In this paper,we prove that Euclid's algorithm,Bezout's equation and Divi-sion algorithm are equivalent to each other.Our result shows that Euclid has preliminarily established the theory of divisibility and t...In this paper,we prove that Euclid's algorithm,Bezout's equation and Divi-sion algorithm are equivalent to each other.Our result shows that Euclid has preliminarily established the theory of divisibility and the greatest common divisor.We further provided several suggestions for teaching.展开更多
This study directs the discussion of HIV disease with a novel kind of complex dynamical generalized and piecewise operator in the sense of classical and Atangana Baleanu(AB)derivatives having arbitrary order.The HIV i...This study directs the discussion of HIV disease with a novel kind of complex dynamical generalized and piecewise operator in the sense of classical and Atangana Baleanu(AB)derivatives having arbitrary order.The HIV infection model has a susceptible class,a recovered class,along with a case of infection divided into three sub-different levels or categories and the recovered class.The total time interval is converted into two,which are further investigated for ordinary and fractional order operators of the AB derivative,respectively.The proposed model is tested separately for unique solutions and existence on bi intervals.The numerical solution of the proposed model is treated by the piece-wise numerical iterative scheme of Newtons Polynomial.The proposed method is established for piece-wise derivatives under natural order and non-singular Mittag-Leffler Law.The cross-over or bending characteristics in the dynamical system of HIV are easily examined by the aspect of this research having a memory effect for controlling the said disease.This study uses the neural network(NN)technique to obtain a better set of weights with low residual errors,and the epochs number is considered 1000.The obtained figures represent the approximate solution and absolute error which are tested with NN to train the data accurately.展开更多
Assessing the behaviour and concentration of waste pollutants deposited between two parallel plates is essential for effective environmental management.Determining the effectiveness of treatment methods in reducing po...Assessing the behaviour and concentration of waste pollutants deposited between two parallel plates is essential for effective environmental management.Determining the effectiveness of treatment methods in reducing pollution scales is made easier by analysing waste discharge concentrations.The waste discharge concentration analysis is useful for assessing how effectively wastewater treatment techniques reduce pollution levels.This study aims to explore the Casson micropolar fluid flow through two parallel plates with the influence of pollutant concentration and thermophoretic particle deposition.To explore the mass and heat transport features,thermophoretic particle deposition and thermal radiation are considered.The governing equations are transformed into ordinary differential equations with the help of suitable similarity transformations.The Runge-Kutta-Fehlberg’s fourthfifth order technique and shooting procedure are used to solve the reduced set of equations and boundary conditions.The integration of a neural network model based on the Levenberg-Marquardt algorithm serves to improve the accuracy of predictions and optimize the analysis of parameters.Graphical outcomes are displayed to analyze the characteristics of the relevant dimensionless parameters in the current problem.Results reveal that concentration upsurges as the micropolar parameter increases.The concentration reduces with an upsurge in the thermophoretic parameter.An upsurge in the external pollutant source variation and the local pollutant external source parameters enhances mass transport.The surface drag force declines for improved values of porosity and micropolar parameters.展开更多
In this paper,we delve into a generalized higher order Camassa-Holm type equation,(or,an ghmCH equation for short).We establish local well-posedness for this equation under the condition that the initial data uo belon...In this paper,we delve into a generalized higher order Camassa-Holm type equation,(or,an ghmCH equation for short).We establish local well-posedness for this equation under the condition that the initial data uo belongs to the Sobolev space H'(R)for some s>2.In addition,we obtain the weak formulation of this equation and prove the existence of both single peakon solution and a multi-peakon dynamic system.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
In this paper,we define the spectral Einstein functional associated with the Dirac operator for manifolds with boundary.And we give the proof of Kastler-Kalau-Walze type theorem for the spectral Einstein functional as...In this paper,we define the spectral Einstein functional associated with the Dirac operator for manifolds with boundary.And we give the proof of Kastler-Kalau-Walze type theorem for the spectral Einstein functional associated with the Dirac operator on 4-dimensional manifolds with boundary.展开更多
