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Research on the refinement algorithm of surface loading deformation based on Green's function
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作者 Chenfeng Li Tengxu Zhang +3 位作者 Peibing Yang Lin He Yu Xia Wei Luan 《Geodesy and Geodynamics》 2025年第2期230-239,共10页
Surface deformation calculations due to environmental loading typically rely on the Preliminary Reference Earth Model(PREM),which assumes a homogeneous and isotropic Earth structure,leading to noticeable errors.To enh... Surface deformation calculations due to environmental loading typically rely on the Preliminary Reference Earth Model(PREM),which assumes a homogeneous and isotropic Earth structure,leading to noticeable errors.To enhance accuracy,the high-precision crustal model CRUST 1.0 is used to refine calculations of regional surface deformation caused by hydrological and non-tidal atmospheric loading.The improved model is applied to 27 Global Navigation Satellite System(GNSS)reference stations in the first phase of the Crustal Movement Observation Network of China(CMONOC),considering their geographical locations.Green's functions are employed to compute surface deformation at each site.Results indicate relative discrepancies of 11.78%and 14.14%for non-tidal atmospheric and hydrological loading compared to PREM,with vertical deformation differences reaching an average of 18.95%.Additionally,the distinct spatial distribution characteristics of the relative differences in each direction indicate that the improved RPREM model is more responsive to the mass variations derived from Gravity Recovery and Climate Experiment(GRACE).The results suggest that the improved PRREM model demonstrates higher sensitivity to loading variations than the PREM model.Utilizing the enhanced method of calculating surface deformation through the utilization of Green's function at the site could effectively reduce the calculation error caused by regional structure,leading to enhanced uniformity and isotropy of PREM. 展开更多
关键词 Loading deformation GNSS green's function PREM GRACE
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GENERALIZED COUNTING FUNCTIONS AND COMPOSITION OPERATORS ON WEIGHTED BERGMAN SPACES OF DIRICHLET SERIES
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作者 Min HE Maofa WANG Jiale CHEN 《Acta Mathematica Scientia》 2025年第2期291-309,共19页
In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditio... In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditions for a composition operator with zero characteristic to be bounded or compact on weighted Bergman spaces of Dirichlet series.The corresponding sufficient condition for compactness in the case of positive characteristics is also obtained. 展开更多
关键词 generalized counting function Dirichlet series composition operator weighted Bergman space
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Generalized multiple-mode prolate spheroidal wave functions multi-carrier waveform with index modulation
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作者 XU Zhichao LU Faping +5 位作者 ZHANG Lifan YANG Dongkai LIU Chuanhui KANG Jiafang AN Qi ZHANG Zhilin 《Journal of Systems Engineering and Electronics》 2025年第2期311-322,共12页
A generalized multiple-mode prolate spherical wave functions (PSWFs) multi-carrier with index modulation approach is proposed with the purpose of improving the spectral efficiency of PSWFs multi-carrier systems. The p... A generalized multiple-mode prolate spherical wave functions (PSWFs) multi-carrier with index modulation approach is proposed with the purpose of improving the spectral efficiency of PSWFs multi-carrier systems. The proposed method,based on the optimized multi-index modulation, does not limit the number of signals in the first and second constellations and abandons the concept of limiting the number of signals in different constellations. It successfully increases the spectrum efficiency of the system while expanding the number of modulation symbol combinations and the index dimension of PSWFs signals. The proposed method outperforms the PSWFs multi-carrier index modulation method based on optimized multiple indexes in terms of spectrum efficiency, but at the expense of system computational complexity and bit error performance. For example, with n=10 subcarriers and a bit error rate of 1×10^(-5),spectral efficiency can be raised by roughly 12.4%. 展开更多
关键词 prolate spherical wave function(PSWF) generalized multiple-mode index modulation spectral efficiency.
