Curvature properties are studied for the Sasaki metric on the （1, 1） tensor bundle of a Riemannian manifold. As an application, examples of almost para-Nordenian and para-Kahler-Nordenian B-metrics are constructed o...Curvature properties are studied for the Sasaki metric on the （1, 1） tensor bundle of a Riemannian manifold. As an application, examples of almost para-Nordenian and para-Kahler-Nordenian B-metrics are constructed on the （1, 1） tensor bundle by looking at the Sasaki metric. Also, with respect to the para-Nordenian B-structure, paraholomorphic conditions for the complete lifts of vector fields are analyzed.展开更多
This paper uses Lorenz curve and Gini index with adjustment to per capita historical cumulative emission to construct carbon Gini index to measure inequality in climate change area. The analysis shows that 70% of carb...This paper uses Lorenz curve and Gini index with adjustment to per capita historical cumulative emission to construct carbon Gini index to measure inequality in climate change area. The analysis shows that 70% of carbon space in the atmosphere has been used for unequal distribution, which is almost the same as that of incomes in a country with the biggest gap between the rich and the poor in the world. The carbon equity should be an urgency and priority in the climate agenda. Carbon Gini index established in this paper can be used to measure inequality in the distribution of carbon space and provide a quantified indicator for measurement of carbon equity among different proposals.展开更多
To develop a unitary quantum theory with probabilistic description for pseudo-Hermitian systems one needs to consider the theories in a different Hilbert space endowed with a positive definite metric operator. There a...To develop a unitary quantum theory with probabilistic description for pseudo-Hermitian systems one needs to consider the theories in a different Hilbert space endowed with a positive definite metric operator. There are different approaches to find such metric operators. We compare the different approaches of calculating positive definite metric operators in pseudo-Hermitian theories with the help of several explicit examples in non-relativistic as well as in relativistic situations. Exceptional points and spontaneous symmetry breaking are also discussed in these models.展开更多
We establish the sharp upper and lower bounds of Gaussian type for the heat kernel in the metric measure space satisfying the RCD(0, N)(equivalently, RCD~*(0, N), condition with N∈N\ {1} and having the maximum volume...We establish the sharp upper and lower bounds of Gaussian type for the heat kernel in the metric measure space satisfying the RCD(0, N)(equivalently, RCD~*(0, N), condition with N∈N\ {1} and having the maximum volume growth, and then show its application on the large-time asymptotics of the heat kernel, sharp bounds on the(minimal) Green function, and above all, the large-time asymptotics of the Perelman entropy and the Nash entropy, where for the former the monotonicity of the Perelman entropy is proved. The results generalize the corresponding ones in the Riemannian manifolds, and some of them appear more explicit and sharper than the ones in metric measure spaces obtained recently by Jiang et al.(2016).展开更多
The authors extend the notion of statistical structure from Riemannian geometry to the general framework of path spaces endowed with a nonlinear connection and a generalized metric.Two particular cases of statistical ...The authors extend the notion of statistical structure from Riemannian geometry to the general framework of path spaces endowed with a nonlinear connection and a generalized metric.Two particular cases of statistical data are defined.The existence and uniqueness of a nonlinear connection corresponding to these classes is proved.Two Koszul tensors are introduced in accordance with the Riemannian approach.As applications,the authors treat the Finslerian (α,β)-metrics and the Beil metrics used in relativity and field theories while the support Riemannian metric is the Fisher-Rao metric of a statistical model.展开更多
基金Project supported by the Scientific and Technological Research Council of Turkey(No.TBAG-108T590)
文摘Curvature properties are studied for the Sasaki metric on the （1, 1） tensor bundle of a Riemannian manifold. As an application, examples of almost para-Nordenian and para-Kahler-Nordenian B-metrics are constructed on the （1, 1） tensor bundle by looking at the Sasaki metric. Also, with respect to the para-Nordenian B-structure, paraholomorphic conditions for the complete lifts of vector fields are analyzed.
基金National Basic Research Programme(No.2010CB955303)
文摘This paper uses Lorenz curve and Gini index with adjustment to per capita historical cumulative emission to construct carbon Gini index to measure inequality in climate change area. The analysis shows that 70% of carbon space in the atmosphere has been used for unequal distribution, which is almost the same as that of incomes in a country with the biggest gap between the rich and the poor in the world. The carbon equity should be an urgency and priority in the climate agenda. Carbon Gini index established in this paper can be used to measure inequality in the distribution of carbon space and provide a quantified indicator for measurement of carbon equity among different proposals.
基金supported by the National Natural Science Foundation of China(Nos.11271330,11261023,11461033,11401269)the Jiangxi Provincial Natural Science Foundation of China(No.20142BAB201003)
文摘In this paper, some endpoint estimates for the generalized multilinear fractional integrals Ia,m on the non-homogeneous metric spaces are established.
文摘To develop a unitary quantum theory with probabilistic description for pseudo-Hermitian systems one needs to consider the theories in a different Hilbert space endowed with a positive definite metric operator. There are different approaches to find such metric operators. We compare the different approaches of calculating positive definite metric operators in pseudo-Hermitian theories with the help of several explicit examples in non-relativistic as well as in relativistic situations. Exceptional points and spontaneous symmetry breaking are also discussed in these models.
基金supported by National Natural Science Foundation of China (Grant No. 11401403)the Australian Research Council (Grant No. DP130101302)
文摘We establish the sharp upper and lower bounds of Gaussian type for the heat kernel in the metric measure space satisfying the RCD(0, N)(equivalently, RCD~*(0, N), condition with N∈N\ {1} and having the maximum volume growth, and then show its application on the large-time asymptotics of the heat kernel, sharp bounds on the(minimal) Green function, and above all, the large-time asymptotics of the Perelman entropy and the Nash entropy, where for the former the monotonicity of the Perelman entropy is proved. The results generalize the corresponding ones in the Riemannian manifolds, and some of them appear more explicit and sharper than the ones in metric measure spaces obtained recently by Jiang et al.(2016).
基金Project supported by the Romanian National Authority for Scientific Research,CNCS UEFISCDI(No.PN-II-ID-PCE-2012-4-0131)
文摘The authors extend the notion of statistical structure from Riemannian geometry to the general framework of path spaces endowed with a nonlinear connection and a generalized metric.Two particular cases of statistical data are defined.The existence and uniqueness of a nonlinear connection corresponding to these classes is proved.Two Koszul tensors are introduced in accordance with the Riemannian approach.As applications,the authors treat the Finslerian (α,β)-metrics and the Beil metrics used in relativity and field theories while the support Riemannian metric is the Fisher-Rao metric of a statistical model.