In the present paper,we give a systematic study of the discrete correspondence the-ory and topological correspondence theory of modal meet-implication logic and moda1 meet-semilattice logic,in the semantics provided i...In the present paper,we give a systematic study of the discrete correspondence the-ory and topological correspondence theory of modal meet-implication logic and moda1 meet-semilattice logic,in the semantics provided in[21].The special features of the present paper include the following three points:the first one is that the semantic structure used is based on a semilattice rather than an ordinary partial order,the second one is that the propositional vari-ables are interpreted as filters rather than upsets,and the nominals,which are the“first-order counterparts of propositional variables,are interpreted as principal filters rather than principal upsets;the third one is that in topological correspondence theory,the collection of admissi-ble valuations is not closed under taking disjunction,which makes the proof of the topological Ackermann 1emma different from existing settings.展开更多
In this paper,using the property of uniform Fredholm non-positive index of bounded linear operators,we give criteria for operators and their functions to possess property(ω),and several equivalent conditions for the ...In this paper,using the property of uniform Fredholm non-positive index of bounded linear operators,we give criteria for operators and their functions to possess property(ω),and several equivalent conditions for the stability of property(ω),and investigate the relationship between the stability of property(ω)and the(ω)-property of operator functions.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
When dealing with imbalanced datasets,the traditional support vectormachine(SVM)tends to produce a classification hyperplane that is biased towards the majority class,which exhibits poor robustness.This paper proposes...When dealing with imbalanced datasets,the traditional support vectormachine(SVM)tends to produce a classification hyperplane that is biased towards the majority class,which exhibits poor robustness.This paper proposes a high-performance classification algorithm specifically designed for imbalanced datasets.The proposed method first uses a biased second-order cone programming support vectormachine(B-SOCP-SVM)to identify the support vectors(SVs)and non-support vectors(NSVs)in the imbalanced data.Then,it applies the synthetic minority over-sampling technique(SV-SMOTE)to oversample the support vectors of the minority class and uses the random under-sampling technique(NSV-RUS)multiple times to undersample the non-support vectors of the majority class.Combining the above-obtained minority class data set withmultiple majority class datasets can obtainmultiple new balanced data sets.Finally,SOCP-SVM is used to classify each data set,and the final result is obtained through the integrated algorithm.Experimental results demonstrate that the proposed method performs excellently on imbalanced datasets.展开更多
In this paper,the authors prove that the parameterized area integralμ_(Ω,S)^(ρ)and the parameterized Littlewood-Paley g_(δ)^(*)-functionμ_(Ω,δ)^(*,ρ)are bounded on two-weight grand homogeneous variable Herz-Mo...In this paper,the authors prove that the parameterized area integralμ_(Ω,S)^(ρ)and the parameterized Littlewood-Paley g_(δ)^(*)-functionμ_(Ω,δ)^(*,ρ)are bounded on two-weight grand homogeneous variable Herz-Morrey spaces MK_(p),θ,q(·))^(α(·),λ)(ω_(1),ω_(2)),where θ>0,λ∈(2,∞),q(·)∈B(R^(n)),α(·)∈L^(∞)(R^(n)),ω_(1)∈A_(p_(ω_(1)))for p_(ω_(1))∈[1,∞]and ω_(2) is a weight.Furthermore,the authors prove that the commutators[b,μ_(Ω,S)^(ρ)]which is formed by b∈BMO(R^(n))and the μ_(Ω,S)^(ρ),and the[b,μ_(Ω,δ)^(*,ρ)]generated by b∈BMO(R^(n))and theμ_(Ω,δ)^(*,ρ)are bounded on MK_(p),θ,q(·))^(α(·),λ)(ω_(1),ω_(2)),respectively.展开更多
The successful application of perimeter control of urban traffic system strongly depends on the macroscopic fundamental diagram of the targeted region.Despite intensive studies on the partitioning of urban road networ...The successful application of perimeter control of urban traffic system strongly depends on the macroscopic fundamental diagram of the targeted region.Despite intensive studies on the partitioning of urban road networks,the dynamic partitioning of urban regions reflecting the propagation of congestion remains an open question.This paper proposes to partition the network into homogeneous sub-regions based on random walk algorithm.Starting from selected random walkers,the road network is partitioned from the early morning when congestion emerges.A modified Akaike information criterion is defined to find the optimal number of partitions.Region boundary adjustment algorithms are adopted to optimize the partitioning results to further ensure the correlation of partitions.The traffic data of Melbourne city are used to verify the effectiveness of the proposed partitioning method.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
