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
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
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
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
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
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
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
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 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
In this paper,we shall study structures of even lattice vertex operator algebras by using the geometry of the varieties of their semi-conformal vectors.We first give the varieties of semi-conformal vectors of a family...In this paper,we shall study structures of even lattice vertex operator algebras by using the geometry of the varieties of their semi-conformal vectors.We first give the varieties of semi-conformal vectors of a family of vertex operator algebras V_(√kA_(1)) associated to rank-one positive definite even lattices √kA_(1) for arbitrary positive integers k to characterize these even lattice vertex operator algebras.In such a family of lattice vertex operator algebras V_(√kA_(1)),the vertex operator algebra V_(√2A_(1)) is different from others.Hence we describe the varieties of semi-conformal vectors of V_(√2A_(1)) and the fixed vertex operator subalgebra V^(+)√2A_(1).Moreover,as applications,we study the relations between vertex operator algebras V_(√kA_(1) )and L_(sl_(2))(k,0)for arbitrary positive integers k by the viewpoint of semi-conformal homomorphisms of vertex operator algebras.For case k=2,in the series of rational simple affine vertex operator algebras L_(sl_(2))(k,0)for positive integers k,we show that L_(sl_(2))(2,0)is a unique frame vertex operator algebra with rank 3.展开更多
In this paper,we first introduce the notion of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras and define a cohomology of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras w...In this paper,we first introduce the notion of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras and define a cohomology of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras with coefficients in a suitable representation.Next,we introduce and study 3-Hom-post-Lie-algebras as the underlying structure of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras.Finally,we investigate relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras induced by Hom-Lie algebras.展开更多
The long-term Mittag-Leffler stability of solutions to multi-term timefractional diffusion equations with constant coefficients was rigorously established,which demonstrated that the algebraic decay rate of the soluti...The long-term Mittag-Leffler stability of solutions to multi-term timefractional diffusion equations with constant coefficients was rigorously established,which demonstrated that the algebraic decay rate of the solution,characterized by||u_(n)||L^(2)(Ω)=O(t^(−αs)) as t→∞,is determined by the minimum order α_(s) of the time-fractional derivatives.Building on this foundational result,this article pursues two primary objectives.First,we introduce a strongly A-stable fractional linear multistep method and derive the numerical stability region for the governing equation.Second,we rigorously prove the long-term decay rate of the numerical solution through a detailed singularity analysis of its generating function.Notably,the numerical decay rate||u_(n)||L^(2)(Ω)=O(t_(n)^(−α_(s)) as t_(n)→∞aligns precisely with the continuous case.Theoretical findings are further validated through comprehensive numerical simulations,underscoring the robustness of our proposed method.展开更多
In this paper,we introduce non-abelian cohomology groups and classify the nonabelian extensions of Rota-Baxter pre-Lie algebras in terms of non-abelian cohomology groups.Next,we explore the inducibility of pairs of au...In this paper,we introduce non-abelian cohomology groups and classify the nonabelian extensions of Rota-Baxter pre-Lie algebras in terms of non-abelian cohomology groups.Next,we explore the inducibility of pairs of automorphisms and derive the analog Wells exact sequences under the circumstance of Rota-Baxter pre-Lie algebras.Finally,we discuss the inducibility problem of pairs of automorphisms about an abelian extensions of Rota-Baxter pre-Lie algebras.展开更多
