In the novel What I Saw and How I Lied （2008）, Judy Blundell presents readers a world of noir where so many lies are around the innocent protagonist, 15-year-old girl Evie. It is a challenge for Evie to probe into t...In the novel What I Saw and How I Lied （2008）, Judy Blundell presents readers a world of noir where so many lies are around the innocent protagonist, 15-year-old girl Evie. It is a challenge for Evie to probe into the heart of the deceptions and make ethical choices between good and evil. After experiencing the path from error to truth, from confusion to clarity, and unconsciousness to consciousness, Evie comes to realize the corruption and evils of the society and in an epiphany, obtains a self-knowledge which leads to her initiation. Through analyzing the ethical predicament and ethical choices of the protagonist Evie as well as the negative living environment around her, the present paper aims to interrogate the moral issues of truth, lie, justice, greed, fidelity, and betrayal so as to give readers a better understanding of the theme of initiation in the novel.展开更多
Lie algebras are special Leibniz algebras,so it is natural to view Lie algebras as Leibniz algebras.In this paper,we calculate all the Leibniz 2 cocycles of the Lie algebra K(1,0),which is helpful to classify one dime...Lie algebras are special Leibniz algebras,so it is natural to view Lie algebras as Leibniz algebras.In this paper,we calculate all the Leibniz 2 cocycles of the Lie algebra K(1,0),which is helpful to classify one dimensional central extensions of K(1,0)as Leibniz algebra.展开更多
In this paper, a Lie group method software package based on a symbolic analytical sys-tem, REDUCE, is established for the solution of the linear and nonlinear O/P DE or O/PDEs. By means of this software package, the g...In this paper, a Lie group method software package based on a symbolic analytical sys-tem, REDUCE, is established for the solution of the linear and nonlinear O/P DE or O/PDEs. By means of this software package, the group analyses for the PDE of the orthogonalanisotropic plates are made. We have obtained a set of ODEs of the reduced dimension andall the exact analysis solutions of the former PDE.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
本文刻画*代数上完全保混合Lie零积的非线性映射,利用该结论得到不含交换中心投影的von Neumann代数上*-同构的等价刻画。In this paper, we characterize nonlinear maps on *-algebras completely preserving mixed Lie zero products...本文刻画*代数上完全保混合Lie零积的非线性映射,利用该结论得到不含交换中心投影的von Neumann代数上*-同构的等价刻画。In this paper, we characterize nonlinear maps on *-algebras completely preserving mixed Lie zero products. As its application, equivalent characterization of *-isomorphism on von Neumann algebra with no abelian center projections is obtained.展开更多
As space equipment become larger in size and more flexible,generalized mechanisms are being widely used in space-deployable structures.Dynamic modeling of large-scale generalized space-deployable mechanisms is challen...As space equipment become larger in size and more flexible,generalized mechanisms are being widely used in space-deployable structures.Dynamic modeling of large-scale generalized space-deployable mechanisms is challenging owing to the coupling between the deformation of flexible links and rigid body motion.This study develops a dynamic modeling method for generalized mechanisms using the local frame of the SE(3)Lie group.The model represents both rigid and flexible links within a unified Lie group setting.The expressions for the velocities of rigid links and deformation of flexible links are derived using the Lie algebra framework.The nonuniqueness of the degrees of freedom of generalized kinematic pairs is considered,and the velocity fields of kinematic pairs in different situations are expressed.The equations of motion are derived using Hamilton’s principle.Because the velocities are expressed in the local frame,the mass matrix in the equation is constant,which yields a compact and unified expression for the dynamic equation.A Lie group generalized-αtime integration method is adopted to ensure numerical stability and efficiency in simulating multibody systems with large rotations and deformations.Two numerical examples are studied to demonstrate a formulation that reflects the motion responses under varying configurations and loading conditions.This study broadens the application of the local frame of the Lie group formulation in space mechanisms and provides a new concept for dynamic modeling of generalized mechanisms.展开更多
