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28 February 2024, Volume 50 Issue 1 Previous Issue    Next Issue

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Materials Science and Engineering

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Effect of ultrasonic treatment on microstructure and properties of degradable Zn-0.5Sr alloy LIU Jian-jun, ZHANG Peng-tao, ZHAO Zhi-xin, ZHANG Jiao, LI Qing-lin, DING Yu-tian 2024, 50 (1):  1-9.  Abstract ( 118 )   PDF (6577KB) ( 232 )   Save The effects of different ultrasonic power (0,300,600,900 W) on the microstructure and corrosion properties of Zn-0.5Sr alloy were studied. The results show that the SrZn13 phase in the as-cast Zn-0.5Sr alloy changes from coarse polygon to fine block after ultrasonic treatment.Compared with the untreated alloy, the electrochemicalcorrosion rate of the alloy increases from 2.078±0.141 mm/a to 5.747±0.390 mm/a when the ultrasonic power is 600 W.The immersion corrosion rates of Zn-0.5Sr alloy after 15 and 30 days are0.090±0.002 1、0.074±0.001 9 mm/a, respectively, which are 1.88 times and 1.95 times higher than that of the untreated alloy. References | Related Articles | Metrics

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Microstructure and properties of H13 steel treated by laser hardening and nitriding CAO Chi, LUO Wei-dong, CHEN Zhi-lin, LUO Li-ping, CHEN Xian-wu 2024, 50 (1):  10-18.  Abstract ( 59 )   PDF (10421KB) ( 70 )   Save H13 steel surface was modified by laser quenching/plasma nitriding compound treatment method, so as to improve the performance of its surface. The influence process and mechanism of plasma nitriding, laser quenching, and the laser quenching/plasma nitriding compound treatment on the microstructure, mechanical properties, and friction and wear properties of H13 steel were studied by X-ray diffraction, optical observation, scanning electron observation, energy spectrum analysis technology, microhardness and nano testing, and high-frequency reciprocating wear test, respectively.The results showed:that the compound treatment process can significantly improve the comprehensive performance of the modified layer. Compared with single nitriding treatment, the hardness of effective case depth of the compound treatmentmodified layer increased from 1 180 HV and 80 μm to 1 360 HV and 550 μm, respectively. and the friction coefficient and wear rate decreased from 0.68 and 5.78×10－8 mm3·N－1·m－1 to 0.59 and 1.35×10－8 mm3·N－1·m－1, respectively. The hardness and wear resistance of the specimen are significantly increased, and the average coefficient of friction is significantly reduced. References | Related Articles | Metrics

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Dendrite growth and bubble formation of Al-Cu alloys under PF-LBM coupling model ZHU Chang-sheng, LEI Yao, LEI Peng, GAO Zi-hao, ZHAO Bo-rui 2024, 50 (1):  19-26.  Abstract ( 32 )   PDF (4510KB) ( 37 )   Save The complex multiphase flow system was simulated by the Lattice Boltzmann Method based on Shan-Chen multiphase flow to explore the growth and motion of bubbles in the liquid phase. The interaction between dendrites and bubbles during solidification of Al-4.0wt% Cu alloys was studied, along with the effect of anisotropy on solidification organization and the variation in solution density when dendrites coexist with bubbles. The results showed that in the directional solidification dendrite growth model, the bubbles initially precipitate at the bottom of the dendrite. Pressure differentials drive bubble ascent, leading to interactions with dendrites during flow, resulting in instances of bubble coalescence and disappearance. In densely channeled regions between dendrites,larger bubbles become worm-shaped. The height-to-length ratio of the simulated area affects the growth of dendrites and bubbles, and the short, small bubbles more is likely to be produced when the height-to-length ratio is small, but the worm-like bubbles more is likely to be produced when the height-to-length ratio is large. In the isometric dendrite growth model, bubbles are precipitated between the dendrites, as the dendrites grow, they also merge, disappear and undergo deformation when they are squeezed. References | Related Articles | Metrics

