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28 December 2024, Volume 50 Issue 6 Previous Issue    Next Issue

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Materials Science and Engineering

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Preparation and tribological properties of Ni-Mo-Y-CaF2 high temperature self-lubricating composites SU Xiao-peng, JIN Wei-wen, YANG Gui-rong, LU Long, WANG Jing-bo 2024, 50 (6):  1-10.  Abstract ( 487 )   PDF (9181KB) ( 76 )   Save Ni-Mo-Y-CaF2 high temperature self-lubricating composites with different CaF2 addition amounts were prepared using spark plasma sintering (SPS) technology. The microstructure, mechanical properties, friction and wear properties of the composites were studied. The results showed that the microstructure of Ni-Mo-Y-CaF2 composites is uniform and dense, and the density, hardness and yield strength of the composites decrease with the amount of CaF2 added increasing. Temperature significantly affects the friction and wear properties of the composites. From room temperature to 800 ℃, the average friction coefficient of the composites decreases initially with increasing temperature, slightly increases between 400 ℃ and 600 ℃, and then decreases again. The average wear rate increases initially with increasing temperature,and then decreases reaching a maximum at 400 ℃. At room temperature,the average wear rate of Ni-Mo-Y-10CaF2 composite has the lowest average wear rate, about 1/5 of that of Ni-Mo-Y alloy. At 800 ℃, the wear rates of the composites are lower than that of the Ni-Mo-Y alloy. A dense and smooth lubricating film forms on the wear surface, mainly composed of calcium molybdate, nickel molybdate, and the oxides of nickel and molybdenum. References | Related Articles | Metrics

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Effect of annealing parameters on microstructure and mechanical properties of 45# steel ZHAO Xiao-long, LUO Xiao-yang, WANG Zheng-zhong, WANG Sheng-dong, JIA Zhi 2024, 50 (6):  11-16.  Abstract ( 641 )   PDF (7252KB) ( 79 )   Save The microstructure characteristics and mechanical properties evolution of 45 steel under different annealing temperatures and heating rates were studied. The orientation, grain boundaries, grain types, geometrically necessary dislocations, and precipitates of samples with different annealing parameterswere analyzed. Combined with tensile mechanical properties testing, the mechanical properties of different samples were explained. The results indicated that the microstructure and mechanical properties of 45 steel have significant differences under different annealing parameters. As the annealing temperature increases, the orientation gradient, low-angle grain boundaries, deformed grains, geometrically necessary dislocations, and cementite content of 45 steel decrease. The effect of annealing heating rate on microstructure is complex. At low temperatures, the slower the heating rate, the greater the degree of recrystallization. However, at high temperatures, the phase transition participates in the static recrystallization nucleation and growth during the annealing process. Under the annealing parameters of 0.08 ℃/s-690 ℃, the tensile mechanical strength and toughness of 45 steel are the best, with the tensile fracture surface exhibiting a plastic fracture mode. References | Related Articles | Metrics

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Electrochemical properties of coral-like nickel-cobalt bimetallic oxide-doped carbon nanohybrid materials MA Ying-xia, LEI Lei, LIU Bing-lu, KANG Xiao-ya, RAN Fen 2024, 50 (6):  17-27.  Abstract ( 315 )   PDF (7268KB) ( 43 )   Save Metal-organic frameworks (MOFs) have received attention as supercapacitor electrode materials due to their large specific surface area, adjustable pore size and abundant redox sites. However, the specific capacitance of MOFs limits their further application. In this paper, employing three-dimensional (3D) spiny cypress-like Ni/Co-MOF as precursors obtained by hydrothermal method using Ni (NO3)2·6H2O and Co (NO3)2·6H2O as the metal ion sources and terephthalic acid as the organic ligand, a series of coral-like nickel-cobalt bimetallic oxide-doped carbon nanohybrid materials (NCPO/C) were prepared in an air atmosphere by regulatingthe heat treatment temperature and isothermal time, and their electrochemical properties as supercapacitor electrode materials were investigated. The results showed that the coral-like NCPO/C sample obtained byheating the 3D spiny cypress-like Ni/Co-MOF precursor at 280 ℃ for 1 h in air atmosphere, has the best electrochemical performance as electrode materials. When the current density expand from 0.5 A·g－1 to 5.0 A·g－1, the specific capacitance of NCPO/C decrease from 852.5 C·g－1 to 720.0 C·g－1, and the capacitance retention 84.5%. References | Related Articles | Metrics