Letϕbe a smooth radial weight that decays faster than the class Gaussian ones.We obtain certain estimates for the reproducing kernels and the Lp-estimates for solutions of theδ-equation on the weighted Fock spaces F_...Letϕbe a smooth radial weight that decays faster than the class Gaussian ones.We obtain certain estimates for the reproducing kernels and the Lp-estimates for solutions of theδ-equation on the weighted Fock spaces F_(ϕ)^(p)(1≤p≤∞),which extends the classical Hörmander Theorem.Furthermore,for a suitable f,we completely characterize the boundedness and compactness of the Hankel operator H_(f):F_(ϕ)^(p)→L^(q)(C,e^(qϕ(·))dm)for all possible 1≤p,q<∞and also characterize the Schatten-p class Hankel operator Hf from F_(ϕ)^(2)to L^(2)(C,E^(-2ϕ)dm) for all 0<p<∞. As an application, we give a complete characterization of the simultaneously bounded, compact and Schatten-p classes Hankel operators H_(f) and h_(f)^(-) on F_(ϕ)^(2).展开更多
The co-infection of corona and influenza viruses has emerged as a significant threat to global public health due to their shared modes of transmission and overlapping clinical symptoms.This article presents a novel ma...The co-infection of corona and influenza viruses has emerged as a significant threat to global public health due to their shared modes of transmission and overlapping clinical symptoms.This article presents a novel mathematical model that addresses the dynamics of this co-infection by extending the SEIR(Susceptible-Exposed-Infectious-Recovered)framework to incorporate treatment and hospitalization compartments.The population is divided into eight compartments,with infectious individuals further categorized into influenza infectious,corona infectious,and co-infection cases.The proposed mathematical model is constrained to adhere to fundamental epidemiological properties,such as non-negativity and boundedness within a feasible region.Additionally,the model is demonstrated to be well-posed with a unique solution.Equilibrium points,including the disease-free and endemic equilibria,are identified,and various properties related to these equilibrium points,such as the basic reproduction number,are determined.Local and global sensitivity analyses are performed to identify the parameters that highly influence disease dynamics and the reproduction number.Knowing the most influential parameters is crucial for understanding their impact on the co-infection’s spread and severity.Furthermore,an optimal control problem is defined to minimize disease transmission and to control strategy costs.The purpose of our study is to identify the most effective(optimal)control strategies for mitigating the spread of the co-infection with minimum cost of the controls.The results illustrate the effectiveness of the implemented control strategies in managing the co-infection’s impact on the population’s health.This mathematical modeling and control strategy framework provides valuable tools for understanding and combating the dual threat of corona and influenza co-infection,helping public health authorities and policymakers make informed decisions in the face of these intertwined epidemics.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
Based on a new bilinear equation,we investigated some new dynamic behaviors of the(2+1)-dimensional shallow water wave model,such as hybridization behavior between different solitons,trajectory equations for lump coll...Based on a new bilinear equation,we investigated some new dynamic behaviors of the(2+1)-dimensional shallow water wave model,such as hybridization behavior between different solitons,trajectory equations for lump collisions,and evolution behavior of multi-breathers.Firstly,the N-soliton solution of Ito equation is studied,and some high-order breather waves can be obtained from the N-soliton solutions through paired-complexification of parameters.Secondly,the high-order lump solutions and the hybrid solutions are obtained by employing the long-wave limit method,and the motion velocity and trajectory equations of high-order lump waves are analyzed.Moreover,based on the trajectory equations of the higher-order lump solutions,we give and prove the trajectory theorem of 1-lump before and after interaction with nsoliton.Finally,we obtain some new lump solutions from the multi-solitons by constructing a new test function and using the parameter limit method.Meanwhile,some evolutionary behaviors of the obtained solutions are shown through a large number of three-dimensional graphs with different and appropriate parameters.展开更多
