Given a finite dimensional special biserial algebra A with normed basis we obtain the dimension formulae of the first Hochschild homology groups of A and the vector space Alt(DA). As a consequence, an explicit dimensi...Given a finite dimensional special biserial algebra A with normed basis we obtain the dimension formulae of the first Hochschild homology groups of A and the vector space Alt(DA). As a consequence, an explicit dimension formula of the first Hochschild cohomology group of trivial extension TA = A × DA in terms of the combinatorics of the quiver and relations is determined.展开更多
The structure of the trivial preference set of group decision making is studied, and the essential characters and generating reasons of the paradox of voting are revealed.
Let A be a finite-dimensional algebra over arbitrary base fieldk. We prove: if the unbounded derived module category D-(Mod-A) admits symmetric recollement relative to unbounded derived module categories of two finite...Let A be a finite-dimensional algebra over arbitrary base fieldk. We prove: if the unbounded derived module category D-(Mod-A) admits symmetric recollement relative to unbounded derived module categories of two finite-dimensionalk-algebras B and C: then the unbounded derived module category D-(Mod - T(A)) admits symmetric recollement relative to the unbounded derived module categories of T(B) and T(C):展开更多
Measuring topological invariants is an essential task in characterizing topological phases of matter.They are usually obtained from the number of edge states due to the bulk-edge correspondence or from interference si...Measuring topological invariants is an essential task in characterizing topological phases of matter.They are usually obtained from the number of edge states due to the bulk-edge correspondence or from interference since they are integrals of the geometric phases in the energy band.It is commonly believed that the bulk band structures could not be directly used to obtain the topological invariants.Here,we implement the experimental extraction of Zak phase from the bulk band structures of a Su-Schrieffer-Heeger(SSH)model in the synthetic frequency dimension.Such synthetic SSH lattices are constructed in the frequency axis of light,by controlling the coupling strengths between the symmetric and antisymmetric supermodes of two bichromatically driven rings.We measure the transmission spectra and obtain the projection of the time-resolved band structure on lattice sites,where a strong contrast between the non-trivial and trivial topological phases is observed.The topological Zak phase is naturally encoded in the bulk band structures of the synthetic SSH lattices,which can hence be experimentally extracted from the transmission spectra in a fiber-based modulated ring platform using a laser with telecom wavelength.Our method of extracting topological phases from the bulk band structure can be further extended to characterize topological invariants in higher dimensions,while the exhibited trivial and non-trivial transmission spectra from the topological transition may find future applications in optical communications.展开更多
We investigate electron transport inside a ring system composed of a quantum dot （QD） coupled to two Majorana bound states confined at the ends of a one-dimensional topological superconductor nanowire. By tuning the...We investigate electron transport inside a ring system composed of a quantum dot （QD） coupled to two Majorana bound states confined at the ends of a one-dimensional topological superconductor nanowire. By tuning the magnetic flux threading through the ring, the model system we consider can be switched into states with or without zero-energy modes when the nanowire is in its topological phase. We find that the Fano profile in the conductance spectrum due to the interference between bound and continuum states exhibits markedly different features for these two different situations, which consequently can be used to detect the Majorana zero-energy mode. Most interestingly, as a periodic function of magnetic flux, the conductance shows 2π periodicity when the two Majorana bound states are nonoverlapping （as in an infinitely long nanowire） but displays 4π periodicity when the overlapping becomes nonzero （as in a finite length nanowire）. We map the model system into a QD-Kitaev ring in the Majorana fermion representation and affirm these different characteristics by checking the energy spectrum.展开更多
Let G be a finite group and assume that a group of automorphisms A is acting on G such that A and G have coprime orders.We prove that the fact of imposing specific properties on the second maximal A-invariant subgroup...Let G be a finite group and assume that a group of automorphisms A is acting on G such that A and G have coprime orders.We prove that the fact of imposing specific properties on the second maximal A-invariant subgroups of G determines that G is either soluble or isomorphic to a fewnon-soluble groups such as PSL(2,5)or SL(2,5).展开更多