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Preparation and properties of montmorillonite nanosheets modified with phosphorylated chitosan GAO Yu, KANG Cheng-hu 2024, 50 (6):  28-32.  Abstract ( 434 )   PDF (2213KB) ( 241 )   Save Nanosizing and surface modification of Na-MMT were carried out using hydroxysilicone oil via mechanical ball milling techniques, and chitosan was phosphorylated. The phosphorylated chitosan was further applied to decorate exfoliated montmorillonite under oil bath treatment. The crystal structure, surface characteristics, specific surface area and thermal stability of MMT before and after surface modification with phosphorylated chitosan were systematically studied using X-ray diffraction (XRD), Fourier transform infrared absorption spectroscopy (FT-IR), contact angle measurement (CA), specific surface area and pore size analyzer (BET), and thermogravimetric analyzer (TGA). The results showed that after modification with hydroxysilicone oil and surface coating with phosphorylated chitosan, the crystal structure of MMT does not significantly changes. Nevertheless, the diffraction peak corresponding to the (001) crystal plane is widened, which means that the layered structure of Na-MMT is deteriorated and exfoliated. Furthermore, the surface hydrophobicity of MMT coated by phosphorylated chitosan is improved, with a water contact angle of 62.7°, and a specific surface area of 13.812 m2/g. In short, the phosphorylated chitosan presents a thicker coating layer on the surface of Na-MMT. References | Related Articles | Metrics

Mechanical Engineering and Power Engineering

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Research on on-machine measurement of tool wear based on machine vision GUO Run-lan, ZHANG Hao, ZHI Xiao-bo, YU Wei-wei 2024, 50 (6):  33-41.  Abstract ( 341 )   PDF (3876KB) ( 574 )   Save In order to solve the problem that it is difficult to measure the wear of small tools in complex machining environments, an on-machine tool wear detection method based on machine vision is proposed. First, a method of adaptive segmentation calculation for knife edge images is designed. The original image is segmented by using the improved Gaussian mixture model segmentation algorithm. Subsequently, the noise is reduced by using the improved nonlinear filter, effectively retaining edge details while reducing error during fuzzy noise reduction process, thus achieving automatic segmentation, denoising, and measurement of tool image. The single camera tool image acquisition mechanism is further designed, and cutting experiments are carried out. The results show that the errors in the tool side, bottom wear area, and the maximum wear bandwidth are 3.88%, 5.41%, and 6.26%, respectively, compared with the traditional electron microscope measurements, achieving micron-level accuracy. Compared with traditional wear measurement methods, this system and algorithm enables faster image denoising with clearer edges. Irregular wear areas are calculated by pixel points, which effectively solves the problem that small tool blades are small and difficult to observe and measure, and can meet the requirements of on-machine detection of small tools. References | Related Articles | Metrics

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Machining accuracy reliability analysis of multi-axis CNC machine tools based on polynomial chaos expansions WANG Zhi-ming, ZHOU Jian, XU Teng 2024, 50 (6):  42-50.  Abstract ( 352 )   PDF (1338KB) ( 97 )   Save To improve the machining accuracy reliability of multi-axis CNC machine tools, an accuracy design method is proposed based on polynomial chaos expansion theory. The comprehensive geometric error model and machining accuracy reliability model of machine tools are built through the use of the coordinate system differential motion matrix method. Through analyzing the reliability sensitivity of machining accuracy, critical geometric error terms which have a large impact on accuracy reliability can be identified. On this basis, combining sensitivity analysis results and accuracy reliability design requirements, the accuracy of machine tools can be optimized to meet the requirement of reliability by adjusting the parameters of geometric error terms with higher sensitivity. Taking a large-scale CNC gantry guideway grinder as an example, the effectiveness of the proposed method is verified. The results show that the proposed method can improve the machining accuracy reliability of machine tools. References | Related Articles | Metrics