Large-grain REBa_(2)Cu_(3)O_(7-δ)(REBCO,RE=rare earth)bulk superconductors offer promising magnetic field trapping capabilities due to their high critical current density,making them ideal for many important applicat...Large-grain REBa_(2)Cu_(3)O_(7-δ)(REBCO,RE=rare earth)bulk superconductors offer promising magnetic field trapping capabilities due to their high critical current density,making them ideal for many important applications such as trapped field magnets.However,for such large-grain superconductor bulks,there are lots of voids and cracks forming during the process of melting preparation,and some of them can be up to hundreds of microns or even millimeters in size.Consequently,these larger size voids/cracks pose a great threat to the strength of the bulks due to the inherent brittleness of superconductor REBCO materials.In order to ensure the operational safety of related superconducting devices with bulk superconductors,it is firstly important to accurately detect these voids/cracks in them.In this paper,we proposed a method for quantitatively evaluating multiple voids/cracks in bulk superconductors through the magnetic field and displacement response signals at superconductor bulk surface.The proposed method utilizes a damage index constructed from the magnetic field signals and displacement responses to identify the number and preliminary location of multiple defects.By dividing the detection area into subdomains and combining the magnetic field signals with displacement responses within each subdomain,a particle swarm algorithm was employed to evaluate the location and size parameters of the defects.In contrast to other evaluation methods using only magnetic field or displacement response signals,the combined evaluation method using both signals can identify the number of cracks effectively.Numerical studies demonstrate that the morphology of voids and cracks reconstructed using the proposed algorithm ideally matches real defects and is applicable to cases where voids and cracks coexist.This study provides a theoretical basis for the quantitative detection of voids/cracks in bulk superconductors.展开更多
Curriculum ideology and politics is the key to carry out the mission of educating people in colleges and universities in the new era.On the problem of integrating the linear algebra course into the ideological and pol...Curriculum ideology and politics is the key to carry out the mission of educating people in colleges and universities in the new era.On the problem of integrating the linear algebra course into the ideological and political education,it was expounded from four aspects:the necessity of integrating the course ideology and politics into the teaching of linear algebra,exploring curriculum ideological and political elements,the case design of integrating the course ideology and politics teaching,and the expected effect of integrating linear algebra courses into ideological and political education in the curriculum,in order to have the reference and help function to the educator.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
基金Supported by the Natural Science Foundation of Chongqing(General Program,NO.CSTB2022NSCQ-MSX0884)Discipline Teaching Special Project of Yangtze Normal University(csxkjx14)。
文摘In this paper,we prove that Euclid's algorithm,Bezout's equation and Divi-sion algorithm are equivalent to each other.Our result shows that Euclid has preliminarily established the theory of divisibility and the greatest common divisor.We further provided several suggestions for teaching.
基金supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University(IMSIU)(grant number IMSIU-RP23066).
文摘This study directs the discussion of HIV disease with a novel kind of complex dynamical generalized and piecewise operator in the sense of classical and Atangana Baleanu(AB)derivatives having arbitrary order.The HIV infection model has a susceptible class,a recovered class,along with a case of infection divided into three sub-different levels or categories and the recovered class.The total time interval is converted into two,which are further investigated for ordinary and fractional order operators of the AB derivative,respectively.The proposed model is tested separately for unique solutions and existence on bi intervals.The numerical solution of the proposed model is treated by the piece-wise numerical iterative scheme of Newtons Polynomial.The proposed method is established for piece-wise derivatives under natural order and non-singular Mittag-Leffler Law.The cross-over or bending characteristics in the dynamical system of HIV are easily examined by the aspect of this research having a memory effect for controlling the said disease.This study uses the neural network(NN)technique to obtain a better set of weights with low residual errors,and the epochs number is considered 1000.The obtained figures represent the approximate solution and absolute error which are tested with NN to train the data accurately.