In this work,a new method to solve the Reynolds equation including mass-conserving cavitation by using the physics informed neural networks(PINNs)is proposed.The complementarity relationship between the pressure and t...In this work,a new method to solve the Reynolds equation including mass-conserving cavitation by using the physics informed neural networks(PINNs)is proposed.The complementarity relationship between the pressure and the void fraction is used.There are several difficulties in problem solving,and the solutions are provided.Firstly,the difficulty for considering the pressure inequality constraint by PINNs is solved by transferring it into one equality constraint without introducing error.While the void fraction inequality constraint is considered by using the hard constraint with the max-min function.Secondly,to avoid the fluctuation of the boundary value problems,the hard constraint method is also utilized to apply the boundary pressure values and the corresponding functions are provided.Lastly,for avoiding the trivial solution the limitation for the mean value of the void fraction is applied.The results are validated against existing data,and both the incompressible and compressible lubricant are considered.Good agreement can be found for both the domain and domain boundaries.展开更多
We first consider properties and basic extensions of symmetric rings. We next argue about the symmetry of some kinds of polynomial rings, and show that if R is a reduced ring then R[x]/（x^n） is a symmetric ring, whe...We first consider properties and basic extensions of symmetric rings. We next argue about the symmetry of some kinds of polynomial rings, and show that if R is a reduced ring then R[x]/（x^n） is a symmetric ring, where （x^n） is the ideal generated by x^n and n is a positive integer. Consequently, we prove that for a right Ore ring R with Q its classical right quotient ring, R is symmetric if and only if Q is symmetric.展开更多
Topological materials refer to solid structures with topo-logically protected electronic states or other degrees of freedom.A prime example is a Chern insulator in which the occupied bands of states are organized with...Topological materials refer to solid structures with topo-logically protected electronic states or other degrees of freedom.A prime example is a Chern insulator in which the occupied bands of states are organized with a non-trivial topology as characterized by a nonzero Chern in-teger,exhibiting gapless chiral excitations on the bound-aries,which are robust against scatterings.展开更多
The authors introduce a notion of a weak graph map homotopy(they call it M-homotopy),discuss its properties and applications.They prove that the weak graph map homotopy equivalence between graphs coincides with the gr...The authors introduce a notion of a weak graph map homotopy(they call it M-homotopy),discuss its properties and applications.They prove that the weak graph map homotopy equivalence between graphs coincides with the graph homotopy equivalence defined by Yau et al in 2001.The difference between them is that the weak graph map homotopy transformation is defined in terms of maps,while the graph homotopy transformation is defined by means of combinatorial operations.They discuss its advantages over the graph homotopy transformation.As its applications,they investigate the mapping class group of a graph and the 1-order M P-homotopy group of a pointed simple graph.Moreover,they show that the 1-order M P-homotopy group of a pointed simple graph is invariant up to the weak graph map homotopy equivalence.展开更多
Some equivalent conditions for double Frobenius algebras to be strict ones are given. Then some examples of （strict or non-strict） double Frobenius algebras are presented. Finally, a sufficient and necessary conditi...Some equivalent conditions for double Frobenius algebras to be strict ones are given. Then some examples of （strict or non-strict） double Frobenius algebras are presented. Finally, a sufficient and necessary condition for the trivial extension of a double Frobenius algebra to be a （strict） double Frobenius algebra is given.展开更多
We give a lower bound of the Loewy length of the projective cover of the trivial module for the group algebra kG of a finite group G of Lie type defined over a finite field of odd characteristic p, where k is an arbit...We give a lower bound of the Loewy length of the projective cover of the trivial module for the group algebra kG of a finite group G of Lie type defined over a finite field of odd characteristic p, where k is an arbitrary field of characteristic p. The proof uses Auslander-Reiten theory.展开更多
Let A be a Koszul algebra, and let M be a graded A-bimodule. We prove that the trivial extension algebra of A by M is also a Koszul algebra whenever M is Koszul as a left A-module. Applications and examples are also p...Let A be a Koszul algebra, and let M be a graded A-bimodule. We prove that the trivial extension algebra of A by M is also a Koszul algebra whenever M is Koszul as a left A-module. Applications and examples are also provided.展开更多
