Exclusive vs Overlapping Viewers in Media Markets

This paper investigates competition for advertisers in media markets when viewers can subscribe to multiple channels. A central feature of the model is that channels are monopolists in selling advertising opportunities toward their exclusive viewers, but they can only obtain a competitive price for advertising opportunities to multi-homing viewers. Strategic incentives of firms in this setting are different than those in former models of media markets. If viewers can only watch one channel, then firms compete for marginal consumers by reducing the amount of advertising on their channels. In our model, channels have an incentive to increase levels of advertising, in order to reduce the overlap in viewership. We take an account of the differences between the predictions of the two types of models and find that our model is more consistent with recent developments in broadcasting markets. We also show that if channels can charge subscription fees on viewers, then symmetric firms can end up in an asymmetric equilibrium in which one collects all or most of its revenues from advertisers, while the other channel collects most of its revenues via viewer fees

The impact of a natural time change on the convergence of the Crank-Nicolson scheme

We first analyse the effect of a square root transformation to the time variable on the convergence of the Crank-Nicolson scheme when applied to the solution of the heat equation with Dirac delta function initial conditions. In the original variables, the scheme is known to diverge as the time step is reduced with the ratio of the time step to space step held constant and the value of this ratio controls how fast the divergence occurs. After introducing the square root of time variable we prove that the numerical scheme for the transformed partial differential equation now always converges and that the ratio of the time step to space step controls the order of convergence, quadratic convergence being achieved for this ratio below a critical value. Numerical results indicate that the time change used with an appropriate value of this ratio also results in quadratic convergence for the calculation of the price, delta and gamma for standard European and American options without the need for Rannacher start-up steps

A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance

We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately, many intuitive (e.g. finite difference based) discretisations can be shown to converge. However, especially when using fully implicit time stepping schemes with their desirable stability properties, one is still faced with the considerable task of solving the resulting nonlinear discrete system. In this paper, we introduce a penalty method which approximates the nonlinear discrete system to first order in the penalty parameter, and we show that an iterative scheme can be used to solve the penalised discrete problem in finitely many steps. We include a number of examples from mathematical finance for which the described approach yields a rigorous numerical scheme and present numerical results.Comment: 18 Pages, 4 Figures. This updated version has a slightly more detailed introduction. In the current form, the paper will appear in SIAM Journal on Numerical Analysi

Epitaxy of Fe3O4 on Si(001) by pulsed laser deposition using a TiN/MgO buffer layer

Epitaxy of oxide materials on silicon (Si) substrates is of great interest for future functional devices using the large variety of physical properties of the oxides as ferroelectricity, ferromagnetism, or superconductivity. Recently, materials with high spin polarization of the charge carriers have become interesting for semiconductor-oxide hybrid devices in spin electronics. Here, we report on pulsed laser deposition of magnetite (Fe3O4) on Si(001) substrates cleaned by an in situ laser beam high temperature treatment. After depositing a double buffer layer of titanium nitride (TiN) and magnesium oxide (MgO), a high quality epitaxial magnetite layer can be grown as verified by RHEED intensity oscillations and high resolution x-ray diffraction.Comment: submitte

Sub-unit cell layer-by-layer growth of Fe3O4, MgO, and Sr2RuO4 thin films

The use of oxide materials in oxide electronics requires their controlled epitaxial growth. Recently, it was shown that Reflection High Energy Electron Diffraction (RHEED) allows to monitor the growth of oxide thin films even at high oxygen pressure. Here, we report the sub-unit cell molecular or block layer growth of the oxide materials Sr2RuO4, MgO, and magnetite using Pulsed Laser Deposition (PLD) from stoichiometric targets. Whereas for perovskites such as SrTiO3 or doped LaMnO3 a single RHEED intensity oscillation is found to correspond to the growth of a single unit cell, in materials where the unit cell is composed of several molecular layers or blocks with identical stoichiometry, a sub-unit cell molecular or block layer growth is established resulting in several RHEED intensity oscillations during the growth of a single unit-cell

Lil3 assembles as chlorophyll-binding protein complex during deetiolation

AbstractDark-grown angiosperm seedlings are etiolated and devoid of chlorophyll. Deetiolation is triggered by light leading to chlorophyll dependent accumulation of the photosynthetic machinery. The transfer of chlorophyll to the chlorophyll-binding proteins is still unclear. We demonstrate here that upon illumination of dark-grown barley seedlings, two new pigment-binding protein complexes are de novo accumulated. Pigments bound to both complexes are identified as chlorophyll a and protochlorophyll a. By auto-fluorescence tracking and mass spectrometry, we show that exclusively Lil3 is the pigment-binding complex subunit in both complexes

The proteome of the heterocyst cell wall in Anabaena sp. PCC 7120

Anabaena sp. PCC 7120 is a filamentous cyanobacterium that serves as a model to analyze prokaryotic cell differentiation, evolutionary development of plastids, and the regulation of nitrogen fixation. The cell wall is the cellular structure in contact with the surrounding medium. To understand the dynamics of the cell wall proteome during cell differentiation, the cell wall from Anabaena heterocysts was enriched and analyzed. In line with the recently proposed continuity of the outer membrane along the Anabaena filament, most of the proteins identified in the heterocyst cell-wall fraction are also present in the cell wall of vegetative cells, even though the lipid content of both membranes is different

Penalty Methods for the Solution of Discrete HJB Equations -- Continuous Control and Obstacle Problems

In this paper, we present a novel penalty approach for the numerical solution of continuously controlled HJB equations and HJB obstacle problems. Our results include estimates of the penalisation error for a class of penalty terms, and we show that variations of Newton's method can be used to obtain globally convergent iterative solvers for the penalised equations. Furthermore, we discuss under what conditions local quadratic convergence of the iterative solvers can be expected. We include numerical results demonstrating the competitiveness of our methods.Comment: 31 Pages, 7 Figure