In this paper, we show a general procedure to nonlinearize bilinear equations by using the Bell polynomials. As applications, we obtain nonlinear forms of some integrable bilinear equations(in the sense of having thre...In this paper, we show a general procedure to nonlinearize bilinear equations by using the Bell polynomials. As applications, we obtain nonlinear forms of some integrable bilinear equations(in the sense of having three-soliton solutions) of the KdV type and mKdV type that were found by Jarmo Hietarinta in the 1980s. Examples of non-integrable bilinear equations of the KdV type are also given.展开更多
The symmetry constraint and binary nonlinearization of Lax pairs for the super classical-Boussinesq hierarchy is obtained. Under the obtained symmetry constraint, the n-th flow of the super classical-Boussinesq hierar...The symmetry constraint and binary nonlinearization of Lax pairs for the super classical-Boussinesq hierarchy is obtained. Under the obtained symmetry constraint, the n-th flow of the super classical-Boussinesq hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.展开更多
In this paper,the translation of the Lax pairs of the Levi equations is pre- sented.Then a symmetry constraint for the Levi equations is given by means of binary nonlinearization method. The spatial part and the tempo...In this paper,the translation of the Lax pairs of the Levi equations is pre- sented.Then a symmetry constraint for the Levi equations is given by means of binary nonlinearization method. The spatial part and the temporal parts of the translated Lax pairs and its adjoint Lax pairs of the Levi equations are all constrainted as finite dimensional Liouville integrable Hamiltonian systems. Finally,the involutive solutions of the Levi equations are presented.展开更多
Under the Bargmann constrained condition, the spatial part of a new Lax pair of the higher order MkdV equation is nonlinearized to be a completely integrable system (R2N,dp^dq, H0=1/2F0)(F0= (^q,p) + (^p,p) + (p,q)2)....Under the Bargmann constrained condition, the spatial part of a new Lax pair of the higher order MkdV equation is nonlinearized to be a completely integrable system (R2N,dp^dq, H0=1/2F0)(F0= (^q,p) + (^p,p) + (p,q)2). While the nonlinearization of the time part leads to its N-involutive system (Fm).展开更多
An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super NLS-MKdV hierarchy. Under the obtained symmetry constraint, the n-th flow of th...An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super NLS-MKdV hierarchy. Under the obtained symmetry constraint, the n-th flow of the super NLS-MKdV hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold R4N|2N with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.展开更多
In this paper, a new equivalent nonlinearization method is developed and used in analysing the response of nonlinear systems to Gaussian while noise excitation. Its basic idea and calculation method are expounded. Wit...In this paper, a new equivalent nonlinearization method is developed and used in analysing the response of nonlinear systems to Gaussian while noise excitation. Its basic idea and calculation method are expounded. With the help of the presented method, several kinds of usual nonlinear random vibration systems are analyzed. The numerical results show that the mean square responses of the proposed approach are much closer to the exact solutions or Monte Carlo solutions, than that obtained from equivalent linearization method.展开更多
This paper deals with a Dirac operator with periodic and finite-bands potentials.Taking advantage of the commutativity of the monodromy operator and the Dirac operator, we define the Bloch functions and multiplicator ...This paper deals with a Dirac operator with periodic and finite-bands potentials.Taking advantage of the commutativity of the monodromy operator and the Dirac operator, we define the Bloch functions and multiplicator curve, which leads to the formula of DubrovinNovikov＇s type. Further, by calculation of residues on the complex sphere and via gauge transformation, we get the trace formulae of eigenfunctions corresponding to the left endpoints and right end-points of the spectral bands, respectively. As an application, we obtain a completely integrable Hamiltonian system in Liouville sense through nonlinearization of the Dirac spectral problem.展开更多
An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super Dirac systems. Under the obtained symmetry constraint, the n-th flow of the sup...An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super Dirac systems. Under the obtained symmetry constraint, the n-th flow of the super Dirac hierarchy is decomposed into two super finite-diinensional integrable Hamiltonian systems, defined over the super- symmetry manifold R^4N{2N with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.展开更多
In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to ...In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.展开更多
By modifying the procedure of binary nonlinearization for the AKNS spectral problem and its adjoint spectral problem under an implicit symmetry constraint, we obtain a finite dimensional system from the Lax pair of th...By modifying the procedure of binary nonlinearization for the AKNS spectral problem and its adjoint spectral problem under an implicit symmetry constraint, we obtain a finite dimensional system from the Lax pair of the nonlinear Schrodinger equation. We show that this system is a completely integrable Hamiltonian system.展开更多
