We classify completely three-generator finite p-groups G such that Ф(G)≤Z(G)and|G′|≤p2.This paper is a part of the classification of finite p-groups with a minimal non-abelian subgroup of index p,and solve partly ...We classify completely three-generator finite p-groups G such that Ф(G)≤Z(G)and|G′|≤p2.This paper is a part of the classification of finite p-groups with a minimal non-abelian subgroup of index p,and solve partly a problem proposed by Berkovich.展开更多
This paper finishes the classification of three-generator finite p-groups G such that Φ(G) Z(G).This paper is a part of classification of finite p-groups with a minimal non-abelian subgroup of index p, and partly sol...This paper finishes the classification of three-generator finite p-groups G such that Φ(G) Z(G).This paper is a part of classification of finite p-groups with a minimal non-abelian subgroup of index p, and partly solves a problem proposed by Berkovich(2008).展开更多
The aim of this article is to extend the theory of several complex variables to the non-commutative realm. Some basic results,such as the Bochner-Martinelli formula,the existence theorem of the solutions to the non-ho...The aim of this article is to extend the theory of several complex variables to the non-commutative realm. Some basic results,such as the Bochner-Martinelli formula,the existence theorem of the solutions to the non-homogeneous Cauchy-Riemann equations,and the Hartogs theorem,are generalized from complex analysis in several variables to Clifford analysis in several paravector variables. In particular,the Bochner-Martinelli formula in several paravector variables unifies the corresponding formulas in the theory of one complex variable,several complex variables,and several quaternionic variables with suitable modifications.展开更多
The generalized Thirring model with impurity coupling is defined on two-dimensional noncommutativespace-time,a modified propagator and free energy are derived by means of functional integrals method.Moreover,quantum f...The generalized Thirring model with impurity coupling is defined on two-dimensional noncommutativespace-time,a modified propagator and free energy are derived by means of functional integrals method.Moreover,quantum fluctuations and excitation energies are calculated on two-dimensional black hole and soliton background.展开更多
In this paper,we give the notion of derivations of Lie 2-algebras using explicit formulas,and construct the associated derivation Lie 3-algebra.We prove that isomorphism classes of non-abelian extensions of Lie 2-alge...In this paper,we give the notion of derivations of Lie 2-algebras using explicit formulas,and construct the associated derivation Lie 3-algebra.We prove that isomorphism classes of non-abelian extensions of Lie 2-algebras are classified by equivalence classes of morphisms from a Lie 2-algebra to a derivation Lie 3-algebra.展开更多
Abstract Let x = （xn）n≥1 be a martingale on a noncommutative probability space （М,τ） and （Wn）n≥1 a sequence of positive numbers such that Wn =∑^n_k=1 wk→∞ as n→∞. We prove that x = （Xn）n≥1 converges...Abstract Let x = （xn）n≥1 be a martingale on a noncommutative probability space （М,τ） and （Wn）n≥1 a sequence of positive numbers such that Wn =∑^n_k=1 wk→∞ as n→∞. We prove that x = （Xn）n≥1 converges bilaterally almost uniformly （b.a.u.） if and only if the weighted average （σan（x））n≥1 of x converges b.a.u, to the same limit under some condition, where σn（x） is given by σn（x）=1/Wn ^n∑_k=1 wkxk,n=1,2,… Furthermore, we prove that x = （xn）n≥1 converges in Lp（М） if and only if （σ＇n（x））n≥1 converges in Lp（М）, where 1 ≤p 〈 ∞ .We also get a criterion of uniform integrability for a family in L1（М）.展开更多
This paper develops a duality theory for connected cochain DG algebras,with particular emphasis on the non-commutative aspects.One of the main items is a dualizing DG module which induces a duality between the derived...This paper develops a duality theory for connected cochain DG algebras,with particular emphasis on the non-commutative aspects.One of the main items is a dualizing DG module which induces a duality between the derived categories of DG left-modules and DG right-modules with finitely generated cohomology.As an application,it is proved that if the canonical module k=A/A≥1 has a semi-free resolution where the cohomological degree of the generators is bounded above,then the same is true for each DG module with finitely generated cohomology.展开更多
In this paper, we apply the tunneling of massive particle through the quantum horizon of a Schwarzschild black hole in noncommutative spaeetime. The tunneling effects lead to modified Hawking radiation due to inclusio...In this paper, we apply the tunneling of massive particle through the quantum horizon of a Schwarzschild black hole in noncommutative spaeetime. The tunneling effects lead to modified Hawking radiation due to inclusion of back-reaction effects. Our calculations show also that noncommutativity effects cause the further modifications to the thermodynamical relations in black hole. We calculate the emission rate of the massive particles＇ tunneling from a Schwarzschild black hole which is modified on account of noncommutativity influences. The issues of information loss and possible correlations between emitted particles are discussed. Unfortunately even by considering noneommutativity view point, there is no correlation between different modes of evaporation at least at late-time. Nevertheless, as a result of spacetime noncommutativity, information may be conserved by a stable black hole remnant.展开更多