Lying in politics has long been seen as both routine and destructive.While some falsehoods appear trivial,others undermine democratic processes,erode trust,and inflict significant harm on society.This essay investigat...Lying in politics has long been seen as both routine and destructive.While some falsehoods appear trivial,others undermine democratic processes,erode trust,and inflict significant harm on society.This essay investigates the moral,legal,and political dimensions of punishing political lies,drawing on Kantian deontological ethics,consequentialist reasoning,and theories of democratic communication.It distinguishes minor misstatements from harmful falsehoods that distort elections,public health responses,and national security.Building on Hannah Arendt’s warning about the collapse of truth and Jürgen Habermas’s emphasis on communicative integrity,the analysis shows how unchecked deception corrodes the foundations of democratic legitimacy.Although legal punishment risks overreach and potential misuse,political and social sanctions remain essential tools of accountability.By examining cases such as misinformation in the Iraq War and the COVID-19 pandemic,the essay argues that meaningful consequences for harmful lies are indispensable to maintaining truth as a shared democratic norm.展开更多
In this paper,a variable-coefficient modified Kadomtsev-Petviashvili(vcm KP)system is investigated by modeling the propagation of electromagnetic waves in an isotropic charge-free infinite ferromagnetic thin film and ...In this paper,a variable-coefficient modified Kadomtsev-Petviashvili(vcm KP)system is investigated by modeling the propagation of electromagnetic waves in an isotropic charge-free infinite ferromagnetic thin film and nonlinear waves in plasma physics and electrodynamics.Painlevéanalysis is given out,and an auto-B?cklund transformation is constructed via the truncated Painlevéexpansion.Based on the auto-B?cklund transformation,analytic solutions are given,including the solitonic,periodic and rational solutions.Using the Lie symmetry approach,infinitesimal generators and symmetry groups are presented.With the Lagrangian,the vcm KP equation is shown to be nonlinearly self-adjoint.Moreover,conservation laws for the vcm KP equation are derived by means of a general conservation theorem.Besides,the physical characteristics of the influences of the coefficient parameters on the solutions are discussed graphically.Those solutions have comprehensive implications for the propagation of solitary waves in nonuniform backgrounds.展开更多
设ℳ和N是无I1或I2型中心直和项的von Neumann代数,其单位元分别为I和I′。本文证明非线性双射Φ:ℳ→N混合Lie可乘,即Φ([ [ A,B ],C ]∗)=[ [ Φ(A),Φ(B) ],Φ(C) ]∗,∀A,B,C∈ℳ,当且仅当存在线性*-同构和共轭线性*-同构的直和Ψ:ℳ→N使...设ℳ和N是无I1或I2型中心直和项的von Neumann代数,其单位元分别为I和I′。本文证明非线性双射Φ:ℳ→N混合Lie可乘,即Φ([ [ A,B ],C ]∗)=[ [ Φ(A),Φ(B) ],Φ(C) ]∗,∀A,B,C∈ℳ,当且仅当存在线性*-同构和共轭线性*-同构的直和Ψ:ℳ→N使得Φ(A)=Φ(I)Ψ(A),∀A∈ℳ,其中Φ(I)∈N是可逆中心元且Φ(I)2=I′。该结论将因子von Neumann代数上的非线性混合Lie可乘双射的结果推广到无I1或I2型中心直和项的von Neumann代数。Let ℳand Nbe von Neumann algebras with no central summands of type I1or I2, Iand I′be the identities of them. This paper proves that a bijective map Φ:ℳ→Nis mixed Lie multiplicative, that is, Φ([ [ A,B ],C ]∗)=[ [ Φ(A),Φ(B) ],Φ(C) ]∗,∀A,B,C∈ℳif and only if Φ(A)=Φ(I)Ψ(A)for all A∈ℳ, where Ψ:ℳ→Nis a direct sum of a linear *-isomorphism and a conjugate linear *-isomorphism, Φ(I)is a central element in Nwith Φ(I)2=I′. The results about mixed Lie multiplicative maps on factor von Neumann algebras are generalized to von Neumann algebras with no central summands of type I1or I2.展开更多
1.Drylands face significant challenges under global change Drylands cover approximately 41%of Earth's terrestrial surface and support about 38%of the global population.They comprise a variety of biomes,and provide...1.Drylands face significant challenges under global change Drylands cover approximately 41%of Earth's terrestrial surface and support about 38%of the global population.They comprise a variety of biomes,and provide essential resources and ecosystem services for humans such as mineral resources,food,livestock products,sand stabilization,and soil and water conservation(Li et al.,2021).However,drylands are characterized by water limitation,and are highly sensitive to global change(Prăvălie et al.,2016).展开更多