文摘Assessing the behaviour and concentration of waste pollutants deposited between two parallel plates is essential for effective environmental management.Determining the effectiveness of treatment methods in reducing pollution scales is made easier by analysing waste discharge concentrations.The waste discharge concentration analysis is useful for assessing how effectively wastewater treatment techniques reduce pollution levels.This study aims to explore the Casson micropolar fluid flow through two parallel plates with the influence of pollutant concentration and thermophoretic particle deposition.To explore the mass and heat transport features,thermophoretic particle deposition and thermal radiation are considered.The governing equations are transformed into ordinary differential equations with the help of suitable similarity transformations.The Runge-Kutta-Fehlberg’s fourthfifth order technique and shooting procedure are used to solve the reduced set of equations and boundary conditions.The integration of a neural network model based on the Levenberg-Marquardt algorithm serves to improve the accuracy of predictions and optimize the analysis of parameters.Graphical outcomes are displayed to analyze the characteristics of the relevant dimensionless parameters in the current problem.Results reveal that concentration upsurges as the micropolar parameter increases.The concentration reduces with an upsurge in the thermophoretic parameter.An upsurge in the external pollutant source variation and the local pollutant external source parameters enhances mass transport.The surface drag force declines for improved values of porosity and micropolar parameters.
文摘In this paper,we delve into a generalized higher order Camassa-Holm type equation,(or,an ghmCH equation for short).We establish local well-posedness for this equation under the condition that the initial data uo belongs to the Sobolev space H'(R)for some s>2.In addition,we obtain the weak formulation of this equation and prove the existence of both single peakon solution and a multi-peakon dynamic system.
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.
文摘In this paper,we define the spectral Einstein functional associated with the Dirac operator for manifolds with boundary.And we give the proof of Kastler-Kalau-Walze type theorem for the spectral Einstein functional associated with the Dirac operator on 4-dimensional manifolds with boundary.
基金supported by the Chinese Ministry of Education of Humanities and Social Science Project(23YJC72040003)the Key Project of Chinese Ministry of Education(22JJD720021)supported by the Natural Science Foundation of Shandong Province,China(project number:ZR2023QF021)。
文摘In the present paper,we give a systematic study of the discrete correspondence the-ory and topological correspondence theory of modal meet-implication logic and moda1 meet-semilattice logic,in the semantics provided in[21].The special features of the present paper include the following three points:the first one is that the semantic structure used is based on a semilattice rather than an ordinary partial order,the second one is that the propositional vari-ables are interpreted as filters rather than upsets,and the nominals,which are the“first-order counterparts of propositional variables,are interpreted as principal filters rather than principal upsets;the third one is that in topological correspondence theory,the collection of admissi-ble valuations is not closed under taking disjunction,which makes the proof of the topological Ackermann 1emma different from existing settings.
基金supported by the National Natural Science Foundation of China(No.11501419)the Nature Science Basic Research Plan in Shaanxi Province of China(No.2021JM-519)。
文摘In this paper,using the property of uniform Fredholm non-positive index of bounded linear operators,we give criteria for operators and their functions to possess property(ω),and several equivalent conditions for the stability of property(ω),and investigate the relationship between the stability of property(ω)and the(ω)-property of operator functions.
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 Natural Science Basic Research Program of Shaanxi(Program No.2024JC-YBMS-026).
文摘When dealing with imbalanced datasets,the traditional support vectormachine(SVM)tends to produce a classification hyperplane that is biased towards the majority class,which exhibits poor robustness.This paper proposes a high-performance classification algorithm specifically designed for imbalanced datasets.The proposed method first uses a biased second-order cone programming support vectormachine(B-SOCP-SVM)to identify the support vectors(SVs)and non-support vectors(NSVs)in the imbalanced data.Then,it applies the synthetic minority over-sampling technique(SV-SMOTE)to oversample the support vectors of the minority class and uses the random under-sampling technique(NSV-RUS)multiple times to undersample the non-support vectors of the majority class.Combining the above-obtained minority class data set withmultiple majority class datasets can obtainmultiple new balanced data sets.Finally,SOCP-SVM is used to classify each data set,and the final result is obtained through the integrated algorithm.Experimental results demonstrate that the proposed method performs excellently on imbalanced datasets.