Through a close reading, this article explores a few aspects of gendered dissent in Li Ang＇s story, ＂The Devil in a Chastity Belt,＂ which reveals the ambivalence and irony of a woman＇s participation in the Taiwan ...Through a close reading, this article explores a few aspects of gendered dissent in Li Ang＇s story, ＂The Devil in a Chastity Belt,＂ which reveals the ambivalence and irony of a woman＇s participation in the Taiwan Residents opposition movement. Instead of writing a stereotypical work of political fiction for the opposition movement that she supports, Li Ang interrogates the problematic intersection of gender and politics, while reclaiming some of the neglected aspects of oppositional history. While recognizing the inevitability of historical contingency, she nevertheless questions the politically-motivated choice of asceticism, heroism, and sacrifice over individual and familial well-being. Li juxtaposes seemingly trivial and disorderly details of ordinary life against the apparently important and grandiose arena of national politics, creating tension through their interaction and contention. She employs images--including the Devil, the female body, and sensory feelings--to perform gendered dissent. While the lyrical and trivial discourse gradually disrupts the political and didactic, the story＇s open-ended conclusion inspires complex interpretations of the enigmatic symbol： the Devil wearing a chastity belt.展开更多
Let T(A)=A?D(A) be a representation-finite trivial extension algebra. We haveproved: (i) every indecomposable module of T(A) is determined by its top and socle, (ii)every indecomposable module of T(A) is determined by...Let T(A)=A?D(A) be a representation-finite trivial extension algebra. We haveproved: (i) every indecomposable module of T(A) is determined by its top and socle, (ii)every indecomposable module of T(A) is determined by its Loewy factors and socal factorsrespectively.展开更多
By means of the method of torus knot theory, this paper gives the complete processes of obtaining the knotted pictures of four Bell b^es from the knotted pictures of four basic two qubit states.
In this paper we give the criteria and constructions of directing compo-nents of a representation-infinite algebra,and the structure of a trivial extension algebraT(A)having Z-component,where A is an iterated-tilted a...In this paper we give the criteria and constructions of directing compo-nents of a representation-infinite algebra,and the structure of a trivial extension algebraT(A)having Z-component,where A is an iterated-tilted algebra.展开更多
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10201004).
文摘Given a finite dimensional special biserial algebra A with normed basis we obtain the dimension formulae of the first Hochschild homology groups of A and the vector space Alt(DA). As a consequence, an explicit dimension formula of the first Hochschild cohomology group of trivial extension TA = A × DA in terms of the combinatorics of the quiver and relations is determined.
文摘The structure of the trivial preference set of group decision making is studied, and the essential characters and generating reasons of the paradox of voting are revealed.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10071062) the Committee of Education Foundation of Fujian(Grant No.K 2001032).
文摘Let A be a finite-dimensional algebra over arbitrary base fieldk. We prove: if the unbounded derived module category D-(Mod-A) admits symmetric recollement relative to unbounded derived module categories of two finite-dimensionalk-algebras B and C: then the unbounded derived module category D-(Mod - T(A)) admits symmetric recollement relative to the unbounded derived module categories of T(B) and T(C):
基金supported by National Natural Science Foundation of China(12104297,12122407,11974245,11825401,12192252,12204304)National Key Research and Development Program of China(2021YFA1400900)+1 种基金Shanghai Municipal Science and Technology Major Project(2019SHZDZX01-Zx06)the Innovation Program for Quantum Science and Technology(2021ZD0302000)。
文摘Measuring topological invariants is an essential task in characterizing topological phases of matter.They are usually obtained from the number of edge states due to the bulk-edge correspondence or from interference since they are integrals of the geometric phases in the energy band.It is commonly believed that the bulk band structures could not be directly used to obtain the topological invariants.Here,we implement the experimental extraction of Zak phase from the bulk band structures of a Su-Schrieffer-Heeger(SSH)model in the synthetic frequency dimension.Such synthetic SSH lattices are constructed in the frequency axis of light,by controlling the coupling strengths between the symmetric and antisymmetric supermodes of two bichromatically driven rings.We measure the transmission spectra and obtain the projection of the time-resolved band structure on lattice sites,where a strong contrast between the non-trivial and trivial topological phases is observed.The topological Zak phase is naturally encoded in the bulk band structures of the synthetic SSH lattices,which can hence be experimentally extracted from the transmission spectra in a fiber-based modulated ring platform using a laser with telecom wavelength.Our method of extracting topological phases from the bulk band structure can be further extended to characterize topological invariants in higher dimensions,while the exhibited trivial and non-trivial transmission spectra from the topological transition may find future applications in optical communications.
