It is well known that mono-implicit Runge-Kutta methods have been applied in the efficient numerical solution of initial or boundary value problems of ordinary differential equations. Burrage (1994) has shown that the...It is well known that mono-implicit Runge-Kutta methods have been applied in the efficient numerical solution of initial or boundary value problems of ordinary differential equations. Burrage (1994) has shown that the order of an s-stage monoimplicit Runge-Kutta method is at most s+1 and the stage order is at most 3. In this paper, it is shown that the order of an s-stage mono-implicit Runge-Kutta method being algebraically stable is at most min((s) over tilde, 4), and the stage order together with the optimal B-convergence order is at most min(s, 2), where [GRAPHICS]展开更多
Loday introduced di-associative algebras and tri-associative algebras motivated by periodicity phenomena in algebraic K-theory.The purpose of this paper is to study the splittings of operations on di-associative algeb...Loday introduced di-associative algebras and tri-associative algebras motivated by periodicity phenomena in algebraic K-theory.The purpose of this paper is to study the splittings of operations on di-associative algebras and tri-associative algebras.We introduce the notion of a quad-dendriform algebra,which is a splitting of a di-associative algebra.We show that a relative averaging operator on dendriform algebras gives rise to a quad-dendriform algebra.Furthermore,we introduce the notion of six-dendriform algebras,which are splittings of the tri-associative algebras,and demonstrate that homomorphic relative averaging operators induce six-dendriform algebras.展开更多
The crossover between short-range and long-range(LR)universal behaviors remains a central theme in the physics of LR interacting systems.The competition between LR coupling and the Berezinskii-Kosterlitz-Thouless mech...The crossover between short-range and long-range(LR)universal behaviors remains a central theme in the physics of LR interacting systems.The competition between LR coupling and the Berezinskii-Kosterlitz-Thouless mechanism makes the problem more subtle and less understood in the two-dimensional(2D)XY model,a cornerstone for investigating low-dimensional phenomena and their implications in quantum computation.We study the 2D XY model with algebraically decaying interaction~1/r^(2+σ).Utilizing an advanced update strategy,we conduct LR Monte Carlo simulations of the model up to a linear size of L=8192.Our results demonstrate continuous phase transitions into a ferromagnetic phase forσ<2,which exhibit the simultaneous emergence of a long-ranged order and a power-law decaying correlation function due to the Goldstone mode.Furthermore,we fnd logarithmic scaling behaviors in the low-temperature phase atσ=2.The observed scaling behaviors in the low-temperature phase forσ≤2 agree with our theoretical analysis.Our fndings request further theoretical understanding and can be of practical application in cutting-edge experiments like Rydberg atom arrays.展开更多
To investigate the forward kinematics problem of parallel mechanisms with complex limbs and to expand the applicability of the powerful tool of Conformal Geometric Algebra(CGA),a CGA-based modeling and solution method...To investigate the forward kinematics problem of parallel mechanisms with complex limbs and to expand the applicability of the powerful tool of Conformal Geometric Algebra(CGA),a CGA-based modeling and solution method for a class of parallel platforms with 3-RE structure after locking the actuated joints is proposed in this paper.Given that the angle between specific joint axes of limbs remains constant,a set of geometric constraints for the forward kinematics of parallel mechanisms(PM)are determined.After translating unit direction vectors of these joint axes to the common starting point,the geometric constraints of the angle between the vectors are transformed into the distances between the endpoints of the vectors,making them easier to handle.Under the framework of CGA,the positions of key points that determine the position and orientation of the moving platform can be intuitively determined by the intersection,division,and duality of basic geometric entities.By employing the tangent half-angle substitution,the forward kinematic analysis of the parallel mechanisms leads to a high-order univariate polynomial equation without the need for any complex algebraic elimination operations.After solving this equation and back substitution,the position and pose of the MP can be obtained indirectly.A numerical case is utilized to confirm the effectiveness of the proposed method.展开更多
