With the implementation of General Senior High School Mathematics Curriculum Standards(2017 Edition,Revised in 2020),probability and statistics,as important carriers of the core mathematical competencies“mathematical...With the implementation of General Senior High School Mathematics Curriculum Standards(2017 Edition,Revised in 2020),probability and statistics,as important carriers of the core mathematical competencies“mathematical modeling”and“data analysis,”have increasingly highlighted their educational value.By summarizing the historical evolution of probability and statistics thinking and combining with teaching practice cases,this study explores its unique role in cultivating students’core mathematical competencies.The research proposes a project-based teaching strategy relying on real scenarios and empowered by technology.Through cases,it demonstrates how to use modern educational technology to realize the whole-process exploration of data collection,model construction,and conclusion verification,so as to promote the transformation of middle school probability and statistics teaching from knowledge imparting to competency development,and provide a practical reference for curriculum reform.展开更多
Under the background of information technology in education,there is insufficient integration of technological knowledge,pedagogical knowledge,and subject content knowledge in the teaching of propositions in high scho...Under the background of information technology in education,there is insufficient integration of technological knowledge,pedagogical knowledge,and subject content knowledge in the teaching of propositions in high school mathematics.Teachers mostly equate information technology with multimedia presentations,and students often memorize formulas mechanically,which leads to difficulties in the application of complex propositions.In this study,we take“the cosine formula of the difference between two angles”as an example.Based on the TPACK framework,we use contextual teaching and geometric drawing board demonstration to integrate subject content,pedagogical knowledge,and technological knowledge in teaching design and practice.It is found that by dynamically displaying the derivation process of the formula and guiding students to explore independently,it can help them understand the logic of the formula and improve their application ability.This study provides a paradigm for teaching propositions in high school mathematics and suggests that the TPACK framework can facilitate knowledge integration and cultivate students’mathematical literacy such as problem posing and creative inquiry,which is of great significance for teaching practice.展开更多
The modifiedλ-differential Lie-Yamaguti algebras are considered,in which a modifiedλ-differential Lie-Yamaguti algebra consisting of a Lie-Yamaguti algebra and a modifiedλ-differential operator.First we introduce t...The modifiedλ-differential Lie-Yamaguti algebras are considered,in which a modifiedλ-differential Lie-Yamaguti algebra consisting of a Lie-Yamaguti algebra and a modifiedλ-differential operator.First we introduce the representation of modifiedλ-differential Lie-Yamaguti algebras.Furthermore,we establish the cohomology of a modifiedλ-differential Lie-Yamaguti algebra with coefficients in a representation.Finally,we investigate the one-parameter formal deformations and Abelian extensions of modifiedλ-differential Lie-Yamaguti algebras using the second cohomology group.展开更多
This paper proposes a novel method for the automatic diagnosis of keratitis using feature vector quantization and self-attention mechanisms(ADK_FVQSAM).First,high-level features are extracted using the DenseNet121 bac...This paper proposes a novel method for the automatic diagnosis of keratitis using feature vector quantization and self-attention mechanisms(ADK_FVQSAM).First,high-level features are extracted using the DenseNet121 backbone network,followed by adaptive average pooling to scale the features to a fixed length.Subsequently,product quantization with residuals(PQR)is applied to convert continuous feature vectors into discrete features representations,preserving essential information insensitive to image quality variations.The quantized and original features are concatenated and fed into a self-attention mechanism to capture keratitis-related features.Finally,these enhanced features are classified through a fully connected layer.Experiments on clinical low-quality(LQ)images show that ADK_FVQSAM achieves accuracies of 87.7%,81.9%,and 89.3% for keratitis,other corneal abnormalities,and normal corneas,respectively.Compared to DenseNet121,Swin transformer,and InceptionResNet,ADK_FVQSAM improves average accuracy by 3.1%,11.3%,and 15.3%,respectively.These results demonstrate that ADK_FVQSAM significantly enhances the recognition performance of keratitis based on LQ slit-lamp images,offering a practical approach for clinical application.展开更多
The widespread popularization and application of laser technology have provided a powerful tool for a deeper understanding of the material world and given birth to several emerging research fields.This study mainly fo...The widespread popularization and application of laser technology have provided a powerful tool for a deeper understanding of the material world and given birth to several emerging research fields.This study mainly focuses on the following three key aspects.First,the classical ensemble method is adopted to conduct a comprehensive and in-depth analysis of two-dimensional(2D)matter–wave pulses in Bose–Fermi mixed gases(including linear and nonlinear pulses).Second,under the strict constraints of unitary systems,a coupled Kd V equation is successfully derived,and the prolongation structure theory is skillfully used to carry out detailed calculations and analyses on this equation.Thus,the prolongation algebra of this equation is accurately determined,and the corresponding Lax pair is rigorously derived.Finally,based on the carefully obtained Lax pair from the prolongation structure theory,the soliton solutions of this equation are further analyzed in depth,and intuitive images of each soliton solution are carefully drawn.This lays a solid foundation for subsequent detailed research on these soliton characteristics and provides great convenience.展开更多