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Linear and Nonlinear Formulation of Phase Field Model with Generalized Polynomial Degradation Functions for Brittle Fractures
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作者 Ala Tabiei Li Meng 《Acta Mechanica Solida Sinica》 SCIE EI CSCD 2024年第5期643-661,共19页
The classical phase field model has wide applications for brittle materials,but nonlinearity and inelasticity are found in its stress-strain curve.The degradation function in the classical phase field model makes it a... The classical phase field model has wide applications for brittle materials,but nonlinearity and inelasticity are found in its stress-strain curve.The degradation function in the classical phase field model makes it a linear formulation of phase field and computationally attractive,but stiffness reduction happens even at low strain.In this paper,generalized polynomial degradation functions are investigated to solve this problem.The first derivative of degradation function at zero phase is added as an extra constraint,which renders higher-order polynomial degradation function and nonlinear formulation of phase field.Compared with other degradation functions(like algebraic fraction function,exponential function,and trigonometric function),this polynomial degradation function enables phase in[0,1](should still avoid the first derivative of degradation function at zero phase to be 0),so there is noconvergence problem.The good and meaningful finding is that,under the same fracture strength,the proposed phase field model has a larger length scale,which means larger element size and better computational efficiency.This proposed phase field model is implemented in LS-DYNA user-defined element and user-defined material and solved by the Newton-Raphson method.A tensile test shows that the first derivative of degradation function at zero phase does impact stress-strain curve.Mode I,mode II,and mixed-mode examples show the feasibility of the proposed phase field model in simulating brittle fracture. 展开更多
关键词 Nonlinear formulation generalized polynomial degradation function Brittle materials Stress-strain curve CONVERGENCE
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Evaluation of Generalized Error Function via Fast-Converging Power Series
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作者 Serdar Beji 《Advances in Pure Mathematics》 2024年第6期495-514,共20页
A generalized form of the error function, Gp(x)=pΓ(1/p)∫0xe−tpdt, which is directly associated with the gamma function, is evaluated for arbitrary real values of p>1and 0x≤+∞by employing a fast-converging power... A generalized form of the error function, Gp(x)=pΓ(1/p)∫0xe−tpdt, which is directly associated with the gamma function, is evaluated for arbitrary real values of p>1and 0x≤+∞by employing a fast-converging power series expansion developed in resolving the so-called Grandi’s paradox. Comparisons with accurate tabulated values for well-known cases such as the error function are presented using the expansions truncated at various orders. 展开更多
关键词 generalized Error function Gamma function Grandi’s Paradox Fast-Converging Power Series
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Ostrowski’s Type Inequalities for Generalized(h,m)−Preinvex Functions with Its Applications
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作者 LI Ran LIAN Tie-yan 《Chinese Quarterly Journal of Mathematics》 2024年第3期270-287,共18页
A new concept generalized(h,m)−preinvex function on Yang’s fractal sets is proposed.Some Ostrowski’s type inequalities with two parameters for generalized(h,m)−preinvex function are established,where three local fra... A new concept generalized(h,m)−preinvex function on Yang’s fractal sets is proposed.Some Ostrowski’s type inequalities with two parameters for generalized(h,m)−preinvex function are established,where three local fractional inequalities involving generalized midpoint type,trapezoid type and Simpson type are derived as consequences.Furthermore,as some applications,special means inequalities and numerical quadratures for local fractional integrals are discussed. 展开更多
关键词 generalized(h m)−preinvex function Hermite−Hadamard inequality Ostrowski inequality Simpson inequality
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Multiparameter generalized universal characters and multiparameter generalized B-type universal characters
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作者 Jingfan Wang Zhaowen Yan 《Chinese Physics B》 2025年第1期215-226,共12页
We construct the quantum fields presentation of the generalized universal character and the generalized B-type universal character,and by acting the quantum fields presentations to the constant 1,the generating functi... We construct the quantum fields presentation of the generalized universal character and the generalized B-type universal character,and by acting the quantum fields presentations to the constant 1,the generating functions are derived.Furthermore,we introduce two integrable systems known as the generalized UC(GUC)hierarchy and the generalized Btype UC(GBUC)hierarchy satisfied by the generalized universal character and the generalized B-type universal character,respectively.Based on infinite sequences of complex numbers,we further establish the multiparameter generalized universal character and the multiparameter generalized B-type universal character,which have been proved to be solutions of the GUC hierarchy and the GBUC hierarchy,respectively. 展开更多