Landslides pose a formidable natural hazard across the Qinghai-Tibet Plateau(QTP),endangering both ecosystems and human life.Identifying the driving factors behind landslides and accurately assessing susceptibility ar...Landslides pose a formidable natural hazard across the Qinghai-Tibet Plateau(QTP),endangering both ecosystems and human life.Identifying the driving factors behind landslides and accurately assessing susceptibility are key to mitigating disaster risk.This study integrated multi-source historical landslide data with 15 predictive factors and used several machine learning models—Random Forest(RF),Gradient Boosting Regression Trees(GBRT),Extreme Gradient Boosting(XGBoost),and Categorical Boosting(CatBoost)—to generate susceptibility maps.The Shapley additive explanation(SHAP)method was applied to quantify factor importance and explore their nonlinear effects.The results showed that:(1)CatBoost was the best-performing model(CA=0.938,AUC=0.980)in assessing landslide susceptibility,with altitude emerging as the most significant factor,followed by distance to roads and earthquake sites,precipitation,and slope;(2)the SHAP method revealed critical nonlinear thresholds,demonstrating that historical landslides were concentrated at mid-altitudes(1400-4000 m)and decreased markedly above 4000 m,with a parallel reduction in probability beyond 700 m from roads;and(3)landslide-prone areas,comprising 13%of the QTP,were concentrated in the southeastern and northeastern parts of the plateau.By integrating machine learning and SHAP analysis,this study revealed landslide hazard-prone areas and their driving factors,providing insights to support disaster management strategies and sustainable regional planning.展开更多
Eucalyptus(Eucalyptus camaldulensis Dehnh.)is an important exotic species in northern Nigeria commonly used for poles and timber.Sustainable management of this resource would require quantifying its volume.Stem taper ...Eucalyptus(Eucalyptus camaldulensis Dehnh.)is an important exotic species in northern Nigeria commonly used for poles and timber.Sustainable management of this resource would require quantifying its volume.Stem taper equations are one of the main and most efficient methods for estimating stem volume to any merchantable limit of a species.There is currently no taper equation for Eucalyptus species in Nigeria.Therefore,this study developed taper equations for E.camaldulensis in northern Nigeria.Data for this study were obtained from a private plantation in Jalingo Local Government Area,Taraba State,Nigeria.68 trees were felled and sectioned into 1-m bolt across the stem to a merchantable limit of 5 cm,which were used as the fitting dataset.An additional 22 trees were felled and used to validate the taper equations for stem volume estimation.Seven taper equations were initially fitted to the dataset using nonlinear least squares.The best taper equation was then refitted using a nonlinear mixed-effects approach and calibrated using diameters of one to five sections from the butt end.The taper equations were numerically integrated to obtain the stem volume,which was compared with empirical volume equations.The result shows that the Kozak(Can J For Res 27(5):619-629.10.1139/x97-011,1997)equation,which included eight parameters,provided the best fit for predicting section diameters for under and over bark.The mixed-effects taper equation(NLME-TE)explained most stem diameter variations in the fitting dataset(pseudo-R2:0.986-0.987;RMSE:0.547-0.578 cm)without substantial residual trends.The validation showed that the prediction accuracy of the integrated NLME-TE improved as the number of sectional diameter measurements increased,with at least a 35%reduction in volume estimate error.For practical implementation,two calibration sectional diameter measurements taken from the butt end per tree are recommended.This approach would reduce measurement effort and cost while improving model performance.展开更多
The goal of this paper is to investigate the long-time dynamics of solutions to a Kirchhoff type suspension bridge equation with nonlinear damping and memory term.For this problem we establish the well-posedness and e...The goal of this paper is to investigate the long-time dynamics of solutions to a Kirchhoff type suspension bridge equation with nonlinear damping and memory term.For this problem we establish the well-posedness and existence of uniform attractor under some suitable assumptions on the nonlinear term g(u),the nonlinear damping f(u_(t))and the external force h(x,t).Specifically,the asymptotic compactness of the semigroup is verified by the energy reconstruction method.展开更多
In this paper,we present a finite volume trigonometric weighted essentially non-oscillatory(TWENO)scheme to solve nonlinear degenerate parabolic equations that may exhibit non-smooth solutions.The present method is de...In this paper,we present a finite volume trigonometric weighted essentially non-oscillatory(TWENO)scheme to solve nonlinear degenerate parabolic equations that may exhibit non-smooth solutions.The present method is developed using the trigonometric scheme,which is based on zero,first,and second moments,and the direct discontinuous Galerkin(DDG)flux is used to discretize the diffusion term.Moreover,the DDG method directly applies the weak form of the parabolic equation to each computational cell,which can better capture the characteristics of the solution,especially the discontinuous solution.Meanwhile,the third-order TVD-Runge-Kutta method is applied for temporal discretization.Finally,the effectiveness and stability of the method constructed in this paper are evaluated through numerical tests.展开更多