In this paper,we call a tuple consisting of 3-Lie algebra and a higher derivation on it a 3-LieHDer pair.We introduce a cohomology theory of 3-LieHDer pairs.Next,we interpret the second cohomology group as the space o...In this paper,we call a tuple consisting of 3-Lie algebra and a higher derivation on it a 3-LieHDer pair.We introduce a cohomology theory of 3-LieHDer pairs.Next,we interpret the second cohomology group as the space of all isomorphism classes of abelian extensions.Finally,we consider formal deformations of 3-LieHDer pairs that are governed by the cohomology with self-coefficient.展开更多
The nonlinear Schrodinger equation(NLSE) is a key tool for modeling wave propagation in nonlinear and dispersive media. This study focuses on the complex cubic NLSE with δ-potential,explored through the Brownian proc...The nonlinear Schrodinger equation(NLSE) is a key tool for modeling wave propagation in nonlinear and dispersive media. This study focuses on the complex cubic NLSE with δ-potential,explored through the Brownian process. The investigation begins with the derivation of stochastic solitary wave solutions using the modified exp(-Ψ(ξ)) expansion method. To illustrate the noise effects, 3D and 2D visualizations are displayed for different non-negative values of noise parameter under suitable parameter values. Additionally, qualitative analysis of both perturbed and unperturbed dynamical systems is conducted using bifurcation and chaos theory. In bifurcation analysis, we analyze the detailed parameter analysis near fixed points of the unperturbed system. An external periodic force is applied to perturb the system, leading to an investigation of its chaotic behavior. Chaos detection tools are employed to predict the behavior of the perturbed dynamical system, with results validated through visual representations.Multistability analysis is conducted under varying initial conditions to identify multiple stable states in the perturbed dynamical system, contributing to chaotic behavior. Also, sensitivity analysis of the Hamiltonian system is performed for different initial conditions. The novelty of this work lies in the significance of the obtained results, which have not been previously explored for the considered equation. These findings offer noteworthy insights into the behavior of the complex cubic NLSE with δ-potential and its applications in fields such as nonlinear optics, quantum mechanics and Bose–Einstein condensates.展开更多
This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the n...This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the novel schemes,without relying on a priori high-order moment bound of the numerical approximation.The expected order-one mean square convergence is attained for the proposed scheme.Moreover,a numerical example is presented to verify our theoretical analysis.展开更多
Compared to single-layer networks,multilayer networks exhibit a more complex node degree composition,comprising both intra-layer and inter-layer degrees.However,the distinct impacts of these degree types on cascading ...Compared to single-layer networks,multilayer networks exhibit a more complex node degree composition,comprising both intra-layer and inter-layer degrees.However,the distinct impacts of these degree types on cascading failures remain underexplored.Distinguishing their effects is crucial for a deeper understanding of network structure,information propagation,and behavior prediction.This paper proposes a capacity-load model to influence and compare the influence of different degree types on cascading failures in multilayer networks.By designing three node removal strategies based on total degree,intra-layer degree,and inter-layer degree,simulation experiments are conducted on four types of networks.Network robustness is evaluated using the maximum number of removable nodes before collapse.The relationships between network robustness and the coupling coefficient,as well as load and capacity adjustment parameters,are also analyzed.The results indicate that the node removal strategy with the least impact on cascading failures varies across different types of networks,revealing the significance of different node degrees in failure propagation.Compared to other models,the proposed model enables networks to maintain a higher maximum number of removable nodes during cascading failures,demonstrating superior robustness.展开更多
Following the work of Li-Shi-Qing, we propose the definition of the relative volume function for an AH manifold. It is not a constant function in general and we study the regularity of this function. We use this funct...Following the work of Li-Shi-Qing, we propose the definition of the relative volume function for an AH manifold. It is not a constant function in general and we study the regularity of this function. We use this function to provide an accurate characterization of the height of the geodesic defining function for the AH manifold with a given boundary metric. Furthermore, it is shown that such functions are uniformly bounded from below at infinity and the bound only depends on the dimension. In the end, we apply this function to study the capacity of balls in AH manifolds and demonstrate that the “relative p—capacity function” coincides with the relative volume function under appropriate curvature conditions.展开更多
