Analytical solution for the evolution of a binary with stable mass transfer from a giant

We derive a simple analytical solution for the evolution of a close binary with nuclear time-scale driven mass transfer from a giant. This solution is based on the well-known fact that the luminosity and the radius of a giant scale to a good approximation as simple power laws of the mass M_c of the degenerate helium core. Comparison with results of numerical calculations by Webbink, Rappaport & Savonije (1983) show the analytical solution and the power law approximation to be quite accurate. The analytical solution presented does also allow (in parametrized form) for non-conservative mass transfer. Furthermore it is shown that the near constancy of the mass transfer rate over most of the mass transfer phase seen in the results by Webbink, Rappaport & Savonije is not a generic feature of this type of evolution but rather a consequence of a particular choice of parameters. The analytical solution also demonstrates that the level of mass transfer is largely set by the core mass of the giant at the onset of mass transfer. Finally we show that the model is selfconsistent and discuss its applicability to low-mass X-ray binaries.Comment: 13 pages, 5 encapsulated figures, LaTeX, minor revisions, accepted by MNRA

Three states, one common past: chance or malediction? The role of history and historiography in the formation of collective identities and mutual relations in Belarus, Lithuania and Poland

Common experiences and a common past offer a special possibility for good relations. But having a common past also can create disharmony. If one has to share traditions with others, it becomes more difficult to find specific elements to call one’s ‘own’. So especially in a situation of intensive search for identity a common past may be harmful to the formation of one’s own identity and to mutual relations as well. In the case of Belarus, Lithuania and Poland after 1989, both generalisations hold true. While Polish-Lithuanian relations are excellent, Lithuanian-Belarusian relations are rather complicated. The reasons for this are not only political or economic, but mainly a consequence of the important role history and historiography play in the process of collective identity formation. The present article will examine the structure of this process

A strong Oka principle for embeddings of some planar domains into CxC*

Gromov, in his seminal 1989 paper on the Oka principle, introduced the notion of an elliptic manifold and proved that every continuous map from a Stein manifold to an elliptic manifold is homotopic to a holomorphic map. We show that a much stronger Oka principle holds in the special case of maps from certain open Riemann surfaces called circular domains into CxC*, namely that every continuous map is homotopic to a proper holomorphic embedding. An important ingredient is a generalisation to CxC* of recent results of Wold and Forstneric on the long-standing problem of properly embedding open Riemann surfaces into C^2, with an additional result on the homotopy class of the embeddings. We also give a complete solution to a question that arises naturally in Larusson's holomorphic homotopy theory, of the existence of acyclic embeddings of Riemann surfaces with abelian fundamental group into 2-dimensional elliptic Stein manifolds.Comment: 25 page

A soft Oka principle for proper holomorphic embeddings of open Riemann surfaces into (C∗)2(\mathbb{C}^*)^2

Let $X$ be an open Riemann surface. We prove an Oka property on the approximation and interpolation of continuous maps $X \to (\mathbb{C}^*)^2$ by proper holomorphic embeddings, provided that we permit a smooth deformation of the complex structure on $X$ outside a certain set. This generalises and strengthens a recent result of Alarcon and Lopez. We also give a Forstneric-Wold theorem for proper holomorphic embeddings (with respect to the given complex structure) of certain open Riemann surfaces into $(\mathbb{C}^*)^2$