Achieving non-centrosymmetric(NCS) configurations in ABX3-type hybrid halides remains a critical challenge for nonlinear optical(NLO) materials due to the conflicting requirements of high second-harmonic generation(SH...Achieving non-centrosymmetric(NCS) configurations in ABX3-type hybrid halides remains a critical challenge for nonlinear optical(NLO) materials due to the conflicting requirements of high second-harmonic generation(SHG) response,wide bandgap,and phase-matching capabilities.Herein,we propose a triplesite modulation strategy by synergistically tailoring the A-site cations(2-methylimidazole cation/1-ethyl-3-methylimidazole cation),B-site metals(Sn^(2+)/Pb^(2+)),and X-site halogens(Cl/Br),which effectively disrupts lattice symmetry and enables NCS crystallization.Our results demonstrate a strong SHG response,an expanded optical bandgap and increased birefringence.The optimized compound C_(6)H_(11)N_(2)PbCl_(3) exhibits a moderately strong SHG efficiency of 3.8 × KDP,a wide bandgap(3.87 eV),and enhanced birefringence(0.139@1064 nm),surpassing majority hybrid NLO materials.The innovative anionic framework introduced here broadens the scope of hybrid NLO crystals,facilitating the integration of various aromatic heterocyclic cations.This research provides a robust strategic framework for the development of advanced NLO materials.展开更多
In this study,a fifth-degree cubature particle filter(5CPF)is proposed to address the limited estimation accuracy in traditional particle filter algorithms for bearings-only tracking(BOT).This algorithm calculates the...In this study,a fifth-degree cubature particle filter(5CPF)is proposed to address the limited estimation accuracy in traditional particle filter algorithms for bearings-only tracking(BOT).This algorithm calculates the recommended density function by introducing a fifth-degree cubature Kalman filter algorithm to guide particle sampling,which effectively alleviates the problem of particle degradation and significantly improves the estimation accuracy of the filter.However,the 5CPF algorithm exhibits high computational complexity,particularly in scenarios with a large number of particles.Therefore,we propose the extended Kalman filter(EKF)-5CPF algorithm,which employs an EKF to replace the time update step for each particle in the 5CPF.This enhances the algorithm’s real-time capability while maintaining the high precision advantage of the 5CPF algorithm.In addition,we construct bearing-only dual-station and single-motion station target tracking systems,and the filtering performances of 5CPF and EKF-5CPF algorithms under different conditions are analyzed.The results show that both the 5CPF algorithm and EKF-5CPF have strong robustness and can adapt to different noise environments.Furthermore,both algorithms significantly outperform traditional nonlinear filtering algorithms in terms of convergence speed,tracking accuracy,and overall stability.展开更多
Transforming urban spatial structures to promote green and low-carbon development is an effective strategy.Although prior studies have examined the impact of urban polycentricity on carbon emissions and economic devel...Transforming urban spatial structures to promote green and low-carbon development is an effective strategy.Although prior studies have examined the impact of urban polycentricity on carbon emissions and economic development,research on its role in the synergistic relationship between these factors regarding carbon emission efficiency is limited.Furthermore,existing literature often overlooks nonlinear effects and interactions with other urban variables.This paper analyzed data from 295 Chinese cities in 2020,calculating urban population polycentricity,population dispersion indices,and carbon emission efficiency.Utilizing local spatial autocorrelation tools,we reveal interactions among urban population polycentricity,dispersion,carbon emissions,and carbon emission efficiency.We then employ a gradient boosting decision tree model(GBDT)to explore nonlinear and synergistic effects of polycentric urbanization.Key findings include:1)polycentric urbanization in Chinese cities exhibits significant spatial differentiation characteristics.The Polycentricity index is relatively high in economically developed eastern coastal regions with an overall low level,carbon emissions are concentrated in industrialized north-central cities and some Yangtze River Delta hubs,and carbon emission efficiency is the highest in the Yangtze River Delta while relatively low in Northeast China;there are significant spatially heterogeneous interaction characteristics among population polycentricity,population dispersion,carbon emissions,and carbon emission efficiency.2)Urban population polycentricity contributes 9.42%to total carbon emissions and 6.24%to carbon emission efficiency.3)The polycentricity index has a nonlinear impact on carbon emissions and carbon emission efficiency:no significant effect when below 0.50 or above 0.55,increased carbon emissions in 0.50-0.53,and reduced carbon emissions with improved efficiency in 0.53-0.55.4)The polycentricity index has an interaction effect with other variables;specifically,when the polycentricity index is between 0.53 and 0.55,its interaction with urban gross domestic product(GDP),urban population,urban built-up area,green coverage rate in built-up areas,urban technological expenditure,and the proportion of the output value of the secondary industry will reduce carbon emissions and improve carbon emission efficiency.These findings enhance the understanding of urban spatial structures and carbon emissions,providing valuable insights for policymakers in developing green and low-carbon strategies.展开更多