The adhesion enhancing effect induced by electro-magnetic loading and the adhesion weakening effect resulting from interfacial shear stress have been observed and widely reported in open literature.However,the adhesio...The adhesion enhancing effect induced by electro-magnetic loading and the adhesion weakening effect resulting from interfacial shear stress have been observed and widely reported in open literature.However,the adhesion behavior of multiferroic composites in the simultaneous presence of these two effects and the competitive mechanism between them are still unclear.In this paper,the non-slipping adhesive contact problem between a multiferroic half-space and a perfectly conducting rigid cylinder subject to multi-field loading is studied.The stated problem is reduced to a system of coupled singular integral equations,which are analytically solved with the analytical function theory.The closed-form solutions of the generalized stress fields including the contact stress,normal electric displacement,and magnetic induction are obtained.The stable equilibrium state of the adhesion system is determined with the Griffith energy balance criterion.The adhesion behavior subject to mechanical-electro-magnetic loading and a mismatch strain is discussed in detail.Numerical results indicate that exerting electro-magnetic loading can enhance the adhesion effect for both two types of multiferroic composites,namely,κ-class(non-oscillatory singularity)andε-class,which is different from the case of piezoelectric materials.It is found that the contact size finally decreases in the simultaneous presence of the electro-magnetic enhancing and shear-stress weakening effects.The results derived from this work not only are helpful to understand the contact behavior of multiferroic composites at micro/nano scale,but also have potential application value in achieving switchable adhesion.展开更多
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
For 1<p<∞,Coifman-Rochberg-Weiss established L^(p) boundedness of commutators of smooth kernels.Later,many works tried to weaken the smooth condition.In this paper,we extend these mentioned results to the case ...For 1<p<∞,Coifman-Rochberg-Weiss established L^(p) boundedness of commutators of smooth kernels.Later,many works tried to weaken the smooth condition.In this paper,we extend these mentioned results to the case of non-homogeneous but with strong H¨ormander condition.Our main skills lie in wavelet decomposition,wavelet commutators,Hardy-Littlewood maximal operator and Fefferman-Stein's vector-valued maximum function Theorem.展开更多
The Pfaffian property of graphs is of fundamental importance in graph theory,as it precisely characterizes those graphs for which the number of perfect matchings can be computed in polynomial time with respect to the ...The Pfaffian property of graphs is of fundamental importance in graph theory,as it precisely characterizes those graphs for which the number of perfect matchings can be computed in polynomial time with respect to the number of edges.The study of Pfaffian graphs originated from the enumeration of perfect matching in planar graphs.References[5,6,8]demonstrated that every planar graph is Pfaffian.Therefore,the Pfaffian property and planarity of graphs play a vital role in modern matching theory.This paper contributes a complete characterization of the Pfaffian property and planarity of connected Cayley graphs over the dicyclic group T_(4n) of order 4n(n≥3),shows that the Cayley graph Cay(T_(4n),S)is Pfaffian if and only if n is odd and S={a^(k_(1)),a^(2n−k_(1)),ba^(k_(2)),ba^(n+k_(2))},where 1≤k_(1)≤n−1,0≤k_(2)≤n−1 and(k_(1),n)=1,and furthermore,shows that Cay(T4n,S)is never planar.展开更多
In this paper, a class of discontinuous neutral-type neural networks (NTNNs) with proportional delays is considered. The targets of the paper are to study the problem of periodic solutions and fixed-time (FXT) stabili...In this paper, a class of discontinuous neutral-type neural networks (NTNNs) with proportional delays is considered. The targets of the paper are to study the problem of periodic solutions and fixed-time (FXT) stabilization of the addressed neural networks. In order to complete the targets, based on set-valued map, differential inclusions theory, coincidence theorem and Hölder inequality technique, some new proportional delay-dependent criteria shown by the inequalities are derived. Based on the fact of the existence of solution, further by applying the FXT stability lemmas and equivalent transformation, the zero solution of closed-loop system achieves FXT stabilization and the corresponding settling-times are estimated. Some previous related works on NTNNs are extended. Finally, one typical example is provided to show the effectiveness of the established results.展开更多
We consider a constrained minimization problem arising in the fractional Schrödinger equation with a trapping potential.By exploring some delicate energy estimates and studying decay properties of solution sequen...We consider a constrained minimization problem arising in the fractional Schrödinger equation with a trapping potential.By exploring some delicate energy estimates and studying decay properties of solution sequences,we obtain the concentration behavior of each minimizer of the fractional Schrödinger energy functional when a↗a^(*):=‖Q‖_(2)^(2s),where Q is the unique positive radial solution of (-△)^(s)u+su-|u|2su=0 in R^(2).Based on the discussion of the concentration phenomenon,we prove the local uniqueness of minimizers by establishing a local Poho zaev identity and studying the blow-up estimates to the nonlocal operator(-△)^(s).展开更多
It is well known that the explicit-invariant energy quadratization(EIEQ)approach can generate fully decoupled,linear and unconditionally energy-stable numerical schemes,so it is favored by many researchers.However,the...It is well known that the explicit-invariant energy quadratization(EIEQ)approach can generate fully decoupled,linear and unconditionally energy-stable numerical schemes,so it is favored by many researchers.However,the undeniable fact is that the numerical method obtained by EIEQ approach preserves the“modified”energy law instead of the original energy.This is mainly due to the introduction of some auxiliary variables in EIEQ scheme,and the truncation error will make the auxiliary variables deviate from the original definition in the process of numerical calculation.The primary objective of this paper is to address this gap by providing the accuracy and consistency of the EIEQ method in the context of the CahnHilliard equation.We introduce a relaxation technique for auxiliary variables and construct two numerical schemes based on EIEQ.The analysis results show that the newly constructed schemes are not only unconditionally energy stable,linear and fully decoupled,but also can effectively correct the errors introduced by auxiliary variables and follow the original energy law.Finally,several 2D and 3D numerical examples illustrate the accuracy and efficiency of the newly constructed numerical schemes.展开更多
