three-tier supply chain of manufacturer-dominated single-channel distribution， the retailer’s optimal ordering strategy， the distributor’s pricing equilibrium and the manufacturer’s pricing strategy were studied. Further， a reseller who provides a repurchase contract was added into the supply chain， and in the three-tier supply chain of retailers’ dual procurement and manufacturers’ differentiated dual-channel distribution， the optimal ordering strategy of a risk-averse retailer and pricing strategy of two competing distributors and a manufacturer were studied. Through the comparative analysis of decisions， a coordination mechanism that benefits all members of the three-tier supply chain with differentiated dual distribution channels was established. The research results show that， compared with the single-channel supply chain， the differentiated dual-channel supply chain can achieve Pareto improvement， which increases the benefits of supply chain members， and the Pareto region will be affected by the degree of retailers’ risk aversion. References | Related Articles | Metrics

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Impact of Governance Structure of Private Multinational Enterprises on Corporate Performance:Based on the Moderating Effect of the Diversification of Enterprises’ Regional Market LIU Ye， GONG Jing-wen， YU Tao， JIN Miao 2021, 42 (2):  290-299.  DOI: 10.12068/j.issn.1005-3026.2021.02.020 Abstract ( 544 )   HTML ( 8)   PDF (455KB) ( 186 )   The proportion of overseas subsidiaries， the number of overseas subsidiaries and the number of countries of overseas subsidiaries were used to measure the degree of market diversification in operating regions， which was used as a moderating variable to study its regulating effect on corporate governance structure and the performance relationship of multinational enterprises.88 listed private companies with overseas M&A experience in the past seven years were selected as the research samples，and the conclusions were as follows: in the private multinational companies with M&A experience， the equity balance degree is significantly positively correlated with the Tobin’s Q; equity concentration， management shareholding ratio， executives’ average salary and employee education level don’t have significantly effect on Tobin’s Q; the proportion of overseas subsidiaries， the number of overseas subsidiaries and the number of countries in which there are overseas subsidiaries can significantly weaken the positive effect of equity balance on Tobin’s Q. References | Related Articles | Metrics

Mathematics

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Generalized Constant Slope Surfaces in E4 YU Yan-hua， JIA Kun 2021, 42 (2):  300-304.  DOI: 10.12068/j.issn.1005-3026.2021.02.021 Abstract ( 626 )   HTML ( 13)   PDF (537KB) ( 296 )   Generalized constant slope surfaces(GCSSs)， whose inner product of the unit position vector and the unit mean curvature vector is constant， are studied in four dimension Euclidean space.Firstly， the position vector is divided into the tangent and normal parts. Then， two special GCSSs， one is that the parallel normal vector field has the mean curvature vector characteristics and the other is that the normal parts has the mean curvature vector characteristics， are studied， respectively， with the existence and classification of the two special GCSSs obtained. The expression and performance of a GCSS of which the normal plane is parallel to the mean curvature vector are discussed， proving that the GCSS can be parameterized with the principal lines and defined as a Chen surface.Finally， some examples of these surfaces and 3-D projection of the surfaces are given by MATLAB. References | Related Articles | Metrics