The nonabelian Jacobian J(X;L,d) of a smooth projective surface X is inspired by the classical theory of Jacobian of curves.It is built as a natural scheme interpolating between the Hilbert scheme X [d] of subschemes ...The nonabelian Jacobian J(X;L,d) of a smooth projective surface X is inspired by the classical theory of Jacobian of curves.It is built as a natural scheme interpolating between the Hilbert scheme X [d] of subschemes of length d of X and the stack M X(2,L,d) of torsion free sheaves of rank 2 on X having the determinant OX(L) and the second Chern class(= number) d.It relates to such influential ideas as variations of Hodge structures,period maps,nonabelian Hodge theory,Homological mirror symmetry,perverse sheaves,geometric Langlands program.These relations manifest themselves by the appearance of the following structures on J(X;L,d):1) a sheaf of reductive Lie algebras;2)(singular) Fano toric varieties whose hyperplane sections are(singular) Calabi-Yau varieties;3) trivalent graphs.This is an expository paper giving an account of most of the main properties of J(X;L,d) uncovered in Reider 2006 and ArXiv:1103.4794v1.展开更多
We study the Klein-Gordon oscillator in commutative, noncommutative space, and phase space with psudoharmonic potential under magnetic field hence the other choice is studying the Klein-Gordon equation oscillator in t...We study the Klein-Gordon oscillator in commutative, noncommutative space, and phase space with psudoharmonic potential under magnetic field hence the other choice is studying the Klein-Gordon equation oscillator in the absence of magnetic field. In this work, we obtain energy spectrum and wave function in different situations by NU method so we show our results in tables.展开更多
This short paper is based on the talk on the conference Operator Algebras and Related Topics held on July 23-27, 2010, Beijing. The author surveys recent developments of the noncommutative gravity in joint works with ...This short paper is based on the talk on the conference Operator Algebras and Related Topics held on July 23-27, 2010, Beijing. The author surveys recent developments of the noncommutative gravity in joint works with Chaichian, Tureanu, Sun, Wang, Xie and Zhang.展开更多
Solutions of a noncommutative nonisospectral Kadomtsev-Petviashvili equation are given in terms of quasiwronskian and quasigrammian respectively. These solutions are verified by direct substitutions. Dynamics of some ...Solutions of a noncommutative nonisospectral Kadomtsev-Petviashvili equation are given in terms of quasiwronskian and quasigrammian respectively. These solutions are verified by direct substitutions. Dynamics of some obtained solutions are illustrated.展开更多
In this paper we apply the assumption of our recent work in noncommutative scalar models to the noncommutative U（1） gauge theories. This assumption is that the noneommutative effects start to be visible continuously...In this paper we apply the assumption of our recent work in noncommutative scalar models to the noncommutative U（1） gauge theories. This assumption is that the noneommutative effects start to be visible continuously from a scale ANC and that below this scale the theory is a commutative one. Based on this assumption and using background field method and loop calculations, an effective action is derived for noncommutative U（1） gauge theory. It will be shown that the corresponding low energy effective theory is asymptotically free and that under this condition the noncommutative quadratic IR divergences will not appear. The effective theory contains higher dimensional terms, which become more important at high energies. These terms predict an elastic photon-photon scattering due to the noncommutativity of space. The coefficients of these higher dimensional terms also satisfy a positivity constraint indicating that in this theory the related diseases of superluminal signal propagating and bad analytic properties of S-matrix do not exist. In the last section, we will apply our method to the noncommutative extra dimension theories.展开更多
In this work, we study the relativistic oscillators in a noncommutative space and in a magnetic field. It is shown that the effect of the magnetic field may compete with that of the noncommutative space and that is ab...In this work, we study the relativistic oscillators in a noncommutative space and in a magnetic field. It is shown that the effect of the magnetic field may compete with that of the noncommutative space and that is able to vanish the effect of the noncommutative space.展开更多
Recently, a new noncommutative geometry inspired solution of the coupled Einstein Maxwell field equations including black holes in 4-dimension is found. In this paper, we generalize some aspects of this model to the R...Recently, a new noncommutative geometry inspired solution of the coupled Einstein Maxwell field equations including black holes in 4-dimension is found. In this paper, we generalize some aspects of this model to the Reissner Nordstrom （RN） like geometries with large extra dimensions. We discuss Hawking radiation process based on noncommutative inspired solutions. In this framework, existence of black hole remnant and possibility of its detection in LHC are investigated.展开更多
This paper presents a criterion for the similarity of length-two elements in a noncommutative principal ideal domain. The criterion enables the authors to develop an algorithm for determining whether B1A1 and B2A2 are...This paper presents a criterion for the similarity of length-two elements in a noncommutative principal ideal domain. The criterion enables the authors to develop an algorithm for determining whether B1A1 and B2A2 are similar, where A1, A2, B1, B2 are first-order differential （difference） operators. The main step in the algorithm is to find a rational solution of a parametric differential （difference） Risch＇s equation, which has been well-studied in symbolic integration （summation）.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 11371232)Natural Science Foundation of Shanxi Province (Grant Nos. 2012011001-3 and 2013011001-1)
文摘We classify completely three-generator finite p-groups G such that Ф(G)≤Z(G)and|G′|≤p2.This paper is a part of the classification of finite p-groups with a minimal non-abelian subgroup of index p,and solve partly a problem proposed by Berkovich.