Cadmium(Cd)contamination of soil is a global environmental issue.Traditional remediation techniques such as immobilization,leaching,and phytoextraction have numerous shortcomings,which has led to growing interest in t...Cadmium(Cd)contamination of soil is a global environmental issue.Traditional remediation techniques such as immobilization,leaching,and phytoextraction have numerous shortcomings,which has led to growing interest in the development of low-cost,high-efficiency,and environmentally friendly agents for removing Cd from soil.In this study,four magnetite(Fe_(3)O_(4))/polyaniline(PANI)nanocomposites,Fe_(3)O_(4)(1.0)/PANI,Fe_(3)O_(4)(1.5)/PANI,Fe_(3)O_(4)(2.0)/PANI,and Fe_(3)O_(4)(2.5)/PANI,were developed using 4 mL aniline monomer and 1.0,1.5,2.0,and 2.5 g Fe_(3)O_(4),respectively,and used as remediation agents with magnetic separation and regeneration capabilities.The Cd adsorption isotherms showed a better fit to the Langmuir model,with Fe_(3)O_(4)(1.5)/PANI exhibiting the highest Cd adsorption capacity of 47.62 mg g^(-1) at 25℃.Then,Fe_(3)O_(4)(1.5)/PANI was used to remediate four Cd-contaminated soils typical in China(black,brown,cinnamon,and red),all with a Cd content of 180 mg kg^(-1) after spiking.The results showed that the total Cd removal efficiency was satisfactory at 25.25%–38.91%and the exchangeable Cd removal efficiency was 36.03%on average.In addition,soil basic properties did not show significant changes after remediation.Regarding the regeneration performance,a higher total Cd removal efficiency(27.89%–44.96%)was achieved after the first regeneration cycle of Fe_(3)O_(4)(1.5)/PANI.After two regeneration cycles,Fe_(3)O_(4)(1.5)/PANI exhibited decreased total Cd removal efficiency compared to after the first regeneration,but its efficiency remained above 95%of or higher than those of virgin Fe_(3)O_(4)(1.5)/PANI.The synthetic process of Fe_(3)O_(4)/PANI was simple and cost-effective,and Fe_(3)O_(4)/PANI exhibited a high Cd removal efficiency with easy recovery and recyclability.Therefore,Fe_(3)O_(4)/PANI is a promising solution for the sustainable and efficient remediation of Cd-contaminated soils,especially for the reclamation of highly contaminated development land.展开更多
The third-order flow Gerdjikov–Ivanov(TOFGI)equation is studied,and the Darboux transformation(DT)is used to obtain the determinant expression of the solution of this equation.On this basis,the soliton solution,ratio...The third-order flow Gerdjikov–Ivanov(TOFGI)equation is studied,and the Darboux transformation(DT)is used to obtain the determinant expression of the solution of this equation.On this basis,the soliton solution,rational solution,positon solution,and breather solution of the TOFGI equation are obtained by taking zero seed solution and non-zero seed solution.The exact solutions and dynamic properties of the Gerdjikov–Ivanov(GI)equation and the TOFGI equation are compared in detail under the same conditions,and it is found that there are some differences in the velocities and trajectories of the solutions of the two equations.展开更多
The unique arrangement of panels and folds in origami structures provides distinct mechanical properties,such as the ability to achieve multiple stable states,reconfigure shapes,and adjust performance.However,combinin...The unique arrangement of panels and folds in origami structures provides distinct mechanical properties,such as the ability to achieve multiple stable states,reconfigure shapes,and adjust performance.However,combining movement and control functions into a simple yet efficient origami-based system remains a challenge.This study introduces a practical and efficient bistable origami mechanism,realized through lightweight and tailored designs in two bio-inspired applications.The mechanism is constructed from two thin materials:a PET sheet with precisely cut flexible hinges and a pre-tensioned elastic band.Its mechanical behavior is studied using nonlinear spring models.These components can be rearranged to create new bistable structures,enabling the integration of movement and partial control features.Inspired by natural systems,the mechanism is applied to two examples:a passive origami gripper that can quickly and precisely grasp moving objects in less than 100 ms,and an active magnetic-driven fish tail capable of high-speed swimming in multiple modes,reaching a maximum straight-line speed of 3.35 body lengths per second and a turning speed of 2.3 radians per second.This bistable origami mechanism highlights its potential for flexible design and high performance,offering useful insights for developing origami-based robotic systems.展开更多
基金2021 Annual Research Project of Yili Normal University(2021YSBS012)。
文摘With the implementation of General Senior High School Mathematics Curriculum Standards(2017 Edition,Revised in 2020),probability and statistics,as important carriers of the core mathematical competencies“mathematical modeling”and“data analysis,”have increasingly highlighted their educational value.By summarizing the historical evolution of probability and statistics thinking and combining with teaching practice cases,this study explores its unique role in cultivating students’core mathematical competencies.The research proposes a project-based teaching strategy relying on real scenarios and empowered by technology.Through cases,it demonstrates how to use modern educational technology to realize the whole-process exploration of data collection,model construction,and conclusion verification,so as to promote the transformation of middle school probability and statistics teaching from knowledge imparting to competency development,and provide a practical reference for curriculum reform.