基金Supported by the National Natural Science Foundation of China(Grant No.12201500)。
文摘In this paper,the authors prove that the parameterized area integralμ_(Ω,S)^(ρ)and the parameterized Littlewood-Paley g_(δ)^(*)-functionμ_(Ω,δ)^(*,ρ)are bounded on two-weight grand homogeneous variable Herz-Morrey spaces MK_(p),θ,q(·))^(α(·),λ)(ω_(1),ω_(2)),where θ>0,λ∈(2,∞),q(·)∈B(R^(n)),α(·)∈L^(∞)(R^(n)),ω_(1)∈A_(p_(ω_(1)))for p_(ω_(1))∈[1,∞]and ω_(2) is a weight.Furthermore,the authors prove that the commutators[b,μ_(Ω,S)^(ρ)]which is formed by b∈BMO(R^(n))and the μ_(Ω,S)^(ρ),and the[b,μ_(Ω,δ)^(*,ρ)]generated by b∈BMO(R^(n))and theμ_(Ω,δ)^(*,ρ)are bounded on MK_(p),θ,q(·))^(α(·),λ)(ω_(1),ω_(2)),respectively.
基金Project supported by the National Natural Science Foundation of China(Grant No.12072340)the Chinese Scholarship Council and the Australia Research Council through a linkage project fund。
文摘The successful application of perimeter control of urban traffic system strongly depends on the macroscopic fundamental diagram of the targeted region.Despite intensive studies on the partitioning of urban road networks,the dynamic partitioning of urban regions reflecting the propagation of congestion remains an open question.This paper proposes to partition the network into homogeneous sub-regions based on random walk algorithm.Starting from selected random walkers,the road network is partitioned from the early morning when congestion emerges.A modified Akaike information criterion is defined to find the optimal number of partitions.Region boundary adjustment algorithms are adopted to optimize the partitioning results to further ensure the correlation of partitions.The traffic data of Melbourne city are used to verify the effectiveness of the proposed partitioning method.
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.
文摘Letϕbe a smooth radial weight that decays faster than the class Gaussian ones.We obtain certain estimates for the reproducing kernels and the Lp-estimates for solutions of theδ-equation on the weighted Fock spaces F_(ϕ)^(p)(1≤p≤∞),which extends the classical Hörmander Theorem.Furthermore,for a suitable f,we completely characterize the boundedness and compactness of the Hankel operator H_(f):F_(ϕ)^(p)→L^(q)(C,e^(qϕ(·))dm)for all possible 1≤p,q<∞and also characterize the Schatten-p class Hankel operator Hf from F_(ϕ)^(2)to L^(2)(C,E^(-2ϕ)dm) for all 0<p<∞. As an application, we give a complete characterization of the simultaneously bounded, compact and Schatten-p classes Hankel operators H_(f) and h_(f)^(-) on F_(ϕ)^(2).
基金supported by NASA Oklahoma Established Program to Stimulate Competitive Research(EPSCoR)Infrastructure Development,“Machine Learning Ocean World Biosignature Detection from Mass Spec”(PI:BrettMcKinney),Grant No.80NSSC24M0109Tandy School of Computer Science,University of Tulsa.