基金supported by National Natural Science Foundation of China(Grant No.11371232)Natural Science Foundation of Shanxi Province(Grant Nos.2012011001-3 and 2013011001-1)
文摘This paper finishes the classification of three-generator finite p-groups G such that Φ(G) Z(G).This paper is a part of classification of finite p-groups with a minimal non-abelian subgroup of index p, and partly solves a problem proposed by Berkovich(2008).
基金supported by National Natural Science Foundation of China(Grant No.11371337)Research Fund for the Doctoral Program of Higher Education of China(Grant No.20123402110068)
文摘The aim of this article is to extend the theory of several complex variables to the non-commutative realm. Some basic results,such as the Bochner-Martinelli formula,the existence theorem of the solutions to the non-homogeneous Cauchy-Riemann equations,and the Hartogs theorem,are generalized from complex analysis in several variables to Clifford analysis in several paravector variables. In particular,the Bochner-Martinelli formula in several paravector variables unifies the corresponding formulas in the theory of one complex variable,several complex variables,and several quaternionic variables with suitable modifications.
基金Supported by the Natural Science Foundation of Sichuan Education Committee under Grant No.08ZA038
文摘The generalized Thirring model with impurity coupling is defined on two-dimensional noncommutativespace-time,a modified propagator and free energy are derived by means of functional integrals method.Moreover,quantum fluctuations and excitation energies are calculated on two-dimensional black hole and soliton background.
基金supported by National Natural Science Foundation of China(Grant Nos.11026046,11101179,10971071)Doctoral Fund of Ministry of Education of China(Grant No.20100061120096)the Fundamental Research Funds for the Central Universities(Grant No.200903294)
文摘In this paper,we give the notion of derivations of Lie 2-algebras using explicit formulas,and construct the associated derivation Lie 3-algebra.We prove that isomorphism classes of non-abelian extensions of Lie 2-algebras are classified by equivalence classes of morphisms from a Lie 2-algebra to a derivation Lie 3-algebra.
基金supported by National Natural Science Foundation of China (Grant No.11071190)
文摘Abstract Let x = （xn）n≥1 be a martingale on a noncommutative probability space （М,τ） and （Wn）n≥1 a sequence of positive numbers such that Wn =∑^n_k=1 wk→∞ as n→∞. We prove that x = （Xn）n≥1 converges bilaterally almost uniformly （b.a.u.） if and only if the weighted average （σan（x））n≥1 of x converges b.a.u, to the same limit under some condition, where σn（x） is given by σn（x）=1/Wn ^n∑_k=1 wkxk,n=1,2,… Furthermore, we prove that x = （xn）n≥1 converges in Lp（М） if and only if （σ＇n（x））n≥1 converges in Lp（М）, where 1 ≤p 〈 ∞ .We also get a criterion of uniform integrability for a family in L1（М）.
文摘This paper develops a duality theory for connected cochain DG algebras,with particular emphasis on the non-commutative aspects.One of the main items is a dualizing DG module which induces a duality between the derived categories of DG left-modules and DG right-modules with finitely generated cohomology.As an application,it is proved that if the canonical module k=A/A≥1 has a semi-free resolution where the cohomological degree of the generators is bounded above,then the same is true for each DG module with finitely generated cohomology.