关键词 symmetric functions quantum fields generating functions multiparameter generalized universal characters
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Integrated spatial generalized additive modeling for forest fire prediction:a case study in Fujian Province,China
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作者 Chunhui Li Zhangwen Su +4 位作者 Rongyu Ni Guangyu Wang Yiyun Ouyang Aicong Zeng Futao Guo 《Journal of Forestry Research》 2025年第3期208-223,共16页
The increasing frequency of extreme weather events raises the likelihood of forest wildfires.Therefore,establishing an effective fire prediction model is vital for protecting human life and property,and the environmen... The increasing frequency of extreme weather events raises the likelihood of forest wildfires.Therefore,establishing an effective fire prediction model is vital for protecting human life and property,and the environment.This study aims to build a prediction model to understand the spatial characteristics and piecewise effects of forest fire drivers.Using monthly grid data from 2006 to 2020,a modeling study analyzed fire occurrences during the September to April fire season in Fujian Province,China.We compared the fitting performance of the logistic regression model(LRM),the generalized additive logistic model(GALM),and the spatial generalized additive logistic model(SGALM).The results indicate that SGALMs had the best fitting results and the highest prediction accuracy.Meteorological factors significantly impacted forest fires in Fujian Province.Areas with high fire incidence were mainly concentrated in the northwest and southeast.SGALMs improved the fitting effect of fire prediction models by considering spatial effects and the flexible fitting ability of nonlinear interpretation.This model provides piecewise interpretations of forest wildfire occurrences,which can be valuable for relevant departments and will assist forest managers in refining prevention measures based on temporal and spatial differences. 展开更多
关键词 Forest fire prediction Logistic regression Spatial generalized additive model Spline functions Piecewise effects
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Formation mechanism of cluster-arranged layers in Mg-Y-Zn alloy:A density functional theory study
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作者 Ryosuke Matsumoto Naoki Uemura 《Journal of Magnesium and Alloys》 2025年第8期3702-3712,共11页
A sparsely introduced basal intrinsic 2-type stacking fault(I_(2)-SF)with a dense segregation of clusters(cluster-arranged layer;CAL)inα-Mg exerts a sufficient strengthening effect with a reduced content of additive ... A sparsely introduced basal intrinsic 2-type stacking fault(I_(2)-SF)with a dense segregation of clusters(cluster-arranged layer;CAL)inα-Mg exerts a sufficient strengthening effect with a reduced content of additive elements.Moreover,the dynamic nucleation and growth of CALs during deformation largely improves the creep resistance.This paper analyzes the cosegregation behaviors of yttrium(Y)and zinc(Zn)atoms at an I_(2)-SF in bulk and at basal edge dislocations using density functional theory calculations.We also study the modification of the generalized stacking-fault energy(GSFE)curves associated with the cosegregation.The segregation energies of Y and Zn atoms in the I_(2)-SF are relatively small during the initial segregation of a cluster,but increases stepwise as the cluster grows.After introducing Y and Zn atoms in the I_(2)-SF in an energetically stable order,we obtain an L1_(2)-type cluster resembling that reported in the literature.Small structural changes driven by vacancy diffusion produce an exact L1_(2)-type cluster.Meanwhile,the core of the Shockley partial dislocation generates sufficient segregation energy for cluster nucleation.Migration of the Shockley partial dislocation and expansion of the I_(2)-SF part are observed at a specific cluster size.The migration is triggered by a large modification of the GSFE curve and destabilization of the hexagonal close-packed stacking(hcp)by the segregated atoms.At this point,the cluster has reached sufficient size and continues to follow the growth in the I_(2)-SF part.According to our findings,the CAL at elevated temperature is formed through repeated synchronized behavior of cluster nucleation at the Shockley partial dislocation,dislocation migration triggered by the destabilized hcp stacking,and following of cluster growth in the I_(2)-SF part of the dislocation. 展开更多
关键词 generalized stacking-fault energy Basal dislocation Segregation Density functional theory Long-period stacking-ordered phase Cluster-arranged layer
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A Basis Function Generation Based Digital Predistortion Concurrent Neural Network Model for RF Power Amplifiers
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作者 SHAO Jianfeng HONG Xi +2 位作者 WANG Wenjie LIN Zeyu LI Yunhua 《ZTE Communications》 2025年第1期71-77,共7页