With the increasing complexity of industrial automation,planetary gearboxes play a vital role in largescale equipment transmission systems,directly impacting operational efficiency and safety.Traditional maintenance s...With the increasing complexity of industrial automation,planetary gearboxes play a vital role in largescale equipment transmission systems,directly impacting operational efficiency and safety.Traditional maintenance strategies often struggle to accurately predict the degradation process of equipment,leading to excessive maintenance costs or potential failure risks.However,existing prediction methods based on statistical models are difficult to adapt to nonlinear degradation processes.To address these challenges,this study proposes a novel condition-based maintenance framework for planetary gearboxes.A comprehensive full-lifecycle degradation experiment was conducted to collect raw vibration signals,which were then processed using a temporal convolutional network autoencoder with multi-scale perception capability to extract deep temporal degradation features,enabling the collaborative extraction of longperiod meshing frequencies and short-term impact features from the vibration signals.Kernel principal component analysis was employed to fuse and normalize these features,enhancing the characterization of degradation progression.A nonlinear Wiener process was used to model the degradation trajectory,with a threshold decay function introduced to dynamically adjust maintenance strategies,and model parameters optimized through maximum likelihood estimation.Meanwhile,the maintenance strategy was optimized to minimize costs per unit time,determining the optimal maintenance timing and preventive maintenance threshold.The comprehensive indicator of degradation trends extracted by this method reaches 0.756,which is 41.2%higher than that of traditional time-domain features;the dynamic threshold strategy reduces the maintenance cost per unit time to 55.56,which is 8.9%better than that of the static threshold optimization.Experimental results demonstrate significant reductions in maintenance costs while enhancing system reliability and safety.This study realizes the organic integration of deep learning and reliability theory in the maintenance of planetary gearboxes,provides an interpretable solution for the predictive maintenance of complex mechanical systems,and promotes the development of condition-based maintenance strategies for planetary gearboxes.展开更多
In this work,the Hierarchical Quadrature Element Method(HQEM)formulation of geometrically exact shells is proposed and applied for geometrically nonlinear analyses of both isotropic and laminated shells.The stress res...In this work,the Hierarchical Quadrature Element Method(HQEM)formulation of geometrically exact shells is proposed and applied for geometrically nonlinear analyses of both isotropic and laminated shells.The stress resultant formulation is developed within the HQEM framework,consequently significantly simplifying the computations of residual force and stiffness matrix.The present formulation inherently avoids shear and membrane locking,benefiting from its high-order approximation property.Furthermore,HQEM’s independent nodal distribution capability conveniently supports local p-refinement and flexibly facilitates mesh generation in various structural configurations through the combination of quadrilateral and triangular elements.Remarkably,in lateral buckling analysis,the HQEM outperforms the weak-form quadrilateral element(QEM)in accuracy with identical nodal degrees of freedom(three displacements and two rotations).Under high-load nonlinear response,the QEM exhibits a maximum relative deviation of approximately 9.5%from the reference,while the HQEM remains closely aligned with the benchmark results.In addition,for the cantilever beam under tip moment,HQEM produces virtually no out-of-plane deviation,compared to a slight deviation of 0.00001 with QEM,confirming its superior numerical reliability.In summary,the method demonstrates high accuracy,superior convergence,and robustness in handling large rotations and complex post-buckling behaviors across a series of benchmark problems.展开更多
The coupled chemo-mechanical impact of supercritical CO_(2)-H_(2)O(ScCO_(2)-H_(2)O)reactions on fracture geometry and nonlinear flow regimes in deep shale under confining pressures remains inadequately quantified.This...The coupled chemo-mechanical impact of supercritical CO_(2)-H_(2)O(ScCO_(2)-H_(2)O)reactions on fracture geometry and nonlinear flow regimes in deep shale under confining pressures remains inadequately quantified.This study systematically investigates the effects of ScCO_(2)-H_(2)O-shale interactions on fracture morphology and flow properties under confining pressures from 15 MPa to 40 MPa by integrating XRD(X-ray diffraction),micro-CT,3D surface profilometry,and multistage steady-state flow experiments.The results demonstrate that ScCO_(2)-H_(2)O exposure drives pyrite/feldspar dissolution and localized clay precipitation,resulting in fracture branching and macroscopic aperture regularization.Critically,confining pressure dictates the net hydraulic response:under low confining pressure(15-25 MPa),dissolution dominates,enhancing permeability,flow efficiency(Q/VP),and pre-linear flow behavior(n<1).At high confining pressures(30-40 MPa)mechanical compaction and mineral precipitation amplify flow resistance,shifting the flow regime toward quasi-linear behavior,as inertial effects become negligible compared to dominant viscous forces and increased flow resistance.Confining pressure thus critically mediates the dissolution-precipitation balance during ScCO_(2)-H_(2)O treatment,with an optimal window of 15-25 MPa identified for enhancing conductivity while minimizing clogging risk.These findings provide a quantitative framework for predicting stress-dependent flow evolution in chemically altered shale fractures.展开更多