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Effect of calcium chloride hexahydrate-based phase change material on energy storage and thermal insulation performance of rock wool insulation board YANG Xiao-tian, WANG Cai-long, LIU Jun-yan, GAO Hui, HE Cheng-jun 2024, 50 (1):  27-34.  Abstract ( 65 )   PDF (4185KB) ( 78 )   Save Using rock wool board as carrier, the self-developed calcium chloride hexahydrate-based phase change energy storage material was uniformly infiltrated into rock wool board to prepare rock wool/calcium chloride hexahydrate-based phase change insulation wall board. The influence of calcium chloride hexahydrate-based phase change material on the energy storage and thermal insulation capacity of rock wool board was studied, and its mechanical strength was tested. The test results showed that the maximum adsorption capacity of rock wool board on calcium chloride hexahydrate-based phase change material is 30 wt.%, and maximum specific heat capacity is 0.700 1 MJ/(m3·K). Although the composite plate show a large thermal conductivity of 0.089 1 W/(m·K) under this adsorption capacity, the corresponding thermal diffusion is the smallest of 0.127 3 mm2/s. Thermal temperature test showed that the maximum indoor temperature drop by 3.4 ℃ under this adsorption capacity, which indicates that thermal conductivity is not the only factor affecting the thermal insulation performance of rock wool board, and it is more reasonableto evaluate thermal insulation performance by using thermal diffusivity.SEM showed that calcium chloride hexahydrate-based phase change material is adhered to rock wool fibers and form a stable spatial grid structure,which effectively improve the compressive strength of rock wool board. References | Related Articles | Metrics

Mechanical Engineering and Power Engineering

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Reliability research of wind turbine based on PAC-FSEM method ZHENG Yu-qiao, LANG Qi-fa, SHI Cheng-long, LIU Yu-hang, LIU Yan-jie 2024, 50 (1):  35-40.  Abstract ( 51 )   PDF (1195KB) ( 82 )   Save Based on the relevant operating data from a wind farm in Northwest China, the reliability of wind turbines is studied. Considering the correlation and redundancy among operating data, Principal Component Analysis (PCA) method was used to reduce dimensionality, and some key reliability indicators were selected. Subsequently, a reliability evaluation model is constructed utilizing fuzzy theory in conjunction with the selected key indicators from operational data. A subset of wind turbine operating data is selected for model verification. The research results show that the PCA method extracts the principal component with a cumulative variance contribution rate of 87.585%, which can comprehensively express the reliability information of wind turbines. In the evaluation of a single reliability index, the availability of B02 is as high as 98%, but its total power generation is the lowest. Conversely, the availability of A04 is the lowest in the available area yet relatively higher power generation, indicating potential discrepancies when assessing reliability based on single reliability index. All indicators of A05 and B03 are high, the actual operation state of which is good, and the power generation is high, indicating that their comprehensive reliability is higher, which is consistent with the research results. Therefore, the fuzzy theoretical evaluation model (FSEM) of wind turbine reliability established based on PCA and fuzzy theory is in line with the actual operating state and has guiding significance for quantitatively evaluating the reliability of wind turbines. References | Related Articles | Metrics

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Optimization of process parameters for multi-feature structural size fusing deposition based on random walk sparrow search algorithm GUO Run-lan, XUE Kai, DENG Wen-qiang, FAN Ya-qiong, WANG Hu-lin 2024, 50 (1):  41-47.  Abstract ( 36 )   PDF (2293KB) ( 68 )   Save In the fused deposition molding process, the printing parameters have an important impact on the accuracy of the molded specimens. In order to improve the overall dimensional accuracy, the random walk sparrow algorithm is employed to obtain the optimal experimental scheme. Firstly, the orthogonal test of four factors and four levels is designed with the delamination thickness, heating temperature, printing speed, and filling rate of melt deposition molding as the experimental variables. Subsequently, the Taguchi-grey correlation method is used to process experimental data, with the relative error of the different characteristic structure sizes of the sample as the optimization object. Finally, the passed Random walk sparrow algorithm is utilized to calculate the optimal parameter scheme. The results indicate that the sample formed by the optimized process parameters has a 20% increase in the comprehensive dimensional accuracy compared with those obtained using Taguchi-gray correlation method, with a 27% increase in the gray correlation value. References | Related Articles | Metrics

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Research on efficiency prediction method of reciprocating air compressor based on digital twin technology YU Jian-ping, HU Shuang, LIU Xing-wang, TIAN You-wen, QIU Hong-wei, AKOTO Emmauel 2024, 50 (1):  48-52.  Abstract ( 71 )   PDF (2613KB) ( 139 )   Save The method for compressor efficiency prediction and parameter optimization by establishing the reciprocating air compressor digital twin model has the advantage of flexibility, low cost, and good versatility. However, the traditional twin model based on the BP neural network (BPNN) has lots of shortcomings, such as longer training time to establish a module, easily falling into the local optimal solution, and difficulty in achieving the global optimal solution. To solve these problems, a novel digital twin model based on the CIWOA-BPNN algorithm is put forward to determine the key indexes by the principal component analysis method, in which a CIWOA algorithm is introduced to improve the BPNN’s performance. The results show that the new CIWOA-BPNN twin model effectively avoids falling the local optimal problem. The relative error of CIWOA-BPNN is less than 0.6%, and the coefficient of determination is 0.997 75, which greatly improves the prediction accuracy compared with the traditional model. References | Related Articles | Metrics

