Set mapping reflection

In this note we will discuss a new reflection principle which follows from the Proper Forcing Axiom. The immediate purpose will be to prove that the bounded form of the Proper Forcing Axiom implies both that 2^omega = omega_2 and that L(P(omega_1)) satisfies the Axiom of Choice. It will also be demonstrated that this reflection principle implies that combinatorial principle Square(kappa) fails for all regular kappa > omega_1.Comment: 11 page

Optical imaging of resonant electrical carrier injection into individual quantum dots

We image the micro-electroluminescence (EL) spectra of self-assembled InAs quantum dots (QDs) embedded in the intrinsic region of a GaAs p-i-n diode and demonstrate optical detection of resonant carrier injection into a single QD. Resonant tunneling of electrons and holes into the QDs at bias voltages below the flat-band condition leads to sharp EL lines characteristic of individual QDs, accompanied by a spatial fragmentation of the surface EL emission into small and discrete light- emitting areas, each with its own spectral fingerprint and Stark shift. We explain this behavior in terms of Coulomb interaction effects and the selective excitation of a small number of QDs within the ensemble due to preferential resonant tunneling paths for carriers.Comment: 4 page

Independence and consistency proofs in quadratic form theory

We consider the following properties of uncountable-dimensional quadratic spaces (E, Φ): (*) For all subspaces U ⊆ E of infinite dimension: dim U ˔ < dim E. (**) For all subspaces U ⊆ E of infinite dimension: dim U ˔ < ℵ0. Spaces of countable dimension are the orthogonal sum of straight lines and planes, so they cannot have (*), but (**) is trivially satisfied. These properties have been considered first in [G/O] in the process of investigating the orthogonal group of quadratic spaces. It has been shown there (in ZFC) that over arbitrary uncountable fields (**)-spaces of uncountable dimension exist. In [B/G], (**)-spaces of dimension ℵ1 (so (*) = (**)) have been constructed over arbitrary finite or countable fields. But this could be done only under the assumption that the continuum hypothesis (CH) holds in the underlying set theor

A second eigenvalue bound for the Dirichlet Schroedinger operator

Let $\lambda_i(\Omega,V)$ be the $i$th eigenvalue of the Schr\"odinger operator with Dirichlet boundary conditions on a bounded domain $\Omega \subset \R^n$ and with the positive potential $V$. Following the spirit of the Payne-P\'olya-Weinberger conjecture and under some convexity assumptions on the spherically rearranged potential $V_\star$, we prove that $\lambda_2(\Omega,V) \le \lambda_2(S_1,V_\star)$. Here $S_1$ denotes the ball, centered at the origin, that satisfies the condition $\lambda_1(\Omega,V) = \lambda_1(S_1,V_\star)$. Further we prove under the same convexity assumptions on a spherically symmetric potential $V$, that $\lambda_2(B_R, V) / \lambda_1(B_R, V)$ decreases when the radius $R$ of the ball $B_R$ increases. We conclude with several results about the first two eigenvalues of the Laplace operator with respect to a measure of Gaussian or inverted Gaussian density

On Some Positivity Properties of the Interquark Potential in QCD

We prove that the Fourier transform of the exponential e^{-\b V(R)} of the {\bf static} interquark potential in QCD is positive. It has been shown by Eliott Lieb some time ago that this property allows in the same limit of static spin independent potential proving certain mass relation between baryons with different quark flavors.Comment: 6 pages, latex with one postscript figur

Hierarchic Superposition Revisited

Many applications of automated deduction require reasoning in first-order logic modulo background theories, in particular some form of integer arithmetic. A major unsolved research challenge is to design theorem provers that are "reasonably complete" even in the presence of free function symbols ranging into a background theory sort. The hierarchic superposition calculus of Bachmair, Ganzinger, and Waldmann already supports such symbols, but, as we demonstrate, not optimally. This paper aims to rectify the situation by introducing a novel form of clause abstraction, a core component in the hierarchic superposition calculus for transforming clauses into a form needed for internal operation. We argue for the benefits of the resulting calculus and provide two new completeness results: one for the fragment where all background-sorted terms are ground and another one for a special case of linear (integer or rational) arithmetic as a background theory

Characterization and tectonic implications of Mesozoic-Cenozoic oceanic assemblages of Costa Rica and Western Panama

The Pacific face of Costa Rica and western Panama has been extensively studied because of the wide occurrence of oceanic assemblages. In Northern Costa Rica, the Santa Elena Nappe made by ultramafic and mafic associations overthrusts the Santa Rosa Accretionary Complex. The Nicoya Complex corresponds to a pre-Campanian oceanic plateau association, cropping out in the Nicoya Peninsula and the outer Herradura Block. The 89 Ma high MgO Tortugal Komatiitic Suite corresponds to 14-km long, 1.5-km wide body, with no clear relation with to the Nicoya Complex. The Tulín Formation (Maastrichtian to Lower Eocene) forms the main edifice of an accreted ancient oceanic island of the Herradura Block. The Quepos Block was formed by the accretion of a late Cretaceous-Paleocene seamount. In the Osa and Burica peninsulas, Caño Island and Golfito area, a series of Upper Cretaceous to Eocene accreted plateau and seamount blocks crop out. In western Panama, the oceanic assemblages range from Upper Cretaceous to Miocene, and their geochemical signature show their oceanic plateau association. The Costa Rica and western Panama oceanic assemblages correspond to a fragmentary and disrupted Jurassic to Miocene sequences with a very complicated geological and geotectonic history. Their presence could be interpreted as a result of accretionary processes rather than tectonic erosion; despite this last process is nowadays active in the Middle American Trench. The whole picture has not been completed yet, but apparently, most of the igneous rocks have a geochemical signature similar to the Galapagos mantle plume. The later has been acting in pulses, or otherwise the outcropping occurrences could be part of several plateaus somehow diachronically formed in the Pacific basin

Real-space imaging of quantum Hall effect edge strips

We use dynamic scanning capacitance microscopy (DSCM) to image compressible and incompressible strips at the edge of a Hall bar in a two-dimensional electron gas (2DEG) in the quantum Hall effect (QHE) regime. This method gives access to the complex local conductance, Gts, between a sharp metallic tip scanned across the sample surface and ground, comprising the complex sample conductance. Near integer filling factors we observe a bright stripe along the sample edge in the imaginary part of Gts. The simultaneously recorded real part exhibits a sharp peak at the boundary between the sample interior and the stripe observed in the imaginary part. The features are periodic in the inverse magnetic field and consistent with compressible and incompressible strips forming at the sample edge. For currents larger than the critical current of the QHE break-down the stripes vanish sharply and a homogeneous signal is recovered, similar to zero magnetic field. Our experiments directly illustrate the formation and a variety of properties of the conceptually important QHE edge states at the physical edge of a 2DEG.Comment: 7 page