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Experimental study on the diffusion spiral mixed flow of multi-stage variable pore size plate ZHAO Ting-hong, WANG Li-qiang 2024, 50 (6):  51-57.  Abstract ( 394 )   PDF (4800KB) ( 105 )   Save The orifice plate energy dissipation device known for its simple structure, high energy dissipation efficiency, and ease of assembly and disassembly, has been widely used in water conservancy projects in China. In the design of the multi-stage orifice plate energy dissipation device, a variable pore diameter aperture plate energy dissipation device is reconstructed. The energy dissipation efficiency, total resistance coefficient, and pressure path change of the device under different shrinkage angles, torsion angles, and Reynolds numbers are analyzed and studied by model tests. The findings suggest that, with constant torsion and contraction angle of the orifice plate remain, the energy dissipation rate of the device increases with the increase of Reynolds number. When the Reynolds number and contraction angle remain unchanged, both the energy dissipation rate and the total resistance coefficient also increase with the increase of the torsion angle. When the Reynolds number and torsion angle remain unchanged, the energy dissipation rate of the device decreases with the increase of contraction angle; In addition, under the same contraction angle and torsion angle, the pressure at the same measuring point increases with the increase of Reynolds number, and under the same Reynolds number, contraction angle and conditions, the pressure at the same measuring point also increases with the increase of torsion angle. In general, the most reasonable combination mode of the orifice plate of the energy dissipation device is the contraction angle of 30 ° and the torsion angle of 6 °. References | Related Articles | Metrics

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Research on meshing impact and meshing energy consumption of spur gear system under time-varying-random excitation HAN Wei, YANG Xing, SHI Jian-fei 2024, 50 (6):  58-64.  Abstract ( 352 )   PDF (4925KB) ( 106 )   Save To study the meshing-impact characteristics of spur gear system under combined time-varying and stochastic excitations, a time-varying and random external excitation model of the gear system is proposed. Based on this, a meshing-impact non-linear dynamic model of spur gear pair, including tooth surface friction and time-varying meshing position under bridge-road excitation, is established. The evolutions of the impact force and the maximum impact energy loss with the meshing frequency and error amplitude are analyzed by constructing the Poincaré mapping section of the contact impact on the tooth surface and the tooth back. The effects of bifurcation and chaos on the dynamic meshing force and maximum impact energy loss are studied using nonlinear vibration theory. Additionally, the distribution characteristics of the maximum impact energy loss in a two-parameter plane are discussed. The results show that the error amplitude, meshing frequency, and their matching law greatly affect the dynamic meshing force and impact energy loss, which in turn critically affect the dynamic performance of the gear system. These findings provide a scientific basis for the dynamic performance improvement and reliability application of this type of gear system. References | Related Articles | Metrics

Chemical Industry and Light Industry

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Hydraulic calculation method and mathematical model of siphon water decanter based on rocker arm water intake head TIAN Bo, LIU Yan-xi, WANG Shao-feng 2024, 50 (6):  65-68.  Abstract ( 309 )   PDF (1123KB) ( 89 )   Save A simplified model of rocker arm intake head is established based on hydraulic equivalence, and a theoretical calculation model is established using the energy conservation equation. A correction factor is introduced in the theoretical model, which is further refined through experimental validation. Statistical analysis of the correction coefficient yields a standard deviation of 0.02, indicating that the modified calculation model $H=\left\{\bar{\varphi}\left(S_{\mathrm{EQ}}+S_{\mathrm{COD}}\right)+\frac{8}{g \pi^{2} d^{4}}\right\} Q_{z}^{2}$ meets the engineering design requirements. References | Related Articles | Metrics