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Research on the effect of inter-stage flow channel on the cavitation characteristics of tandem high speed centrifugal pump WANG Xiao-hui, ZHANG Kai, SONG Xin, HOU Chang-liang, LI Ke-jian 2024, 50 (1):  53-59.  Abstract ( 56 )   PDF (5787KB) ( 39 )   Save In order to analyze the influence of transition flow channels of different shapes on the cavitation characteristics of a tandem high-speed centrifugal pump, the second stage of a certain type of series high-speed centrifugal pump was taken as the research object. Based on the Zwart-Gerber-Belamri cavitation model in ANSYS Fluent, RNG k-ε two-equation turbulence model is used to compare and analyze the pressurization value, blade cavitation area, and cavitation volume in the flow channel under different cavitation numbers of annular and spiral transition channels under the same working conditions. The results show that the pressure increase value of the Secondary pump of the spiral transition channel is increased by about 8.5% in the flow range of 32 000~64 000 L/h, and the efficiency is improved by about 3%~6% under the large flow condition (qV>52 000 L/h). When the secondary impeller is completely cavitated, the cavitation area on the back of the secondary impeller blade in the spiral transition channel and the cavitation volume in the channel decreases to a certain extent compared with the annular transition channel. Consequently, it can be seen that the helical transition flow channel inhibits the generation of cavitation bubbles in the impeller blade and improves the anti-cavitation performance of the secondary impeller. References | Related Articles | Metrics

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Research on configuration optimization design method of hybrid electric vehicle ZHAO Si-li-gen, WANG Jing-yuan, ZHANG Xiao-ming 2024, 50 (1):  60-67.  Abstract ( 57 )   PDF (3271KB) ( 77 )   Save According to the relationship between the structural characteristics and dynamic characteristics of planetary gear vehicle, a theoretical design method of power system configuration of hybrid electric vehicle was proposed. Firstly, all the connections in the configuration are divided into three categories, and the matrix representation is used to represent these connections to reflect the system dynamics and the physical structure of the configuration. Subsequently, a matrix representation method for automatic configuration design is proposed. The speed equation is obtained through matrix operation, and consequently, various configurations of automobile double planetary gear structures are obtained. Finally, the effectiveness of this approach is validated through simulation. Results indicate that with the support of the matrix representation method, the optimal configuration can be selected automatically by computer, which avoids manual calculation and comparison, thereby conserving significant effort and time. References | Related Articles | Metrics

Chemical Industry and Light Industry

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Numerical simulation study of tunnel wastewater treatment technology based on grating-type micro-vortex flocculation ZHANG Dong-hai 2024, 50 (1):  68-75.  Abstract ( 33 )   PDF (5370KB) ( 28 )   Save To explore the feasibility of micro-vortex coagulation technology in tunnel wastewater treatment process, a numerical simulation is conducted to investigate the the characteristics of the coagulation flow field produced by the grid micro vortex generator with different characteristics.Furthermore, a hydraulic flocculation validation experiment is conducted using the optimal combination of grating-types for simulated tunnel wastewater with turbidity of 1 300 NUT. The results show that the thickness of the grid bars primarily affects the turbulent kinetic energy of the fluid in the flow field and the consumption degree of turbulent dissipation in the initial coagulation stage. The square grid bars with a side length of 5 mm are better suited to maintain the kinetic energy required in the whole coagulation process in the flow field. The spacing of the grid bars alter their blocking effect of the grid bars on the fluid. When the spacing is 11 mm, the fluid can provide higher turbulent kinetic energy and turbulent dissipation for flocculation reaction. The length of grid bars mainly affects the energy evolution of the flow field in the axial direction. The grid bars of 400 mm, 600 mm and 800 mm extend the energy distribution distance of the fluid in the flow field, providing sufficient energy for aggregation of the flocs in the rear section of the reactor. The hydraulic flocculation verification experiment of simulated tunnel wastewater with turbidity of 1 300 NTU was carried out using the optimal combination of grid bars, resulting in a stable effluent turbidity of the wastewater of less than 50 NTU. References | Related Articles | Metrics