Semenov-Tian-Shansky has given the solution of the modified classical Yang-Baxter equation, which was called the modified r-matrix. Relevant studies have been extensive in recent times. In this paper, we introduce the...Semenov-Tian-Shansky has given the solution of the modified classical Yang-Baxter equation, which was called the modified r-matrix. Relevant studies have been extensive in recent times. In this paper, we introduce the concept and representations of modified RotaBaxter Hom-Lie algebras. We develop a cohomology of modified Rota-Baxter Hom-Lie algebras with coefficients in a suitable representation. As applications, we study formal deformations and abelian extensions of modified Rota-Baxter Hom-Lie algebras in terms of second cohomology groups.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
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
We classify condensable𝐸E_(2)-algebras in a modular tensor category C up to 2-Morita equivalence.Physically,this classification provides an explicit criterion to determine when distinct condensable𝐸E_(...We classify condensable𝐸E_(2)-algebras in a modular tensor category C up to 2-Morita equivalence.Physically,this classification provides an explicit criterion to determine when distinct condensable𝐸E_(2)-algebras yield the same condensed topological phase under a two-dimensional anyon condensation process.The relations between different condensable algebras can be translated into their module categories,interpreted physically as gapped domain walls in topological orders.As concrete examples,we interpret the categories of quantum doubles of finite groups and examples beyond group symmetries.Our framework fully elucidates the interplay among condensable𝐸E_(1)-algebras in C,condensable𝐸E_(2)-algebras in C up to 2-Morita equivalence,and Lagrangian algebras in C⊠C.展开更多
Let D(n)be the finite dimensional non-pointed and non-semisimple Hopf algebra,which is a quotient of a prime Hopf algebras of GK-dimension one for an odd number n>1.In this paper,we investigate the structure of Yet...Let D(n)be the finite dimensional non-pointed and non-semisimple Hopf algebra,which is a quotient of a prime Hopf algebras of GK-dimension one for an odd number n>1.In this paper,we investigate the structure of Yetter-Drinfeld simple modules over D(n)and give iso-classes of them.展开更多
Many applications for locating a radio signal source employ Global Navigation Satellite System(GNSS)to obtain a sensor’s position.By using GNSS,a sensor can also synchronize with other sensors.For a sensor that is eq...Many applications for locating a radio signal source employ Global Navigation Satellite System(GNSS)to obtain a sensor’s position.By using GNSS,a sensor can also synchronize with other sensors.For a sensor that is equipped with a GNSS receiver,it can be independent and is readily to be loaded on a flexible platform,such as an unmanned aerial vehicle(UAV).In this paper,we consider using such sensors and timeof-arrival(TOA)techniques to locate a radio signal source,and analyze the performance limit of source localization.Besides the performance analysis,this paper provides the geometric interpretation of the performance limit,which can illustrate how a sensor contributes to the source localization accuracy.The performance analysis and the geometric interpretation together give important insights into how to make better use of GNSS receiver for passive localization.Another contribution is we propose a modified closedform solution for this localization problem.Compared with previous literature,this solution takes both sensor position and synchronization uncertainty into account,and it does not need proper initial guess of source position and is computationally efficient.Our simulation results validate the efficiency of this solution.展开更多
A left Leibniz algebra equipped with an invariant nondegenerate skew-symmetric bilinear form(i.e.,a skew-symmetric quadratic Leibniz algebra)is constructed.The notion of T^(*)-extension of Lie-Yamaguti algebras is int...A left Leibniz algebra equipped with an invariant nondegenerate skew-symmetric bilinear form(i.e.,a skew-symmetric quadratic Leibniz algebra)is constructed.The notion of T^(*)-extension of Lie-Yamaguti algebras is introduced and it is observed that the trivial extension of a Lie-Yamaguti algebra is a quadratic Lie-Yamaguti algebra.It is proved that every symmetric(resp.,skew-symmetric)quadratic Leibniz algebra induces a quadratic(resp.,symplectic)LieYamaguti algebra.展开更多
