Equilibrium Configuration of Black Holes and the Inverse Scattering Method

The inverse scattering method is applied to the investigation of the equilibrium configuration of black holes. A study of the boundary problem corresponding to this configuration shows that any axially symmetric, stationary solution of the Einstein equations with disconnected event horizon must belong to the class of Belinskii-Zakharov solutions. Relationships between the angular momenta and angular velocities of black holes are derived.Comment: LaTeX, 14 pages, no figure

A note on the extension of the polar decomposition for the multidimensional Burgers equation

It is shown that the generalizations to more than one space dimension of the pole decomposition for the Burgers equation with finite viscosity and no force are of the form u = -2 viscosity grad log P, where the P's are explicitly known algebraic (or trigonometric) polynomials in the space variables with polynomial (or exponential) dependence on time. Such solutions have polar singularities on complex algebraic varieties.Comment: 3 pages; minor formatting and typos corrected. Submitted to Phys. Rev. E (Rapid Comm.

On asymptotic stability of the Skyrmion

We study the asymptotic behavior of spherically symmetric solutions in the Skyrme model. We show that the relaxation to the degree-one soliton (called the Skyrmion) has a universal form of a superposition of two effects: exponentially damped oscillations (the quasinormal ringing) and a power law decay (the tail). The quasinormal ringing, which dominates the dynamics for intermediate times, is a linear resonance effect. In contrast, the polynomial tail, which becomes uncovered at late times, is shown to be a \emph{nonlinear} phenomenon.Comment: 4 pages, 4 figures, minor changes to match the PRD versio

Induction of Plasminogen Activator in Cultured Cells by Macrocyclic Plant Diterpene Esters and Other Agents Related to Tumor Promotion

In vitro systems that are responsive to tumor-promoting agents may facilitate the identification of such agents and the analysis of their mode of action. We have previously reported that the potent tumor promoter phorbol-12-myristate-13-acetate induces the synthesis of the enzyme plasminogen activator in cultured chick embryo fibroblasts. We have, therefore, tested various compounds for their ability to induce plasminogen activator in chicken embryo fibroblasts. Among these, phorbol esters and other macrocyclic diterpene esters isolated from species of the families Euphorbiaceae and Thymelaeaceae were potent inducers of plasminogen activator. These compounds maximally induced enzyme to the same levels, although they differed in their relative molar potencies. Structural requirements for in vitro activity paralleled the requirements for activity in vivo. These results indicate that induction of plasminogen activator is a useful marker for the biologically active macrocyclic diterpene esters. On the other hand, tumor-promoting agents such as anthralin, cantharidin, Tween 60, and tobacco leaf extract failed to induce plasminogen activator