Aimed at the demand of contingency return at any time during the near-moon phase in the manned lunar landing missions,a fast calculation method for three-impulse contingency return trajectories is proposed.Firstly,a t...Aimed at the demand of contingency return at any time during the near-moon phase in the manned lunar landing missions,a fast calculation method for three-impulse contingency return trajectories is proposed.Firstly,a three-impulse contingency return trajectory scheme is presented by combining the Lambert transfer and maneuver at the special point.Secondly,a calculation model of three-impulse contingency return trajectories is established.Then,fast calculation methods are proposed by adopting the high-order Taylor expansion of differential algebra in the twobody trajectory dynamics model and perturbed trajectory dynamics model.Finally,the performance of the proposed methods is verified by numerical simulation.The results indicate that the fast calculation method of two-body trajectory has higher calculation efficiency compared to the semi-analytical calculation method under a certain accuracy condition.Due to its high efficiency,the characteristics of the three-impulse contingency return trajectories under different contingency scenarios are further analyzed expeditiously.These findings can be used for the design of contingency return trajectories in future manned lunar landing missions.展开更多
With the development of science and technology,the design and optimization of control systems are widely applied.This paper focuses on the application of matrix equations in linear time-invariant systems.Taking the in...With the development of science and technology,the design and optimization of control systems are widely applied.This paper focuses on the application of matrix equations in linear time-invariant systems.Taking the inverted pendulum model as an example,the algebraic Riccati equation is used to solve the optimal control problem,and the system performance and stability are achieved by selecting the closed-loop pole and designing the gain matrix.Then,the numerical methods for solving the stochastic algebraic Riccati equations are applied to practical problems,with Newton’s iteration method as the outer iteration and the solution of the mixed-type Lyapunov equations as the inner iteration.Two methods for solving the Lyapunov equations are introduced,providing references for related research.展开更多
Let R be a commutative ring with unity and T be a triangular algebra over R.Let a sequence G={G_n}_(n∈N)of nonlinear mappings G_n:T→T associated with nonlinear Lie triple higher derivations∆={δ_n}_(n∈N)by local ac...Let R be a commutative ring with unity and T be a triangular algebra over R.Let a sequence G={G_n}_(n∈N)of nonlinear mappings G_n:T→T associated with nonlinear Lie triple higher derivations∆={δ_n}_(n∈N)by local actions be a generalized Lie triple higher derivation by local actions satisfying Gn([[x,y],z])=Σ_(i+j+k=n)[[Gi(x),δj(y)],δk(z)]for all x,y,z∈T with xyz=0.Under some mild conditions on T,we prove in this paper that every nonlinear generalized Lie triple higher derivation by local actions on triangular algebras is proper.As an application we shall give a characterization of nonlinear generalized Lie triple higher derivations by local actions on upper triangular matrix algebras and nest algebras,respectively.At the same time,it also improves some interesting conclusions,such as[J.Algebra Appl.22(3),2023,Paper No.2350059],[Axioms,11,2022,1–16].展开更多
In this paper,various extended contractions are introduced as generalizations of some existing contractions given by Kannan,Ciric,Reich and Gornicki,et al.Then,several meaningful results about asymptotically regular m...In this paper,various extended contractions are introduced as generalizations of some existing contractions given by Kannan,Ciric,Reich and Gornicki,et al.Then,several meaningful results about asymptotically regular mappings in cone metric spaces over Banach algebras are obtained,weakening the completeness of the spaces and the continuity of the mappings.Moreover,some nontrivial examples are showed to verify the innovation of the new concepts and our fxed point theorems.展开更多
In this paper,we study the Hom-structures of a special class of solvable Lie algebras with naturally graded filiform nilradical n_(n,1).Over an algebraically closed field F of zero characteristic,we calculate the Hom-...In this paper,we study the Hom-structures of a special class of solvable Lie algebras with naturally graded filiform nilradical n_(n,1).Over an algebraically closed field F of zero characteristic,we calculate the Hom-structures of these solvable Lie algebras using the Hom-Jacobi identity,obtain the bases of these Hom-structures and observe that there are certain similarities among these bases.展开更多
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.
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 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.
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 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 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.
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 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.
基金Supported by National Natural Science Foundation of China(Grant No.12475002).
