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    Information & Control
    New Output Feedback Design Method for Singular Systems Based on Algebraic Criteria
    QIAO Liang, LI Lin-lin, REN Jun-chao
    2022, 43 (1):  1-7.  DOI: 10.12068/j.issn.1005-3026.2022.01.001
    Abstract ( 835 )   HTML ( 15)   PDF (480KB) ( 433 )  
    A new design method of the static output feedback control for singular systems is proposed. Firstly, by using the matrix trace inequality, the admissibility issue of singular systems is introduced and the algebraic criteria of admissibility for this kind of systems is established. Secondly, based on the admissibility analysis result, the sufficient condition for static output feedback controller design is obtained to ensure the admissibility for closed-loop systems. Meanwhile, the solving method of matrix trace inequality is given to obtain the gain matrix. Different from the design method of static output feedback controller via linear matrix inequalities, the proposed method does not need the special requirement setting of output matrix. Finally, three numerical examples illustrate the feasibility and effectiveness of the proposed theoretical method, which also applies for the output feedback controller design of normal systems.
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    Fault Analysis of Metro Power Supply Module and Prediction Method
    GONG Qi, CHEN Bing-zhi, LI Yong-hua, XIA Qing
    2022, 43 (1):  8-16.  DOI: 10.12068/j.issn.1005-3026.2022.01.002
    Abstract ( 702 )   HTML ( 2)   PDF (782KB) ( 472 )  
    In order to improve the reliability of the metro traction inverter system, the tracking research on the failure of the power supply module in the traction inverter system is carried out. First, during the initial stage of the power module application, the rectification is presented for the burning problem. Then, a new failure prediction method is proposed. Fourier series and Markov theory are used to modify the prediction residuals once and twice, respectively. The improved grey model is established. The metabolism is introduced to make the final prediction. Finally, in order to verify the effectiveness of the method, several prediction methods are compared by the power module fault data of 8.5 years. The results show that the proposed method has a higher prediction accuracy and certain engineering application value.
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    Temperature Control Algorithm of Induction Heating CFRP
    XU Jia-zhong, ZHAO Hui, FU Tian-yu, ZHANG Cheng-dong
    2022, 43 (1):  17-24.  DOI: 10.12068/j.issn.1005-3026.2022.01.003
    Abstract ( 612 )   HTML ( 4)   PDF (4093KB) ( 321 )  
    In order to solve the problem of poor molding quality of CFRP(carbon fiber reinforced polymer) caused by the system’s weak anti-interference, slow response speed during the induction heating of CFRP, a Fuzzy-PID algorithm based on improved particle swarm optimization (IPF-PID) was proposed. IPF was used to optimize and self-adjust the three parameters of PID. The algorithm combines the advantages of PSO and Fuzzy-PID algorithm, while avoiding falling into the local optimum, it ensures the control accuracy and the best optimization performance. The results show that the algorithm used to enhance the adaptive ability of the controller and reduce the adjustment time has a significant effect. Compared with the traditional PID algorithm, it has smaller overshoot and steady-state error, and it is more suitable for induction heating CFRP temperature control system.
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    Diagnosis Algorithm of Pulmonary Nodules Malignancy Based on Generative Adversarial Network
    LUO Jia-jian, FENG Bao, CHEN Xiang-meng, GU Zheng-hui
    2022, 43 (1):  24-32.  DOI: 10.12068/j.issn.1005-3026.2022.01.004
    Abstract ( 812 )   HTML ( 5)   PDF (1783KB) ( 329 )  
    To solve the problem of data scarcity and expensive costs in manual labeling of CT images of solid pulmonary nodules, a computer aided diagnosis algorithm for classification between lung tuberculosis and lung adenocarcinoma of solid pulmonary nodules by combining generative adversarial network and ensemble learning was proposed. Firstly, the original CT image dataset was augmented using Wasserstein generative adversarial network with gradient penalty(WGAN-GP), in order to relieve the problem of overfitting caused by small-scale dataset and class imbalance. Then, feature extraction was performed using convolutional neural network, followed by a dimension reduction procedure using principal component analysis(PCA). Finally, deep features concatenated with effective subjective features were classified by an ensemble learning model to give final prediction of the patient.Analysis based on multi-center clinical data indicated that the proposed algorithm has better performance compared to traditional convolutional neural network method.
