We give two alternative proofs leading to di erent generalizations of the following theorem of [1]. Given n convex sets in the plane, such that the boundaries of each pair of sets cross at most twice, then the boundary of their union consists of at most 6n 12 arcs. (An arc is a connected piece of the boundary of one of the sets.) In the generalizations we allow pairs of boundaries to cross more...

An analytical treatment of the electron screening effect within an active-electron model is given for positronium formation from helium atoms. A first-order distorted wave approximation with correct boundary conditions is applied to evaluate the transition amplitude. In the range of impact energy for which the introduced perturbative approach is valid, both the total and differential cross sect...

The non-orthogonal boundary-fitted coordinate transformation method is applied to the solution of steady three-dimensional conservation equations of mass, momentum, energy and speciescontinuity to obtain the laminar velocity, temperature and concentration fields for simulation of polymerization of styrene in arbitrary cross-sectional duct reactors. Variable physical properties (except for speci...

The non-orthogonal boundary-fitted coordinate transformation method is applied to the solution of steady three-dimensional momentum and energy equations in laminar flow to obtain temperature field and Nusselt numbers in the thermal entry region of straight ducts of different cross sectional geometries. The conservation equations originally written in Cartesian coordinates are parabolized in the...

In this study an investigation using log-files of teachers’ Collections of educational resources in two different platform was conducted. The goal was to find empirical evidence from the field that teachers use and reuse learning resources that are in a language other than their mother tongue and originate from different countries than they do, for this, the term cross-boundary use of learning ...

Open boundary conditions. Since the source current, Eq. 1, extends from z = −∞ to +∞ whereas our computational domain is finite, one has to apply suitable boundary conditions (see also [2]). Consider some accelerator component, residing in a vacuum cavity with attached beam pipe of smaller cross section than the cavity. Generally, the transitions from the pipe to the module have to be included ...

Under labels such as global value chains, global production networks, interconnected firms, or outsourcing cross-boundary business processes have gained significant attention in practice and research. However, only little research has yet systematically examined the implications of cross-boundary business processes for Business Process Management (BPM). These cross-boundary business processes t...

We propose a novel framework to segment vessels on their cross-sections. It starts with a probabilistic vessel axis tracing in a gray-scale three-dimensional angiogram, followed by vessel boundary delineation on cross-sections derived from the extracted axis. It promotes a more intuitive delineation of vessel boundaries which are mostly round on the cross-sections. The prior probability density...

The volume information extracted from computed tomography angiogram is very useful for cardiologists to diagnose various diseases. An approach is presented to segment human coronary artery trees from the volumetric datasets. The coronary arteries’ surfaces are recovered by triangle mesh with the boundary points extracted from the coronary artery voxels segmented. The positions where the calcifi...

We have measured the stability boundary for steady electroconvection in thin, freely suspended liquid crystal lms. As the voltage across the lm, or the lm length, is varied, convective vortices are created or destroyed at the ends of the lm to keep the pattern wave number within a stable range. The measured stability boundary lies substantially inside the Eckhaus boundary calculated for this sy...