This study mainly focuses on the triangle bounded L⁃algebras and triangle ideals.Firstly,the definition of triangle bounded L⁃algebras is presented,and several examples with different conditions are outlined along wit...This study mainly focuses on the triangle bounded L⁃algebras and triangle ideals.Firstly,the definition of triangle bounded L⁃algebras is presented,and several examples with different conditions are outlined along with an exploration of their properties.Moreover,we investigate the structure of triangle bounded L⁃algebra with a special condition.Secondly,we define the concept of triangle ideals of triangle bounded L⁃algebra and explore the connection between the triangle ideals of triangle bounded L⁃algebra L and the ideals of bounded L⁃algebra E(L).In addition,we classified and studied various classes of triangle ideals,including Stonean triangle ideals,extended Stonean triangle ideals,and lattice ideals,and by introducing the notion of Stonean triangle bounded L algebras,we examine the relationship between Stonean triangle bounded L⁃algebras and Stonean triangle ideals.Finally,we investigate the interrelationships among these various types of triangle ideals.展开更多
Several aspects of the internal structure of pseudoscalar mesons,accessible through generalized parton distri-butions in their zero-skewness limit,are examined.These include electromagnetic and gravitational form fact...Several aspects of the internal structure of pseudoscalar mesons,accessible through generalized parton distri-butions in their zero-skewness limit,are examined.These include electromagnetic and gravitational form factors related to charge and mass densities;and distributions in the impact parameter space.To this end,we employ an algebraically viable framework that is based upon the valence-quark generalized parton distribution expressed explicitly in terms of the associated distribution function and a profile function that governs the off-forward dynamics.The predominantly analytical nature of this scheme yields several algebraic results and relations while also facilitating the exploration of insightful limiting cases.With a suitable input distribution function,guided either by experiment or theory,and with an appropriate choice of the profile function,it is possible to provide testable predictions for spatial distributions of valence quarks inside pseudoscalar mesons.When comparison is possible,these predictions align well with existing experimental data as well as the findings of reliable theoretical approaches and lattice QCD.展开更多
This paper presents a systematic comparison of the curriculum design and application orientation of the linear algebra curriculum in our country and abroad.It explains mainly differences in course objectives,teaching ...This paper presents a systematic comparison of the curriculum design and application orientation of the linear algebra curriculum in our country and abroad.It explains mainly differences in course objectives,teaching content,approaches,and feedback mechanisms,reflecting divergent understandings of the discipline’s value within distinct educational ecosystems.Forward-looking and practical conclusions are proposed across five main directions:optimizing course structure,strengthening practical components,deepening interdisciplinary integration,building faculty capacity,and developing teaching resources.The aim is to provide strong conceptual help and realistic guidance for getting real progress in linear algebra education in China.展开更多
This article proposes an algebraic model predictive control(MPC)method for automatic landing.While defining the constraint functions in the optimization problem,the tangent hyperbolic function is preferred.Therefore,t...This article proposes an algebraic model predictive control(MPC)method for automatic landing.While defining the constraint functions in the optimization problem,the tangent hyperbolic function is preferred.Therefore,the optimization problem turns into an unconstrained,continuous,and differentiable form.An analytical two-step method is also proposed to solve the rest of the problem.In the first step,it is assumed that only input constraints are active and states are unconstrained.The optimal solution for this case is calculated directly with the optimality condition.The calculated control signal is revised in the second step according to system dynamics and state constraints.Simulation results of the auto-landing system show that the MPC computation speed is significantly increased by the new algebraic MPC(AMPC)without compromising the control performance,which makes the method realistic for using MPC in systems with high-speed changing dynamics.展开更多
A bottleneck algebra is a linearly ordered set(B,≤)with two operations a⊕b=max{a,b}and a⊗b=min{a,b}.A finite nonempty set of vectors of order m over a bottleneck algebra B is said to be 2 B-independent if each vecto...A bottleneck algebra is a linearly ordered set(B,≤)with two operations a⊕b=max{a,b}and a⊗b=min{a,b}.A finite nonempty set of vectors of order m over a bottleneck algebra B is said to be 2 B-independent if each vector of order m over B can be expressed as a linear combination of vectors in this set in at most one way.In 1996,Cechlárováand Plávka posed an open problem:Find a necessary and sufficient condition for a finite nonempty set of vectors of order m over B to be 2 B-independent.In this paper,we derive some necessary and sufficient conditions for a finite nonempty set of vectors of order m over a bounded bottleneck algebra to be 2 B-independent and answer this open problem.展开更多
