Some Second Thoughts on Monopolistic Distortions and Endogenous Growth

The most fundamental proposition about growth and competition is that there is a tradeoff between static welfare and long-term growth. This paper reconsiders this basic proposition in an increasing product variety endogenous growth model with competitive markets for “old” innovative products and for a traditional good. We shed light on some implications of monopolistic distortions which tend to be ignored by standard models. First, no growth may be better than some growth, since modest positive growth potentially requires sizeable static welfare losses. Second, the economy may converge to a steady state with zero growth, even though another (saddle-point stable) steady state with positive growth exists if the initial share of “cheap” competitive markets is sufficiently high, as this implies a relatively low demand for “expensive” innovative goods. Third, such a “no-growth trap” may happen in a world economy made up of several countries engaged in free trade with each other. The policy implications are that growth-enhancing policies may be misguided and that quick deregulation as well as quick trade liberalization can lead to stagnation in the long term.endogenous growth, competition, deregulation, poverty trap, trade liberalization

Projections of Virasoro Singular Vectors

We use recently derived explicit formulae for the Virasoro algebra's singular vectors to give constructive proofs of three results due to Feigin and Fuchs. The main result, which is needed for a rigorous treatment of fusion, describes the action of the singular vectors on conformal fields.Comment: 11 p

Reactive ion beam figuring of optical aluminium surfaces

Ultra-smooth and arbitrarily shaped reflective optics are necessary for further progress in EUV/XUV lithography, x-ray and synchrotron technology. As one of the most important technological mirror optic materials, aluminium behaves in a rather difficult way in ultra-precision machining with such standard techniques as diamond-turning and subsequent ion beam figuring (IBF). In particular, in the latter, a strong surface roughening is obtained. Hence, up to now it has not been possible to attain the surface qualities required for UV or just visible spectral range applications. To overcome the limitations mainly caused by the aluminium alloy structural and compositional conditions, a reactive ion beam machining process using oxygen process gas is evaluated. To clarify the principle differences in the effect of oxygen gas contrary to oxygen ions on aluminium surface machining, we firstly focus on chemical-assisted ion beam etching (CAIBE) and reactive ion beam etching (RIBE) experiments in a phenomenological manner. Then, the optimum process route will be explored within a more quantitative analysis applying the concept of power spectral density (PSD) for a sophisticated treatment of the surface topography. Eventually, the surface composition is examined by means of dynamic secondary ion mass spectrometry (SIMS) suggesting a characteristic model scheme for the chemical modification of the aluminium surface during oxygen ion beam machining. Monte Carlo simulations were applied to achieve a more detailed process conception

Local and Global Well-posedness of the fractional order EPDiff equation on Rd\mathbb{R}^{d}

Of concern is the study of fractional order Sobolev--type metrics on the group of $H^{\infty}$-diffeomorphism of $\mathbb{R}^{d}$ and on its Sobolev completions $\mathcal{D}^{q}(\mathbb{R}^{d})$. It is shown that the $H^{s}$-Sobolev metric induces a strong and smooth Riemannian metric on the Banach manifolds $\mathcal{D}^{s}(\mathbb{R}^{d})$ for $s >1 + \frac{d}{2}$. As a consequence a global well-posedness result of the corresponding geodesic equations, both on the Banach manifold $\mathcal{D}^{s}(\mathbb{R}^{d})$ and on the smooth regular Fr\'echet-Lie group of all $H^{\infty}$-diffeomorphisms is obtained. In addition a local existence result for the geodesic equation for metrics of order $\frac{1}{2} \leq s < 1 + d/2$ is derived.Comment: 37 page

Deciphering Consumer Commitment: Exploring the Dual Influence of Self-Brand and Self-Group Relationships

Consumer-brand relationships are highly valued as brand-committed consumers are thought to deliver many positive outcomes for affiliated brands. However, in addition to connections between individuals and brands, consumer-brand relationships also involve relationships between individuals and other brand users. Little attention has been given to the potential consequences associated with commitment to other brand users as compared to the brand itself. Therefore, our framework establishes two distinct types of consumer-brand relationships (i.e., self-brand relationships vs. self-group relationships) that differentially influence brand commitment versus group commitment, leading to contrasting effects on both desirable and undesirable brand outcomes. Specifically, our studies illuminate that while brand commitment is largely associated with favorable brand-related outcomes, group commitment does not protect against brand switching and is negatively related to willingness to pay price premiums and positive word-of-mouth. Our main contribution is uncovering how consumer-brand relationships face tradeoffs between brand and group attachments, whereby commitment provides both conditional benefits as well as unintended consequences

Improved ion beam tools for ultraprecision figure correction of curved aluminum mirror surfaces

Aluminum mirrors offer great potential for satisfying the increasing demand in high-performance optical components for visible and ultraviolet applications. Ion beam figuring is an established finishing technology and in particular a promising technique for direct aluminum figure error correction. For the machining of strongly curved or arbitrarily shaped surfaces as well as the correction of low-to-mid spatial frequency figure errors, the usage of a high-performance ion beam source with low tool width is mandatory. For that reason, two different concepts of ion beam generation with high ion current density and narrow beam width are discussed. (1) A concave ion beam extraction grid system is used for apertureless constriction of ion beams in the low millimeter range. An oxygen ion beam with a full-width at half-maximum (FWHM) of 4.0 mm with an ion current density of 29.8  mA  /  cm2 was achieved. (2) For even smaller ion beams, a conic aperture design with a submillimeter-sized exit opening was tested. A nitrogen ion beam with an FWHM down to 0.62 mm with an ion current density of 4.6  mA  /  cm2 was obtained. In situ ion current density mapping is performed by scanning Faraday probe measurements. Special interest is set on the data evaluation for submillimeter ion beam analysis

Effects of boundary roughness on a Q-factor of whispering-gallery-mode lasing microdisk cavities

We perform numerical studies of the effect of sidewall imperfections on the resonant state broadening of the optical microdisk cavities for lasing applications. We demonstrate that even small edge roughness causes a drastic degradation of high-Q whispering gallery (WG) mode resonances reducing their Q-values by many orders of magnitude. At the same time, low-Q WG resonances are rather insensitive to the surface roughness. The results of numerical simulation obtained using the scattering matrix technique, are analyzed and explained in terms of wave reflection at a curved dielectric interface combined with the examination of Poincare surface of sections in the classical ray picture.Comment: 4 pages, 3 figure

Charge localization instability in a highly deformable dielectric elastomer

This paper shows that a highly deformable capacitor made of a soft dielectric and two conformal electrodes can switch between two states discontinuously, by a first-order transition, as the total charge varies gradually. When the total charge is small, it spreads evenly over the area of the capacitor, and the capacitor deforms homogeneously. When the total charge is large, it localizes in a small region of the capacitor, and this region thins down preferentially. The capacitor will survive the localization without electrical breakdown if the area of the electrode is small. Such a bistable system may lead to useful devices.Engineering and Applied Science