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    Materials & Metallurgy
    Removal Behavior of Carbonate in Bauxite Digestion Process
    WU Shi-peng, PAN Xiao-lin, WU Hong-fei, YU Hai-yan
    2022, 43 (1):  33-39.  DOI: 10.12068/j.issn.1005-3026.2022.01.005
    Abstract ( 718 )   HTML ( 3)   PDF (966KB) ( 199 )  
    The changing rule and removal mechanism of carbonate from sodium aluminate solution with lime addition, digestion temperature, seed addition and carbonate concentration were systematically investigated by XRD, XRF, SEM-EDS and PSD methods. The results show that when the mass concentration of carbonate in sodium aluminate solution is 25g·L-1, the optimum digestion conditions of alumina and removal conditions of carbonate were lime addition of 11% and reaction temperature of 270℃, and the corresponding digestion rate of alumina and removal rate of carbonate were 72.47% and 68.95% respectively. Cancrinite (Na6(Al6Si6O24)·Na2CO3·2H2O) with panel structure is the main product in the carbonate removing process. Carbonate is easier to be removed from sodium aluminate solution when its concentration is lower than 25g·L-1.
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    Numerical Analysis of Gas-Solid Heat Transfer Characteristics in Shaft Furnace for Calcination of Sintered Magnesia
    ZHANG Xiao-hu, ZHANG Sheng, ZHAO Liang, DONG Hui
    2022, 43 (1):  40-47.  DOI: 10.12068/j.issn.1005-3026.2022.01.006
    Abstract ( 590 )   HTML ( 7)   PDF (857KB) ( 384 )  
    Based on the theory of porous media, a three-dimensional heat transfer model for steady gas-solid flow was established for a shaft furnace of sintered magnesia with annual output of 5×104t. The influences of thermal parameters of the shaft furnace on the gas-solid heat transfer process in the bed were simulated. The results show that, with increasing the cooling air flow by 10%, the outlet flue gas temperature decreases by 50℃, and the outlet pellet temperature decreases by 80℃. When the cooling section length increases by 5%, the outlet pellet temperature decreases by 25℃. Taking the flue gas temperature and pellet temperature at the shaft furnace outlet as the optimization objective functions, the optimum structure and operation parameters of shaft furnace are obtained, including the calcination air flow of 2606.67m3/h, the cooling air flow of 2203.34m3/h, the preheating calcination section of 6.64m, and the cooling section of 11.70m. Under this working condition of the shaft furnace, the outlet pellet temperature is 288.75℃, and the outlet flue gas temperature is 414.32℃.
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    Mechanical Engineering
    Gradual Reliability Sensitivity Analysis of Thermal-Mechanical Coupling of Disc Brakes
    YANG Zhou, PAK Un-song, KWON Chol-u
    2022, 43 (1):  48-56.  DOI: 10.12068/j.issn.1005-3026.2022.01.007
    Abstract ( 712 )   HTML ( 2)   PDF (1837KB) ( 303 )  
    In order to solve the problem of reliability decrease due to high friction temperatures, the thermal-mechanical coupling gradual reliability sensitivity analysis is carried out. Taking a car disc brake for example, “Coupled Field Transient” module of Workbench is used to conduct the thermal-mechanical coupling analysis, and transient temperature field distribution of the brake under emergency braking condition is obtained. The accuracy of the finite element model is confirmed by comparing with the experimental results. The adaptive Kriging surrogate model theory is used to establish the reliability performance function model, and the AK-MCS method is used to conduct the gradual reliability sensitivity analysis of thermal-mechanical coupling, and then Monte Carlo method is used to verify calculation results. The results show that the thickness of brake discs has the most obvious influence on the reliability, followed by the thermal conductivity and the specific heat of brake discs, and the thickness of heat-dissipation stiffeners, while influence of the density of brake discs on the reliability is the smallest.