文摘Under the background of information technology in education,there is insufficient integration of technological knowledge,pedagogical knowledge,and subject content knowledge in the teaching of propositions in high school mathematics.Teachers mostly equate information technology with multimedia presentations,and students often memorize formulas mechanically,which leads to difficulties in the application of complex propositions.In this study,we take“the cosine formula of the difference between two angles”as an example.Based on the TPACK framework,we use contextual teaching and geometric drawing board demonstration to integrate subject content,pedagogical knowledge,and technological knowledge in teaching design and practice.It is found that by dynamically displaying the derivation process of the formula and guiding students to explore independently,it can help them understand the logic of the formula and improve their application ability.This study provides a paradigm for teaching propositions in high school mathematics and suggests that the TPACK framework can facilitate knowledge integration and cultivate students’mathematical literacy such as problem posing and creative inquiry,which is of great significance for teaching practice.
基金National Natural Science Foundation of China(12161013)Research Projects of Guizhou University of Commerce in 2024。
文摘The modifiedλ-differential Lie-Yamaguti algebras are considered,in which a modifiedλ-differential Lie-Yamaguti algebra consisting of a Lie-Yamaguti algebra and a modifiedλ-differential operator.First we introduce the representation of modifiedλ-differential Lie-Yamaguti algebras.Furthermore,we establish the cohomology of a modifiedλ-differential Lie-Yamaguti algebra with coefficients in a representation.Finally,we investigate the one-parameter formal deformations and Abelian extensions of modifiedλ-differential Lie-Yamaguti algebras using the second cohomology group.
基金supported by the National Natural Science Foundation of China(Nos.62276210,82201148 and 62376215)the Key Research and Development Project of Shaanxi Province(No.2025CY-YBXM-044)+3 种基金the Natural Science Foundation of Zhejiang Province(No.LQ22H120002)the Medical Health Science and Technology Project of Zhejiang Province(Nos.2022RC069 and 2023KY1140)the Natural Science Foundation of Ningbo(No.2023J390)the Ningbo Top Medical and Health Research Program(No.2023030716).
文摘This paper proposes a novel method for the automatic diagnosis of keratitis using feature vector quantization and self-attention mechanisms(ADK_FVQSAM).First,high-level features are extracted using the DenseNet121 backbone network,followed by adaptive average pooling to scale the features to a fixed length.Subsequently,product quantization with residuals(PQR)is applied to convert continuous feature vectors into discrete features representations,preserving essential information insensitive to image quality variations.The quantized and original features are concatenated and fed into a self-attention mechanism to capture keratitis-related features.Finally,these enhanced features are classified through a fully connected layer.Experiments on clinical low-quality(LQ)images show that ADK_FVQSAM achieves accuracies of 87.7%,81.9%,and 89.3% for keratitis,other corneal abnormalities,and normal corneas,respectively.Compared to DenseNet121,Swin transformer,and InceptionResNet,ADK_FVQSAM improves average accuracy by 3.1%,11.3%,and 15.3%,respectively.These results demonstrate that ADK_FVQSAM significantly enhances the recognition performance of keratitis based on LQ slit-lamp images,offering a practical approach for clinical application.
基金Project supported by the National Natural Science Foundation of China(Grant No.12261072)。
文摘The widespread popularization and application of laser technology have provided a powerful tool for a deeper understanding of the material world and given birth to several emerging research fields.This study mainly focuses on the following three key aspects.First,the classical ensemble method is adopted to conduct a comprehensive and in-depth analysis of two-dimensional(2D)matter–wave pulses in Bose–Fermi mixed gases(including linear and nonlinear pulses).Second,under the strict constraints of unitary systems,a coupled Kd V equation is successfully derived,and the prolongation structure theory is skillfully used to carry out detailed calculations and analyses on this equation.Thus,the prolongation algebra of this equation is accurately determined,and the corresponding Lax pair is rigorously derived.Finally,based on the carefully obtained Lax pair from the prolongation structure theory,the soliton solutions of this equation are further analyzed in depth,and intuitive images of each soliton solution are carefully drawn.This lays a solid foundation for subsequent detailed research on these soliton characteristics and provides great convenience.
基金Supported by the National Natural Science Foundation of China(Grant No.12161013)the Basic Research Program(Natural Science)of Guizhou Province(Grant No.ZK[2023]025).
