最新刊期
      卷 62 ， 期 6 ， 2023

        Research articles

      • CHEN Zishen,YANG fang,GAO Shiyou
        Vol. 62, Issue 6, Pages: 1-10(2023) DOI: 10.13471/j.cnki.acta.snus.2023D020
        摘要：The hourly rainfall of the four central cities in the Guangdong-Hong Kong-Macao Greater Bay Area （GBA） during the pre-and post-flood seasons over a period of about 60 years is studied in this paper. The maximum 1-hour rainfall （rain peak）， the maximum 6-hour rainfall， and the maximum 24-hour rainfall are taken as samples. The asymmetric Archimedean Gumbel-Hougaard extreme copula is used to construct a typical design of rainstorm hydrographs for the joint distribution of rainfall in three durations. The main conclusions are as follows： （1） The urban design rainstorm value calculated from the joint distribution of 3 durations of rainfall is greater than the combined distribution of 2 durations and the design rainstorm value of a single period， and the overall effect of the design rainstorm hydrograph with the same frequency amplification is relatively optimal， which provides a new idea for the research method of urban design rainstorm hydrograph. （2） The design of rainstorm hydrographs for 4 cities based on the joint distribution of 3 rainfall durations more objectively represents the rain pattern characteristics of the cities in which they are located， providing a new method for further research on the design of rain patterns. （3） The typical design of rainstorm hydrographs constructed with the maximum rainfall of 24 hours is representative. The typical design of rainstorm hydrographs amplified with the same frequency can be used as a reference for the city design of drainage and waterlogging control engineering in flood season.  
        关键词：asymmetrical extreme value Copula;design rainstorm hydrographs;‘OR’ return period;rainfall patterns   
        232
        |
        65
        |
        0
        <HTML>
        <L-PDF><Meta-XML>
        <引用本文> <批量引用> 40080518 false
        发布时间：2023-12-08
      • GAO Xue,GAO Yan,SUN Ketian,SHI Tiangen
        Vol. 62, Issue 6, Pages: 11-21(2023) DOI: 10.13471/j.cnki.acta.snus.2023D023
        摘要：Particle breakage affects the macro-mechanical properties of calcareous sand and also changes the mechanism of energy dissipation at the micro-scale. To explore the relationship between particle breakage and energy evolution of calcareous sand during shearing， PFC2D simulations of shearing tests of calcareous sand were performed considering particle breakage. The results show that： 1） Particles continually break during the entire shearing process. With the progress of shearing， the same crushing requires more input work and the particle crushing makes the shear band disperse. 2） The friction energy dissipation plays an important role in the whole shearing process. Particle breakage not only affects the accumulation of strain energy but also influences the distribution of friction energy consumption. 3） The friction energy of calcareous sand with a low crushing rate is mainly produced by particle rearrangement in the shear band， while the friction dissipation of calcareous sand with a high crushing rate is more attributed to the movement of sub-particles produced by the breakage. 4） The change of energy also corresponds to the macroscopic development of stress and strain. With the increase of breakage dissipation， the strain energy decreases， and the energy of particle transition also decreases， which finally leads to the shear response of dense sand changing to that of loose sand.  
        关键词：calcareous sand;DEM;energy dissipation;particle breakage;shear band   
        113
        |
        27
        |
        0
        <HTML>
        <L-PDF><Meta-XML>
        <引用本文> <批量引用> 38800258 false
        发布时间：2023-12-08
      • XIONG Mei,ZHOU Qiuwen,SUN Rongguo
        Vol. 62, Issue 6, Pages: 22-30(2023) DOI: 10.13471/j.cnki.acta.snus.2023D014
        摘要：To explore the characteristics of temperature and rainfall in Guizhou Province, the daily temperature and rainfall data of Guizhou weather stations from 1951-2021 were analyzed at different time scales by using methods such as linear trend, cumulative anomaly, Mann-Kendal(M-K) test, and R/S (re-scale range analysis). The results show that the increasing rate of the annual mean, annual maximum, and minimum temperature were 0.08 °C/10a, 0.11 °C/10a, and 0.25 °C/10a, respectively, and the annual minimum temperature was the most sensitive to global warming. The autumn and winter seasons contributed the most to the annual mean temperature increase, mainly influenced by Siberian high pressure and East Asian winter winds. The temperature evolution of Guizhou was generally consistent with that of China and has increased significantly since the 1990s. The annual mean temperature in 2009 showed a significant increase. The annual rainfall decreased significantly at a rate of 23.46 mm/10a. The rainfall in spring, summer, and autumn showed a downward trend, while in winter it showed an upward trend. The rainfall in summer accounted for 51% of the annual rainfall. The annual rainfall has declined obviously since the 1980s. 1986, 1990, and 1992 showed sharp decrease in annual, spring, and autumn precipitation, respectively. The annual rainfall is negatively correlated with temperature. The Hurst index of temperature and rainfall indicated that the temperature in Guizhou continued to rise and the rainfall continued to decline, and the climate in Guizhou may continue to be warm and dry. This study provided a reference for predicting the future temperature and rainfall in Guizhou Province.  
