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
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
Based on reanalysis data from 1979 to 2021,this study explores the spatial distribution of the Southern Indian Ocean Dipole(SIOD)and its individual and synergistic effects with the El Niño-Southern Oscillation(EN...Based on reanalysis data from 1979 to 2021,this study explores the spatial distribution of the Southern Indian Ocean Dipole(SIOD)and its individual and synergistic effects with the El Niño-Southern Oscillation(ENSO)on summer precipitation in China.The inverse phase spatial distribution of sea surface temperature anomalies(SSTAs)in the southwest and northeast of the southern Indian Ocean is defined as the SIOD.Positive SIOD events(positive SSTAs in the southwest,negative SSTAs in the northeast)are associated with La Niña events(Central Pacific(CP)type),while negative SIOD events(negative SSTAs in the southwest,positive SSTAs in the northeast)are associated with El Niño events(Eastern Pacific(EP)type).Both SIOD and ENSO have certain impacts on summer precipitation in China.Precipitation in the Yangtze River basin decreases,while precipitation in southern China increases during pure positive SIOD(P_PSIOD)events.During pure negative SIOD(P_NSIOD)events,the changes in precipitation are exactly the opposite of those during P_PSIOD events,which may be due to differences in the cross-equatorial flow in the southern Indian Ocean,particularly in low-level Australian cross-equatorial flow.When positive SIOD and CP-type La Niña events occur simultaneously(PSIOD+La_Niña),precipitation increases in the Yangtze-Huaihe River basin,while it decreases in northern China.When negative SIOD and EP-type El Niño events occur simultaneously(NSIOD+El_Niño),precipitation in the Yangtze-Huaihe River basin is significantly lower than during P_NSIOD events.This is caused by differences in water vapor originating from the Pacific Ocean during different events.展开更多
Teaching goal design is an important link of teaching design, which has the teaching, learning and measurement function. How to establish the appropriate teaching goal and properly state to enhance its guidance and de...Teaching goal design is an important link of teaching design, which has the teaching, learning and measurement function. How to establish the appropriate teaching goal and properly state to enhance its guidance and detection function are the important tasks of teaching design. This paper makes a programming and systematic analysis on the aspects of teaching goal design theory, teaching goal statement mode and technology, teaching goal statement and design and teaching goal design detection.展开更多
Hypergeometric functions have been increasingly present in several disciplines including Statistics, but there is much confusion on their proper uses, as well as on their existence and domain of definition. In this ar...Hypergeometric functions have been increasingly present in several disciplines including Statistics, but there is much confusion on their proper uses, as well as on their existence and domain of definition. In this article, we try to clarify several points and give a general overview of the topic, going from the univariate case to the matrix case, in one and then in several arguments. We also survey some results in fields close to Statistics, where hypergeometric functions are actively used, studied and developed.展开更多
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 this paper,we show that an ideal generated by matching Rota-Baxter equations is a bideal of a Hopf algebra on decorated rooted forests.We then get a bialgebraic structure on the space of decorated rooted forests mo...In this paper,we show that an ideal generated by matching Rota-Baxter equations is a bideal of a Hopf algebra on decorated rooted forests.We then get a bialgebraic structure on the space of decorated rooted forests modulo this biideal.As an application,a connected graded bialgebra and so a graded Hopf algebra on matching Rota-Baxter algebras are constructed,which simplifies the Hopf algebraic structure proposed by[Pacific J.Math.,2022,317(2):441-475].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
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
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.
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[grant numbers 41975087,U2242212,and 41975085]supported by the National Natural Science Foundation of China[grant number U2242212]。
文摘Based on reanalysis data from 1979 to 2021,this study explores the spatial distribution of the Southern Indian Ocean Dipole(SIOD)and its individual and synergistic effects with the El Niño-Southern Oscillation(ENSO)on summer precipitation in China.The inverse phase spatial distribution of sea surface temperature anomalies(SSTAs)in the southwest and northeast of the southern Indian Ocean is defined as the SIOD.Positive SIOD events(positive SSTAs in the southwest,negative SSTAs in the northeast)are associated with La Niña events(Central Pacific(CP)type),while negative SIOD events(negative SSTAs in the southwest,positive SSTAs in the northeast)are associated with El Niño events(Eastern Pacific(EP)type).Both SIOD and ENSO have certain impacts on summer precipitation in China.Precipitation in the Yangtze River basin decreases,while precipitation in southern China increases during pure positive SIOD(P_PSIOD)events.During pure negative SIOD(P_NSIOD)events,the changes in precipitation are exactly the opposite of those during P_PSIOD events,which may be due to differences in the cross-equatorial flow in the southern Indian Ocean,particularly in low-level Australian cross-equatorial flow.When positive SIOD and CP-type La Niña events occur simultaneously(PSIOD+La_Niña),precipitation increases in the Yangtze-Huaihe River basin,while it decreases in northern China.When negative SIOD and EP-type El Niño events occur simultaneously(NSIOD+El_Niño),precipitation in the Yangtze-Huaihe River basin is significantly lower than during P_NSIOD events.This is caused by differences in water vapor originating from the Pacific Ocean during different events.
文摘Teaching goal design is an important link of teaching design, which has the teaching, learning and measurement function. How to establish the appropriate teaching goal and properly state to enhance its guidance and detection function are the important tasks of teaching design. This paper makes a programming and systematic analysis on the aspects of teaching goal design theory, teaching goal statement mode and technology, teaching goal statement and design and teaching goal design detection.
文摘Hypergeometric functions have been increasingly present in several disciplines including Statistics, but there is much confusion on their proper uses, as well as on their existence and domain of definition. In this article, we try to clarify several points and give a general overview of the topic, going from the univariate case to the matrix case, in one and then in several arguments. We also survey some results in fields close to Statistics, where hypergeometric functions are actively used, studied and developed.
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 NSFC(No.12101316)Belt and Road Innovative Talents Exchange Foreign Experts project(No.DL2023014002L)。
文摘In this paper,we show that an ideal generated by matching Rota-Baxter equations is a bideal of a Hopf algebra on decorated rooted forests.We then get a bialgebraic structure on the space of decorated rooted forests modulo this biideal.As an application,a connected graded bialgebra and so a graded Hopf algebra on matching Rota-Baxter algebras are constructed,which simplifies the Hopf algebraic structure proposed by[Pacific J.Math.,2022,317(2):441-475].
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.
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.