Automation Technique and Computer Technology

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Fault-tolerant consensus control for time-delay multi-agent systems with model uncertainties WANG Jun, YANG Jia-qi 2024, 50 (6):  69-75.  Abstract ( 321 )   PDF (2167KB) ( 54 )   Save In this paper, the fault-tolerant consensus control for model-uncertain multi-agent systems with time delays is studied in the case of possible failure of any agent and the external finite energy disturbance. Firstly, the fault-tolerant consensus control of multi-agent systems with time-delay model uncertainty is transformed into an asymptotic stability problem of closed-loop fault systems by matrix transformation method. Then, Lyapunov stability theory was used to design a fault-tolerant consensus controller for possible actuator faults. On this basis, the sufficient condition for fault-tolerant consistency in model uncertain delayed multi-agent systems subject to directed communication topologies and limited external energy disturbances is deduced, based on linear matrix inequality (LMI). These conditions ensure the convergence of position and velocity state information towards consensus. Finally, a leaderless system model consisting of six agents is used to verify the feasibility and effectiveness of the proposed method. References | Related Articles | Metrics

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Semi-global output containment control for discrete-time descriptor multi-agent systems with input saturation WANG Zhi-wen, WANG Yu-ying, LU Yan-rong, DU Nan, LI Xiao-fang 2024, 50 (6):  76-84.  Abstract ( 239 )   PDF (2749KB) ( 180 )   Save The semi-global output containment control for discrete-time descriptor multi-agent systems with input saturation under a directed communication topology. Firstly, the original problem is transformed into an output regulation problem with a distributed observer. Secondly, the explicit solution of a descriptor system is obtained by a parametric discrete-time Riccati equation, the constrained equivalent decomposition of a descriptor system. Thirdly, the semi-global output containment control protocols are constructed based on a distributed state observer and an output regulator, and sufficient conditions for the stability of the system are given by selecting an appropriate Lyapunov function. It is proved that the output of all followers can converge to the convex hull formed by the leaders under the designed control protocol. Finally, the effectiveness of the proposed distributed protocols is verified by a numerical example. References | Related Articles | Metrics

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Soft measurement model of effluent BOD based on improved seagull optimization algorithm and LSTM neural network DU Xian-jun, CHAI Jun-wei 2024, 50 (6):  85-91.  Abstract ( 438 )   PDF (2101KB) ( 305 )   Save Aimed at the problem that the biochemical oxygen demand (BOD) of effluent in the sewage treatment process is difficult to accurately measure online, a soft measurement method based on the combination of random forest (RF) importance assessment and improved seagull optimization algorithm (ISOA) optimized long short-term memory neural network (LSTM) is proposed to predict the effluent BOD. The predictors affecting the effluent BOD were evaluated by the random forest algorithm, and the predictors with high importance scores were screened out as input variables of the soft measurement model.Secondary, an improved seagull optimization algorithm is presented for optimizing the LSTM network. The chaos mapping and new search mechanisms are introduced to overcome the problems of poor diversity and easy to fall into local optima of the seagull optimization algorithm. The ISOA is employed to optimize four hyperparameters of the LSTM network: the network iteration number, the number of nodes in the hidden layer, initial learning rate, and learning rate degradation factor. Finally, the proposed soft measurement models are applied to actual wastewater treatment processes. The results show that the prediction error of the model has been reduced and the prediction accuracy has been improved, achieving the accurate prediction of effluent BOD. References | Related Articles | Metrics