In this paper,we study anti-derivations and anti-left multipliers.For a class of algebras,which contains triangular algebras,matrix algebras,embedded algebras,Cuntz algebras,nest algebras,P-lattice algebras,and linear...In this paper,we study anti-derivations and anti-left multipliers.For a class of algebras,which contains triangular algebras,matrix algebras,embedded algebras,Cuntz algebras,nest algebras,P-lattice algebras,and linear transformation algebras L(X),we show that every anti-left multiplier on these algebras is zero.Furthermore,let A be a zero product determined algebra andδbe a linear mapping from A into itself,satisfying that for any a,b in A,ab=0 impliesδ(b)a+bδ(a)=0.We show thatδ(x)=D(x)+δ(1)x,where D is an anti-derivation andδ(1)∈Z(A).展开更多
In this paper,we propose a new full-Newton step feasible interior-point algorithm for the special weighted linear complementarity problems.The proposed algorithm employs the technique of algebraic equivalent transform...In this paper,we propose a new full-Newton step feasible interior-point algorithm for the special weighted linear complementarity problems.The proposed algorithm employs the technique of algebraic equivalent transformation to derive the search direction.It is shown that the proximity measure reduces quadratically at each iteration.Moreover,the iteration bound of the algorithm is as good as the best-known polynomial complexity for these types of problems.Furthermore,numerical results are presented to show the efficiency of the proposed algorithm.展开更多
文摘It is well known that mono-implicit Runge-Kutta methods have been applied in the efficient numerical solution of initial or boundary value problems of ordinary differential equations. Burrage (1994) has shown that the order of an s-stage monoimplicit Runge-Kutta method is at most s+1 and the stage order is at most 3. In this paper, it is shown that the order of an s-stage mono-implicit Runge-Kutta method being algebraically stable is at most min((s) over tilde, 4), and the stage order together with the optimal B-convergence order is at most min(s, 2), where [GRAPHICS]
基金Supported by the Science and Technology Program of Guizhou Province(Grant No.QKHJC QN[2025]362)the National Natural Science Foundation of China(Grant No.12361005).
文摘Loday introduced di-associative algebras and tri-associative algebras motivated by periodicity phenomena in algebraic K-theory.The purpose of this paper is to study the splittings of operations on di-associative algebras and tri-associative algebras.We introduce the notion of a quad-dendriform algebra,which is a splitting of a di-associative algebra.We show that a relative averaging operator on dendriform algebras gives rise to a quad-dendriform algebra.Furthermore,we introduce the notion of six-dendriform algebras,which are splittings of the tri-associative algebras,and demonstrate that homomorphic relative averaging operators induce six-dendriform algebras.
基金supported by the National Natural Science Foundation of China(Grant Nos.12204173 and 12275263)the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0301900)supported by the Natural Science Foundation of Fujian Province 802 of China(Grant No.2023J02032)。
文摘The crossover between short-range and long-range(LR)universal behaviors remains a central theme in the physics of LR interacting systems.The competition between LR coupling and the Berezinskii-Kosterlitz-Thouless mechanism makes the problem more subtle and less understood in the two-dimensional(2D)XY model,a cornerstone for investigating low-dimensional phenomena and their implications in quantum computation.We study the 2D XY model with algebraically decaying interaction~1/r^(2+σ).Utilizing an advanced update strategy,we conduct LR Monte Carlo simulations of the model up to a linear size of L=8192.Our results demonstrate continuous phase transitions into a ferromagnetic phase forσ<2,which exhibit the simultaneous emergence of a long-ranged order and a power-law decaying correlation function due to the Goldstone mode.Furthermore,we fnd logarithmic scaling behaviors in the low-temperature phase atσ=2.The observed scaling behaviors in the low-temperature phase forσ≤2 agree with our theoretical analysis.Our fndings request further theoretical understanding and can be of practical application in cutting-edge experiments like Rydberg atom arrays.