文摘In this paper, we show a general procedure to nonlinearize bilinear equations by using the Bell polynomials. As applications, we obtain nonlinear forms of some integrable bilinear equations(in the sense of having three-soliton solutions) of the KdV type and mKdV type that were found by Jarmo Hietarinta in the 1980s. Examples of non-integrable bilinear equations of the KdV type are also given.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.61072147 and 11071159)the Natural Science Foundation of Shanghai,China (Grant No.09ZR1410800)+2 种基金the Science Foundation of the Key Laboratory of Mathematics Mechanization,China (Grant No.KLMM0806)the Shanghai Leading Academic Discipline Project,China (Grant No.J50101)the Key Disciplines of Shanghai Municipality of China (Grant No.S30104)
文摘The symmetry constraint and binary nonlinearization of Lax pairs for the super classical-Boussinesq hierarchy is obtained. Under the obtained symmetry constraint, the n-th flow of the super classical-Boussinesq hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.
文摘In this paper,the translation of the Lax pairs of the Levi equations is pre- sented.Then a symmetry constraint for the Levi equations is given by means of binary nonlinearization method. The spatial part and the temporal parts of the translated Lax pairs and its adjoint Lax pairs of the Levi equations are all constrainted as finite dimensional Liouville integrable Hamiltonian systems. Finally,the involutive solutions of the Levi equations are presented.
文摘Under the Bargmann constrained condition, the spatial part of a new Lax pair of the higher order MkdV equation is nonlinearized to be a completely integrable system (R2N,dp^dq, H0=1/2F0)(F0= (^q,p) + (^p,p) + (p,q)2). While the nonlinearization of the time part leads to its N-involutive system (Fm).
文摘An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super NLS-MKdV hierarchy. Under the obtained symmetry constraint, the n-th flow of the super NLS-MKdV hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold R4N|2N with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.
文摘In this paper, a new equivalent nonlinearization method is developed and used in analysing the response of nonlinear systems to Gaussian while noise excitation. Its basic idea and calculation method are expounded. With the help of the presented method, several kinds of usual nonlinear random vibration systems are analyzed. The numerical results show that the mean square responses of the proposed approach are much closer to the exact solutions or Monte Carlo solutions, than that obtained from equivalent linearization method.
基金Supported by the National Natural Science Foundation of China(Grant No.61473332)the Natural Science Foundation of Zhejiang Province(Grant No.LQ14A010009)the Natural Science Foundation of Huzhou City(Grant No.2013YZ06)
文摘This paper deals with a Dirac operator with periodic and finite-bands potentials.Taking advantage of the commutativity of the monodromy operator and the Dirac operator, we define the Bloch functions and multiplicator curve, which leads to the formula of DubrovinNovikov＇s type. Further, by calculation of residues on the complex sphere and via gauge transformation, we get the trace formulae of eigenfunctions corresponding to the left endpoints and right end-points of the spectral bands, respectively. As an application, we obtain a completely integrable Hamiltonian system in Liouville sense through nonlinearization of the Dirac spectral problem.
基金Project supported by the Hangdian Foundation (No. KYS075608072)the National Natural Science Foundation of China (Nos. 10671187, 10971109)the Program for New Century Excellent Talents in University of China (No. NCET-08-0515)
文摘An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super Dirac systems. Under the obtained symmetry constraint, the n-th flow of the super Dirac hierarchy is decomposed into two super finite-diinensional integrable Hamiltonian systems, defined over the super- symmetry manifold R^4N{2N with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.
基金Supported in part by Natural Science Foundation of Guangxi(2023GXNSFAA026246)in part by the Central Government's Guide to Local Science and Technology Development Fund(GuikeZY23055044)in part by the National Natural Science Foundation of China(62363003)。
文摘In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.
基金Supported by the National Natural Science Foundation of China(No.11001069,61273077,11271210 and 10971109)Program for NCET under Grant No.NCET-08-0515Zhejiang Provincial Natural Science Foun-dation of China under Grant No.LQ12A01002 and LQ12A01003
文摘By modifying the procedure of binary nonlinearization for the AKNS spectral problem and its adjoint spectral problem under an implicit symmetry constraint, we obtain a finite dimensional system from the Lax pair of the nonlinear Schrodinger equation. We show that this system is a completely integrable Hamiltonian system.