        关键词：rainfall;temperature;trend analysis;Guizhou province   
        105
        |
        18
        |
        0
        <HTML>
        <L-PDF><Meta-XML>
        <引用本文> <批量引用> 40165277 false
        发布时间：2023-12-08
      • FAN Yongzhuo,LI Xinguo
        Vol. 62, Issue 6, Pages: 31-39(2023) DOI: 10.13471/j.cnki.acta.snus.2023D024
        摘要：To more accurately understand the soil salinity of different land use types in the lakeside oasis of Bosten Lake， Xinjiang， three methods of competitive adaptive reweighted sampling （CARS）， successive projection algorithm （SPA）， and competitive adaptive reweighted-successive projection algorithm （CARS-SPA） were applied to screen the characteristic bands of soil conductivity hyperspectral data of different land use types， based on the full band and characteristic bands. The estimation models of soil conductivity of the lakeshore oasis were constructed based on the full band and characteristic bands combined with BP neural network to compare the accuracy of estimation models in different ways. The results showed that： （1） the mean values of soil conductivity of cropland， forest land， wasteland， and overall land are 0.84， 5.43， 5.78， and 3.26 mS/cm， respectively； the overall soil conductivity of the lakeshore oasis is 2.42 mS/cm higher than the mean value of cropland， 2.17 and 2.52 mS/cm lower than forest land and wasteland. （2） The CARS-SPA method can reduce the number of bands input to the model and improve the efficiency of the model. The number of characteristic bands for screening the electrical conductivity of cropland， forestland， wasteland， and overall land soil only accounts for 0.71%， 0.59%， 0.06%， and 1.00% of the full bands. （3） Constructing separate estimation models for soil conductivity of cropland， forest land， and wasteland significantly improves the estimation accuracy of soil conductivity in the study area. Among the three models of FDR-CARS-BP， FDR-SPA-BP， and FDR-CARS-SPA-BP， the average R2 of soil conductivity modeling for cropland， forest land， and wasteland increased by 0.12， 0.14， and 0.15， respectively， compared with the overall soil modeling， the FDR-CARS-SPA-BP model is the optimal model for hyperspectral estimation of soil conductivity in the study area.  
        关键词：soil conductivity;land use types;hyperspectral data;CARS-SPA;BP neural network   
        57
        |
        12
        |
        0
        <HTML>
        <L-PDF><Meta-XML>
        <引用本文> <批量引用> 40165251 false
        发布时间：2023-12-08
      • MA Xi,LI Chuanhao
        Vol. 62, Issue 6, Pages: 40-49(2023) DOI: 10.13471/j.cnki.acta.snus.2023C011
        摘要：Development of an efficient technique for nitrate treatment is urgent in view of the toxicity and potential carcinogenicity of nitrate nitrogen stably present in wastewater. The electrochemical method， with the advantages of high efficiency， stability and product controllability， has become the most promising wastewater purification process for purifying nitrate pollution in wastewater. However， traditional powder electrocatalysts are easily inhibited in complex water bodies， and finding a more efficient electrocatalytic material is necessary. In this study， two-dimensional cobalt-based nanosheet cathodes （Co NS/CC） were prepared using template and calcination methods， and investigated the performance of electrocatalytic reduction of nitrate. The experimental results showed that Co NS/CC with a calcination temperature of 700 ℃ exhibited the best electrocatalytic denitrification performance with a high reaction rate constant （2.88 h-1） and nitrate removal efficiency （95%） in 1 h. In addition， Co NS/CC-700 exhibited excellent electrocatalytic denitrification for a high concentration of nitrate， different pH values of solutions and wastewater with complex components. Electron paramagnetic resonance （EPR） and tertiary butyl alcohol （TBA） capture experiments confirmed that Co NS/CC-700 facilitates nitrate reduction through the generation of adsorbed hydrogen （H*）. In addition， Co NS/CC-700 has high stability and environmental adaptability. In conclusion， Co NS/CC-700 is an electrocatalytic material with high catalytic activity and stability， which is potentially applicable for electrocatalytic treatment of nitrate-containing wastewater.  
