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
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
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
The BCK/BCI/BCH-algebras finds general algebra system than Boolean algebras system. This paper presents a novel class of algebras of type (2, 0) called BCL-algebras. We found the BCL-algebras to be more extensive clas...The BCK/BCI/BCH-algebras finds general algebra system than Boolean algebras system. This paper presents a novel class of algebras of type (2, 0) called BCL-algebras. We found the BCL-algebras to be more extensive class than BCK/BCI/BCH-algebras in the abstract algebra. The BCL-algebras as a class of logical algebras are the algebraic formulations of the set difference together with its properties in set theory and the propositional calculus in logical systems. It is important that the BCL-algebras play an independent role in the axiom algebra system.展开更多
In this paper, two new kinds of B-basis functions called algebraic hyperbolic （AH） Bézier basis and AH B-Spline basis are presented in the space Гk=span{ l,t ……f^k-3,sinht,cosht}, in which K is an arbitrary ...In this paper, two new kinds of B-basis functions called algebraic hyperbolic （AH） Bézier basis and AH B-Spline basis are presented in the space Гk=span{ l,t ……f^k-3,sinht,cosht}, in which K is an arbitrary integer larger than or equal to 3. They share most optimal properties as those of the Bézier basis and B-Spline basis respectively and can represent exactly some remarkable curves and surfaces such as the hyperbola, catenary, hyperbolic spiral and the hyperbolic paraboloid. The generation of tensor product surfaces of the AH B-Spline basis have two forms： AH B-Spline surface and AH T-Spline surface.展开更多
The purpose of this paper is to give a brief introduction to the category of Lie Rinehart algebras and introduces the concept of smooth manifolds associated with a unitary, commutative, associative algebra A. It espec...The purpose of this paper is to give a brief introduction to the category of Lie Rinehart algebras and introduces the concept of smooth manifolds associated with a unitary, commutative, associative algebra A. It especially shows that the A-extended algebra as well as the action algebra can be realized as the space of A-left invariant vector fields on a Lie group, analogous to the well known relationship of Lie algebras and Lie groups.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 present the(co)sine n-algebra which is indexed by the d-dimensional integer lattice.Due to the associative operators,this generalized(co)sine n-algebra is the higher order Lie algebra for the n even case.The partic...We present the(co)sine n-algebra which is indexed by the d-dimensional integer lattice.Due to the associative operators,this generalized(co)sine n-algebra is the higher order Lie algebra for the n even case.The particular cases are the d-dimensional lattice sine 3 and cosine 5-algebras with the special parameter values.We find that the corresponding d-dimensional lattice sine 3 and cosine 5-algebras are the Nambu 3-algebra and higher order Lie algebra,respectively.The limiting case of the d-dimensional lattice(co)sine n-algebra is also discussed.Moreover we construct the super sine n-algebra,which is the super higher order Lie algebra for the n even case.展开更多
In this paper,we introduce the notion of a generalized weak group-like algebra which is designed to cover finite groupoid algebras and group-like algebras.Then we construct a list of examples and show that a generaliz...In this paper,we introduce the notion of a generalized weak group-like algebra which is designed to cover finite groupoid algebras and group-like algebras.Then we construct a list of examples and show that a generalized weak group-like algebra can be regarded as a generalized weak bi-Frobenius algebra.Moreover,we discuss when a generalized weak bi-Frobenius algebra is a groupoid algebra.Finally,we give the classifications of low-dimensional generalized weak group-like algebras.展开更多
In this paper,we give an explicit and systematic study on the double constructions of Frobenius Hom-algebras and introduce the close relations between O-operators and Homdendriform algebras.Furthermore,we study the do...In this paper,we give an explicit and systematic study on the double constructions of Frobenius Hom-algebras and introduce the close relations between O-operators and Homdendriform algebras.Furthermore,we study the double constructions of Connes cocycles in terms of Hom-dendriform algebras.Finally,we give a clear analogy between antisymmetric infinitesimal Hom-bialgebras and Hom-dendriform D-bialgebras.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
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
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
Parallel mechanisms with fewer degrees of freedom that incorporate two or more SPR limbs have been widely adopted in industrial applications in recent years.However,notable theoretical gaps persist,particularly in the...Parallel mechanisms with fewer degrees of freedom that incorporate two or more SPR limbs have been widely adopted in industrial applications in recent years.However,notable theoretical gaps persist,particularly in the field of analytical solutions for forward kinematics.To address this,this paper proposes an innovative forward kinematics analysis method based on Conformal Geometric Algebra(CGA)for complex hybrid mechanisms formed by serial concatenation of such parallel mechanisms.The method efficiently represents geometric elements and their operational relationships by defining appropriate unknown parameters.It constructs fundamental geometric objects such as spheres and planes,derives vertex expressions through intersection and dual operations,and establishes univariate high-order equations via inner product operations,ultimately obtaining complete analytical solutions for the forward kinematics of hybrid mechanisms.Using the(2-SPR+RPS)+(3-SPR)serial-parallel hybrid mechanism as a validation case,three configuration tests implemented in Mathematica demonstrate that:for each configuration,the upper 3-SPR mechanism yields 15 mathematical solutions,while the lower 2-SPR+RPS mechanism yields 4 mathematical solutions.After geometric constraint filtering,a unique physically valid solution is obtained for each mechanism.SolidWorks simulations further verify the correctness and reliability of the model.This research provides a reliable analytical method for forward kinematics of hybrid mechanisms,holding significant implications for advancing their applications in high-precision scenarios.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
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 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.
