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
Exploring new material systems and enhancing the birefringence of compounds is a highly valuable endeavor.In this study,we introduce a novel method to enhance the birefringence of inorganic compounds by inducing struc...Exploring new material systems and enhancing the birefringence of compounds is a highly valuable endeavor.In this study,we introduce a novel method to enhance the birefringence of inorganic compounds by inducing structural alignment through linear groups and fluoride ions.We report on two new compounds:HgGa_(2)(SeO_(3))_(4) and Hg_(2)Ga(Se_(O)_(3))_(2)F.HgGa_(2)(SeO_(3))_(4) crystallizes in a non-centrosymmetric(NCS)space group,exhibiting a second harmonic generation(SHG)efficiency of approximately 60% that of commercial KH2PO4(KDP),with a birefringence of 0.032@546 nm.Hg_(2)Ga(Se_(O)_(3))_(2)F,on the other hand,crystallizes in a centrosymmetric space(CS)group and represents the first reported HgI-based selenite birefringent material.Due to the influence of the linear group Hg_(2)O_(2),its birefringence is significantly enhanced to 0.111@546 nm,which is 3.5 times that of HgGa_(2)(SeO_(3))_(4).Moreover,both compounds demonstrate high stability and a broad optical transparency window.These findings indicate that Hg_(2)Ga(Se_(O)_(3))_(2)F is a promising candidate for birefringent material in the mid-infrared(MIR)range.Our research provides an innovative strategy for improving the birefringence of compounds.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
This paper aims to explore and quantify the nonlinear vibration response of tri-directional functionally graded sandwich(3D-FGSW)plates partially supported by a Pasternak foundation(PF)subjected to blast loading(BL).A...This paper aims to explore and quantify the nonlinear vibration response of tri-directional functionally graded sandwich(3D-FGSW)plates partially supported by a Pasternak foundation(PF)subjected to blast loading(BL).A key objective is to develop a computationally efficient finite element framework capable of accurately capturing the complex behavior of 3D-FGSW plates.The studied configuration features a two-dimensional functionally graded material(2D-FGM)core between two threedimensional functionally graded material(3D-FGM)face layers.Nonlinear geometric effects,including mid-plane stretching,are modeled using von K arm an-type assumptions,and the governing equations are formulated via Hamilton's principle within an improved first-order shear deformation theory(iFSDT).The accuracy and computational efficiency of the proposed method are validated through comparison with existing benchmark solutions.Subsequently,a comprehensive parametric study is carried out to examine the effects of geometric dimensions,material properties,foundation sizes,and boundary conditions(BCs)on the nonlinear vibration of 3D-FGSW plates.The findings of this work are expected to provide valuable insights for the design and manufacturing of advanced sandwich structures subjected to BL.展开更多
Elliptic curve(EC)based cryptosystems gained more attention due to enhanced security than the existing public key cryptosystems.A substitution box(S-box)plays a vital role in securing modern symmetric key cryptosystem...Elliptic curve(EC)based cryptosystems gained more attention due to enhanced security than the existing public key cryptosystems.A substitution box(S-box)plays a vital role in securing modern symmetric key cryptosystems.However,the recently developed EC based algorithms usually trade off between computational efficiency and security,necessitating the design of a new algorithm with the desired cryptographic strength.To address these shortcomings,this paper proposes a new scheme based onMordell elliptic curve(MEC)over the complex field for generating distinct,dynamic,and highly uncorrelated S-boxes.Furthermore,we count the exact number of the obtained S-boxes,and demonstrate that the permuted version of the presented S-box is statistically optimal.The nonsingularity of the presented algorithm and the injectivity of the resultant output are explored.Rigorous theoretical analysis and experimental results demonstrate that the proposedmethod is highly effective in generating a large number of dynamic S-boxes with adequate cryptographic properties,surpassing current state-of-the-art S-box generation algorithms in terms of security.Apart fromthis,the generated S-box is benchmarked using side-channel attacks,and its