基金The National Key Research and Development Program of China,No.2023YFC3206601。
文摘Landslides pose a formidable natural hazard across the Qinghai-Tibet Plateau(QTP),endangering both ecosystems and human life.Identifying the driving factors behind landslides and accurately assessing susceptibility are key to mitigating disaster risk.This study integrated multi-source historical landslide data with 15 predictive factors and used several machine learning models—Random Forest(RF),Gradient Boosting Regression Trees(GBRT),Extreme Gradient Boosting(XGBoost),and Categorical Boosting(CatBoost)—to generate susceptibility maps.The Shapley additive explanation(SHAP)method was applied to quantify factor importance and explore their nonlinear effects.The results showed that:(1)CatBoost was the best-performing model(CA=0.938,AUC=0.980)in assessing landslide susceptibility,with altitude emerging as the most significant factor,followed by distance to roads and earthquake sites,precipitation,and slope;(2)the SHAP method revealed critical nonlinear thresholds,demonstrating that historical landslides were concentrated at mid-altitudes(1400-4000 m)and decreased markedly above 4000 m,with a parallel reduction in probability beyond 700 m from roads;and(3)landslide-prone areas,comprising 13%of the QTP,were concentrated in the southeastern and northeastern parts of the plateau.By integrating machine learning and SHAP analysis,this study revealed landslide hazard-prone areas and their driving factors,providing insights to support disaster management strategies and sustainable regional planning.
文摘Eucalyptus(Eucalyptus camaldulensis Dehnh.)is an important exotic species in northern Nigeria commonly used for poles and timber.Sustainable management of this resource would require quantifying its volume.Stem taper equations are one of the main and most efficient methods for estimating stem volume to any merchantable limit of a species.There is currently no taper equation for Eucalyptus species in Nigeria.Therefore,this study developed taper equations for E.camaldulensis in northern Nigeria.Data for this study were obtained from a private plantation in Jalingo Local Government Area,Taraba State,Nigeria.68 trees were felled and sectioned into 1-m bolt across the stem to a merchantable limit of 5 cm,which were used as the fitting dataset.An additional 22 trees were felled and used to validate the taper equations for stem volume estimation.Seven taper equations were initially fitted to the dataset using nonlinear least squares.The best taper equation was then refitted using a nonlinear mixed-effects approach and calibrated using diameters of one to five sections from the butt end.The taper equations were numerically integrated to obtain the stem volume,which was compared with empirical volume equations.The result shows that the Kozak(Can J For Res 27(5):619-629.10.1139/x97-011,1997)equation,which included eight parameters,provided the best fit for predicting section diameters for under and over bark.The mixed-effects taper equation(NLME-TE)explained most stem diameter variations in the fitting dataset(pseudo-R2:0.986-0.987;RMSE:0.547-0.578 cm)without substantial residual trends.The validation showed that the prediction accuracy of the integrated NLME-TE improved as the number of sectional diameter measurements increased,with at least a 35%reduction in volume estimate error.For practical implementation,two calibration sectional diameter measurements taken from the butt end per tree are recommended.This approach would reduce measurement effort and cost while improving model performance.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11961059,1210502)the University Innovation Project of Gansu Province(Grant No.2023B-062)the Gansu Province Basic Research Innovation Group Project(Grant No.23JRRA684).
文摘The goal of this paper is to investigate the long-time dynamics of solutions to a Kirchhoff type suspension bridge equation with nonlinear damping and memory term.For this problem we establish the well-posedness and existence of uniform attractor under some suitable assumptions on the nonlinear term g(u),the nonlinear damping f(u_(t))and the external force h(x,t).Specifically,the asymptotic compactness of the semigroup is verified by the energy reconstruction method.
基金The Natural Science Foundation of Xinjiang Uygur Autonomous Region of China“RBF-Hermite difference scheme for the time-fractional kdv-Burgers equation”(2024D01C43)。
文摘In this paper,we present a finite volume trigonometric weighted essentially non-oscillatory(TWENO)scheme to solve nonlinear degenerate parabolic equations that may exhibit non-smooth solutions.The present method is developed using the trigonometric scheme,which is based on zero,first,and second moments,and the direct discontinuous Galerkin(DDG)flux is used to discretize the diffusion term.Moreover,the DDG method directly applies the weak form of the parabolic equation to each computational cell,which can better capture the characteristics of the solution,especially the discontinuous solution.Meanwhile,the third-order TVD-Runge-Kutta method is applied for temporal discretization.Finally,the effectiveness and stability of the method constructed in this paper are evaluated through numerical tests.