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Path planning of target tracking sensor based on intelligent optimization decision ZHANG Wen-xu, WANG Xiao-qing, CHEN Hui, ZHAO Yong-hong 2024, 50 (6):  92-98.  Abstract ( 221 )   PDF (2687KB) ( 117 )   Save Aiming at the estimation and optimization problem of target tracking systems managed by sensor control, this paper proposes a sensor path planning method based on reinforcement learning in the discrete space. First, the estimated position and the covariance of the target at the next time are obtained by nonlinear optimal filtering. Then, a target tracking optimization model based on reinforcement learning is established, and the target covariance trace after sensor path planning is calculated based on the SARSA (state-action-reward-state-action) algorithm. Finally, a single-step cycle is performed on the sensor position selection the next time. The optimal moving position is obtained by comparison of the covariance traces before and after the sensor path planning in each cycle. In the simulation experiment, the motion trajectories of the sensor in different learning episodes were compared and analyzed, and the results show that the effect of target tracking optimization was significantly improved. References | Related Articles | Metrics

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Research on lossless transmission of Barker coded ultrasonic excitation system in rail environment HUANG Ling, XU Zi-jian, WEI Xiao-yuan, WANG Gang 2024, 50 (6):  99-106.  Abstract ( 213 )   PDF (5566KB) ( 38 )   Save The ultrasonic guided wave (UGW) testing has the problem of the dispersion effect and interference in the transmission medium, which degrades signal-to-noise ratio (SNR) and range resolution in the rail detection. To solve this issue, a Barker-coded excitation technology is applied to UGW rail damage detection. The comparison of the effects of square pulse, sinusoidal pulse, Hanning window sinusoidal pulse waveforms, and carrier cycles on UGW signals is performed by simulation. It is shown that the 10-cycle carrier exhibits the widest main lobe width with a peak-to-side lobe ratio of about －24.0 dB. Field experiments were conducted to validate the findings. The results show that the peak sidelobe level of the ultrasonic guided wave signal excited by Barker coding is －14.40 dB after pulse compression processing, which is 3.26 dB higher than that of a single pulse excitation signal. These findings indicate that ultrasonic-guided wave transmission using the coding excitation technology in the rail environment is reliable. References | Related Articles | Metrics

Architectural Sciences

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Study on damage mechanism of core concrete defect location on CFST bearing capacity DONG Jun, GE Shi-chao, LI Guo-hua, XIANGXue-jian, LIU Dian-yuan 2024, 50 (6):  107-112.  Abstract ( 297 )   PDF (3115KB) ( 138 )   Save Relying on the engineering background of a concrete-filled steel tubular single-pylon cable-stayed bridge under construction, aiming at the loss problem that the bearing capacity of concrete-filled steel tubular members may be reduced due to the different defect positions of core concrete, a numerical finite element model is established and analyzed by combining the bearing capacity tests of concrete-filled steel tubular members under different typical defect positions in this paper. The stress law of concrete-filled steel tube bearing capacity under different defect conditions is analyzed and discussed, and compared with the test results. The results show that the existence of core concrete defects inevitably reduce the bearing capacity of members Compared with the members with defects in the lower part, the members with defects in the upper or middle part are more likely to be destroyed. Additionally, defects located at the edge of the core concrete lead to greater loss in load-bearing capacity compared to defects in the central region, due to a weakened confinement effect, which is caused by the hoop effect of the structure. References | Related Articles | Metrics

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Study on the influence of limestone powder on the strength of sustainable UHPC cementitious material system NAN Xue-li, WNAG Yi, CHEN Hao, LI Mei, TNAG Wei-bin 2024, 50 (6):  113-118.  Abstract ( 278 )   PDF (4015KB) ( 128 )   Save In order to investigate the effect of limestone powder (LP) on the strength of sustainable ultra-high performance concrete (UHPC) cementitious material systems, the compressive strength, pore structure, phase composition, and microstructure of UHPC cementitious material systems after 4%, 8% and 12% replacement of cement by LP were investigated. Additionally, the environmental effects were quantitatively assessed using life cycle theory (LCA). The results showed that as the LP substitution rate increases, the compressive strength initially increased and then decreased with an inverse trend observed for the total porosity. The optimal substitution rate was 4%, which resulted in a 16.7% increase in compressive strength and a 28% reduction in total porosity compared to the blank group (LPC). LP does not participate in hydration but contributes to pore structure refinement through filler and nucleation effects. When the substitution rate exceeds 4%, dilution effects predominate. LP substitution rate greater than 4% significantly reduces the adverse effect on the environment but will have a negative effect on the strength and internal structure of the specimen. Therefore, the LP substitution rate should be increased as much as possible under the condition of ensuring the strength of the specimen. References | Related Articles | Metrics