This paper proposes a concurrent neural network model to mitigate non-linear distortion in power amplifiers using a basis function generation approach.The model is designed using polynomial expansion and comprises a f... This paper proposes a concurrent neural network model to mitigate non-linear distortion in power amplifiers using a basis function generation approach.The model is designed using polynomial expansion and comprises a feedforward neural network(FNN)and a convolutional neural network(CNN).The proposed model takes the basic elements that form the bases as input,defined by the generalized memory polynomial(GMP)and dynamic deviation reduction(DDR)models.The FNN generates the basis function and its output represents the basis values,while the CNN generates weights for the corresponding bases.Through the concurrent training of FNN and CNN,the hidden layer coefficients are updated,and the complex multiplication of their outputs yields the trained in-phase/quadrature(I/Q)signals.The proposed model was trained and tested using 300 MHz and 400 MHz broadband data in an orthogonal frequency division multiplexing(OFDM)communication system.The results show that the model achieves an adjacent channel power ratio(ACPR)of less than-48 d B within a 100 MHz integral bandwidth for both the training and test datasets. 展开更多
关键词 basis function generation digital predistortion generalized memory polynomial dynamic deviation reduction neural network
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Prevalence and risk factors of depressive and anxiety symptoms and functional constipation among university students in Eastern China
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作者 Bo-Chen Jiang Jing Zhang +2 位作者 Man Yang Hai-Dong Yang Xiao-Bin Zhang 《World Journal of Psychiatry》 2025年第6期220-233,共14页
BACKGROUND Depression and anxiety are prevalent among university students worldwide,often coexisting with functional constipation(FC).Family relationships have been identified as crucial factors affecting mental healt... BACKGROUND Depression and anxiety are prevalent among university students worldwide,often coexisting with functional constipation(FC).Family relationships have been identified as crucial factors affecting mental health,yet the gender-specific associations between these conditions remain underexplored.AIM To assess prevalence of depressive symptoms,anxiety symptoms,and FC among Chinese university students and explore their associations.METHODS Using a cross-sectional survey design,data were collected from 12721 students at two universities in Jiangsu Province and Shandong Province.Depressive symptoms were assessed using the Patient Health Questionnaire-9,anxiety symptoms using the Generalized Anxiety Disorder-7 scale,and FC using the ROME IV.Gender-stratified analyses and population attributable risk proportions were calculated to evaluate risk factor patterns and population impact.RESULTS The prevalence of self-reported depressive,anxiety,and comorbid depressive and anxiety symptoms was 16.3%,24.9%,and 13.3%,respectively,whereas that of FC was 22%.Students with depressive symptoms were 1.811 times more likely to have FC than those without.Female gender,parental relationships,and lower household income were significant risk factors for both mental health conditions.For depressive symptoms,females experienced stronger effects from both parental conflict[odds ratio(OR)=8.006 vs OR=7.661 in males]and FC(OR=1.954 vs OR=1.628 in males).For anxiety symptoms,conflicted parental relationships had stronger effects in males(OR=5.946)than females(OR=4.262).Overall,poor parental relationships contributed to 38.6%of depressive and 33.5%of anxiety symptoms.CONCLUSION Family relationships significantly impact student mental health,with gender-specific patterns.Targeted interventions addressing family dynamics could reduce mental health burden in university settings. 展开更多
关键词 University students DEPRESSION ANXIETY functional constipation Patient Health Questionnaire-9 generalized Anxiety Disorder-7
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Compositional and functional succession of soil bacterial communities during long-term rice cultivation on saline-alkali soils:Insights derived from a new perspective on core bacterial taxa
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作者 Yu SUN Li JI +4 位作者 Jingjing CHANG Yingxin LI Hongbin WANG Deliang LU Chunjie TIAN 《Pedosphere》 2025年第4期641-654,共14页
The conversion of saline-alkali soils into paddy fields for long-term rice cultivation involves multiple disturbances,and as a result,soil microbial communities are altered to adapt to changing environmental condition... The conversion of saline-alkali soils into paddy fields for long-term rice cultivation involves multiple disturbances,and as a result,soil microbial communities are altered to adapt to changing environmental conditions.However,a comprehensive understanding of the succession of soil bacterial communities that occurs during this process is still lacking.In the present study,we utilized data obtained from paddy fields of different rice cultivation years(0-23 years)to investigate the compositional and functional succession of soil bacterial communities.We focused on core bacterial taxa that were specifically enriched at different successional stages.Generalized joint attribute modeling(GJAM)was used to identify core bacterial taxa.Results indicated that the bare saline-alkali soil(0 year,prior to any rice cultivation)shared few core amplicon sequence variants(ASVs)with paddy fields.In the bare saline-alkali soil,Longimicrobiaceae from the phylum Gemmatimonadetes was dominant,while the dominance was subsequently replaced by Burkholderiaceae and Pedosphaeraceae--phyla affiliated with Proteobacteria and Verrucomicrobia--after 5 and 23 years of rice cultivation,respectively.The relative abundances of nitrogen metabolism functions in the core bacterial communities of the bare saline-alkali soil were higher than those at other successional stages,while sulfur metabolism functions exhibited the opposite trend.These indicated that the role of the core bacterial taxa in mediating nutrient cycling also evolved and adapted to changing soil conditions as rice cultivation was established.Redundancy analysis(RDA)indicated that the composition of the core bacterial community in paddy fields with rice cultivation for 0,2 and 4,6,8,10,and 12,and 20 and 23 years were driven by soil nitrate nitrogen content,pH,available phosphorus content,and the ratio of total carbon to total nitrogen,respectively.In summary,the present study provides insights into the succession of soil bacterial communities and core bacterial taxa that occurs during long-term rice cultivation. 展开更多