文摘In this paper,we shall study structures of even lattice vertex operator algebras by using the geometry of the varieties of their semi-conformal vectors.We first give the varieties of semi-conformal vectors of a family of vertex operator algebras V_(√kA_(1)) associated to rank-one positive definite even lattices √kA_(1) for arbitrary positive integers k to characterize these even lattice vertex operator algebras.In such a family of lattice vertex operator algebras V_(√kA_(1)),the vertex operator algebra V_(√2A_(1)) is different from others.Hence we describe the varieties of semi-conformal vectors of V_(√2A_(1)) and the fixed vertex operator subalgebra V^(+)√2A_(1).Moreover,as applications,we study the relations between vertex operator algebras V_(√kA_(1) )and L_(sl_(2))(k,0)for arbitrary positive integers k by the viewpoint of semi-conformal homomorphisms of vertex operator algebras.For case k=2,in the series of rational simple affine vertex operator algebras L_(sl_(2))(k,0)for positive integers k,we show that L_(sl_(2))(2,0)is a unique frame vertex operator algebra with rank 3.
基金Supported by the National Natural Science Foundation of China(Grant No.12161013)the School-Level Student Research Project of Guizhou University of Finance and Economics(Grant No.2024ZXSY231)。
文摘In this paper,we first introduce the notion of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras and define a cohomology of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras with coefficients in a suitable representation.Next,we introduce and study 3-Hom-post-Lie-algebras as the underlying structure of relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras.Finally,we investigate relative Rota-Baxter operators of nonzero weight on 3-Hom-Lie algebras induced by Hom-Lie algebras.
文摘The long-term Mittag-Leffler stability of solutions to multi-term timefractional diffusion equations with constant coefficients was rigorously established,which demonstrated that the algebraic decay rate of the solution,characterized by||u_(n)||L^(2)(Ω)=O(t^(−αs)) as t→∞,is determined by the minimum order α_(s) of the time-fractional derivatives.Building on this foundational result,this article pursues two primary objectives.First,we introduce a strongly A-stable fractional linear multistep method and derive the numerical stability region for the governing equation.Second,we rigorously prove the long-term decay rate of the numerical solution through a detailed singularity analysis of its generating function.Notably,the numerical decay rate||u_(n)||L^(2)(Ω)=O(t_(n)^(−α_(s)) as t_(n)→∞aligns precisely with the continuous case.Theoretical findings are further validated through comprehensive numerical simulations,underscoring the robustness of our proposed method.
基金Supported by the National Natural Science Foundation of China(Grant No.12161013)the School-Level Student Research Project of Guizhou University of Finance and Economics(Grant No.2024ZXSY239).
文摘In this paper,we introduce non-abelian cohomology groups and classify the nonabelian extensions of Rota-Baxter pre-Lie algebras in terms of non-abelian cohomology groups.Next,we explore the inducibility of pairs of automorphisms and derive the analog Wells exact sequences under the circumstance of Rota-Baxter pre-Lie algebras.Finally,we discuss the inducibility problem of pairs of automorphisms about an abelian extensions of Rota-Baxter pre-Lie algebras.
基金co-supported by the National Natural Science Foundation of China(No.12072365)the Technology Innovation Team of Manned Space Engineering,China。
文摘Aimed at the demand of contingency return at any time during the near-moon phase in the manned lunar landing missions,a fast calculation method for three-impulse contingency return trajectories is proposed.Firstly,a three-impulse contingency return trajectory scheme is presented by combining the Lambert transfer and maneuver at the special point.Secondly,a calculation model of three-impulse contingency return trajectories is established.Then,fast calculation methods are proposed by adopting the high-order Taylor expansion of differential algebra in the twobody trajectory dynamics model and perturbed trajectory dynamics model.Finally,the performance of the proposed methods is verified by numerical simulation.The results indicate that the fast calculation method of two-body trajectory has higher calculation efficiency compared to the semi-analytical calculation method under a certain accuracy condition.Due to its high efficiency,the characteristics of the three-impulse contingency return trajectories under different contingency scenarios are further analyzed expeditiously.These findings can be used for the design of contingency return trajectories in future manned lunar landing missions.