文摘We investigate electron transport inside a ring system composed of a quantum dot （QD） coupled to two Majorana bound states confined at the ends of a one-dimensional topological superconductor nanowire. By tuning the magnetic flux threading through the ring, the model system we consider can be switched into states with or without zero-energy modes when the nanowire is in its topological phase. We find that the Fano profile in the conductance spectrum due to the interference between bound and continuum states exhibits markedly different features for these two different situations, which consequently can be used to detect the Majorana zero-energy mode. Most interestingly, as a periodic function of magnetic flux, the conductance shows 2π periodicity when the two Majorana bound states are nonoverlapping （as in an infinitely long nanowire） but displays 4π periodicity when the overlapping becomes nonzero （as in a finite length nanowire）. We map the model system into a QD-Kitaev ring in the Majorana fermion representation and affirm these different characteristics by checking the energy spectrum.
文摘Let G be a finite group and assume that a group of automorphisms A is acting on G such that A and G have coprime orders.We prove that the fact of imposing specific properties on the second maximal A-invariant subgroups of G determines that G is either soluble or isomorphic to a fewnon-soluble groups such as PSL(2,5)or SL(2,5).
基金the funding from Anhui University of Science and Technology(No.2022yjrc15)the Key Project of National Natural Science Foundation of China(Nos.U21A20125 and U21A20122)+1 种基金the Key Research and Development Projects of Anhui Province(No.2022a05020043)the National Natural Science Foundation of China(Nos.51805410 and 51804007).
文摘In this work,a new method to solve the Reynolds equation including mass-conserving cavitation by using the physics informed neural networks(PINNs)is proposed.The complementarity relationship between the pressure and the void fraction is used.There are several difficulties in problem solving,and the solutions are provided.Firstly,the difficulty for considering the pressure inequality constraint by PINNs is solved by transferring it into one equality constraint without introducing error.While the void fraction inequality constraint is considered by using the hard constraint with the max-min function.Secondly,to avoid the fluctuation of the boundary value problems,the hard constraint method is also utilized to apply the boundary pressure values and the corresponding functions are provided.Lastly,for avoiding the trivial solution the limitation for the mean value of the void fraction is applied.The results are validated against existing data,and both the incompressible and compressible lubricant are considered.Good agreement can be found for both the domain and domain boundaries.
文摘We first consider properties and basic extensions of symmetric rings. We next argue about the symmetry of some kinds of polynomial rings, and show that if R is a reduced ring then R[x]/（x^n） is a symmetric ring, where （x^n） is the ideal generated by x^n and n is a positive integer. Consequently, we prove that for a right Ore ring R with Q its classical right quotient ring, R is symmetric if and only if Q is symmetric.
基金The author wishes thank Prof.Shengyuan Yang and Prof.Di Xiao for sharing their views and providing critical comments,and to thank the financial support from DoE(DE FG02-02ER45958,Division of Materials Science and Engineering).
文摘Topological materials refer to solid structures with topo-logically protected electronic states or other degrees of freedom.A prime example is a Chern insulator in which the occupied bands of states are organized with a non-trivial topology as characterized by a nonzero Chern in-teger,exhibiting gapless chiral excitations on the bound-aries,which are robust against scatterings.