        关键词：electrocatalytic reduction of nitrate;two-dimensional cobalt-based nanosheet cathode;purification of nitrate containing wastewater   
        69
        |
        13
        |
        0
        <HTML>
        <L-PDF><Meta-XML>
        <引用本文> <批量引用> 43085613 false
        发布时间：2023-12-08
      • ZHAO Lihong,PENG Guoqiang,HAO Chengxin,SU Dan,JIANG Chunxu,WANG Zuocheng
        Vol. 62, Issue 6, Pages: 50-60(2023) DOI: 10.13471/j.cnki.acta.snus.2022C023
        摘要：The enantiomerism of amphoteric phenylalanine （S-Phe） with divalent calcium （Ca2+） complex （Phe·Ca2+） in aqueous solution was studied by using M06-2X and MN15 methods based on DFT （density functional theory） and SMD model method to deal with solvent effect. The study of reaction channel found that enantiomerism of S-Phe·Ca2+ can be realized on three channels in which protons use N as bridge， O as bridge ， O and N combine to form a bridge. The calculation shows that the reaction channel of H proton transfer with amino N as bridge has advantages under the effect of recessive solvent and its energy barrier is 227.5 kJ/mol， and the barrier is reduced to between 108.0 and 117.6 kJ/mol under the dominant solvent effect. According to the research results， chiral Phe·Ca2+ complex is hard to racemize in aqueous solution， and it might be safer to be used for life supplementing phenylalanine and calcium.  
        关键词：phenylalanine;calcium ion （Ca2+）;DFT（density functional theory）;optical isomerism;energy barrier   
        25
        |
        10
        |
        0
        <HTML>
        <L-PDF><Meta-XML>
        <引用本文> <批量引用> 34790960 false
        发布时间：2023-12-08
      • WANG Di,YANG Ying,CHEN Yu,FEI Weifan,LI Weihua
        Vol. 62, Issue 6, Pages: 61-70(2023) DOI: 10.13471/j.cnki.acta.snus.2023C002
        摘要：BiFeO3 was prepared by carbon adsorption co-precipitation method， and then BiFeO3/H2O2 Fenton-like system was constructed to degrade tetracycline in wastewater. The effects of initial pH value， catalyst BiFeO3 dosing and H2O2 concentration on the degradation of tetracycline in wastewater were investigated by setting single-factor conditions. The samples were characterized using X-ray diffraction （XRD）， field emission scanning electron microscopy （SEM）， X-ray photoelectron spectroscopy （XPS）， and fully automated surface area and porosity analyzer （BET） etc. The experimental results showed that the optimal reaction conditions for the degradation of tetracycline were the initial pH value of 4， BiFeO3 injection amount of 1.0 g/L and H2O2 concentration of 20 mmol/L， under which the degradation rate of tetracycline was 95.18%. The degradation rate of tetracycline in wastewater by the Fenton-like system did not change significantly after four reapplications of BiFeO3， indicating that it is stable and reusable. The radical capture experiments showed that the most important active species for the degradation of tetracycline in this system are hydroxyl radicals （·OH） and superoxide radicals （·O2-） . Based on the findings， we proposed a mechanism for the degradation of tetracycline by BiFeO3 activated H2O2. This study provides a reference for the application of advanced oxidation technology on H2O2 in the field of wastewater treatment.  