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    Dynamic Simulation of Drilling String System Based on Fluid-Structure Coupling
    WANG Rong-peng, SONG Gui-qiu, ZHOU Shi-hua
    2022, 43 (1):  56-64.  DOI: 10.12068/j.issn.1005-3026.2022.01.008
    Abstract ( 699 )   HTML ( 3)   PDF (2754KB) ( 358 )  
    The nonlinear dynamics of the drilling string system is studied, and the fluid-structure coupling dynamic equation of the drilling string system is established. With the Galerkin truncation method, a set of partial differential equations are diverted into ordinary differential equations. Numerical simulation is carried out by using the Runge-Kutta integration method and the effects of parameters such as pulsating frequency, pulsation amplitude and mass ratio on the dynamic characteristics of the drilling string system are investigated. The results show that there are various dynamic behaviors for the model in different parametric excitation such as periodic motion, quasi-periodic motion, chaotic motion and jump discontinuous phenomenon. Besides, the path from chaotic motion to periodic motion is in the form of period-doubling inverse bifurcation, and the support stiffness can cause a certain change in the inherent characteristics of the system, which has a complex impact on the nonlinear dynamic behavior of the system.
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    Theoretical and Experimental Study on Tensile Properties of Fused Filament Fabrication Thin Plates
    JIANG Shi-jie, DONG Tian-kuo, DAI Wei-bing, ZHAN Ming
    2022, 43 (1):  65-70.  DOI: 10.12068/j.issn.1005-3026.2022.01.009
    Abstract ( 538 )   HTML ( 1)   PDF (791KB) ( 133 )  
    Due to the manufacturing layer-by-layer deposition process of the fused filament fabrication (FFF) technology, the tensile properties of the products have obvious limitations. In order to put forward effective improvement measures, the corresponding mechanism of FFF products should be clarified, that is, establishing theoretical constitutive model. Based on the classical elastic mechanics theory, the constitutive model of FFF thin plate samples is set up, and the theoretical analysis on the tensile properties of the samples are completed. Then, the experimental tensile properties of the samples were obtained by using the tensile testing machine.Finally, by comparing the theoretical and experimental results of stress-strain curves of the samples built in both X and Z direction, it is shown that they are in good consistence, verifying the correctness and accuracy of the theoretical model.
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    Vertical Compressive Sealing Performance of Automobile Sealing Strips
    TONG Meng-han, XIU Shi-chao, CHEN Xiao-shan, CHEN Si-yu
    2022, 43 (1):  71-76.  DOI: 10.12068/j.issn.1005-3026.2022.01.010
    Abstract ( 472 )   HTML ( 4)   PDF (1110KB) ( 209 )  
    The quality of sealing plays an important role in the sustainability of vehicle NVH. Sealing at inner corner is more prone to failure compared to the straight lines and outer corners. In order to improve the sealing quality at the inner corner, the additional pressure on the bonding substrate generated by compressive sealing strips was studied, and a model for calculating the pressure on the inner corner of the bonding substrate provided by compressive sealing strips was proposed and the finite element simulation of the process was carried out. The results showed that compressive sealing can provide additional pressure on the bonding substrate steadily and evenly.The pressure exerted on the bonding substrate by the sealing strip is proportional to the compression ratio. The distribution of pressure is related to the section shape along the width and it is not immutable. The pressure is distributed uniformly along the circumference, and the difference is less than 8%. It is proved that compressive sealing can obviously improve the sealing quality at the inner corner, and it has good process stability.
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    Effects of Different Interbody Fusion Methods on Dynamic Characteristics of Lumbar Spines
    WANG Qing-dong, GUO Li-xin, ZHANG Chi, ZHANG Dong-xiang
    2022, 43 (1):  76-82.  DOI: 10.12068/j.issn.1005-3026.2022.01.011
    Abstract ( 675 )   HTML ( 0)   PDF (1139KB) ( 113 )  
    Based on the finite element method, the effects of four different methods of lumbar interbody fusion (ALIF, PLIF, TLIF and DLIF) on the lumbar fusion segments and adjacent segments under the condition of whole-body vibration were compared. Some important indexes related to complications such as stress distribution, stress peak and stress amplitude were introduced and compared. The results showed that ALIF can provide a more stable environment for the adjacent segments in the whole-body vibration state among the four different methods, and this method has better anti-vibration performance. Compared with the other methods, DLIF can reduce the risk of cage subsidence and failure. Besides, DLIF can provide a more stable and suitable environment for the growth of vertebral cells in the state of whole-body vibration, which is more conducive to the success of vertebral fusion.