文摘In this paper,we call a tuple consisting of 3-Lie algebra and a higher derivation on it a 3-LieHDer pair.We introduce a cohomology theory of 3-LieHDer pairs.Next,we interpret the second cohomology group as the space of all isomorphism classes of abelian extensions.Finally,we consider formal deformations of 3-LieHDer pairs that are governed by the cohomology with self-coefficient.
基金Supporting Project under Grant No.RSP2025R472,King Saud University,Riyadh,Saudi Arabia。
文摘The nonlinear Schrodinger equation(NLSE) is a key tool for modeling wave propagation in nonlinear and dispersive media. This study focuses on the complex cubic NLSE with δ-potential,explored through the Brownian process. The investigation begins with the derivation of stochastic solitary wave solutions using the modified exp(-Ψ(ξ)) expansion method. To illustrate the noise effects, 3D and 2D visualizations are displayed for different non-negative values of noise parameter under suitable parameter values. Additionally, qualitative analysis of both perturbed and unperturbed dynamical systems is conducted using bifurcation and chaos theory. In bifurcation analysis, we analyze the detailed parameter analysis near fixed points of the unperturbed system. An external periodic force is applied to perturb the system, leading to an investigation of its chaotic behavior. Chaos detection tools are employed to predict the behavior of the perturbed dynamical system, with results validated through visual representations.Multistability analysis is conducted under varying initial conditions to identify multiple stable states in the perturbed dynamical system, contributing to chaotic behavior. Also, sensitivity analysis of the Hamiltonian system is performed for different initial conditions. The novelty of this work lies in the significance of the obtained results, which have not been previously explored for the considered equation. These findings offer noteworthy insights into the behavior of the complex cubic NLSE with δ-potential and its applications in fields such as nonlinear optics, quantum mechanics and Bose–Einstein condensates.
基金supported by the National Natural Science Foundation of China(Nos.12471394,12371417)Natural Science Foundation of Changsha(No.kq2502101)。
文摘This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the novel schemes,without relying on a priori high-order moment bound of the numerical approximation.The expected order-one mean square convergence is attained for the proposed scheme.Moreover,a numerical example is presented to verify our theoretical analysis.
基金supported by the National Social Science Fund Project(No.23&ZD115)the Graduate Student Research Innovation Project of the School of Mathematics and Statistics,Hubei Minzu University(No.STK2023011)。
文摘Compared to single-layer networks,multilayer networks exhibit a more complex node degree composition,comprising both intra-layer and inter-layer degrees.However,the distinct impacts of these degree types on cascading failures remain underexplored.Distinguishing their effects is crucial for a deeper understanding of network structure,information propagation,and behavior prediction.This paper proposes a capacity-load model to influence and compare the influence of different degree types on cascading failures in multilayer networks.By designing three node removal strategies based on total degree,intra-layer degree,and inter-layer degree,simulation experiments are conducted on four types of networks.Network robustness is evaluated using the maximum number of removable nodes before collapse.The relationships between network robustness and the coupling coefficient,as well as load and capacity adjustment parameters,are also analyzed.The results indicate that the node removal strategy with the least impact on cascading failures varies across different types of networks,revealing the significance of different node degrees in failure propagation.Compared to other models,the proposed model enables networks to maintain a higher maximum number of removable nodes during cascading failures,demonstrating superior robustness.
文摘Following the work of Li-Shi-Qing, we propose the definition of the relative volume function for an AH manifold. It is not a constant function in general and we study the regularity of this function. We use this function to provide an accurate characterization of the height of the geodesic defining function for the AH manifold with a given boundary metric. Furthermore, it is shown that such functions are uniformly bounded from below at infinity and the bound only depends on the dimension. In the end, we apply this function to study the capacity of balls in AH manifolds and demonstrate that the “relative p—capacity function” coincides with the relative volume function under appropriate curvature conditions.
基金Project supported by the National Natural Science Foundation of China(Nos.12272269,11972257,and 11472193)the Shanghai Pilot Program for Basic Researchthe Shanghai Gaofeng Project for University Academic Program Development。
文摘The adhesion enhancing effect induced by electro-magnetic loading and the adhesion weakening effect resulting from interfacial shear stress have been observed and widely reported in open literature.However,the adhesion behavior of multiferroic composites in the simultaneous presence of these two effects and the competitive mechanism between them are still unclear.In this paper,the non-slipping adhesive contact problem between a multiferroic half-space and a perfectly conducting rigid cylinder subject to multi-field loading is studied.The stated problem is reduced to a system of coupled singular integral equations,which are analytically solved with the analytical function theory.The closed-form solutions of the generalized stress fields including the contact stress,normal electric displacement,and magnetic induction are obtained.The stable equilibrium state of the adhesion system is determined with the Griffith energy balance criterion.The adhesion behavior subject to mechanical-electro-magnetic loading and a mismatch strain is discussed in detail.Numerical results indicate that exerting electro-magnetic loading can enhance the adhesion effect for both two types of multiferroic composites,namely,κ-class(non-oscillatory singularity)andε-class,which is different from the case of piezoelectric materials.It is found that the contact size finally decreases in the simultaneous presence of the electro-magnetic enhancing and shear-stress weakening effects.The results derived from this work not only are helpful to understand the contact behavior of multiferroic composites at micro/nano scale,but also have potential application value in achieving switchable adhesion.