基金Supported by National Natural Science Foundation of China(Grant No.12571388)the Visiting Scholar Program of National Natural Science Foundation of China(Grant No.12426616)Natural Science Research Start-up Foundation of Recruiting Talents of Nanjing University of Posts and Telecommunications(Grant No.NY223127).
文摘With the development of science and technology,the design and optimization of control systems are widely applied.This paper focuses on the application of matrix equations in linear time-invariant systems.Taking the inverted pendulum model as an example,the algebraic Riccati equation is used to solve the optimal control problem,and the system performance and stability are achieved by selecting the closed-loop pole and designing the gain matrix.Then,the numerical methods for solving the stochastic algebraic Riccati equations are applied to practical problems,with Newton’s iteration method as the outer iteration and the solution of the mixed-type Lyapunov equations as the inner iteration.Two methods for solving the Lyapunov equations are introduced,providing references for related research.
基金Supported by Open Research Fund of Hubei Key Laboratory of Mathematical Sciences(Central China Normal University)the Natural Science Foundation of Anhui Province(Grant No.2008085QA01)the University Natural Science Research Project of Anhui Province(Grant No.KJ2019A0107)。
文摘Let R be a commutative ring with unity and T be a triangular algebra over R.Let a sequence G={G_n}_(n∈N)of nonlinear mappings G_n:T→T associated with nonlinear Lie triple higher derivations∆={δ_n}_(n∈N)by local actions be a generalized Lie triple higher derivation by local actions satisfying Gn([[x,y],z])=Σ_(i+j+k=n)[[Gi(x),δj(y)],δk(z)]for all x,y,z∈T with xyz=0.Under some mild conditions on T,we prove in this paper that every nonlinear generalized Lie triple higher derivation by local actions on triangular algebras is proper.As an application we shall give a characterization of nonlinear generalized Lie triple higher derivations by local actions on upper triangular matrix algebras and nest algebras,respectively.At the same time,it also improves some interesting conclusions,such as[J.Algebra Appl.22(3),2023,Paper No.2350059],[Axioms,11,2022,1–16].
基金Supported by Yunnan Provincial Reserve Talent Program for Young and Middle-aged Academic and Technical Leaders(202405AC350086)the Special Basic Cooperative Research Programs of Yunnan Provincial Undergraduate Universities’Association(202301BA070001-095,202301BA070001-092)+3 种基金the Natural Science Foundation of Guangdong Province(2023A1515010997)Xingzhao Talent Support ProgramEducation and Teaching Reform Research Project of Zhaotong University(Ztjx202405,Ztjx202403,Ztjx202414)2024 First-class Undergraduate Courses of Zhaotong University(Ztujk202405,Ztujk202404).
文摘In this paper,various extended contractions are introduced as generalizations of some existing contractions given by Kannan,Ciric,Reich and Gornicki,et al.Then,several meaningful results about asymptotically regular mappings in cone metric spaces over Banach algebras are obtained,weakening the completeness of the spaces and the continuity of the mappings.Moreover,some nontrivial examples are showed to verify the innovation of the new concepts and our fxed point theorems.
基金Supported by National Natural Science Foundation of China(12271085)Supported by National Natural Science Foundation of Heilongjiang Province(LH2022A019)+3 种基金Basic Scientic Research Operating Funds for Provincial Universities in Heilongjiang Province(2020 KYYWF 1018)Heilongjiang University Outstanding Youth Science Foundation(JCL202103)Heilongjiang University Educational and Teaching Reform Research Project(2024C43)Heilongjiang University Postgraduate Education Reform Project(JGXM_YJS_2024010).
文摘In this paper,we study the Hom-structures of a special class of solvable Lie algebras with naturally graded filiform nilradical n_(n,1).Over an algebraically closed field F of zero characteristic,we calculate the Hom-structures of these solvable Lie algebras using the Hom-Jacobi identity,obtain the bases of these Hom-structures and observe that there are certain similarities among these bases.