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    Experimental Study on Surface Quality in Micro-scale Grinding of Zirconia Ceramics
    ZHOU Yun-guang, TIAN Chuan-chuan, MA Lian-jie, BI Chang-bo
    2022, 43 (1):  83-88.  DOI: 10.12068/j.issn.1005-3026.2022.01.012
    Abstract ( 629 )   HTML ( 2)   PDF (1206KB) ( 263 )  
    To improve the surface quality of zirconia ceramic parts in the process of micro machining and improve the service life of zirconia ceramic parts, orthogonal experiments of three factors and five levels on zirconia ceramics were performed using a micro-grinding tool with 500# grains and 0.9mm diameter. Firstly, through range analysis and variance analysis, the main influencing factors for the micro-grinding surface roughness of zirconia ceramics were studied. Then, the micro-grinding process was optimized to obtain the minimum surface roughness. Finally, the effect of process parameters on the surface roughness of micro-grinding zirconia ceramics was analyzed through the single-factor experiment. The results showed that the major and minor order of the effect of various process parameters on the surface roughness is the grinding depth, the feed speed and the spindle speed. The optimized parameter combination was as follows: the spindle speed v○s=40000r/min, the feed rate v○w=20μm/s and the grinding depth a○p=3μm, the surface roughness being minimum. The surface roughness decreases first and then increases with the increase of spindle speed, and increases with the increase of feed speed and grinding depth.
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    Modeling and Parameter Identification of Friction Characteristics of Harmonic Reducer
    SHI Yin, YIN Hua-chuan, LI Jun-yang, TANG Ting
    2022, 43 (1):  89-97.  DOI: 10.12068/j.issn.1005-3026.2022.01.013
    Abstract ( 1237 )   HTML ( 16)   PDF (1152KB) ( 812 )  
    In order to improve the control precision of the robot joint of the harmonic reducer(HD)and adapt to its use under complex working conditions, the friction torque characteristics of HD are studied. By introducing the models of elastohydrodynamic lubrication relationship, the nonlinear stiffness relationship and equivalent dissipation relationship of flexspline elastic deformation, a friction torque model of HD coupled with parameters such as speed, load torque and temperature is established. The genetic algorithm is used to process the test data of the SHF-20-80-2UJ harmonic reducer, the identification results of the parameters to be identified are obtained, and the accuracy of the model is verified. The maximum and average deviations between the simulated and experimental values of friction torque are 8.05% and 4.26% respectively; with full load and input speed being 2000r/min, the maximum deviation between the simulated value and the experimental value of the friction torque at different temperatures is 1.12%. The model effectively reflects the nonlinear relationship between the friction torque of the harmonic reducer with respect to the rotating speed, load torque and temperature changes. The measured elastic deformation energy loss accounts for about 20% and 50% of the total energy loss at no-load and full-load respectively.
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    Resources & Civil Engineering
    Preparation and Photocatalytic Properties of AgCl/Bi25FeO40 Composites
    YIN Wen-yue, LI Ying-hua, NAN Rui-bin, LI Meng-xi
    2022, 43 (1):  97-102.  DOI: 10.12068/j.issn.1005-3026.2022.01.014
    Abstract ( 581 )   HTML ( 2)   PDF (985KB) ( 204 )  
    AgCl/Bi25FeO40 composites loaded with different mass fractions of AgCl were prepared by the hydrothermal-sonochemical method. The microstructure, crystal phase composition and optical absorption properties of the composites were characterized by XRD, SEM-EDS, UV-Vis DRS and PL spectra. The photocatalytic degradation of Rhodamine B was also carried out. The results showed that Bi25FeO40was a cubic structure with a diameter of 0.8~10μm. AgCl was uniformly loaded on Bi25FeO40 with a diameter of 90~130nm. The combination of the two materials broadens the photo response range of the single material and improves the photocatalytic activity of Bi25FeO40. 0.1g AgCl/Bi25FeO40 was added to degrade 100mL 15mg/L Rhodamine B solution, when the mass fraction of loaded AgCl was 51.8 %, the degradation rate reached 94.4% in 75 min and Rhodamine B could be completely degraded in 90min. In addition, the degradation mechanism of AgCl /Bi25FeO40 was analyzed. It was considered that h+, e-,H2O2 and ·O-2 are the main active groups of the photocatalysis system to degrade Rhodamine B.