基金Supported by National Natural Science Foundation of China (Grant No. 52175019)Beijing Municipal Natural Science Foundation of China (Grant No. L222038)+3 种基金Beijing Nova Programme Interdisciplinary Cooperation Project of China (Grant No. 20240484699)Joint Funds of Industry-University-Research of Shanghai Academy of Spaceflight Technology of China (Grant No. SAST2022-017)Beijing Municipal Key Laboratory of Space-ground Interconnection and Convergence of ChinaKey Laboratory of IoT Monitoring and Early Warning,Ministry of Emergency Management of China
文摘To investigate the forward kinematics problem of parallel mechanisms with complex limbs and to expand the applicability of the powerful tool of Conformal Geometric Algebra(CGA),a CGA-based modeling and solution method for a class of parallel platforms with 3-RE structure after locking the actuated joints is proposed in this paper.Given that the angle between specific joint axes of limbs remains constant,a set of geometric constraints for the forward kinematics of parallel mechanisms(PM)are determined.After translating unit direction vectors of these joint axes to the common starting point,the geometric constraints of the angle between the vectors are transformed into the distances between the endpoints of the vectors,making them easier to handle.Under the framework of CGA,the positions of key points that determine the position and orientation of the moving platform can be intuitively determined by the intersection,division,and duality of basic geometric entities.By employing the tangent half-angle substitution,the forward kinematic analysis of the parallel mechanisms leads to a high-order univariate polynomial equation without the need for any complex algebraic elimination operations.After solving this equation and back substitution,the position and pose of the MP can be obtained indirectly.A numerical case is utilized to confirm the effectiveness of the proposed method.
基金Supported by the Universities Key Laboratory of System Modeling and Data Mining in Guizhou Province(Grant No.2023013)the National Natural Science Foundation of China(Grant No.12161013)the Science and Technology Program of Guizhou Province(Grant No.ZK[2023]025)。
文摘Semenov-Tian-Shansky has given the solution of the modified classical Yang-Baxter equation, which was called the modified r-matrix. Relevant studies have been extensive in recent times. In this paper, we introduce the concept and representations of modified RotaBaxter Hom-Lie algebras. We develop a cohomology of modified Rota-Baxter Hom-Lie algebras with coefficients in a suitable representation. As applications, we study formal deformations and abelian extensions of modified Rota-Baxter Hom-Lie algebras in terms of second cohomology groups.
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 Research Grants Council(RGC),University Grants Committee(UGC)of Hong Kong(ECS No.24304722)。
文摘We classify condensable𝐸E_(2)-algebras in a modular tensor category C up to 2-Morita equivalence.Physically,this classification provides an explicit criterion to determine when distinct condensable𝐸E_(2)-algebras yield the same condensed topological phase under a two-dimensional anyon condensation process.The relations between different condensable algebras can be translated into their module categories,interpreted physically as gapped domain walls in topological orders.As concrete examples,we interpret the categories of quantum doubles of finite groups and examples beyond group symmetries.Our framework fully elucidates the interplay among condensable𝐸E_(1)-algebras in C,condensable𝐸E_(2)-algebras in C up to 2-Morita equivalence,and Lagrangian algebras in C⊠C.
