On the properties of contact binary stars

A catalogue of light curve solutions of contact binary stars has been compiled. It contains the results of 159 light curve solutions. Properties of contact binary stars were studied by using the catalogue data. As it is well known since Lucy's (1968a,b) and Mochnacki's (1981) works, primary components transfer their own energy to the secondary star via the common envelope around the two stars. This transfer was parameterized by a transfer parameter (ratio of the observed and intrinsic luminosities of the primary star). We proved that this transfer parameter is a simple function of the mass and luminosity ratio. This newly found relation is valid for all systems except H type systems which have a different relation. We introduced a new type of contact binary stars: H subtype systems which have a large mass ratio ($q>0.72$). These systems show highly different behaviour on the luminosity ratio - transfer parameter diagram from other systems and according to our results the energy transfer rate is less efficient in them than in other type of contact binary stars. We also show that different types of contact binaries have well defined locations on the mass ratio - luminosity ratio diagram. All contact binary systems do not follow Lucy's relation ($L_2/L_1 = (M_2/M_1)^{0.92}$). No strict mass ratio - luminosity ratio relation of contact binary stars exists.Comment: 5 pages, 4 figures, accepted for publication in A&

Script geometry

In this paper we describe the foundation of a new kind of discrete geometry and calculus called Script Geometry. It allows to work with more general meshes than classic simplicial complexes. We provide the basic denitions as well as several examples, like the Klein bottle and the projective plane. Furthermore, we also introduce the corresponding Dirac and Laplace operators which should lay the groundwork for the development of the corresponding discrete function theory

Modern trends in hypercomplex analysis

This book contains a selection of papers presented at the session "Quaternionic and Clifford Analysis" at the 10th ISAAC Congress held in Macau in August 2015. The covered topics represent the state-of-the-art as well as new trends in hypercomplex analysis and its applications

On the solution of spatial generalizations of Beltrami equations

With the help of functional analytical methods complex analysis is a powerful tool in treating non-linear first-order partial differential equations in the plane. Some of the most important of these equations are the Beltrami equations. This is due to the fact that the theory of Beltrami systems is related to many problems of geometry and analysis, like non-linear subsonic two-dimensional hydrodynamics, problems of conformal and quasiconformal mappings of two-dimensional Riemannian manifolds, or complex analytic dynamics. The theory of Beltrami equations is strongly connected with the -operator. This singular integral operator is immediately recognized as two-dimensional Hilbert-transform, known also under the name of integral operator with Beurling kernel, acting as an isometry of L2(C) onto L2(C). In hypercomplex function theory the Beltrami equations have not yet this importance, but nevertheless, they are a basic condition for the transfer of complex methods and efforts for solving partial differential equations, especially of non-linear type, to the spatial case. Here we deal with hypercomplex Beltrami systems. For this we restrict ourselves to the quaternionic case, but without any loss of generality. We will show how a spatial generalization of the complex -operator can be used to solve systems of non-linear partial differential equations, in particular different types of spatial Beltrami systems. Also, the for practical purposes so important norm estimates will be derived. Some of our results are stronger as known results in the complex case, but they are applicable in the complex situation, too