Let An be the n-th Weyl algebra over a field of characteristic 0 and M a finitely generated module over An. By further exploring the relationship between the Poincare series and the dimension and the multiplicity of M...Let An be the n-th Weyl algebra over a field of characteristic 0 and M a finitely generated module over An. By further exploring the relationship between the Poincare series and the dimension and the multiplicity of M, we are able to prove that the tensor product of two finitely generated modules over An has the multiplicity equal to the product of the multiplicities of both modules. It turns out that we can compute the dimensions and the multiplicities of some homogeneous subquotient modules of An.展开更多
The main aim of the article is to investigate the irrational and transcendental properties of certain real numbers by means of the factorial series and the factorial number system. The difference between the factorial...The main aim of the article is to investigate the irrational and transcendental properties of certain real numbers by means of the factorial series and the factorial number system. The difference between the factorial series and the factorial system is that the factorial series does not set an upper bound at a given place after the radix point, while in the factorial system (i – 1) is the maximal possible value for r<sub>i</sub> after the radix point. I give an extended definition of periodic numbers, and show the relationship between periodic and irrational numbers. I prove the transcendence of e by means of the factorial series and the factorial number system.展开更多
After we modified raw data for anomalies, we conducted spectral analysis using the data. In the frequency, the spectrum is best described by a decaying exponential function. For this reason, stochastic models characte...After we modified raw data for anomalies, we conducted spectral analysis using the data. In the frequency, the spectrum is best described by a decaying exponential function. For this reason, stochastic models characterized by a spectrum attenuated according to a power law cannot be used to model precipitation anomaly. We introduced a new model, the e-model, which properly reproduces the spectrum of the precipitation anomaly. After using the data to infer the parameter values of the e-model, we used the e-model to generate synthetic daily precipitation time series. Comparison with recorded data shows a good agreement. This e-model resembles fractional Brown motion (fBm)/fractional Lévy motion (fLm), especially the spectral method. That is, we transform white noise Xt to the precipitation daily time series. Our analyses show that the frequency of extreme precipitation events is best described by a Lévy law and cannot be accounted with a Gaussian distribution.展开更多
This paper is to extend the Poincar’e Lemma for differential forms in a bounded, convex domain [1] in Rn to a more general domain that, we call, is deformable to every point in itself. Then we extend the homotopy ope...This paper is to extend the Poincar’e Lemma for differential forms in a bounded, convex domain [1] in Rn to a more general domain that, we call, is deformable to every point in itself. Then we extend the homotopy operator T in [1] to the domain defromed to every point of itself.展开更多
基金Supported by the National Natural Science Foundation of China (10771182)
文摘Let An be the n-th Weyl algebra over a field of characteristic 0 and M a finitely generated module over An. By further exploring the relationship between the Poincare series and the dimension and the multiplicity of M, we are able to prove that the tensor product of two finitely generated modules over An has the multiplicity equal to the product of the multiplicities of both modules. It turns out that we can compute the dimensions and the multiplicities of some homogeneous subquotient modules of An.
文摘The main aim of the article is to investigate the irrational and transcendental properties of certain real numbers by means of the factorial series and the factorial number system. The difference between the factorial series and the factorial system is that the factorial series does not set an upper bound at a given place after the radix point, while in the factorial system (i – 1) is the maximal possible value for r<sub>i</sub> after the radix point. I give an extended definition of periodic numbers, and show the relationship between periodic and irrational numbers. I prove the transcendence of e by means of the factorial series and the factorial number system.
文摘After we modified raw data for anomalies, we conducted spectral analysis using the data. In the frequency, the spectrum is best described by a decaying exponential function. For this reason, stochastic models characterized by a spectrum attenuated according to a power law cannot be used to model precipitation anomaly. We introduced a new model, the e-model, which properly reproduces the spectrum of the precipitation anomaly. After using the data to infer the parameter values of the e-model, we used the e-model to generate synthetic daily precipitation time series. Comparison with recorded data shows a good agreement. This e-model resembles fractional Brown motion (fBm)/fractional Lévy motion (fLm), especially the spectral method. That is, we transform white noise Xt to the precipitation daily time series. Our analyses show that the frequency of extreme precipitation events is best described by a Lévy law and cannot be accounted with a Gaussian distribution.
文摘This paper is to extend the Poincar’e Lemma for differential forms in a bounded, convex domain [1] in Rn to a more general domain that, we call, is deformable to every point in itself. Then we extend the homotopy operator T in [1] to the domain defromed to every point of itself.
基金Supported by the National Natural Science Foundation of China(1146103211401267)+2 种基金the Foundation of Jiangxi University of Science and Technology(NSFJ2015-G25)the Youth Foundation of Jiangxi Provincial Education Department of China(GJJ150646GJJ151356)