        关键词：BiFeO3;H2O2;Fenton-like;tetracycline;wastewater   
        44
        |
        5
        |
        0
        <HTML>
        <L-PDF><Meta-XML>
        <引用本文> <批量引用> 38804887 false
        发布时间：2023-12-08
      • LI Zhenyu,YE Lefu,GAN Yangguang,CHI Yang,WANG Liqing,XU Zhen,FU Xue
        Vol. 62, Issue 6, Pages: 71-79(2023) DOI: 10.13471/j.cnki.acta.snus.2023E026
        摘要：Through exploring whether wood vinegar has a synergic effect on the control of Myzus persicae with two kinds of internal absorption agents， dinotefuran and spirulin ethyl， so as to provide certain research basis for green control of Myzus persicae.The synergistic effect of wood vinegar on two pesticides was determined， and the effect of wood vinegar on the detoxification enzyme activity in Myzus persicae was also measured. The efficacy of wood vinegar combined with two pesticides on Myzus persicae populations and potted plants was then tested. The results show that：1） The synergic ratio of 5 mL/L wood vinegar to dinontefuran control Myzus persicae was 25.9， and the synergic ratio of 20 mL/L wood vinegar to spiralate control Myzus persicae was 20.3. 2） Wood vinegar reduces the resistance of Myzus persicae to insecticides by inhibiting the activity of detoxifying enzymes （GST， AChE， CarE） in their bodies， thereby facilitating the effectiveness of the two insecticides. 3） Through pot experiment， it was found that the wood vinegar diluted 200 times significantly enhanced the control effect of dinotefuran at three concentrations against Myzus persicae， and played a synergistic role. The wood vinegar diluted by 100 or 200 times has a significant improvement on the control of spirochete against Myzus persicae. 4） High concentration of wood vinegar could inhibit the growth of Chinese cabbage plants， and wood vinegar inhibits the synthesis of chlorophyll in chinese cabbage leaves. The main impact on the Myzus persicae population is a decrease in population fertility. In conclusion， wood vinegar can be used as a green synergist to delay the resistance of peach aphid to spiralate and dinotefuran and enhance the control effect.  
        关键词：wood vinegar;Myzus persicae;synergism;detoxification enzyme   
        28
        |
        4
        |
        0
        <HTML>
        <L-PDF><Meta-XML>
        <引用本文> <批量引用> 40166686 false
        发布时间：2023-12-08
      • LI Yetao,HUANG Min,HUANG Chunting,ZHANG Xiaolan
        Vol. 62, Issue 6, Pages: 80-88(2023) DOI: 10.13471/j.cnki.acta.snus.2023D010
        摘要：In this paper， we propose a path splicing model to estimate the long path travel time on urban roads using the automatic vehicle identification （AVI） data. The model requires two conditions to be met when splicing the sub-paths： public nodes exist and the traffic status is similar. A target path is split into a splicing scheme composed of several subpaths whose variance is the least. Based on the proposed traffic state， the travel time distributions are obtained by fitting the travel time under different states using the Burr distribution. Next， the method assigns target travel time to the sub-paths， thus， the travel time probability of the target path is the accumulation of the probability of all time assignments. The study shows that the error between the average path travel time of the proposed method and the real path is 3.04%， and the JS divergence between the travel time distribution of the method and the real path is 0.05. The estimated path travel time is reliable， which can provide a data basis for subsequent research.  
        关键词：path travel time;path splicing;traffic status;distribution of travel time   
        28
        |
        4
        |
        0
        <HTML>
        <L-PDF><Meta-XML>
        <引用本文> <批量引用> 40166624 false
        发布时间：2023-12-08
      • DAI Beibing,DENG Linjie,CHEN Zhigang
        Vol. 62, Issue 6, Pages: 89-97(2023) DOI: 10.13471/j.cnki.acta.snus.2023B009
        摘要：In this study， 3D DEM simulations have been conducted to investigate the effect of inter-particle friction on the macro and micro properties of granular heaps such as the angle of repose， stress distribution at the bottom， distribution of projected contact force， and number of strong and weak force chains， etc. The results indicate that increasing the inter-particle friction coefficient leads to an increase in the angle of repose, which eventually reaches a stable value. Additionally, the peak stress at the bottom migrates from the center outward, and the degree of reduction in contact force at the bottom center relative to the peak value increases. This results in a more pronounced stress dip and arching effect. The orientation angle of the conical surface, along which the maximum projection of contact forces occurs, increases with the increasing inter-particle friction coefficient and eventually stabilizes. The preferential direction for the mobilization of arching effect is oriented at 15°~25° relative to the vertical direction.  