performance is compared with highly nonlinear S-boxes,demonstrating comparable results.In addition,we present an application of our proposed S-box generator by incorporating it into an image encryption technique.The encrypted and decrypted images are tested by employing extensive standard security metrics,including the Number of Pixel Change Rate,the Unified Average Changing Intensity,information entropy,correlation coefficient,and histogram analysis.Moreover,the analysis is extended beyond conventional metrics to validate the new method using advanced tests,such as the NIST statistical test suite,robustness analysis,and noise and cropping attacks.Experimental outcomes show that the presented algorithm strengthens the existing encryption scheme against various well-known cryptographic attacks.展开更多
The bipartite containment control problem for heterogeneous nonlinear multi-agent systems(HNMASs)within multi-group networks under signed digraphs is investigated,where the first-order and second-order nonlinear dynam...The bipartite containment control problem for heterogeneous nonlinear multi-agent systems(HNMASs)within multi-group networks under signed digraphs is investigated,where the first-order and second-order nonlinear dynamic agents belong to distinct groups.Interactions are cooperative-antagonistic within each group and sign-in-degree balanced across the inter-groups.Firstly,a state feedback control protocol is designed to ensure that the trajectories of followers in diverse groups can converge to distinct convex hulls formed by their corresponding leaders,respectively.As an extension,the bipartite control problem with time-variant formation for the multi-agent system(MAS)is also considered,and a corresponding control protocol with formation compensation vectors is given.Finally,in view of Lyapunov stability theory and matrix inequality,the sufficient conditions for realizing the bipartite containment control are obtained,and several simulations are provided to verify the validity of the above methods.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
With the development of the semiconductor industry below the 7 nm scale,critical dimension small-angle X-ray scattering(CD-SAXS)has emerged as a powerful tool for quantitatively measuring nanoscale deviations.In this ...With the development of the semiconductor industry below the 7 nm scale,critical dimension small-angle X-ray scattering(CD-SAXS)has emerged as a powerful tool for quantitatively measuring nanoscale deviations.In this study,the effects of X-ray beam size and photon energy on the accuracy of critical dimension measurements were investigated.Critical dimensions measured using beams with different spot sizes showed different deviations from the expected values.Beam sizes that were either too large or too small did not improve confidence intervals.As the incident energy increased,the X-ray transmission rate increased,while the scattering cross section decreased,resulting in a gradual decrease in the signal-to-noise ratio of the diffraction peaks,which reduced the accuracy of the CD-SAXS measurements.An optimal accuracy was obtained at 12 keV with a smaller beam size.Using an effective trapezoid model,the results yielded an average pitch of 100.4±0.2 nm,width of 49.8±0.2 nm,height of 130.0±0.2 nm,and a sidewall angle below 1.1°±0.1°.These results provide crucial guidance for the future development of CD-SAXS laboratories and the construction of X-ray machines as well as robust support for research in related fields.展开更多
Trajectory tracking for nonlinear robotic systems remains a fundamental yet challenging problem in control engineering,particularly when both precision and efficiency must be ensured.Conventional control methods are o...Trajectory tracking for nonlinear robotic systems remains a fundamental yet challenging problem in control engineering,particularly when both precision and efficiency must be ensured.Conventional control methods are often effective for stabilization but may not directly optimize long-term performance.To address this limitation,this study develops an integrated framework that combines optimal control principles with reinforcement learning for a single-link robotic manipulator.The proposed scheme adopts an actor–critic structure,where the critic network approximates the value function associated with the Hamilton–Jacobi–Bellman equation,and the actor network generates near-optimal control signals in real time.This dual adaptation