基金Supported by the Fundamental Research Program of Shanxi Province(Grant No.202303021212147)the National Natural Science Foundation of China(Grant No.12471038)。
文摘Let D(n)be the finite dimensional non-pointed and non-semisimple Hopf algebra,which is a quotient of a prime Hopf algebras of GK-dimension one for an odd number n>1.In this paper,we investigate the structure of Yetter-Drinfeld simple modules over D(n)and give iso-classes of them.
基金supported by the National Natural Science Foundation of China(Grant No.61973181)Tsinghua University Initiative Scientific Research Program(Grant No.2018Z05JZY004).
文摘Many applications for locating a radio signal source employ Global Navigation Satellite System(GNSS)to obtain a sensor’s position.By using GNSS,a sensor can also synchronize with other sensors.For a sensor that is equipped with a GNSS receiver,it can be independent and is readily to be loaded on a flexible platform,such as an unmanned aerial vehicle(UAV).In this paper,we consider using such sensors and timeof-arrival(TOA)techniques to locate a radio signal source,and analyze the performance limit of source localization.Besides the performance analysis,this paper provides the geometric interpretation of the performance limit,which can illustrate how a sensor contributes to the source localization accuracy.The performance analysis and the geometric interpretation together give important insights into how to make better use of GNSS receiver for passive localization.Another contribution is we propose a modified closedform solution for this localization problem.Compared with previous literature,this solution takes both sensor position and synchronization uncertainty into account,and it does not need proper initial guess of source position and is computationally efficient.Our simulation results validate the efficiency of this solution.
文摘A left Leibniz algebra equipped with an invariant nondegenerate skew-symmetric bilinear form(i.e.,a skew-symmetric quadratic Leibniz algebra)is constructed.The notion of T^(*)-extension of Lie-Yamaguti algebras is introduced and it is observed that the trivial extension of a Lie-Yamaguti algebra is a quadratic Lie-Yamaguti algebra.It is proved that every symmetric(resp.,skew-symmetric)quadratic Leibniz algebra induces a quadratic(resp.,symplectic)LieYamaguti algebra.
基金Sponsored by Foreign Expert Program of China(Grant No.DL2023041002L)Yulin City Industry University Research Project(Grant No.CXY-2022-59).
文摘This study mainly focuses on the triangle bounded L⁃algebras and triangle ideals.Firstly,the definition of triangle bounded L⁃algebras is presented,and several examples with different conditions are outlined along with an exploration of their properties.Moreover,we investigate the structure of triangle bounded L⁃algebra with a special condition.Secondly,we define the concept of triangle ideals of triangle bounded L⁃algebra and explore the connection between the triangle ideals of triangle bounded L⁃algebra L and the ideals of bounded L⁃algebra E(L).In addition,we classified and studied various classes of triangle ideals,including Stonean triangle ideals,extended Stonean triangle ideals,and lattice ideals,and by introducing the notion of Stonean triangle bounded L algebras,we examine the relationship between Stonean triangle bounded L⁃algebras and Stonean triangle ideals.Finally,we investigate the interrelationships among these various types of triangle ideals.
基金supported by the Spanish MICINN grant PID2022-140440NB-C22the regional Andalusian project P18-FR-5057+3 种基金the Coordinación de la Investigación Científica of the Universidad Michoacana de San Nicolás de Hidalgo,Morelia,Mexico,Grant No.4.10the Consejo Nacional de Humanidades,Ciencias y Tecnologías,Mexico,project CBF2023-2024-3544the Beatriz-Galindo support during his current scientific stay at the University of Huelva,Huelva,Spainthe Chair d'excellence within the program d'Alembert supporting a visiting professorship in the Universitéde Paris-Saclay,France。
文摘Several aspects of the internal structure of pseudoscalar mesons,accessible through generalized parton distri-butions in their zero-skewness limit,are examined.These include electromagnetic and gravitational form factors related to charge and mass densities;and distributions in the impact parameter space.To this end,we employ an algebraically viable framework that is based upon the valence-quark generalized parton distribution expressed explicitly in terms of the associated distribution function and a profile function that governs the off-forward dynamics.The predominantly analytical nature of this scheme yields several algebraic results and relations while also facilitating the exploration of insightful limiting cases.With a suitable input distribution function,guided either by experiment or theory,and with an appropriate choice of the profile function,it is possible to provide testable predictions for spatial distributions of valence quarks inside pseudoscalar mesons.When comparison is possible,these predictions align well with existing experimental data as well as the findings of reliable theoretical approaches and lattice QCD.