基金supported by the National Natural Science Foundation of China (No.22275052)Department of Science and Technology of Hubei Province (Nos.2025AFA111 and 2024CSA076)。
文摘Achieving non-centrosymmetric(NCS) configurations in ABX3-type hybrid halides remains a critical challenge for nonlinear optical(NLO) materials due to the conflicting requirements of high second-harmonic generation(SHG) response,wide bandgap,and phase-matching capabilities.Herein,we propose a triplesite modulation strategy by synergistically tailoring the A-site cations(2-methylimidazole cation/1-ethyl-3-methylimidazole cation),B-site metals(Sn^(2+)/Pb^(2+)),and X-site halogens(Cl/Br),which effectively disrupts lattice symmetry and enables NCS crystallization.Our results demonstrate a strong SHG response,an expanded optical bandgap and increased birefringence.The optimized compound C_(6)H_(11)N_(2)PbCl_(3) exhibits a moderately strong SHG efficiency of 3.8 × KDP,a wide bandgap(3.87 eV),and enhanced birefringence(0.139@1064 nm),surpassing majority hybrid NLO materials.The innovative anionic framework introduced here broadens the scope of hybrid NLO crystals,facilitating the integration of various aromatic heterocyclic cations.This research provides a robust strategic framework for the development of advanced NLO materials.
基金Supported by the Guangxi Special Program for Technological Innovation Guidance(No.GuiKeAC25069006).
文摘In this study,a fifth-degree cubature particle filter(5CPF)is proposed to address the limited estimation accuracy in traditional particle filter algorithms for bearings-only tracking(BOT).This algorithm calculates the recommended density function by introducing a fifth-degree cubature Kalman filter algorithm to guide particle sampling,which effectively alleviates the problem of particle degradation and significantly improves the estimation accuracy of the filter.However,the 5CPF algorithm exhibits high computational complexity,particularly in scenarios with a large number of particles.Therefore,we propose the extended Kalman filter(EKF)-5CPF algorithm,which employs an EKF to replace the time update step for each particle in the 5CPF.This enhances the algorithm’s real-time capability while maintaining the high precision advantage of the 5CPF algorithm.In addition,we construct bearing-only dual-station and single-motion station target tracking systems,and the filtering performances of 5CPF and EKF-5CPF algorithms under different conditions are analyzed.The results show that both the 5CPF algorithm and EKF-5CPF have strong robustness and can adapt to different noise environments.Furthermore,both algorithms significantly outperform traditional nonlinear filtering algorithms in terms of convergence speed,tracking accuracy,and overall stability.
基金Under the auspices of National Natural Science Foundation of China(No.42571300)。
文摘Transforming urban spatial structures to promote green and low-carbon development is an effective strategy.Although prior studies have examined the impact of urban polycentricity on carbon emissions and economic development,research on its role in the synergistic relationship between these factors regarding carbon emission efficiency is limited.Furthermore,existing literature often overlooks nonlinear effects and interactions with other urban variables.This paper analyzed data from 295 Chinese cities in 2020,calculating urban population polycentricity,population dispersion indices,and carbon emission efficiency.Utilizing local spatial autocorrelation tools,we reveal interactions among urban population polycentricity,dispersion,carbon emissions,and carbon emission efficiency.We then employ a gradient boosting decision tree model(GBDT)to explore nonlinear and synergistic effects of polycentric urbanization.Key findings include:1)polycentric urbanization in Chinese cities exhibits significant spatial differentiation characteristics.The Polycentricity index is relatively high in economically developed eastern coastal regions with an overall low level,carbon emissions are concentrated in industrialized north-central cities and some Yangtze River Delta hubs,and carbon emission efficiency is the highest in the Yangtze River Delta while relatively low in Northeast China;there are significant spatially heterogeneous interaction characteristics among population polycentricity,population dispersion,carbon emissions,and carbon emission efficiency.2)Urban population polycentricity contributes 9.42%to total carbon emissions and 6.24%to carbon emission efficiency.3)The polycentricity index has a nonlinear impact on carbon emissions and carbon emission efficiency:no significant effect when below 0.50 or above 0.55,increased carbon emissions in 0.50-0.53,and reduced carbon emissions with improved efficiency in 0.53-0.55.4)The polycentricity index has an interaction effect with other variables;specifically,when the polycentricity index is between 0.53 and 0.55,its interaction with urban gross domestic product(GDP),urban population,urban built-up area,green coverage rate in built-up areas,urban technological expenditure,and the proportion of the output value of the secondary industry will reduce carbon emissions and improve carbon emission efficiency.These findings enhance the understanding of urban spatial structures and carbon emissions,providing valuable insights for policymakers in developing green and low-carbon strategies.
基金funded by scientific research projects under Grant JY2024B011.
