No abstract available

[en] It is shown that Ward's two-monopole ansatz possesses a non-linear (twisted) generalization of axial symmetry, and this symmetry is used to show that, for any finite value of the intrinsic parameter, the ansatz describes separated monopoles and is non-singular everywhere if it is non-singular on one of the coordinate planes. (orig.)

No abstract available

[en] We give sufficient conditions for the rigid body in the presence of an axisymmetric force field and a gyroscopic torque to admit a Hamilton-Poisson formulation. Even if by adding a gyroscopic torque we initially lose one of the conserved Casimirs, we recover another conservation law as a Casimir function for a modified Poisson structure. We apply this frame to several well-known results in the literature. -- Highlights: → Gyroscopic torques and sufficient conditions for a Hamilton-Poisson formulation. → An algorithm to find a third constant of motion as a Casimir function. → A unitary framework that encompasses well-known gyroscopic torques from literature.

[en] The field enhancement factor at the emitter tip and its variation in a close neighbourhood determines the emitter current in a Fowler–Nordheim like formulation. For an axially symmetric emitter with a smooth tip, it is shown that the variation can be accounted by a $\cos \tilde{\theta }$ factor in appropriately defined normalized co-ordinates. This is shown analytically for a hemiellipsoidal emitter and confirmed numerically for other emitter shapes with locally quadratic tips.

[en] By considering suitable axially symmetric slices on the Kruskal spacetime, we construct a counterexample to a recent version of the Penrose inequality in terms of so-called generalized apparent horizons. (fast track communication)

[en] A graphical method for the analysis of relaxation data is presented. It allows a fast estimation of the range of values of the components of the axially symmetric rotational diffusion tensor that are compatible with the experimental relaxation data. The graphical method clearly shows the contribution of different experimental relaxation parameters to the measured anisotropy. In particular, for proteins with moderate anisotropy, data from at least two N-H bonds forming angles close to 0 deg. and 90 deg. with respect to the principal axis of the rotational diffusional tensor are needed. For very anisotropic systems, combination of different relaxation parameters from a single residue is enough to characterize the local anisotropy

[en] The relation between the black hole shadow and the black hole thermodynamics is investigated. We find that the phase structure can be reflected by the shadow radius for the spherically symmetric black hole. We also find that the shadow size gives correct information but the distortion of the shadow gives wrong information of the phase structure for the axially symmetric black hole.

No abstract available

[en] We demonstrate how one should transform correctly quasi-isotropic coordinates to Weyl-Papapetrou coordinates in order to compare the metric around a rotating star, which has been constructed numerically in the former coordinates, with an axially symmetric stationary metric, which is given through an analytical form in the latter coordinates. (comments, replies and notes)