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Numerical simulation comparative analysis of temperature field of different freezing and strengthening schemes for replacement of shield tail brush YANG Ning, ZHAO Mei-xia, CHEN Lu, HU Jun 2024, 50 (6):  119-126.  Abstract ( 298 )   PDF (5576KB) ( 563 )   Save How to prevent shield tail leakage when replacing shield tail brushes is an important and difficult pointduring shield tunnel construction. In this paper, the shield tail brushes were replaced by ‘directly drilling a circle of radioactive holes on the pipe segment’ (scheme 1), ‘shield tail freezing tube and pre-embedded freezing tube segment’ (scheme 2) and ‘setting 2 annular freezing tubes’ (scheme 3), and a numerical model was established to compare and analyze the development law of the temperature field of the frozen soil curtain formed by each scheme. The results show that the frozen soil curtain formed by the three schemes can effectively prevent shield tail leakage, and the volume of the frozen soil curtain formed by scheme 3 is greater than scheme 2 and scheme 1. The sealing time for the gap between the shield tail and the ring is 17 days, 2 days, and 5 days, respectively. The freezing effect at this location of scheme 2 is greater than scheme 3, and the scheme 1 has the worst effect.The improvement measure for scheme 1 is to arrange a radial freezing tube as close as possible to the gap between the shield tails. Scheme 2 and scheme 3 can be adopted in practical engineering,and it is recommended to adopt scheme 3 for freezing reinforcement during the replacement of the shield tail brush. References | Related Articles | Metrics

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Study on the regeneration mechanism of SBS modified asphalt based on DSR and FTIR WANG Zhao-li, LIN Mei, WANG Guo-wei, LEI Yu-tao, ZHANG Lei 2024, 50 (6):  127-134.  Abstract ( 429 )   PDF (4028KB) ( 84 )   Save In order to investigate the high and low temperature properties of SBS modified bitumen and the changes of functional groups after aging and regeneration, this paper tested the high and low temperature properties of bitumen based on softening point test, dynamic shear rheology test (DSR), multi-stress repetitive creep test (MSCR) and bending beam rheology test (BBR), and investigated the changes of characteristic peaks and functional groups using infrared spectroscopy (FTIR). The results show that: the ageing process of SBS modified bitumen includes not only the ageing of asphalt but also the ageing degradation of SBS modifier, the softening point, G*, G*/sin δ and R decrease, δ and Jnr increase, the low temperature performance is improved, but the high temperature resistance is decreased, and the increase in the amount of regenerant will make this phenomenon more obvious. Under the same conditions, the sensitivity of the high temperature performance of the recycled SBS modified bitumen to the stress level is weaker than that of the original SBS modified bitumen; in addition, the results of the infrared spectroscopy tests show that the effect of the recycled agent on the repair of SBS modified bitumen is limited. References | Related Articles | Metrics

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Research on stability of row piles and plugging local jetted pile-prestressed anchor supporting system influenced by the existing buildings JIN Gao-ming 2024, 50 (6):  135-143.  Abstract ( 216 )   PDF (6941KB) ( 24 )   Save Based on the foundation pit project of the scientific research base of Gansu coalfield geology bureau, through the combination of on-site monitoring and numerical calculation, this paper analyzes the influence of the composite support system of prestressed anchor cable and row pile local plug high-pressure jet grouting pile on the seepage, deformation characteristics and potential failure forms of foundation pit slope during the excavation process under the action of existing buildings. The results show that the combined water stop curtain of row piles and local high-pressure jet grouting piles can effectively extend the groundwater seepage path and significantly reduce the groundwater seepage velocity. Although the existing buildings limit the vertical settlement of the surface soil in the excavation process to a certain extent, they also aggravate the lateral displacement of the soil, which increases the internal pressure of the jet grouting pile and greatly reduces the overall stability of the foundation pit. Under the action of existing buildings, the formation of two groups of potential fracture surfaces at the bottom of the foundation pit is the main reason for the great reduction of the stability of the foundation pit slope. References | Related Articles | Metrics