文摘The co-infection of corona and influenza viruses has emerged as a significant threat to global public health due to their shared modes of transmission and overlapping clinical symptoms.This article presents a novel mathematical model that addresses the dynamics of this co-infection by extending the SEIR(Susceptible-Exposed-Infectious-Recovered)framework to incorporate treatment and hospitalization compartments.The population is divided into eight compartments,with infectious individuals further categorized into influenza infectious,corona infectious,and co-infection cases.The proposed mathematical model is constrained to adhere to fundamental epidemiological properties,such as non-negativity and boundedness within a feasible region.Additionally,the model is demonstrated to be well-posed with a unique solution.Equilibrium points,including the disease-free and endemic equilibria,are identified,and various properties related to these equilibrium points,such as the basic reproduction number,are determined.Local and global sensitivity analyses are performed to identify the parameters that highly influence disease dynamics and the reproduction number.Knowing the most influential parameters is crucial for understanding their impact on the co-infection’s spread and severity.Furthermore,an optimal control problem is defined to minimize disease transmission and to control strategy costs.The purpose of our study is to identify the most effective(optimal)control strategies for mitigating the spread of the co-infection with minimum cost of the controls.The results illustrate the effectiveness of the implemented control strategies in managing the co-infection’s impact on the population’s health.This mathematical modeling and control strategy framework provides valuable tools for understanding and combating the dual threat of corona and influenza co-infection,helping public health authorities and policymakers make informed decisions in the face of these intertwined epidemics.
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Project supported by the National Natural Science Foundation of China(Grant No.12461047)the Scientific Research Project of the Hunan Education Department(Grant No.24B0478).
文摘Based on a new bilinear equation,we investigated some new dynamic behaviors of the(2+1)-dimensional shallow water wave model,such as hybridization behavior between different solitons,trajectory equations for lump collisions,and evolution behavior of multi-breathers.Firstly,the N-soliton solution of Ito equation is studied,and some high-order breather waves can be obtained from the N-soliton solutions through paired-complexification of parameters.Secondly,the high-order lump solutions and the hybrid solutions are obtained by employing the long-wave limit method,and the motion velocity and trajectory equations of high-order lump waves are analyzed.Moreover,based on the trajectory equations of the higher-order lump solutions,we give and prove the trajectory theorem of 1-lump before and after interaction with nsoliton.Finally,we obtain some new lump solutions from the multi-solitons by constructing a new test function and using the parameter limit method.Meanwhile,some evolutionary behaviors of the obtained solutions are shown through a large number of three-dimensional graphs with different and appropriate parameters.
基金supported by the National Natural Science Foundation of China(Grant Nos.12232005 and 12072101).
文摘Large-grain REBa_(2)Cu_(3)O_(7-δ)(REBCO,RE=rare earth)bulk superconductors offer promising magnetic field trapping capabilities due to their high critical current density,making them ideal for many important applications such as trapped field magnets.However,for such large-grain superconductor bulks,there are lots of voids and cracks forming during the process of melting preparation,and some of them can be up to hundreds of microns or even millimeters in size.Consequently,these larger size voids/cracks pose a great threat to the strength of the bulks due to the inherent brittleness of superconductor REBCO materials.In order to ensure the operational safety of related superconducting devices with bulk superconductors,it is firstly important to accurately detect these voids/cracks in them.In this paper,we proposed a method for quantitatively evaluating multiple voids/cracks in bulk superconductors through the magnetic field and displacement response signals at superconductor bulk surface.The proposed method utilizes a damage index constructed from the magnetic field signals and displacement responses to identify the number and preliminary location of multiple defects.By dividing the detection area into subdomains and combining the magnetic field signals with displacement responses within each subdomain,a particle swarm algorithm was employed to evaluate the location and size parameters of the defects.In contrast to other evaluation methods using only magnetic field or displacement response signals,the combined evaluation method using both signals can identify the number of cracks effectively.Numerical studies demonstrate that the morphology of voids and cracks reconstructed using the proposed algorithm ideally matches real defects and is applicable to cases where voids and cracks coexist.This study provides a theoretical basis for the quantitative detection of voids/cracks in bulk superconductors.
文摘Curriculum ideology and politics is the key to carry out the mission of educating people in colleges and universities in the new era.On the problem of integrating the linear algebra course into the ideological and political education,it was expounded from four aspects:the necessity of integrating the course ideology and politics into the teaching of linear algebra,exploring curriculum ideological and political elements,the case design of integrating the course ideology and politics teaching,and the expected effect of integrating linear algebra courses into ideological and political education in the curriculum,in order to have the reference and help function to the educator.
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.