Automation Technique and Computer Technology

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Image blind restoration based on edge constraint and norm ratio ZHAO Xiao-qiang, WANG Tao 2024, 50 (1):  76-83.  Abstract ( 39 )   PDF (1595KB) ( 38 )   Save The image blur caused by motion has always been a challenging problem. The image prior information used in the classical moving image blind restoration algorithm is often too simple. The sparse theory has a good restoration effect, and it usually estimates the point spread function directly using the gradient edges of the degraded image. But the gradient edge of the degraded image contains many weak edges and pseudo edges, which can affect the estimation of the point spread function. To solve the above problems, a blind image restoration algorithm based on edge constraint and norm ratio is proposed. First, the edge of the degraded image is constrained to obtain strong edge structure of the image, which improves the accuracy of point spread function estimation. Then, the sparse penalty constraint of norm ratio is constructed for the clear image to be estimated, and the obtained strong edge information is combined with the constructed norm ratio penalty constraint to guide the restoration of point spread function. When restoring the point spread function, the coarse to fine multiscale iterative estimation of the point spread function makes the iterative maximum scale more accurate. Finally, the image is solved by non-blind deconvolution to restore it. The algorithm combines the edge information of the degraded image with the constructed norm ratio penalty constraint to guide the restoration of the point spread function. It can suppress a large number of artifacts generated in the process of image restoration. Experimental results show that the algorithm has a good effect on restoring the edge details of the image, which can get a high-quality restored image. References | Related Articles | Metrics

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Sliding mode predictive control of Vienna rectifier based on grid voltage sensorless JIANG Ya-fei, ZHAO Gang 2024, 50 (1):  84-89.  Abstract ( 35 )   PDF (3706KB) ( 40 )   Save The control system design of the Vienna rectifier is inseparable from the parameters of grid voltage. However, conventional voltage sensors increase the cost and complexity of the system. Therefore, a model predictive control strategy for the Vienna rectifier without a grid voltage sensor is proposed in this paper. First, the mathematical model of virtual flux for the Vienna rectifier was established to estimate the power grid voltage. A second-order low-pass filter was adopted to eliminate the initial integral value and DC bias problem, which in turn improved the observation effect. Secondly, combined with the direct power mode predictive control(DPMPC),the switching sequence of the three-bridge arm was obtained to minimize the power tracking error. The results show that the proposed control strategy has low harmonic content. The voltage can accurately track the given value. It has good steady-state and dynamic performance. References | Related Articles | Metrics

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Power equalization method of CHB multilevel inverter based on carrier reconfiguration GENG Zhan-quan, XING Yue 2024, 50 (1):  90-95.  Abstract ( 30 )   PDF (4851KB) ( 34 )   Save Aiming at the disadvantage of the unbalanced output power of four units of Cascaded H-bridge (CHB) nine-level inverter under traditional carrier amplitude shift modulation, an improved power equalization strategy is proposed based on carrier reconstruction in this paper, which can effectively reduce the number of carriers. Through the secondary power equalization process, the output power equalization among the four units of the cascaded H-bridge nine-level inverter is realized. First, the power balance between the four units is realized by the carrier reconstruction method, and then the actual drive signal of the switch tube is obtained by performing a 1/4 cycle logic interchange of the drive signal of the switch tube, to realize the power balance of the whole unit under full modulation Simulation and experimental results show that this strategy can achieve a power balance of four cascaded H-bridge units based on effectively reducing the number of carriers. References | Related Articles | Metrics

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3D handwriting recognition of smartphone based on LSTM ZHANG Le, BAO Guang-bin, GUO Lin, WU Li 2024, 50 (1):  96-103.  Abstract ( 51 )   PDF (4345KB) ( 76 )   Save Traditional sensors are prone to receive the interference of external environmental factors due to achieving human-machine interaction in specific spatial area. 3D handwriting recognition of smartphones based on the long short-term memory (LSTM) neural network is proposed, which can be used in human-machine interaction in non-specific 3D spaces. First, three-axis acceleration sensors of smartphones are used to collect data which perform pre-processing operations to construct a 3D handwriting recognition dataset. Then, the 3D handwriting recognition model based on LSTMis constructed and pre-trained by adopting the constructed datasets. Finally, the trained model is applied to implement 3D handwriting classification recognition for smartphones. By testing on a self-built non-dependent user dataset, experimental results show that the proposed model can achieve the accuracy rate of 86.4%, recall rate of 88.1%, precision rate of 88.4%, and F1 score of 88.0%. References | Related Articles | Metrics