Scientific

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Enumerations of 3 di-sk trees TIAN Zhen-ji, DOU Shu-ping 2024, 50 (6):  144-149.  Abstract ( 235 )   PDF (790KB) ( 64 )   Save The study investigates several counting problems related to 3 di-sk trees, which are characterized as a hybrid ternary tree without the left edge labeled (2,2). Obtaining several enumeration results with respect to certain statistics of 3 di-sk trees. A bijection between the set of all 3 di-sk trees with n internal nodes and the set of all 3-Schröder paths from (0,0) to (3n,0) is given. References | Related Articles | Metrics

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Gorenstein homological dimensions with respect to cotosion pairs WU De-jun, YUAN Yuan 2024, 50 (6):  150-156.  Abstract ( 262 )   PDF (462KB) ( 71 )   Save Let $\mathscr{C}$ be an abelian category with enough projectives and injectives and let ($\mathscr{A}$,$\mathscr{B}$) be a complete hereditary cotorsion pair in $\mathscr{C}$. The definition and equivalent characterizations of Gorenstein $\mathscr{A}-\mathscr{B}$ objects in abelian category $\mathscr{C}$ are given. Additionally, the related properties of Gorenstein $\mathscr{A}-\mathscr{B}$ dimensions in module category are studied. References | Related Articles | Metrics

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Asymptotic behavior of solution for Kirchhoff suspension bridge equations with state-dependent delay WANG Su-ping, MA Qiao-zhen, QI Yuan, ZHAO Hua-ni 2024, 50 (6):  157-163.  Abstract ( 229 )   PDF (484KB) ( 49 )   Save The asymptotic behavior of the solution for the Kirchhoff suspension bridge equation with state-dependent delay was investigated. By virtue of Banach fixed-point theorem, the locally unique mild solution was obtained. The asymptotic compactness of the evolution operator was demonstrated through the method of contraction function, which leaded to the establishment of the existence of a globalattractor. References | Related Articles | Metrics

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Base-submesocompact spaces CAI Qi-rong 2024, 50 (6):  164-166.  Abstract ( 256 )   PDF (404KB) ( 23 )   Save The notion of base-submesocompact spaces is introduced and the nature of the question is discussed: if X is a base-submesocompact space, Y is a closed subset of X, and ω(X)=ω(Y), then Y is a base-submesocompact space. Let X be base-submesocompact space and X′ be an Fσ subset of X, then X′ is base-submesocompact reative to X. Under perfect mapping, the inverse image of base-submesocompact space remains base-submesocompact space. References | Related Articles | Metrics

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On r-hued coloring of Cartesian product graphs YANG Xiao-mei, TANG Meng, LIU Bo-yu 2024, 50 (6):  167-172.  Abstract ( 253 )   PDF (774KB) ( 52 )   Save The r-hued chromatic number of a graph G is the minimum number k of all (k,r)-colorings, denoted by χr(G). The Cartesian product of G and H is denoted by G□H with vertex set V(G)×V(H), where two vertices (u,v) and (x,y) are adjacent if and only if either u=x and vy∈E(H) or v=y and ux∈E(G). The r-hued chromatic number of the Cartesian product graph C2m□Pn is discussed. By applying a constructive method and considering the structural relationships of C2m□Pn, the r-hued chromatic number of C2m□Pn is obtained for r=2,3. References | Related Articles | Metrics