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    Remediation of Lead-Contaminated Soil by Single and Compound Environment-Friendly Leaching Agents
    LI Ying-hua, WU Ji-guo, QIAN Jie, SUN Jia-ru
    2022, 43 (1):  103-110.  DOI: 10.12068/j.issn.1005-3026.2022.01.015
    Abstract ( 665 )   HTML ( 4)   PDF (1535KB) ( 267 )  
    The leaching characteristics of ethylenediamine tetra methylene phosphonic acid(EDTMPA), polyamic acid(PAA) and rhamnolipid on removing Pb from contaminated soil were studied to develop a high-efficiency and environment-friendly leaching agent for Pb contaminated soil by horizontal experiments, and response surface methodology(RSM)was applied to optimize the parameters of these two eluents. For the first time, combinations of the biosurfactant rhamnolipid and two chelating agents EDTMPA and PAA were used to leach contaminated soil of Pb. The results showed that EDTMPA has the best leaching effect among these three eluents, and the optimal operation parameters were concentration 2.3%, pH 5.7, leaching time 167min and the removal rate of Pb can reach 57.6%. The highest removal rate of rhamnolipid combined with EDTMPA was 70.9%, which was 12% higher than that of EDTMPA alone. The highest removal rate of rhamnolipid compound PAA was 63.3%, which was 16% higher than that of PAA alone. Rhamnolipid combined with EDTMPA is an environment-friendly eluent with the highest removal rate.
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    Effect of Pulsed Electric Field on Growth Metabolism of Aerobic Denitrifiers
    WANG Fan, HU Xiao-min, LI Xue-jie, ZHANG Bo
    2022, 43 (1):  111-117.  DOI: 10.12068/j.issn.1005-3026.2022.01.016
    Abstract ( 514 )   HTML ( 4)   PDF (869KB) ( 170 )  
    Pulsed electric field(PEF)technology was applied to aerobic denitrification treatment of nitrate wastewater. By comparing the changes of growth metabolism of aerobic denitrifiers under different PEF strength, frequency, electrode distance and inoculation volume, the optimal process parameters of PEF treatment were determined. The results indicated that under the conditions of PEF strength 0.8V·cm-1, frequency 1000Hz, electrode distance 5cm and inoculation volume 5%, the optical density at 600nm wavelengths (OD600), removal efficiency of COD and NO-3-N of aerobic denitrifiers Pseudomonas putida W207-14 treated with PEF can reach the maximum value in 24h, which were 1.926±0.04,(97.67±1.12)% and(90.34±0.73)%, respectively. Compared with the untreated aerobic denitrifiers, the growth time of the treated aerobic denitrifiers is significantly reduced, and the nitrate removal rate is increased by 115.76%.
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    Study on Limited Conditions and Calculation Formula of BQ Classification Based on Graphic Method
    ZHAO Wen, JIN Chen, LU Bo, YANG Nan
    2022, 43 (1):  117-123.  DOI: 10.12068/j.issn.1005-3026.2022.01.017
    Abstract ( 859 )   HTML ( 4)   PDF (586KB) ( 229 )  
    The calculation formula of BQ (basic quality) classification index in GB 50218—1994 is modified in the revised Standard for Engineering Classification of Rock Mass(GB/T 50218—2014), but its two limiting conditions(saturated uniaxial compressive strength of rock and rock mass integrity coefficient)were not modified simultaneously. Through a large number of data studies, it is found that the calculation results are inconsistent with the qualitative and quantitative calculation results when the data are directly reduced by Rc and Kv constraints. Therefore, the limited conditions are modified and analyzed based on simplified graphical method. According to the analysis results that are widely affected by Rc constraints, 54 sets of new data in the database are taken as samples, and a new calculation formula is established by regression analysis of the data reduced by Rc constraints. The revised limit conditions and new section calculation formula obtained are analyzed and demonstrated on the basis of actual engineering data. The results show that the revised limited conditions and the calculation formula proposed in this study improve the agreement between the qualitative classification and the quantitative classification, and a more accurate classification result is obtained.
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    Management Science
    Research on Impacts of Manufacturers’ Innovation Investment Decision-Making Under Different Competition Modes
    GUO Xiao-ling, LI Kai
    2022, 43 (1):  124-132.  DOI: 10.12068/j.issn.1005-3026.2022.01.018
    Abstract ( 524 )   HTML ( 0)   PDF (544KB) ( 131 )  
    Based on the game models under different market structures, the impacts of different competition modes on upstream manufacturers’ innovation investment decision-making in horizontal and vertical dimensions were discussed. The results showed that the horizontal market competition intensity has a negative effect on upstream manufacturers’ innovation investment willingness, while the vertical market power has a positive effect on upstream manufacturers’ innovation investment willingness. However, compared with the benchmark situation without competition pressure, both horizontal and vertical competition will reduce manufacturers’ motivation to invest in research and development innovation, and the double competition pressure from the horizontal and vertical dimensions will aggravate this inhibition. Finally, through numerical analysis, the correctness of the obtained results is verified.
