Comments on "Inverse scattering method and soliton solution family for the Einstein-Maxwell theory with multiple Abelian gauge fields"

This paper points out that equations （18a） and （18b） in Ref. [7] [Gao Y J 2008 Chin. Phys. B 17 3574] only possess the solutions M = ργc. So, there does not exist the so-called soliton solution family for the Einstein-Maxwell theory with multiple Abelian gauge fields shown in Ref. [7].

New infinite-dimensional symmetry groups for the stationary axisymmetric Einstein-Maxwell equations with multiple Abelian gauge fields

The so-called extended hyperbolic complex （EHC） function method is used to study further the stationary axisymmetric Einstein Maxwell theory with p Abelian gauge fields （EM-p theory, for short）, Two EHC structural Riemann- Hilbert （RH） transformations are constructed and are then shown to give an infinite-dimensional symmetry group of the EM-p theory. This symmetry group is verified to have the structure of semidirect product of Kac-Moody group SU（p ＋ 1, 1） and Virasoro group. Moreover, the infinitesimal forms of these two RH transformations are calculated and found to give exactly the same infinitesimal transformations as in previous author＇s paper by a different scheme, This demonstrates that the results obtained in the present paper provide some exponentiations of all the infinitesimal symmetry transformations obtained before.

Balls in complex hyperbolic manifolds

We get an explicit lower bound for the radius of a Bergman ball contained in the Dirichlet fundamental polyhedron of a torsion free discrete group G PU（n,1）acting on complex hyperbolic space.As an application,we also give a lower bound for the volumes of complex hyperbolic n-manifolds.

Teichmller space of negatively curved metrics on complex hyperbolic manifolds is not contractible

We prove that for all n = 4k- 2 and k 2 there exists a closed smooth complex hyperbolic manifold M with real dimension n having non-trivial π1(T<0(M)). T<0(M) denotes the Teichm¨uller space of all negatively curved Riemannian metrics on M, which is the topological quotient of the space of all negatively curved metrics modulo the space of self-diffeomorphisms of M that are homotopic to the identity.

On the Cohomology of Some Complex Hyperbolic Arithmetic 3-Manifolds

Given an arithmetic lattice of the unitary group U(3,1)arising from a hermitian form over a CM-field,we show that all unitary representations of U(3,1)with nonzero cohomology contribute to the cohomology of the attached arithmetic complex 3-manifold,at least when we pass to a finite-index subgroup of the given arithmetic lattice.

Stability Analysis of Multi-paralleled Grid-connected Inverters Including Distribution Parameter Characteristics of Transmission Lines

The sparse distribution characteristics of renewable energy resources can lead to there being tens of kilometers of transmission lines between a grid-connected inverter and the actual grid.Accurate analysis of the stability of such gridconnected inverter systems currently involves using a complex hyperbolic function to shaped model of the transmission line circuit.This has proved to be problematic,so,drawing upon the distribution parameter characteristics of transmission lines,this paper looks at how to use impedance-based stability criteria to assess the stability of multi-paralleled grid-connected inverters.First,the topology of multi-paralleled inverters connected to the grid via transmission lines is established,using each transmission line terminal as a grid connection point.Each grid-connected system is taken to be equivalent to a small-signal circuit model of the“current source-grid”.Euler’s formula and the Nyquist stability criterion are combined to assess the stability of the associated grid-connected current transfer functions and evaluate the stability of the grid-connected current.Finally,a simulation analysis circuit is constructed to verify whether power line intervention will cause stability problems in the grid-connected system.Overall,it is found that long-distance transmission lines are more likely to cause unstable output of the grid-connected current.It is also found that the number of grid-connected inverters,the short-circuit ratio(SCR),the distorted grid and the inverter parameters can all have a significant impact on the stability of the grid-connected current.

Note on a Theorem of Bangert

We generalize Bangert＇s non-hyperbolicity result for uniformly tamed almost complex structures on standard symplectic R^2n to asymptotically standard symplectic manifolds.