We compute the Dirac indexes for the two spin structures κ_0 and κ_1 forEguchi-Hanson metrics with nonzero total mass. It shows that the Dirac indexes do not vanish ingeneral, and axial anomaly exists. When the metr...We compute the Dirac indexes for the two spin structures κ_0 and κ_1 forEguchi-Hanson metrics with nonzero total mass. It shows that the Dirac indexes do not vanish ingeneral, and axial anomaly exists. When the metric has zero total mass, the Dirac index vanishes forthe spin structure κ_0 , and no axial anomaly exists in this case.展开更多
We study a coupled nonlinear evolution system arising from the Ginzburg-Landau theory for atomic Fermi gases near the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover.First,we prove that the ...We study a coupled nonlinear evolution system arising from the Ginzburg-Landau theory for atomic Fermi gases near the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover.First,we prove that the initial boundary value problem generates a strongly continuous semigroup on a suitable phase-space which possesses a global attractor.Then we establish the existence of an exponential attractor.As a consequence,we show that the global attractor is of finite fractal dimension.展开更多
Consider a sequence of i.i.d.positive random variables with the underlying distribution in the domain of attraction of a stable distribution with an exponent in (1,2].A universal result in the almost sure limit theore...Consider a sequence of i.i.d.positive random variables with the underlying distribution in the domain of attraction of a stable distribution with an exponent in (1,2].A universal result in the almost sure limit theorem for products of partial sums is established. Our results significantly generalize and improve those on the almost sure central limit theory previously obtained by Gonchigdanzan and Rempale and by Gonchigdanzan.In a sense,our results reach the optimal form.展开更多
文摘We compute the Dirac indexes for the two spin structures κ_0 and κ_1 forEguchi-Hanson metrics with nonzero total mass. It shows that the Dirac indexes do not vanish ingeneral, and axial anomaly exists. When the metric has zero total mass, the Dirac index vanishes forthe spin structure κ_0 , and no axial anomaly exists in this case.
基金partially supported by National Natural Science Foundation of China (Grant No.11001058)Specialized Research Fund for the Doctoral Program of Higher Educationthe Fundamental Research Funds for the Central Universities
文摘We study a coupled nonlinear evolution system arising from the Ginzburg-Landau theory for atomic Fermi gases near the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover.First,we prove that the initial boundary value problem generates a strongly continuous semigroup on a suitable phase-space which possesses a global attractor.Then we establish the existence of an exponential attractor.As a consequence,we show that the global attractor is of finite fractal dimension.
基金Project supported by the National Natural Science Foundation of China(No.11061012)the NaturalScience Foundation of Guangxi Province(No.2012GXNSFAA053010)
文摘Consider a sequence of i.i.d.positive random variables with the underlying distribution in the domain of attraction of a stable distribution with an exponent in (1,2].A universal result in the almost sure limit theorem for products of partial sums is established. Our results significantly generalize and improve those on the almost sure central limit theory previously obtained by Gonchigdanzan and Rempale and by Gonchigdanzan.In a sense,our results reach the optimal form.