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    Method of Service Level Classification of Station Spacing for Bus Rapid Transit
    HUO Yue-ying , QIU Zhi-xuan, CHEN Guo-qing, GUO Chen
    2022, 43 (1):  133-140.  DOI: 10.12068/j.issn.1005-3026.2022.01.019
    Abstract ( 515 )   HTML ( 1)   PDF (899KB) ( 220 )  
    A method for determining the classification thresholds of service levels based on the ordinal Logistic regression model was proposed. The passenger volume estimation method of different station spacing for bus rapid transit(BRT)was proposed, and the cubic function of station spacing and bus running speed was established to calibrate the BRT simulation parameters. The software of VISSIM was used to establish BRT simulation systems with different station spacing of 500~1500m. Based on this, the BRT travel video clips including four stages of arrival, waiting, boarding and departure were produced. The video experiments were carried out and the data of service levels under different station spacings were collected with the sample size of 126. The service level classification of BRT station spacing was established using the proposed classification thresholds method. The thresholds of A~F service levels are 300, 460, 850, 1300 and 1900m respectively. The built service level classification can guide the setting of station spacing under BRT planning and construction, and can be used to evaluate the service levels provided by the current station spacing.
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    Analysis and Countermeasures of Spatial-Temporal Evolution of Cultivated Land Use in Liaoning Province
    WANG Yu-feng
    2022, 43 (1):  141-146.  DOI: 10.12068/j.issn.1005-3026.2022.01.020
    Abstract ( 579 )   HTML ( 3)   PDF (1471KB) ( 185 )  
    The models of cultivated land kernel density, dynamic degree and influence mechanism were used to discuss the evolution and influence mechanism of cultivated land’s spatial distribution from 1990 to 2020 in Liaoning Province. The results showed that the characteristics of cultivated land agglomeration in Liaoning Province are significant, showing a spatial distribution pattern of "dense in the northwest and sparse in the southeast", with a variation range of 0~10.17hm2/km2. The relative index of cultivated land change gradually transformed from the high in the western and eastern regions in 1990 to the high in the central region in 2020. In the 1990s, the average annual increase of cultivated land was 1.88×104hm2, but decreased by 2.72×104hm2 after the 21st century. The area of cultivated land decreased in Shenyang, Dalian and Anshan but increased in Panjin and Tieling. Natural factors are a prerequisite for cultivated land use, but socio-economic and regional policies play an important role. The intensification of drought and the reduction of agricultural population led to a reduction of 3.576×105hm2 of cultivated land. With the social development, the average output value increased by 302%, and the social fixed investment increased by 9.4 times. It is suggested that the government should encourage diversified cultivation of cultivated land, establish a mechanism for the circulation of cultivated land, strengthen the construction of new countryside, and encourage the young labor force to return home to develop science and technology agriculture.
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    Mathematics
    Harnack Inequality for Equi-Affine Curve Shortening Flow
    YU Yan-hua, JIN Ling
    2022, 43 (1):  147-152.  DOI: 10.12068/j.issn.1005-3026.2022.01.021
    Abstract ( 439 )   HTML ( 4)   PDF (327KB) ( 245 )  
    The Harnack inequalities of a family of closed convex equi-affine curves based on equi-affine curve shortening flow were studied. Firstly, according to the geometric evolution property of the equi-affine curve, a new type of Harnack quantity on the closed convex equi-affine curve was defined, then the evolution equation about the Harnack quantity of the closed convex equi-affine curve was discovered. Secondly, by the maximum principle, the non-negativity of the Harnack quantity, i.e., the Harnack inequality of the closed convex equi-affine curve, was investigated. Moreover, the constraint conditions of parameters in the Harnack quantity were found. Then, the Hamilton’s Harnack inequality of the closed convex equi-affine curve was further explored using the newly defined Harnack quantity.Finally, the classical Harnack inequality was derived based on Harnack inequality of the closed convex equi-affine curve and Cauchy-Schwarz inequality.
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