文摘This paper presents a systematic comparison of the curriculum design and application orientation of the linear algebra curriculum in our country and abroad.It explains mainly differences in course objectives,teaching content,approaches,and feedback mechanisms,reflecting divergent understandings of the discipline’s value within distinct educational ecosystems.Forward-looking and practical conclusions are proposed across five main directions:optimizing course structure,strengthening practical components,deepening interdisciplinary integration,building faculty capacity,and developing teaching resources.The aim is to provide strong conceptual help and realistic guidance for getting real progress in linear algebra education in China.
文摘This article proposes an algebraic model predictive control(MPC)method for automatic landing.While defining the constraint functions in the optimization problem,the tangent hyperbolic function is preferred.Therefore,the optimization problem turns into an unconstrained,continuous,and differentiable form.An analytical two-step method is also proposed to solve the rest of the problem.In the first step,it is assumed that only input constraints are active and states are unconstrained.The optimal solution for this case is calculated directly with the optimality condition.The calculated control signal is revised in the second step according to system dynamics and state constraints.Simulation results of the auto-landing system show that the MPC computation speed is significantly increased by the new algebraic MPC(AMPC)without compromising the control performance,which makes the method realistic for using MPC in systems with high-speed changing dynamics.
基金Supported by National Natural Science Foundation of China(Grant Nos.11771004 and 11971111).
文摘A bottleneck algebra is a linearly ordered set(B,≤)with two operations a⊕b=max{a,b}and a⊗b=min{a,b}.A finite nonempty set of vectors of order m over a bottleneck algebra B is said to be 2 B-independent if each vector of order m over B can be expressed as a linear combination of vectors in this set in at most one way.In 1996,Cechlárováand Plávka posed an open problem:Find a necessary and sufficient condition for a finite nonempty set of vectors of order m over B to be 2 B-independent.In this paper,we derive some necessary and sufficient conditions for a finite nonempty set of vectors of order m over a bounded bottleneck algebra to be 2 B-independent and answer this open problem.
基金Supported by the General Program of Shanghai Natural Science Foundation(Grant No.24ZR1415600)the National Natural Science Foundation of China(Grant Nos.1232637412401157)。
文摘In this paper,we study anti-derivations and anti-left multipliers.For a class of algebras,which contains triangular algebras,matrix algebras,embedded algebras,Cuntz algebras,nest algebras,P-lattice algebras,and linear transformation algebras L(X),we show that every anti-left multiplier on these algebras is zero.Furthermore,let A be a zero product determined algebra andδbe a linear mapping from A into itself,satisfying that for any a,b in A,ab=0 impliesδ(b)a+bδ(a)=0.We show thatδ(x)=D(x)+δ(1)x,where D is an anti-derivation andδ(1)∈Z(A).
基金Supported by the Optimisation Theory and Algorithm Research Team(Grant No.23kytdzd004)University Science Research Project of Anhui Province(Grant No.2024AH050631)the General Programs for Young Teacher Cultivation of Educational Commission of Anhui Province(Grant No.YQYB2023090).
文摘In this paper,we propose a new full-Newton step feasible interior-point algorithm for the special weighted linear complementarity problems.The proposed algorithm employs the technique of algebraic equivalent transformation to derive the search direction.It is shown that the proximity measure reduces quadratically at each iteration.Moreover,the iteration bound of the algorithm is as good as the best-known polynomial complexity for these types of problems.Furthermore,numerical results are presented to show the efficiency of the proposed algorithm.