基金supported by the National Natural Science Foundation of China(12171373)Chen's work also supported by the Fundamental Research Funds for the Central Universities of China(GK202207018).
文摘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.
基金partially supported by the research grant of Macao University of Science and Technology(FRG-22-075-MCMS)the Macao Government Research Funding(FDCT0128/2022/A)+2 种基金the Science and Technology Development Fund of Macao SAR(005/2022/ALC)the Science and Technology Development Fund of Macao SAR(0045/2021/A)Macao University of Science and Technology(FRG-20-021-MISE)。
文摘For 1<p<∞,Coifman-Rochberg-Weiss established L^(p) boundedness of commutators of smooth kernels.Later,many works tried to weaken the smooth condition.In this paper,we extend these mentioned results to the case of non-homogeneous but with strong H¨ormander condition.Our main skills lie in wavelet decomposition,wavelet commutators,Hardy-Littlewood maximal operator and Fefferman-Stein's vector-valued maximum function Theorem.
基金supported by NSFC(No.12201202)NSF of Hunan Province(No.2023JJ30180)NSFC(No.12471022)。
文摘The Pfaffian property of graphs is of fundamental importance in graph theory,as it precisely characterizes those graphs for which the number of perfect matchings can be computed in polynomial time with respect to the number of edges.The study of Pfaffian graphs originated from the enumeration of perfect matching in planar graphs.References[5,6,8]demonstrated that every planar graph is Pfaffian.Therefore,the Pfaffian property and planarity of graphs play a vital role in modern matching theory.This paper contributes a complete characterization of the Pfaffian property and planarity of connected Cayley graphs over the dicyclic group T_(4n) of order 4n(n≥3),shows that the Cayley graph Cay(T_(4n),S)is Pfaffian if and only if n is odd and S={a^(k_(1)),a^(2n−k_(1)),ba^(k_(2)),ba^(n+k_(2))},where 1≤k_(1)≤n−1,0≤k_(2)≤n−1 and(k_(1),n)=1,and furthermore,shows that Cay(T4n,S)is never planar.
基金supported by Social Science Fund of Hunan province(Grant No.22JD074)the Research Foundation of Education Bureau of Hunan province(Grant No.22B0912).
文摘In this paper, a class of discontinuous neutral-type neural networks (NTNNs) with proportional delays is considered. The targets of the paper are to study the problem of periodic solutions and fixed-time (FXT) stabilization of the addressed neural networks. In order to complete the targets, based on set-valued map, differential inclusions theory, coincidence theorem and Hölder inequality technique, some new proportional delay-dependent criteria shown by the inequalities are derived. Based on the fact of the existence of solution, further by applying the FXT stability lemmas and equivalent transformation, the zero solution of closed-loop system achieves FXT stabilization and the corresponding settling-times are estimated. Some previous related works on NTNNs are extended. Finally, one typical example is provided to show the effectiveness of the established results.
基金supported by the Fundamental Research Program of Shanxi Province(202403021222126)supported by the Fundamental Research Program of Shanxi Province(202303021211056)supported by the National Natural Science Foundation of China(12071486)。
文摘We consider a constrained minimization problem arising in the fractional Schrödinger equation with a trapping potential.By exploring some delicate energy estimates and studying decay properties of solution sequences,we obtain the concentration behavior of each minimizer of the fractional Schrödinger energy functional when a↗a^(*):=‖Q‖_(2)^(2s),where Q is the unique positive radial solution of (-△)^(s)u+su-|u|2su=0 in R^(2).Based on the discussion of the concentration phenomenon,we prove the local uniqueness of minimizers by establishing a local Poho zaev identity and studying the blow-up estimates to the nonlocal operator(-△)^(s).
基金Supported by the National Natural Science Foundation of China(Grant No.11901100)the Scientific Research Foundation of Guizhou University of Finance and Economics(Grant No.2022XSXMB11).
文摘It is well known that the explicit-invariant energy quadratization(EIEQ)approach can generate fully decoupled,linear and unconditionally energy-stable numerical schemes,so it is favored by many researchers.However,the undeniable fact is that the numerical method obtained by EIEQ approach preserves the“modified”energy law instead of the original energy.This is mainly due to the introduction of some auxiliary variables in EIEQ scheme,and the truncation error will make the auxiliary variables deviate from the original definition in the process of numerical calculation.The primary objective of this paper is to address this gap by providing the accuracy and consistency of the EIEQ method in the context of the CahnHilliard equation.We introduce a relaxation technique for auxiliary variables and construct two numerical schemes based on EIEQ.The analysis results show that the newly constructed schemes are not only unconditionally energy stable,linear and fully decoupled,but also can effectively correct the errors introduced by auxiliary variables and follow the original energy law.Finally,several 2D and 3D numerical examples illustrate the accuracy and efficiency of the newly constructed numerical schemes.