enables the controller to refine its policy online without explicit system knowledge.Stability of the closed-loop system is analyzed through Lyapunov theory,ensuring boundedness of the tracking error.Numerical simulations on the single-link manipulator demonstrate that themethod achieves accurate trajectory followingwhile maintaining lowcontrol effort.The results further showthat the actor–critic learning mechanism accelerates convergence of the control policy compared with conventional optimization-based strategies.This work highlights the potential of reinforcement learning integrated with optimal control for robotic manipulators and provides a foundation for future extensions to more complex multi-degree-of-freedom systems.The proposed controller is further validated in a physics-based virtual Gazebo environment,demonstrating stable adaptation and real-time feasibility.展开更多
The equilibrium dynamics and nonlinear rheology of unentangled polymer blends remain inadequately understood,especially regarding the influence of short-chain matrix length N_(S) on the structure and rheological behav...The equilibrium dynamics and nonlinear rheology of unentangled polymer blends remain inadequately understood,especially regarding the influence of short-chain matrix length N_(S) on the structure and rheological behavior of dispersed long chains.Using molecular dynamics simulations based on the Kremer-Grest model,we systematically explore the N_(S)-dependence of static conformations,equilibrium dynamics,and nonlinear shear responses in unentangled long-chain/short-chain polymer blends.Our results demonstrate a decoupling between the static and dynamic sensitivity to N_(S):while the static chain size,R_g,follows Flory theory with slight swelling at small N_(S) due to incomplete excluded volume screening,the diffusion coefficient,D,and the relaxation time,τ_(0),exhibit a strong,non-monotonic N_(S)-dependence,transitioning from monomeric friction dominance at small N_(S) to collective segmental rearrangement at large N_(S).Additionally,we observe partial decoupling between the viscous and normal stress responses:while the zero-shear viscosity,η,is strongly N_(S)-dependent,the first and second normal stress coefficients,Ψ_(1) and Ψ_(2),collapse onto universal curves when scaled by the dimensionless shear rate,γτ_(0),suggesting a common mechanism of orientation and stretching.Under shear,long chains compress in the vorticity direction λ_(z)~Wi^(-0.2),which reduces collision frequency and contributes to shear thinning,while the scaling of weaker orientation resistance m_(G)~Wi^(0.35)reflects hydrodynamic screening by the short-chain matrix.These findings highlight the limitations of single-chain models and emphasize the necessity of considering N_(S)-dependent matrix dynamics and flow-induced structural changes in understanding the rheology of unentangled polymer blends.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supported by the National Natural Science Foundation of China(Nos.22475215,22031009 and 21921001)the NSF of Fujian Province(Nos.2023J01216,2024J010039)the Selfdeployment Project Research Program of Haixi Institutes,Chinese Academy of Sciences(No.CXZX-2022-GH06).
文摘Exploring new material systems and enhancing the birefringence of compounds is a highly valuable endeavor.In this study,we introduce a novel method to enhance the birefringence of inorganic compounds by inducing structural alignment through linear groups and fluoride ions.We report on two new compounds:HgGa_(2)(SeO_(3))_(4) and Hg_(2)Ga(Se_(O)_(3))_(2)F.HgGa_(2)(SeO_(3))_(4) crystallizes in a non-centrosymmetric(NCS)space group,exhibiting a second harmonic generation(SHG)efficiency of approximately 60% that of commercial KH2PO4(KDP),with a birefringence of 0.032@546 nm.Hg_(2)Ga(Se_(O)_(3))_(2)F,on the other hand,crystallizes in a centrosymmetric space(CS)group and represents the first reported HgI-based selenite birefringent material.Due to the influence of the linear group Hg_(2)O_(2),its birefringence is significantly enhanced to 0.111@546 nm,which is 3.5 times that of HgGa_(2)(SeO_(3))_(4).Moreover,both compounds demonstrate high stability and a broad optical transparency window.These findings indicate that Hg_(2)Ga(Se_(O)_(3))_(2)F is a promising candidate for birefringent material in the mid-infrared(MIR)range.Our research provides an innovative strategy for improving the birefringence of compounds.
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.