        关键词：granular heaps;discrete element method;friction coefficient;angle of repose;arching effect   
        27
        |
        5
        |
        0
        <HTML>
        <L-PDF><Meta-XML>
        <引用本文> <批量引用> 39125607 false
        发布时间：2023-12-08
      • QIN Yingquan,LIU Zuoqiu,LIU Jike,LIU Guang
        Vol. 62, Issue 6, Pages: 98-106(2023) DOI: 10.13471/j.cnki.acta.snus.2023B031
        摘要：The semi-analytical periodic solution of a nonlinear aeroelastic system with freeplay was solved by the time-domain minimum residual method. First， the periodic solution of the aeroelastic system is expanded into the Fourier series， and the first N term is truncated as the approximate analytical solution. Then， the velocity and acceleration of the system are obtained by taking the derivative of the approximate solution in the time. And the displacement， velocity and acceleration functions are substituted back into the original aeroelastic system. Then，the problem of solving the semi-analytical solution is transformed into a nonlinear least-square optimization problem. Finally， such minimum value optimization problem is iteratively solved by the enhanced response sensitivity approach. In the above iteration， the Tikhonov regularization and “trust-region constraint” are used to enhance the algorithm’s convergence. Numerical examples show that the time-domain minimum residual method can quickly obtain high-precision semi-analytical solutions.  
        关键词：freeplay nonlinearity;the time-domain minimum residual method;periodic solution;Tikhonov regularization   
        24
        |
        3
        |
        0
        <HTML>
        <L-PDF><Meta-XML>
        <引用本文> <批量引用> 41909631 false
        发布时间：2023-12-08
      • WANG Xin,CHEN Zesen
        Vol. 62, Issue 6, Pages: 107-115(2023) DOI: 10.13471/j.cnki.acta.snus.2023B049
        摘要：Mild cognitive impairment （MCI） is both an intermediate state between normal aging and Alzheimer's disease and the key stage in the diagnosis of Alzheimer's disease. Therefore， early detection and treatment for potential elderly can delay the occurrence of dementia. In this study， a neural network-based multi-feature detection model for mild cognitive impairment was proposed， which exploits the characteristics of patients with obvious changes in linguistic performance. The model is based on extracting the linguistic features in natural speech and integrating the T-W matrix of the LDA model with the subject data and other multi-feature information as the input tensor of the TextCNN network. It achieved an accuracy of 0.93， a sensitivity of 1.00， a specificity of 0.8， and a precision of 0.9 on the DementiaBank dataset， which effectively improved the accuracy of cognitive impairment detection in the elderly by using natural speech.  
        关键词：mild cognitive impairment;natural speech;neural network model;multi-feature detection;speech analysis   
        46
        |
        13
        |
        0
        <HTML>
        <L-PDF><Meta-XML>
        <引用本文> <批量引用> 43400089 false
        发布时间：2023-12-08
      • PENG Yi,MA Xiaolin,YANG Qingqing
        Vol. 62, Issue 6, Pages: 116-126(2023) DOI: 10.13471/j.cnki.acta.snus.2023B051
        摘要：Aiming at the problems of energy limitation and physical layer security in the process of information transmission in CR-NOMA systems， a full-duplex multi-relay cooperative CR-NOMA system model based on wireless power transfer is constructed. Firstly， an optimal relay selection strategy is proposed based on multi-relay. Secondly，the approximate expressions of system security outage probability and security throughput are derived. Finally， the correctness of the theoretical analysis is verified by simulation. The effects of relay number， target security rate， interference power threshold， self-interference channel coefficient， and power splitting coefficient on system security performance are analyzed， which provides a feasible transmission strategy for CR-NOMA network security communication.  
        关键词：physical layer security;cognitive radio;non-orthogonal multiple access;simultaneous wireless information and power transfer;full duplex;artificial noise   
        26
        |
        4
        |
        0
        <HTML>
        <L-PDF><Meta-XML>
        <引用本文> <批量引用> 43004545 false
        发布时间：2023-12-08
      • WU Sha,WU Kuilin
        Vol. 62, Issue 6, Pages: 127-134(2023) DOI: 10.13471/j.cnki.acta.snus.2022A083
        摘要：The number of limit cycles bifurcated from the periodic annulus of two quadratic reversible Lotka-Volterra systems with non-genus 1 under small bifurcations is studied. Using the properties of complete Chebyshev systems to estimate the number of zeros of second-order Melnikov function， it is proven that the number of limit cycles bifurcated from the periodic annulus of the two quadratic reversible Lotka-Volterra systems are both 2 under quadratic perturbations.  