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.
文摘The BCK/BCI/BCH-algebras finds general algebra system than Boolean algebras system. This paper presents a novel class of algebras of type (2, 0) called BCL-algebras. We found the BCL-algebras to be more extensive class than BCK/BCI/BCH-algebras in the abstract algebra. The BCL-algebras as a class of logical algebras are the algebraic formulations of the set difference together with its properties in set theory and the propositional calculus in logical systems. It is important that the BCL-algebras play an independent role in the axiom algebra system.
基金Projects supported by the National Natural Science Foundation of China (No. 10371110) and the National Basic Research Program (973) of China (No.G2002CB312101)
文摘In this paper, two new kinds of B-basis functions called algebraic hyperbolic （AH） Bézier basis and AH B-Spline basis are presented in the space Гk=span{ l,t ……f^k-3,sinht,cosht}, in which K is an arbitrary integer larger than or equal to 3. They share most optimal properties as those of the Bézier basis and B-Spline basis respectively and can represent exactly some remarkable curves and surfaces such as the hyperbola, catenary, hyperbolic spiral and the hyperbolic paraboloid. The generation of tensor product surfaces of the AH B-Spline basis have two forms： AH B-Spline surface and AH T-Spline surface.
基金the China Postdoctoral Science Foundation(20060400017)
文摘The purpose of this paper is to give a brief introduction to the category of Lie Rinehart algebras and introduces the concept of smooth manifolds associated with a unitary, commutative, associative algebra A. It especially shows that the A-extended algebra as well as the action algebra can be realized as the space of A-left invariant vector fields on a Lie group, analogous to the well known relationship of Lie algebras and Lie groups.
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 National Natural Science Foundation of China under Grant Nos.11375119 and 11475116
文摘We present the(co)sine n-algebra which is indexed by the d-dimensional integer lattice.Due to the associative operators,this generalized(co)sine n-algebra is the higher order Lie algebra for the n even case.The particular cases are the d-dimensional lattice sine 3 and cosine 5-algebras with the special parameter values.We find that the corresponding d-dimensional lattice sine 3 and cosine 5-algebras are the Nambu 3-algebra and higher order Lie algebra,respectively.The limiting case of the d-dimensional lattice(co)sine n-algebra is also discussed.Moreover we construct the super sine n-algebra,which is the super higher order Lie algebra for the n even case.
基金Supported by the National Natural Science Foundation of China(Grant No.12001174)the Natural Science Foundation of Shandong Province(Grant No.ZR2023MA008)。
文摘In this paper,we introduce the notion of a generalized weak group-like algebra which is designed to cover finite groupoid algebras and group-like algebras.Then we construct a list of examples and show that a generalized weak group-like algebra can be regarded as a generalized weak bi-Frobenius algebra.Moreover,we discuss when a generalized weak bi-Frobenius algebra is a groupoid algebra.Finally,we give the classifications of low-dimensional generalized weak group-like algebras.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11761017,11801150)the Science and Technology Foundation of Guizhou Province(Grant No.20201Y005)。
文摘In this paper,we give an explicit and systematic study on the double constructions of Frobenius Hom-algebras and introduce the close relations between O-operators and Homdendriform algebras.Furthermore,we study the double constructions of Connes cocycles in terms of Hom-dendriform algebras.Finally,we give a clear analogy between antisymmetric infinitesimal Hom-bialgebras and Hom-dendriform D-bialgebras.
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 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 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 Hebei Provincial Natural Science Foundation(Grant No.F2024202052)National Natural Science Foundation of China(Grant No.52175019)+3 种基金Beijing Municipal Natural Science Foundation(Grant No.L222038)Beijing Nova Programme Interdisciplinary Cooperation Project(Grant No.20240484699)Joint Funds of Industry-University-Research of Shanghai Academy of Spaceflight Technology(Grant No.SAST2022-017)Beijing Municipal Key Laboratory of Space-ground Interconnection and Convergence of China and Key Laboratory of IoT Monitoring and Early Warning,Ministry of Emergency Management。
文摘Parallel mechanisms with fewer degrees of freedom that incorporate two or more SPR limbs have been widely adopted in industrial applications in recent years.However,notable theoretical gaps persist,particularly in the field of analytical solutions for forward kinematics.To address this,this paper proposes an innovative forward kinematics analysis method based on Conformal Geometric Algebra(CGA)for complex hybrid mechanisms formed by serial concatenation of such parallel mechanisms.The method efficiently represents geometric elements and their operational relationships by defining appropriate unknown parameters.It constructs fundamental geometric objects such as spheres and planes,derives vertex expressions through intersection and dual operations,and establishes univariate high-order equations via inner product operations,ultimately obtaining complete analytical solutions for the forward kinematics of hybrid mechanisms.Using the(2-SPR+RPS)+(3-SPR)serial-parallel hybrid mechanism as a validation case,three configuration tests implemented in Mathematica demonstrate that:for each configuration,the upper 3-SPR mechanism yields 15 mathematical solutions,while the lower 2-SPR+RPS mechanism yields 4 mathematical solutions.After geometric constraint filtering,a unique physically valid solution is obtained for each mechanism.SolidWorks simulations further verify the correctness and reliability of the model.This research provides a reliable analytical method for forward kinematics of hybrid mechanisms,holding significant implications for advancing their applications in high-precision scenarios.
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.