基金financially supported by the National Natural Science Foundation of China(No.41807116)the Natural Science Foundation of Fujian Province,China(Nos.2023J01418,2019J05035,and 2022N0024)+2 种基金the Scientific and Technological Innovation Project of China Metallurgical Geology Bureau(No.CMGBKY202301)the Independent Innovation Foundation of Tianjin University and Fuzhou University,China(No.TF2023-3)the Fuzhou University Testing Fund of Precious Apparatus,China(No.2023T014).
文摘Cadmium(Cd)contamination of soil is a global environmental issue.Traditional remediation techniques such as immobilization,leaching,and phytoextraction have numerous shortcomings,which has led to growing interest in the development of low-cost,high-efficiency,and environmentally friendly agents for removing Cd from soil.In this study,four magnetite(Fe_(3)O_(4))/polyaniline(PANI)nanocomposites,Fe_(3)O_(4)(1.0)/PANI,Fe_(3)O_(4)(1.5)/PANI,Fe_(3)O_(4)(2.0)/PANI,and Fe_(3)O_(4)(2.5)/PANI,were developed using 4 mL aniline monomer and 1.0,1.5,2.0,and 2.5 g Fe_(3)O_(4),respectively,and used as remediation agents with magnetic separation and regeneration capabilities.The Cd adsorption isotherms showed a better fit to the Langmuir model,with Fe_(3)O_(4)(1.5)/PANI exhibiting the highest Cd adsorption capacity of 47.62 mg g^(-1) at 25℃.Then,Fe_(3)O_(4)(1.5)/PANI was used to remediate four Cd-contaminated soils typical in China(black,brown,cinnamon,and red),all with a Cd content of 180 mg kg^(-1) after spiking.The results showed that the total Cd removal efficiency was satisfactory at 25.25%–38.91%and the exchangeable Cd removal efficiency was 36.03%on average.In addition,soil basic properties did not show significant changes after remediation.Regarding the regeneration performance,a higher total Cd removal efficiency(27.89%–44.96%)was achieved after the first regeneration cycle of Fe_(3)O_(4)(1.5)/PANI.After two regeneration cycles,Fe_(3)O_(4)(1.5)/PANI exhibited decreased total Cd removal efficiency compared to after the first regeneration,but its efficiency remained above 95%of or higher than those of virgin Fe_(3)O_(4)(1.5)/PANI.The synthetic process of Fe_(3)O_(4)/PANI was simple and cost-effective,and Fe_(3)O_(4)/PANI exhibited a high Cd removal efficiency with easy recovery and recyclability.Therefore,Fe_(3)O_(4)/PANI is a promising solution for the sustainable and efficient remediation of Cd-contaminated soils,especially for the reclamation of highly contaminated development land.
基金Project supported by the National Natural Science Foundation of China(Grant No.12201329)the Zhejiang Provincial Natural Science Foundation of China(Grant No.LY24A010002)the Natural Science Foundation of Ningbo(Grant No.2023J126)。
文摘The third-order flow Gerdjikov–Ivanov(TOFGI)equation is studied,and the Darboux transformation(DT)is used to obtain the determinant expression of the solution of this equation.On this basis,the soliton solution,rational solution,positon solution,and breather solution of the TOFGI equation are obtained by taking zero seed solution and non-zero seed solution.The exact solutions and dynamic properties of the Gerdjikov–Ivanov(GI)equation and the TOFGI equation are compared in detail under the same conditions,and it is found that there are some differences in the velocities and trajectories of the solutions of the two equations.
基金supported in part by the Fundamental Research Funds for the Central Universities under Grant CSA-TS202404in part by the National Natural Science Foundation of China under Grant 12172226.
文摘The unique arrangement of panels and folds in origami structures provides distinct mechanical properties,such as the ability to achieve multiple stable states,reconfigure shapes,and adjust performance.However,combining movement and control functions into a simple yet efficient origami-based system remains a challenge.This study introduces a practical and efficient bistable origami mechanism,realized through lightweight and tailored designs in two bio-inspired applications.The mechanism is constructed from two thin materials:a PET sheet with precisely cut flexible hinges and a pre-tensioned elastic band.Its mechanical behavior is studied using nonlinear spring models.These components can be rearranged to create new bistable structures,enabling the integration of movement and partial control features.Inspired by natural systems,the mechanism is applied to two examples:a passive origami gripper that can quickly and precisely grasp moving objects in less than 100 ms,and an active magnetic-driven fish tail capable of high-speed swimming in multiple modes,reaching a maximum straight-line speed of 3.35 body lengths per second and a turning speed of 2.3 radians per second.This bistable origami mechanism highlights its potential for flexible design and high performance,offering useful insights for developing origami-based robotic systems.