关键词 bacterial compositional analysis ecosystem functions generalized joint attribute modeling paddy field soil bacterial succession
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Optimizing basis wave functions in the generator coordinate method for microscopic cluster models (Ⅰ)
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作者 Yi‑Fan Liu Bo Zhou Yu‑Gang Ma 《Nuclear Science and Techniques》 2025年第10期183-191,共9页
We employed random distributions and gradient descent methods for the Generator Coordinate Method(GCM)to identify effective basis wave functions,taking halo nuclei ^(6)He and ^(6)Li as examples.By comparing the ground... We employed random distributions and gradient descent methods for the Generator Coordinate Method(GCM)to identify effective basis wave functions,taking halo nuclei ^(6)He and ^(6)Li as examples.By comparing the ground state(0^(+))energy of ^(6)He and the excited state(0^(+))energy of 6 Li calculated with various random distributions and manually selected generation coordinates,we found that the heavy tail characteristic of the logistic distribution better describes the features of the halo nuclei.Subsequently,the Adam algorithm from machine learning was applied to optimize the basis wave functions,indicating that a limited number of basis wave functions can approximate the converged values.These results offer some empirical insights for selecting basis wave functions and contribute to the broader application of machine learning methods in predicting effective basis wave functions. 展开更多
关键词 Generator Coordinate Method Effective basis wave functions Nuclear cluster model Machine learning Halo nuclei
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Chattering-free terminal sliding mode control based on adaptive exponential reaching barrier function for a chaotic permanent magnet synchronous generator in offshore wind turbine system
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作者 Aissa Benabdeseelam Manal Messadi +1 位作者 Karim Kemih Hamid Hamiche 《Chinese Physics B》 2025年第9期104-113,共10页
This paper introduces a novel chattering-free terminal sliding mode control(SMC)strategy to address chaotic behavior in permanent magnet synchronous generators(PMSG)for offshore wind turbine systems.By integrating an ... This paper introduces a novel chattering-free terminal sliding mode control(SMC)strategy to address chaotic behavior in permanent magnet synchronous generators(PMSG)for offshore wind turbine systems.By integrating an adaptive exponential reaching law with a continuous barrier function,the proposed approach eliminates chattering and ensures robust performance under model uncertainties.The methodology combines adaptive SMC with dynamic switching to estimate and compensates for unknown uncertainties,providing smooth and stable control.Finally,the performance and effectiveness of the proposed approach are compared with those of a previous study. 展开更多
关键词 permanent magnet synchronous generator chaotic system terminal sliding mode control exponential reaching adaptive barrier function chattering-free unknown uncertainty
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Analysis of a Cavity Used for Medical Purposes with the Dyadic Green's Functions and the Moment method
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作者 薛正辉 刘永善 +1 位作者 李德生 王堃 《Journal of Beijing Institute of Technology》 EI CAS 1996年第1期19-26,共8页
The structure of a microwave radiator used for medical purposes is described. The dyadic Green's function and the method are used to analyze this Kind of multimode rectangular medium-filled cavity. The distributio... The structure of a microwave radiator used for medical purposes is described. The dyadic Green's function and the method are used to analyze this Kind of multimode rectangular medium-filled cavity. The distribution of electromagnetic field intensity and the power density,as well as the temperature effect in the biological sample load are obtained.OPtimization of the size of cavity and the position of the input aperture have been performed with the computer to optimize the uniformity or microwave effect and the input VSWR.Necessary experiments were performed to compare the data obtained with theoretical analysis. 展开更多
关键词 microwave therapy apparatus moment problems dyadic green's function
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Generalized Numerical Radius of Real Quaternion Matrices with Symmetric Function
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作者 夏铁成 张鸿庆 《Chinese Quarterly Journal of Mathematics》 CSCD 2000年第3期34-38,共5页
In the paper the generalized numerical radiuses of real quaternion matrices with symmetric function are defined and theirs inequalities are given.