文摘With the increasing complexity of industrial automation,planetary gearboxes play a vital role in largescale equipment transmission systems,directly impacting operational efficiency and safety.Traditional maintenance strategies often struggle to accurately predict the degradation process of equipment,leading to excessive maintenance costs or potential failure risks.However,existing prediction methods based on statistical models are difficult to adapt to nonlinear degradation processes.To address these challenges,this study proposes a novel condition-based maintenance framework for planetary gearboxes.A comprehensive full-lifecycle degradation experiment was conducted to collect raw vibration signals,which were then processed using a temporal convolutional network autoencoder with multi-scale perception capability to extract deep temporal degradation features,enabling the collaborative extraction of longperiod meshing frequencies and short-term impact features from the vibration signals.Kernel principal component analysis was employed to fuse and normalize these features,enhancing the characterization of degradation progression.A nonlinear Wiener process was used to model the degradation trajectory,with a threshold decay function introduced to dynamically adjust maintenance strategies,and model parameters optimized through maximum likelihood estimation.Meanwhile,the maintenance strategy was optimized to minimize costs per unit time,determining the optimal maintenance timing and preventive maintenance threshold.The comprehensive indicator of degradation trends extracted by this method reaches 0.756,which is 41.2%higher than that of traditional time-domain features;the dynamic threshold strategy reduces the maintenance cost per unit time to 55.56,which is 8.9%better than that of the static threshold optimization.Experimental results demonstrate significant reductions in maintenance costs while enhancing system reliability and safety.This study realizes the organic integration of deep learning and reliability theory in the maintenance of planetary gearboxes,provides an interpretable solution for the predictive maintenance of complex mechanical systems,and promotes the development of condition-based maintenance strategies for planetary gearboxes.
基金supported by the National Natural Science Foundation of China(Grant Nos.12472194,12002018,11972004,11772031,11402015).
文摘In this work,the Hierarchical Quadrature Element Method(HQEM)formulation of geometrically exact shells is proposed and applied for geometrically nonlinear analyses of both isotropic and laminated shells.The stress resultant formulation is developed within the HQEM framework,consequently significantly simplifying the computations of residual force and stiffness matrix.The present formulation inherently avoids shear and membrane locking,benefiting from its high-order approximation property.Furthermore,HQEM’s independent nodal distribution capability conveniently supports local p-refinement and flexibly facilitates mesh generation in various structural configurations through the combination of quadrilateral and triangular elements.Remarkably,in lateral buckling analysis,the HQEM outperforms the weak-form quadrilateral element(QEM)in accuracy with identical nodal degrees of freedom(three displacements and two rotations).Under high-load nonlinear response,the QEM exhibits a maximum relative deviation of approximately 9.5%from the reference,while the HQEM remains closely aligned with the benchmark results.In addition,for the cantilever beam under tip moment,HQEM produces virtually no out-of-plane deviation,compared to a slight deviation of 0.00001 with QEM,confirming its superior numerical reliability.In summary,the method demonstrates high accuracy,superior convergence,and robustness in handling large rotations and complex post-buckling behaviors across a series of benchmark problems.
基金support from the Science and Technology Innovation Program of Hunan Province(Grant No.2023RC1021)the Natural Science Foundation of Sichuan Province(Grant No.2025YFHZ0323).-。
文摘The coupled chemo-mechanical impact of supercritical CO_(2)-H_(2)O(ScCO_(2)-H_(2)O)reactions on fracture geometry and nonlinear flow regimes in deep shale under confining pressures remains inadequately quantified.This study systematically investigates the effects of ScCO_(2)-H_(2)O-shale interactions on fracture morphology and flow properties under confining pressures from 15 MPa to 40 MPa by integrating XRD(X-ray diffraction),micro-CT,3D surface profilometry,and multistage steady-state flow experiments.The results demonstrate that ScCO_(2)-H_(2)O exposure drives pyrite/feldspar dissolution and localized clay precipitation,resulting in fracture branching and macroscopic aperture regularization.Critically,confining pressure dictates the net hydraulic response:under low confining pressure(15-25 MPa),dissolution dominates,enhancing permeability,flow efficiency(Q/VP),and pre-linear flow behavior(n<1).At high confining pressures(30-40 MPa)mechanical compaction and mineral precipitation amplify flow resistance,shifting the flow regime toward quasi-linear behavior,as inertial effects become negligible compared to dominant viscous forces and increased flow resistance.Confining pressure thus critically mediates the dissolution-precipitation balance during ScCO_(2)-H_(2)O treatment,with an optimal window of 15-25 MPa identified for enhancing conductivity while minimizing clogging risk.These findings provide a quantitative framework for predicting stress-dependent flow evolution in chemically altered shale fractures.