文摘This paper aims to explore and quantify the nonlinear vibration response of tri-directional functionally graded sandwich(3D-FGSW)plates partially supported by a Pasternak foundation(PF)subjected to blast loading(BL).A key objective is to develop a computationally efficient finite element framework capable of accurately capturing the complex behavior of 3D-FGSW plates.The studied configuration features a two-dimensional functionally graded material(2D-FGM)core between two threedimensional functionally graded material(3D-FGM)face layers.Nonlinear geometric effects,including mid-plane stretching,are modeled using von K arm an-type assumptions,and the governing equations are formulated via Hamilton's principle within an improved first-order shear deformation theory(iFSDT).The accuracy and computational efficiency of the proposed method are validated through comparison with existing benchmark solutions.Subsequently,a comprehensive parametric study is carried out to examine the effects of geometric dimensions,material properties,foundation sizes,and boundary conditions(BCs)on the nonlinear vibration of 3D-FGSW plates.The findings of this work are expected to provide valuable insights for the design and manufacturing of advanced sandwich structures subjected to BL.
文摘Elliptic curve(EC)based cryptosystems gained more attention due to enhanced security than the existing public key cryptosystems.A substitution box(S-box)plays a vital role in securing modern symmetric key cryptosystems.However,the recently developed EC based algorithms usually trade off between computational efficiency and security,necessitating the design of a new algorithm with the desired cryptographic strength.To address these shortcomings,this paper proposes a new scheme based onMordell elliptic curve(MEC)over the complex field for generating distinct,dynamic,and highly uncorrelated S-boxes.Furthermore,we count the exact number of the obtained S-boxes,and demonstrate that the permuted version of the presented S-box is statistically optimal.The nonsingularity of the presented algorithm and the injectivity of the resultant output are explored.Rigorous theoretical analysis and experimental results demonstrate that the proposedmethod is highly effective in generating a large number of dynamic S-boxes with adequate cryptographic properties,surpassing current state-of-the-art S-box generation algorithms in terms of security.Apart fromthis,the generated S-box is benchmarked using side-channel attacks,and its performance is compared with highly nonlinear S-boxes,demonstrating comparable results.In addition,we present an application of our proposed S-box generator by incorporating it into an image encryption technique.The encrypted and decrypted images are tested by employing extensive standard security metrics,including the Number of Pixel Change Rate,the Unified Average Changing Intensity,information entropy,correlation coefficient,and histogram analysis.Moreover,the analysis is extended beyond conventional metrics to validate the new method using advanced tests,such as the NIST statistical test suite,robustness analysis,and noise and cropping attacks.Experimental outcomes show that the presented algorithm strengthens the existing encryption scheme against various well-known cryptographic attacks.
基金National Natural Science Foundation of China(No.12071370)。
文摘The bipartite containment control problem for heterogeneous nonlinear multi-agent systems(HNMASs)within multi-group networks under signed digraphs is investigated,where the first-order and second-order nonlinear dynamic agents belong to distinct groups.Interactions are cooperative-antagonistic within each group and sign-in-degree balanced across the inter-groups.Firstly,a state feedback control protocol is designed to ensure that the trajectories of followers in diverse groups can converge to distinct convex hulls formed by their corresponding leaders,respectively.As an extension,the bipartite control problem with time-variant formation for the multi-agent system(MAS)is also considered,and a corresponding control protocol with formation compensation vectors is given.Finally,in view of Lyapunov stability theory and matrix inequality,the sufficient conditions for realizing the bipartite containment control are obtained,and several simulations are provided to verify the validity of the above methods.