关键词 numerical radius generalized numerical radius symmetric function
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The Fourier Transform of a Sort of Generalized Function
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作者 祝同江 《Journal of Beijing Institute of Technology》 EI CAS 1996年第2期106+101-106,共7页
The Fourier transforms of functions X ln e are given. where λ is a complex constant (λ≠-1,-2. …), a is a complex number. m=0. 1. 2,…,and
关键词 Fourier transform generalized function analytic exextension
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Dynamic stiffness matrix of a poroelastic multi-layered site and its Green's functions 被引量:20
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作者 梁建文 尤红兵 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2004年第2期273-282,共10页
Few studies of wave propagation in layered saturated soils have been reported in the literature.In this paper,a general solution of the equation of wave motion in saturated soils,based on one kind of practical Blot... Few studies of wave propagation in layered saturated soils have been reported in the literature.In this paper,a general solution of the equation of wave motion in saturated soils,based on one kind of practical Blot's equation, was deduced by introducing wave potentials.Then exact dynamic-stiffness matrices for a poroelastic soil layer and half- space were derived,which extended Wolf's theory for an elastic layered site to the case of poroelasticity,thus resolving a fundamental problem in the field of wave propagation and soil-structure interaction in a poroelastic layered soil site.By using the integral transform method,Green's functions of horizontal and vertical uniformly distributed loads in a poroelastic layered soil site were given.Finally,the theory was verified by numerical examples and dynamic responses by comparing three different soil sites.This study has the following advantages:all parameters in the dynamic-stiffness matrices have explicitly physical meanings and the thickness of the sub-layers does not affect the precision of the calculation which is very convenient for engineering applications.The present theory can degenerate into Wolf's theory and yields numerical results approaching those for an ideal elastic layered site when porosity tends to zero. 展开更多
关键词 Biot's equation poroelastic layered site dynamic-stiffness matrix green's function
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Some new exact solutions of Jacobian elliptic function about the generalized Boussinesq equation and Boussinesq-Burgers equation 被引量:9
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作者 张亮 张立凤 李崇银 《Chinese Physics B》 SCIE EI CAS CSCD 2008年第2期403-410,共8页
By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic functio... By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions. 展开更多
关键词 generalized Boussinesq equation Boussinesq-Burgers equation Jacobian elliptic function modified mapping method
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The generalized Chapman-Richards function and applications to tree and stand growth 被引量:10
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作者 刘兆刚 李凤日 《Journal of Forestry Research》 SCIE CAS CSCD 2003年第1期19-26,共8页
The generalized Chapman-Richards model was derived from the Chapman-Richards function in which parameters h, k and m were unconstrained. Based on the structure of solutions and biological interpretations, the model co... The generalized Chapman-Richards model was derived from the Chapman-Richards function in which parameters h, k and m were unconstrained. Based on the structure of solutions and biological interpretations, the model could be classified into eight cases (three categories) at all and among them only 4 kinds of cases are suitable in forestry that represent four typical growth patterns of trees and stands. For each of 4 equations, the model properties and biological interpretations for parameters were discussed in detail. The generalized Chapman-Richards model was capable of describing a wide range of growth curves that was asymptotic or nonasymptotic, with or without inflection point. In order to illustrate the versatility of the model, it was fitted to a group of data sets concerning the DBH growth of cryptomeria plantations with 4 initial densities and the DBH and height growth of natural Korean pine tree. Comparing the generalized Chapman-Richards function and the Schnute model, it was found that the parameters and expressions of the two models were interchangeable in theory, and the fitting results were explicitly identical in empirical applications. 展开更多
关键词 generalized Chapman-Richards function Schnute model Growth model Growth pattern Cryptomeria japonica Pinus koraiensis
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