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

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

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

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

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

Rapid, Precise, and High-Sensitivity Acquisition of Paleomagnetic and Rock-Magnetic Data: Development of a Low-Noise Automatic Sample Changing System for Superconducting Rock Magnetometers

Among Earth sciences, paleomagnetism is particularly linked to the statistics of large sample sets as a matter of historical development and logistical necessity. Because the geomagnetic field varies over timescales relevant to sedimentary deposition and igneous intrusion, while the fidelity of recorded magnetization is modulated by original properties of rock units and by alteration histories, "ideal" paleomagnetic results measure remanent magnetizations of hundreds of samples at dozens of progressive demagnetization levels, accompanied by tests of magnetic composition on representative sister specimens. We present an inexpensive, open source system for automating paleomagnetic and rock magnetic measurements. Using vacuum pick-and-place technology and a quartz-glass sample holder, the system can in one hour measure remanent magnetizations, as weak as a few pAm2, of ~30 specimens in two vertical orientations with measurement errors comparable to those of the best manual systems. The system reduces the number of manual manipulations required per specimen ~8 fold

Exploring the variability of media multitasking choice behaviour using a network approach

Many researchers have used the Media Multitasking Index (MMI) for investigating media multitasking behaviour. While useful as a means to compare inter-individual multitasking levels, the MMI disregards the variability in media multitasking choice behaviour: certain media combinations are more likely to be selected than others, and these patterns might differ from one population to another. The aim of the present study was to examine media multitasking choices in different populations. For this means, we employed a social network approach to render MMI responses collected in eight different populations into networks. The networks showed that the level of media multitasking as measured by the network densities differed across populations, yet, the pattern of media multitasking behaviour was similar. Specifically, media combinations which involved texting/IMing, listening to music, browsing, and social media were prominent in most datasets. Overall the findings indicate that media multitasking behaviours might be confined within a smaller set of media activities. Accordingly, instead of assessing a large number of media combinations, future studies might consider focusing on a more limited set of media types

Carbon nanotube quantum dots on hexagonal boron nitride

We report the fabrication details and low-temperature characteristics of the first carbon nanotube (CNT) quantum dots on flakes of hexagonal boron nitride (hBN) as substrate. We demonstrate that CNTs can be grown on hBN by standard chemical vapor deposition and that standard scanning electron microscopy imaging and lithography can be employed to fabricate nanoelectronic structures when using optimized parameters. This proof of concept paves the way to more complex devices on hBN, with more predictable and reproducible characteristics and electronic stability.Comment: 4 pages, 4 figure