基金supported by the National Natural Science Foundation of China(No.11771116)。
文摘The authors introduce a notion of a weak graph map homotopy(they call it M-homotopy),discuss its properties and applications.They prove that the weak graph map homotopy equivalence between graphs coincides with the graph homotopy equivalence defined by Yau et al in 2001.The difference between them is that the weak graph map homotopy transformation is defined in terms of maps,while the graph homotopy transformation is defined by means of combinatorial operations.They discuss its advantages over the graph homotopy transformation.As its applications,they investigate the mapping class group of a graph and the 1-order M P-homotopy group of a pointed simple graph.Moreover,they show that the 1-order M P-homotopy group of a pointed simple graph is invariant up to the weak graph map homotopy equivalence.
基金This work was supported by the National Natural Science Foundation of China （Grant No. 11471282）, the China Postdoctoral Science Foundation （Grant No. 2017M610316）, and the Natural Science Foundation of Jiangsu Province （Grant No. BK20170589）.
文摘Some equivalent conditions for double Frobenius algebras to be strict ones are given. Then some examples of （strict or non-strict） double Frobenius algebras are presented. Finally, a sufficient and necessary condition for the trivial extension of a double Frobenius algebra to be a （strict） double Frobenius algebra is given.
基金the Japan Society for Promotion of Science （JSPS）, Grant-in-Aid for Scientific Research （C）15K04776, 2015-2018, and by the CIB in EPFL. The second author was supported by the German Science Foundation （DFG） Scientific Priority Programme SPP-1489 ＂Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory＂.
文摘We give a lower bound of the Loewy length of the projective cover of the trivial module for the group algebra kG of a finite group G of Lie type defined over a finite field of odd characteristic p, where k is an arbitrary field of characteristic p. The proof uses Auslander-Reiten theory.
基金The author is very grateful to the referees for helpful comments. He thanks Professor Yu Ye for numerous discussion and suggestions. This work was supported in part by the National Natural Science Foundation of China （Grant No. 11471017）, Doctoral Research Foundation, and the Research Culture Foundation of Anhui Normal University （No. 2014xmpyll）.
文摘Let A be a Koszul algebra, and let M be a graded A-bimodule. We prove that the trivial extension algebra of A by M is also a Koszul algebra whenever M is Koszul as a left A-module. Applications and examples are also provided.
文摘Through a close reading, this article explores a few aspects of gendered dissent in Li Ang＇s story, ＂The Devil in a Chastity Belt,＂ which reveals the ambivalence and irony of a woman＇s participation in the Taiwan Residents opposition movement. Instead of writing a stereotypical work of political fiction for the opposition movement that she supports, Li Ang interrogates the problematic intersection of gender and politics, while reclaiming some of the neglected aspects of oppositional history. While recognizing the inevitability of historical contingency, she nevertheless questions the politically-motivated choice of asceticism, heroism, and sacrifice over individual and familial well-being. Li juxtaposes seemingly trivial and disorderly details of ordinary life against the apparently important and grandiose arena of national politics, creating tension through their interaction and contention. She employs images--including the Devil, the female body, and sensory feelings--to perform gendered dissent. While the lyrical and trivial discourse gradually disrupts the political and didactic, the story＇s open-ended conclusion inspires complex interpretations of the enigmatic symbol： the Devil wearing a chastity belt.
基金Project supported by the National Natural Science Foundation of China.
文摘Let T(A)=A?D(A) be a representation-finite trivial extension algebra. We haveproved: (i) every indecomposable module of T(A) is determined by its top and socle, (ii)every indecomposable module of T(A) is determined by its Loewy factors and socal factorsrespectively.
文摘By means of the method of torus knot theory, this paper gives the complete processes of obtaining the knotted pictures of four Bell b^es from the knotted pictures of four basic two qubit states.
基金Project supported by the National Natural Science Foundation of China.
文摘In this paper we give the criteria and constructions of directing compo-nents of a representation-infinite algebra,and the structure of a trivial extension algebraT(A)having Z-component,where A is an iterated-tilted algebra.