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Research on automatic generation method of test cases for charging device communication protocol conformance test HE Xue-feng, JIA Jun-guo, LI Xu-ling 2024, 50 (1):  104-109.  Abstract ( 30 )   PDF (588KB) ( 21 )   Save Current communication protocol consistency test methods between the charger and battery management system (BMS) is mainly designed according to expert experience, which lacks theoretical support, resulting in weak test coverage and unconvincing test results. To effectively solve the above problem, a communication protocol consistency test method was designed here based on a finite state machine (FSM). First, through a detailed interpretation of Protocol GB/T 27930—2015, the communication process between the charger and BMS was analyzed using the proposed method to ensure the consistency of communication between different entities of the protocol. Secondly, the unique input/output (UIO) was exploited on FSM to get the test sequence and the final test case set. The recursive algorithm was adopted to consider the pre-test cases so that each test case had complete input and output. The results show that the consistency testing method based on FSM not only provides theoretical support for the communication protocol consistency testing process between charger and BMS, but also has strong reuse ability compared to the experience-based method. References | Related Articles | Metrics

Architectural Sciences

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Non-stationary random response of pedestrian bridge under pedestrian load excitation ZHU Qian-kun, ZENG Xin 2024, 50 (1):  110-115.  Abstract ( 39 )   PDF (2727KB) ( 54 )   Save The differential quadrature-probabilistic collocation (DQ-PEM) method, which combines the virtual excitation method and differential quadrature method, is used to study the non-stationary random response of pedestrian bridges under pedestrian excitation. Different from the previous virtual excitation method, this method, based on the simplified spectral model, establishes the spectral density of the pedestrian forcing function, to obtain the multi-modal of the multi-degree of freedom system under pedestrian load. The accuracy and effectiveness of the proposed method are verified by the engineering case. Furthermore, the stochastic vibration problems of beam-type structures under pedestrian loading at different velocities and under various constraint conditions are discussed. References | Related Articles | Metrics

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Dynamic model establishment and response analysis of frame anchors supporting structure YE Shuai-hua, FENG Wen-gang, LI Jing-bang, TAO Hui 2024, 50 (1):  116-122.  Abstract ( 40 )   PDF (2252KB) ( 49 )   Save In order to analyze the dynamic response of frame anchors supporting structure under seismic effect, a mid span column element was taken as the object, and the dynamic earth pressure was analyzed by considering the amplification effect of slope acceleration. Then the column was simplified as a vertical member with uniform bending stiffness. According to the working mechanism of the anchor rod, the free section was simplified as a line spring, and the anchor section was simplified as a line spring and a Newton viscous pot under the consideration of the influence of soil damping. The slope foot of the support structure was simplified as a fixed end constraint, then the simplified dynamic response model of supporting structure was established. The dynamic response of the supporting structure was solved by the force method and graph multiplication method, and the relationship between the dynamic bending moment as well as dynamic displacement of the supporting structure and the slope height was established. The alogorithm was compared with the result of Geo-Studio finite element software to verify the rationality and feasibility of the model, which can provide corresponding reference for such engineering design and dynamic research of supporting structure under earthquake. References | Related Articles | Metrics

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Damage identification of transverse connection members of T-beam bridges based on damage factors WANG Li-xian, ZHAO Jun-hao, DI Sheng-kui, XIANG Chang-sheng, DANG Cong 2024, 50 (1):  123-131.  Abstract ( 36 )   PDF (3580KB) ( 63 )   Save In recent years, prefabricated T-girder Bridges have been widely used in China. Damage identification of transverse connection members, which is the most vulnerable locations of Bridges, has become a hot issue. This study simplifies the transverse diaphragms of T-beam bridges into equally rigid bridge decks, employing a spring system to simulate the force and deformation of transverse connection components. The theoretical calculation of damage factors for transverse connection components in prefabricated T-beam bridges is proposed, considering the effects of shear force, lateral force, and flange deformation. The theoretical calculation results by MATLAB were compared with the numerical simulation results by ANSYS to verify the effectiveness of the damage factor. Furthermore, through the comparison between 7 simulated conditions and 3 actual conditions, it is found that the closer the load position is to the damaged transverse connection member, the higher the accuracy of damage identification. References | Related Articles | Metrics