In this paper,the Lie symmetry analysis method is applied to the(2+1)-dimensional time-fractional Heisenberg ferromagnetic spin chain equation.We obtain all the Lie symmetries admitted by the governing equation and re...In this paper,the Lie symmetry analysis method is applied to the(2+1)-dimensional time-fractional Heisenberg ferromagnetic spin chain equation.We obtain all the Lie symmetries admitted by the governing equation and reduce the corresponding(2+1)-dimensional fractional partial differential equations with the Riemann–Liouville fractional derivative to(1+1)-dimensional counterparts with the Erdélyi–Kober fractional derivative.Then,we obtain the power series solutions of the reduced equations,prove their convergence and analyze their dynamic behavior graphically.In addition,the conservation laws for all the obtained Lie symmetries are constructed using the new conservation theorem and the generalization of Noether operators.展开更多
文摘In the novel What I Saw and How I Lied （2008）, Judy Blundell presents readers a world of noir where so many lies are around the innocent protagonist, 15-year-old girl Evie. It is a challenge for Evie to probe into the heart of the deceptions and make ethical choices between good and evil. After experiencing the path from error to truth, from confusion to clarity, and unconsciousness to consciousness, Evie comes to realize the corruption and evils of the society and in an epiphany, obtains a self-knowledge which leads to her initiation. Through analyzing the ethical predicament and ethical choices of the protagonist Evie as well as the negative living environment around her, the present paper aims to interrogate the moral issues of truth, lie, justice, greed, fidelity, and betrayal so as to give readers a better understanding of the theme of initiation in the novel.
基金National Natural Science Foundation of China(11971315)。
文摘Lie algebras are special Leibniz algebras,so it is natural to view Lie algebras as Leibniz algebras.In this paper,we calculate all the Leibniz 2 cocycles of the Lie algebra K(1,0),which is helpful to classify one dimensional central extensions of K(1,0)as Leibniz algebra.
基金Project supported by the National Natural Science Foundation of China.
文摘In this paper, a Lie group method software package based on a symbolic analytical sys-tem, REDUCE, is established for the solution of the linear and nonlinear O/P DE or O/PDEs. By means of this software package, the group analyses for the PDE of the orthogonalanisotropic plates are made. We have obtained a set of ODEs of the reduced dimension andall the exact analysis solutions of the former PDE.
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].
文摘本文刻画*代数上完全保混合Lie零积的非线性映射,利用该结论得到不含交换中心投影的von Neumann代数上*-同构的等价刻画。In this paper, we characterize nonlinear maps on *-algebras completely preserving mixed Lie zero products. As its application, equivalent characterization of *-isomorphism on von Neumann algebra with no abelian center projections is obtained.
基金Supported by National Natural Science Foundation of China(Grant No.52475280)Key Laboratory Project of the Key Program of the Natural Science Basic Research Program of Shaanxi Province of China(Grant No.2025SYS-SYSZD-105)+1 种基金Natural Science Foundation of Shaanxi Province of China(Grant No.2025JC-YBQN-505)China Postdoctoral Science Foundation(Grant No.2024M752510).
文摘As space equipment become larger in size and more flexible,generalized mechanisms are being widely used in space-deployable structures.Dynamic modeling of large-scale generalized space-deployable mechanisms is challenging owing to the coupling between the deformation of flexible links and rigid body motion.This study develops a dynamic modeling method for generalized mechanisms using the local frame of the SE(3)Lie group.The model represents both rigid and flexible links within a unified Lie group setting.The expressions for the velocities of rigid links and deformation of flexible links are derived using the Lie algebra framework.The nonuniqueness of the degrees of freedom of generalized kinematic pairs is considered,and the velocity fields of kinematic pairs in different situations are expressed.The equations of motion are derived using Hamilton’s principle.Because the velocities are expressed in the local frame,the mass matrix in the equation is constant,which yields a compact and unified expression for the dynamic equation.A Lie group generalized-αtime integration method is adopted to ensure numerical stability and efficiency in simulating multibody systems with large rotations and deformations.Two numerical examples are studied to demonstrate a formulation that reflects the motion responses under varying configurations and loading conditions.This study broadens the application of the local frame of the Lie group formulation in space mechanisms and provides a new concept for dynamic modeling of generalized mechanisms.