文摘In this paper, we apply the tunneling of massive particle through the quantum horizon of a Schwarzschild black hole in noncommutative spaeetime. The tunneling effects lead to modified Hawking radiation due to inclusion of back-reaction effects. Our calculations show also that noncommutativity effects cause the further modifications to the thermodynamical relations in black hole. We calculate the emission rate of the massive particles＇ tunneling from a Schwarzschild black hole which is modified on account of noncommutativity influences. The issues of information loss and possible correlations between emitted particles are discussed. Unfortunately even by considering noneommutativity view point, there is no correlation between different modes of evaporation at least at late-time. Nevertheless, as a result of spacetime noncommutativity, information may be conserved by a stable black hole remnant.
文摘The nonabelian Jacobian J(X;L,d) of a smooth projective surface X is inspired by the classical theory of Jacobian of curves.It is built as a natural scheme interpolating between the Hilbert scheme X [d] of subschemes of length d of X and the stack M X(2,L,d) of torsion free sheaves of rank 2 on X having the determinant OX(L) and the second Chern class(= number) d.It relates to such influential ideas as variations of Hodge structures,period maps,nonabelian Hodge theory,Homological mirror symmetry,perverse sheaves,geometric Langlands program.These relations manifest themselves by the appearance of the following structures on J(X;L,d):1) a sheaf of reductive Lie algebras;2)(singular) Fano toric varieties whose hyperplane sections are(singular) Calabi-Yau varieties;3) trivalent graphs.This is an expository paper giving an account of most of the main properties of J(X;L,d) uncovered in Reider 2006 and ArXiv:1103.4794v1.
文摘We study the Klein-Gordon oscillator in commutative, noncommutative space, and phase space with psudoharmonic potential under magnetic field hence the other choice is studying the Klein-Gordon equation oscillator in the absence of magnetic field. In this work, we obtain energy spectrum and wave function in different situations by NU method so we show our results in tables.
基金supported by National Natural Science Foundation of China (Grant Nos. 10725105, 10731080, 11021091)and Chinese Academy of Sciences
文摘This short paper is based on the talk on the conference Operator Algebras and Related Topics held on July 23-27, 2010, Beijing. The author surveys recent developments of the noncommutative gravity in joint works with Chaichian, Tureanu, Sun, Wang, Xie and Zhang.
基金Supported by the National Natural Science Foundation of China under Grant No.11071157Shanghai Leading Academic Discipline Project under Grant No.J50101Beijing Natural Science Foundation under Grant No.1101024 and PHR(IHLB)
文摘Solutions of a noncommutative nonisospectral Kadomtsev-Petviashvili equation are given in terms of quasiwronskian and quasigrammian respectively. These solutions are verified by direct substitutions. Dynamics of some obtained solutions are illustrated.
文摘In this paper we apply the assumption of our recent work in noncommutative scalar models to the noncommutative U（1） gauge theories. This assumption is that the noneommutative effects start to be visible continuously from a scale ANC and that below this scale the theory is a commutative one. Based on this assumption and using background field method and loop calculations, an effective action is derived for noncommutative U（1） gauge theory. It will be shown that the corresponding low energy effective theory is asymptotically free and that under this condition the noncommutative quadratic IR divergences will not appear. The effective theory contains higher dimensional terms, which become more important at high energies. These terms predict an elastic photon-photon scattering due to the noncommutativity of space. The coefficients of these higher dimensional terms also satisfy a positivity constraint indicating that in this theory the related diseases of superluminal signal propagating and bad analytic properties of S-matrix do not exist. In the last section, we will apply our method to the noncommutative extra dimension theories.
文摘In this work, we study the relativistic oscillators in a noncommutative space and in a magnetic field. It is shown that the effect of the magnetic field may compete with that of the noncommutative space and that is able to vanish the effect of the noncommutative space.
基金supported partially by Research Institute for Astronomy and Astrophysics of Maragha,Iran
文摘Recently, a new noncommutative geometry inspired solution of the coupled Einstein Maxwell field equations including black holes in 4-dimension is found. In this paper, we generalize some aspects of this model to the Reissner Nordstrom （RN） like geometries with large extra dimensions. We discuss Hawking radiation process based on noncommutative inspired solutions. In this framework, existence of black hole remnant and possibility of its detection in LHC are investigated.
基金supported by a 973 key project under Grant No.2004CB318000the National Natural Science Foundation under Grant No.76596100
文摘This paper presents a criterion for the similarity of length-two elements in a noncommutative principal ideal domain. The criterion enables the authors to develop an algorithm for determining whether B1A1 and B2A2 are similar, where A1, A2, B1, B2 are first-order differential （difference） operators. The main step in the algorithm is to find a rational solution of a parametric differential （difference） Risch＇s equation, which has been well-studied in symbolic integration （summation）.
