Generators of simple modular Lie superalgebras

Let $X$ be one of the finite-dimensional simple graded Lie superalgebras of Cartan type $W, S, H, K, HO, KO, SHO$ or $SKO$ over an algebraically closed field of characteristic $p>3$. In this paper we prove that $X$ can be generated by one element except the ones of type $W,$ $HO$, $KO$ or $SKO$ in certain exceptional cases, in which $X$ can be generated by two elements. As a subsidiary result, we also prove that certain classical Lie superalgebras or their relatives can be generated by one or two elements

Representation of SO(3) Group by a Maximally Entangled State

A representation of the SO(3) group is mapped into a maximally entangled two qubit state according to literatures. To show the evolution of the entangled state, a model is set up on an maximally entangled electron pair, two electrons of which pass independently through a rotating magnetic field. It is found that the evolution path of the entangled state in the SO(3) sphere breaks an odd or even number of times, corresponding to the double connectedness of the SO(3) group. An odd number of breaks leads to an additional $\pi$ phase to the entangled state, but an even number of breaks does not. A scheme to trace the evolution of the entangled state is proposed by means of entangled photon pairs and Kerr medium, allowing observation of the additional $\pi$ phase.Comment: 4 pages, 3 figure

Climate change impact on China food security in 2050

Climate change is now affecting global agriculture and food production worldwide. Nonetheless the direct link between climate change and food security at the national scale is poorly understood. Here we simulated the effect of climate change on food security in China using the CERES crop models and the IPCC SRES A2 and B2 scenarios including CO2 fertilization effect. Models took into account population size, urbanization rate, cropland area, cropping intensity and technology development. Our results predict that food crop yield will increase +3-11 % under A2 scenario and +4 % under B2 scenario during 2030-2050, despite disparities among individual crops. As a consequence China will be able to achieve a production of 572 and 615 MT in 2030, then 635 and 646 MT in 2050 under A2 and B2 scenarios, respectively. In 2030 the food security index (FSI) will drop from +24 % in 2009 to -4.5 % and +10.2 % under A2 and B2 scenarios, respectively. In 2050, however, the FSI is predicted to increase to +7.1 % and +20.0 % under A2 and B2 scenarios, respectively, but this increase will be achieved only with the projected decrease of Chinese population. We conclude that 1) the proposed food security index is a simple yet powerful tool for food security analysis; (2) yield growth rate is a much better indicator of food security than yield per se; and (3) climate change only has a moderate positive effect on food security as compared to other factors such as cropland area, population growth, socio-economic pathway and technology development. Relevant policy options and research topics are suggested accordingly

Biderivations, commuting mappings and (2-)local derivations of N\mathbb{N}-graded Lie algebras of maximal class

In Fialowski's classification for algebras of maximal class, there are three Lie algebras of maximal class with 1-dimensional homogeneous components: $\mathfrak{m}_0$, $L_1$ and $\mathfrak{m}_2$. In this paper, we studied their biderivations by considering the embedded mapping to derivation algebras. Then we determined commuting mappings on these algebras as an application of biderivations. Finally, local and 2-local derivations for these three algebras were characterized as the given gradings.Comment: 15 pages. Comments welcom