文摘Lying in politics has long been seen as both routine and destructive.While some falsehoods appear trivial,others undermine democratic processes,erode trust,and inflict significant harm on society.This essay investigates the moral,legal,and political dimensions of punishing political lies,drawing on Kantian deontological ethics,consequentialist reasoning,and theories of democratic communication.It distinguishes minor misstatements from harmful falsehoods that distort elections,public health responses,and national security.Building on Hannah Arendt’s warning about the collapse of truth and Jürgen Habermas’s emphasis on communicative integrity,the analysis shows how unchecked deception corrodes the foundations of democratic legitimacy.Although legal punishment risks overreach and potential misuse,political and social sanctions remain essential tools of accountability.By examining cases such as misinformation in the Iraq War and the COVID-19 pandemic,the essay argues that meaningful consequences for harmful lies are indispensable to maintaining truth as a shared democratic norm.
文摘In this paper,a variable-coefficient modified Kadomtsev-Petviashvili(vcm KP)system is investigated by modeling the propagation of electromagnetic waves in an isotropic charge-free infinite ferromagnetic thin film and nonlinear waves in plasma physics and electrodynamics.Painlevéanalysis is given out,and an auto-B?cklund transformation is constructed via the truncated Painlevéexpansion.Based on the auto-B?cklund transformation,analytic solutions are given,including the solitonic,periodic and rational solutions.Using the Lie symmetry approach,infinitesimal generators and symmetry groups are presented.With the Lagrangian,the vcm KP equation is shown to be nonlinearly self-adjoint.Moreover,conservation laws for the vcm KP equation are derived by means of a general conservation theorem.Besides,the physical characteristics of the influences of the coefficient parameters on the solutions are discussed graphically.Those solutions have comprehensive implications for the propagation of solitary waves in nonuniform backgrounds.
文摘设ℳ和N是无I1或I2型中心直和项的von Neumann代数,其单位元分别为I和I′。本文证明非线性双射Φ:ℳ→N混合Lie可乘,即Φ([ [ A,B ],C ]∗)=[ [ Φ(A),Φ(B) ],Φ(C) ]∗,∀A,B,C∈ℳ,当且仅当存在线性*-同构和共轭线性*-同构的直和Ψ:ℳ→N使得Φ(A)=Φ(I)Ψ(A),∀A∈ℳ,其中Φ(I)∈N是可逆中心元且Φ(I)2=I′。该结论将因子von Neumann代数上的非线性混合Lie可乘双射的结果推广到无I1或I2型中心直和项的von Neumann代数。Let ℳand Nbe von Neumann algebras with no central summands of type I1or I2, Iand I′be the identities of them. This paper proves that a bijective map Φ:ℳ→Nis mixed Lie multiplicative, that is, Φ([ [ A,B ],C ]∗)=[ [ Φ(A),Φ(B) ],Φ(C) ]∗,∀A,B,C∈ℳif and only if Φ(A)=Φ(I)Ψ(A)for all A∈ℳ, where Ψ:ℳ→Nis a direct sum of a linear *-isomorphism and a conjugate linear *-isomorphism, Φ(I)is a central element in Nwith Φ(I)2=I′. The results about mixed Lie multiplicative maps on factor von Neumann algebras are generalized to von Neumann algebras with no central summands of type I1or I2.
基金supported by the 111 projectthe Fundamental Research Funds for the Central Universities of China。
文摘1.Drylands face significant challenges under global change Drylands cover approximately 41%of Earth's terrestrial surface and support about 38%of the global population.They comprise a variety of biomes,and provide essential resources and ecosystem services for humans such as mineral resources,food,livestock products,sand stabilization,and soil and water conservation(Li et al.,2021).However,drylands are characterized by water limitation,and are highly sensitive to global change(Prăvălie et al.,2016).
基金supported by the State Key Program of the National Natural Science Foundation of China(72031009).
文摘In this paper,the Lie symmetry analysis method is applied to the(2+1)-dimensional time-fractional Heisenberg ferromagnetic spin chain equation.We obtain all the Lie symmetries admitted by the governing equation and reduce the corresponding(2+1)-dimensional fractional partial differential equations with the Riemann–Liouville fractional derivative to(1+1)-dimensional counterparts with the Erdélyi–Kober fractional derivative.Then,we obtain the power series solutions of the reduced equations,prove their convergence and analyze their dynamic behavior graphically.In addition,the conservation laws for all the obtained Lie symmetries are constructed using the new conservation theorem and the generalization of Noether operators.