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supported by the National Natural Science Foundation of China(No.12175295)the National Key R&D Program of China(2021YFA1601000)the Shanghai Municipal Science and Technology Major Project。
文摘With the development of the semiconductor industry below the 7 nm scale,critical dimension small-angle X-ray scattering(CD-SAXS)has emerged as a powerful tool for quantitatively measuring nanoscale deviations.In this study,the effects of X-ray beam size and photon energy on the accuracy of critical dimension measurements were investigated.Critical dimensions measured using beams with different spot sizes showed different deviations from the expected values.Beam sizes that were either too large or too small did not improve confidence intervals.As the incident energy increased,the X-ray transmission rate increased,while the scattering cross section decreased,resulting in a gradual decrease in the signal-to-noise ratio of the diffraction peaks,which reduced the accuracy of the CD-SAXS measurements.An optimal accuracy was obtained at 12 keV with a smaller beam size.Using an effective trapezoid model,the results yielded an average pitch of 100.4±0.2 nm,width of 49.8±0.2 nm,height of 130.0±0.2 nm,and a sidewall angle below 1.1°±0.1°.These results provide crucial guidance for the future development of CD-SAXS laboratories and the construction of X-ray machines as well as robust support for research in related fields.
基金supported in part by the National Science and Technology Council under Grant NSTC 114-2221-E-027-104.
文摘Trajectory tracking for nonlinear robotic systems remains a fundamental yet challenging problem in control engineering,particularly when both precision and efficiency must be ensured.Conventional control methods are often effective for stabilization but may not directly optimize long-term performance.To address this limitation,this study develops an integrated framework that combines optimal control principles with reinforcement learning for a single-link robotic manipulator.The proposed scheme adopts an actor–critic structure,where the critic network approximates the value function associated with the Hamilton–Jacobi–Bellman equation,and the actor network generates near-optimal control signals in real time.This dual adaptation enables the controller to refine its policy online without explicit system knowledge.Stability of the closed-loop system is analyzed through Lyapunov theory,ensuring boundedness of the tracking error.Numerical simulations on the single-link manipulator demonstrate that themethod achieves accurate trajectory followingwhile maintaining lowcontrol effort.The results further showthat the actor–critic learning mechanism accelerates convergence of the control policy compared with conventional optimization-based strategies.This work highlights the potential of reinforcement learning integrated with optimal control for robotic manipulators and provides a foundation for future extensions to more complex multi-degree-of-freedom systems.The proposed controller is further validated in a physics-based virtual Gazebo environment,demonstrating stable adaptation and real-time feasibility.
基金financially supported by the National Natural Science Foundation of China(Nos.22341304,22303100 and 12205270)the National Key R&D Program of China(Nos.2023YFA1008800 and 2020YFA0713601)the Strategic Priority Research Program of the Chinese Academy of Sciences(No.XDC0180303)。
文摘The equilibrium dynamics and nonlinear rheology of unentangled polymer blends remain inadequately understood,especially regarding the influence of short-chain matrix length N_(S) on the structure and rheological behavior of dispersed long chains.Using molecular dynamics simulations based on the Kremer-Grest model,we systematically explore the N_(S)-dependence of static conformations,equilibrium dynamics,and nonlinear shear responses in unentangled long-chain/short-chain polymer blends.Our results demonstrate a decoupling between the static and dynamic sensitivity to N_(S):while the static chain size,R_g,follows Flory theory with slight swelling at small N_(S) due to incomplete excluded volume screening,the diffusion coefficient,D,and the relaxation time,τ_(0),exhibit a strong,non-monotonic N_(S)-dependence,transitioning from monomeric friction dominance at small N_(S) to collective segmental rearrangement at large N_(S).Additionally,we observe partial decoupling between the viscous and normal stress responses:while the zero-shear viscosity,η,is strongly N_(S)-dependent,the first and second normal stress coefficients,Ψ_(1) and Ψ_(2),collapse onto universal curves when scaled by the dimensionless shear rate,γτ_(0),suggesting a common mechanism of orientation and stretching.Under shear,long chains compress in the vorticity direction λ_(z)~Wi^(-0.2),which reduces collision frequency and contributes to shear thinning,while the scaling of weaker orientation resistance m_(G)~Wi^(0.35)reflects hydrodynamic screening by the short-chain matrix.These findings highlight the limitations of single-chain models and emphasize the necessity of considering N_(S)-dependent matrix dynamics and flow-induced structural changes in understanding the rheology of unentangled polymer blends.