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Wavelet ridge extraction based on improved Carazy Climber algorithm ZHAO Li-jie, LI Wen-wen, LIU Jin, JIN Dong-li 2024, 50 (1):  132-138.  Abstract ( 44 )   PDF (4298KB) ( 28 )   Save For the problems of time-consuming and low efficiency of extracting multiple wavelet ridges using the traditional Crazy Climber algorithm, an improved Crazy Climber algorithm in simulating normalizing cooling was proposed. The continuous wavelet transform is applied to the response of the structural vibration. In the time-frequency plane composed of the wavelet coefficients amplitudes, the wavelet ridge points are tracked by the simulating normalizing cooling algorithm to make each random point gather on the ridge line, eliminating the operation time. Through the numerical simulation of single-degree of freedom and multi-degree of freedom system, the computational efficiency and recognition accuracy of the proposed algorithm are compared with that of the traditional Crazy Climber algorithm, and the advantages of the proposed algorithm are demonstrated. References | Related Articles | Metrics

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Influence of activated coal gangue powder on performance of coal gangue coarse aggregate concrete YAN Jie, SHAN Dou-dou, WANG Xiao-tian, YU Xu-tao, LIU Xing-long, XIE Jun 2024, 50 (1):  139-145.  Abstract ( 48 )   PDF (2925KB) ( 55 )   Save Activated coal gangue powder (CGP) was prepared by thermal activation method, which was mixed with coal gangue coarse aggregate (CGA) as mineral admixture to form coal gangue coarse aggregate concrete. The effects of CGP content on the pore structure and microstructure of concrete with different gangue coarse aggregate replacement rates were studied by mercury injection, nitrogen adsorption and scanning electron microscopy. The results show that the compressive strength of coal gangue coarse aggregate concrete is affected by different CGP content and CGA replacement rate. When CGP replacement rate is 15% and CGA replacement rate is 100%, the compressive strength of all coal gangue coarse aggregate concrete increases the most compared with the reference group. The addition of CGP reduces the chloride ion diffusion coefficient of coal gangue coarse aggregate concrete and improves the chloride ion permeability resistance of specimens. CGP can reduce the concentration of alkali ion in the hydration system, promote the hydration reaction of cement clinker, and increase the harmless holes, and optimize the internal pore structure of coarse aggregate concrete with coal gangue. References | Related Articles | Metrics

Scientific

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Interior elements in topological systems with its applications BAI Rong-rong, WU Hong-bo 2024, 50 (1):  146-151.  Abstract ( 39 )   PDF (421KB) ( 44 )   Save The concept of interior elements of subsets has been introduced in topological systems, and the related properties of interior elements have been discussed. The operator of interior elements has been defined by extent mapping and interior element mapping between a set and a frame, and the method determining topological system by the operator of interior elements has been given. The continuous mapping between topological systems is characterized by the interior elements of topological systems. References | Related Articles | Metrics

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Minimal norm least square Toeplitz solution of quaternion matrix equation (A1XB1,…,AkXBk)=(C1,…,Ck) SHI Jun-ling, LI Ying, WANG Tao, ZHANG Dong-hui, QIU Xin 2024, 50 (1):  152-157.  Abstract ( 48 )   PDF (426KB) ( 52 )   Save Based on the real representation of the quaternion matrix, combined with the matrix H-representation and semi-tensor product of matrices, an effective method for solving the minimal norm least square Toeplitz solution of the quaternion matrix equation (A1XB1,…,AkXBk)=(C1,…,Ck) is proposed in this paper. The necessary and sufficient condition for the existence of Toeplitz solution to the quaternion matrix equation are provided, and a general expression of solutions is also obtained. The numerical algorithm is given, and examples are given to verify the effectiveness of the method in terms of error and computation time. References | Related Articles | Metrics

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Some characterizations on odd deficient-perfect numbers ZHANG Si-bao 2024, 50 (1):  158-167.  Abstract ( 34 )   PDF (484KB) ( 81 )   Save In order to study the existence of odd-deficient perfect numbers with five different prime factors, the problem whether odd positive integer n with five different prime factors satisfy the definition of the odd deficient perfect number is discussed by using the elementary method. Several conclusions indicating that there are three classes of odd positive integers n with five different prime factors are not odd deficient perfect number. References | Related Articles | Metrics

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Enumeration of height restricted Dyck paths WANG Ya-qin 2024, 50 (1):  168-172.  Abstract ( 41 )   PDF (434KB) ( 43 )   Save For the enumerative question of a type of height-restricted Dyck paths from (0,0) to (n,k), the system of linear equations of the associated generating functions are derived by applying the recurrence relations, and the corresponding enumerative formulas are obtained by the linear algebraic method. References | Related Articles | Metrics