        关键词：reversible Lotka-Volterra system;Abelian integral;limit cycles;genus one   
        24
        |
        6
        |
        0
        <HTML>
        <L-PDF><Meta-XML>
        <引用本文> <批量引用> 40166594 false
        发布时间：2023-12-08
      • FAN Xinman,GAO Xing,ZHANG Zhaotai
        Vol. 62, Issue 6, Pages: 135-142(2023) DOI: 10.13471/j.cnki.acta.snus.2022A050
        摘要：The Koszulity of the operad 𝒜sLC■𝒟end in terms of the method of rewriting systems is proven, where 𝒜sLC■𝒟end is the Manin black product of the linear compatible operad of the associative 𝒜s and the dendriform operad 𝒟end.  
        关键词：operad;Koszulity;linear compatible operad;dendriform operad;Manin black product   
        25
        |
        3
        |
        0
        <HTML>
        <L-PDF><Meta-XML>
        <引用本文> <批量引用> 40983366 false
        发布时间：2023-12-08
      • NIU Bingjie,LAN Shiyi
        Vol. 62, Issue 6, Pages: 143-151(2023) DOI: 10.13471/j.cnki.acta.snus.2022A026
        摘要：For 0<κ<8， an expression of the probability that the trace of dipolar SLEκ in the upper half-plane H={z : Im z>0} from 1 to interval (-∞,-1] intersects a disk is derived. Next， we obtain an estimate of the probability that the trace of dipolar SLEκ in the strip domain Sπ={z : 0<Im z<π} from 0 to the upper boundary Rπ={z : Im z=π} intersects a disk is obtained. This generalizes the estimate of corresponding probability for chordal SLEκ in H to the case of dipolar SLEκ.  
        关键词：chordal SLEκ;dipolar SLEκ;intersection probability   
        26
        |
        6
        |
        0
        <HTML>
        <L-PDF><Meta-XML>
        <引用本文> <批量引用> 42220070 false
        发布时间：2023-12-08
      • ZHENG Weishan
        Vol. 62, Issue 6, Pages: 152-158(2023) DOI: 10.13471/j.cnki.acta.snus.2022A077
        摘要：Spectral methods are developed for solving fractional differential equations with vanishing delay numerically. Sharp error estimates are carried out， which indicates that the error of solution and the error of exact fractional derivative decay exponentially in both L∞ and Lω-μ,-μ2 . In the end， a numerical example is presented to confirm our theoretical findings.  
        关键词：fractional Volterra integro-differential equation;Jacobi collocation method;delay;sharp error estimate   
        36
        |
        14
        |
        0
        <HTML>
        <L-PDF><Meta-XML>
        <引用本文> <批量引用> 42220009 false
        发布时间：2023-12-08
      • ZHU Xuezhi,ZHANG Hong
        Vol. 62, Issue 6, Pages: 159-170(2023) DOI: 10.13471/j.cnki.acta.snus.2022A085
        摘要：Instrumental variables(IVs) are widely used in mediation analysis to effectively reduce causal effect bias due to unobserved confounding factors and reverse causal direction that cannot be handled with conventional causal inference methods. Most IV methods in the literature are designed for cross-sectional studies. Longitudinal data can better reflect causal paths than cross-sectional data, which provides observations of individual patterns of changes and measurements of event duration. To our knowledge, there is no IV method specifically tailored for longitudinal mediation analysis in the literature. A new IV method is proposed to estimate longitudinal mediation effects. Large sample properties, including consistency and asymptotic normality, are established for the new IV method. Simulation studies are provided to demonstrate the desired finite sample properties of the new method.  
        关键词：causal inference;Mendelian randomization;mediation analysis;longitudinal data   
        26
        |
        5
        |
        0
        <HTML>
        <L-PDF><Meta-XML>
        <引用本文> <批量引用> 42233277 false
        发布时间：2023-12-08
      • ZHAO Yali,CHEN Tianlan
        Vol. 62, Issue 6, Pages: 171-176(2023) DOI: 10.13471/j.cnki.acta.snus.2021A077
        摘要：By using the fixed point theorem in cones， the existence of negative convex solutions for a discrete mixed boundary value problem of p-Laplacian operator △φp△ut-1=ft,-u(t),  t∈2,T-1Z,△u1=0, uT=0 is studied， where  φps=sp-2s， p>1， f : 2,T-1Z×[0,+∞)→[0,+∞) is continuous.  
        关键词：p-Laplacian operator;discrete mixed boundary value problem;negative convex solutions;fixed point theorem;cone   
        43
        |
        14
        |
        0
        <HTML>
        <L-PDF><Meta-XML>
        <引用本文> <批量引用> 43168166 false
        发布时间：2023-12-08
      0