Represented Value Sets for Integral Binary Quadratic Forms and Lattices

A characterization is given for the integral binary quadratic forms for which the set of represented values is closed under products. It is also proved that for an integral binary quadratic lattice over the ring of integers of a global field, the product of three values represented by the form is again a value represented by the form. This generalizes the trigroup property discovered by V. Arnold for the case of integral binary quadratic forms

Multiplicative Properties of Integral Binary Quadratic Forms

In this paper, the integral binary quadratic forms for which the set of represented values is closed under k-fold products, for even positive integers k, will be characterized. This property will be seen to distinguish the elements of odd order in the form class group of a fixed discriminant. Further, it will be shown that this closure under k-fold products can always be expressed by a k-linear mapping from (Z2)k to Z2. In the case k = 2, this resolves a conjecture of Aicardi and Timorin

Polarized Magnetic Wire Induced by Tunneling Through a Magnetic Impurity

Using the zero mode method we compute the conductance of a wire consisting of a magnetic impurity coupled to two Luttinger liquid leads characterized by the Luttinger exponent $\alpha(\leq 1)$. We find for resonance conditions, in which the Fermi energy of the leads is close to a single particle energy of the impurity, the conductance as a function of temperature is $G \sim \frac{e^2}{h} (T/T_F)^{2(\alpha-2)}$, whereas for off-resonance conditions the conductance is $G \sim \frac{e^2}{h} (T/T_F)^{2(\alpha-1)}$. By applying a gate voltage and/or a magnetic field, one of the spin components can be in resonance while the other is off-resonance causing a strong asymmetry between the spin-up and spin-down conductances.Comment: 8 pages, submitted to PR

A Ring of Warm Dust in the HD 32297 Debris Disk

We report the detection of a ring of warm dust in the edge-on disk surrounding HD 32297 with the Gemini-N/MICHELLE mid-infrared imager. Our N'-band image shows elongated structure consistent with the orientation of the scattered-light disk. The Fnu(11.2 um) = 49.9+/-2.1 mJy flux is significantly above the 28.2+/-0.6 mJy photosphere. Subtraction of the stellar point spread function reveals a bilobed structure with peaks 0.5"-0.6" from the star. An analysis of the stellar component of the SED suggests a spectral type later than A0, in contrast to commonly cited literature values. We fit three-dimensional, single-size grain models of an optically thin dust ring to our image and the SED using a Markov chain Monte Carlo algorithm in a Bayesian framework. The best-fit effective grain sizes are submicron, suggesting the same dust population is responsible for the bulk of the scattered light. The inner boundary of the warm dust is located 0.5"-0.7" (~65 AU) from the star, which is approximately cospatial with the outer boundary of the scattered-light asymmetry inward of 0.5". The addition of a separate component of larger, cooler grains that provide a portion of the 60 um flux improves both the fidelity of the model fit and consistency with the slopes of the scattered-light brightness profiles. Previous indirect estimates of the stellar age (~30 Myr) indicate the dust is composed of debris. The peak vertical optical depths in our models (~0.3-1 x 1e-2) imply that grain-grain collisions likely play a significant role in dust dynamics and evolution. Submicron grains can survive radiation pressure blow-out if they are icy and porous. Similarly, the inferred warm temperatures (130-200 K) suggest that ice sublimation may play a role in truncating the inner disk.Comment: ApJ accepted, 8 pages, 4 figure

Doubly Special Relativity with a minimum speed and the Uncertainty Principle

The present work aims to search for an implementation of a new symmetry in the space-time by introducing the idea of an invariant minimum speed scale ($V$). Such a lowest limit $V$, being unattainable by the particles, represents a fundamental and preferred reference frame connected to a universal background field (a vacuum energy) that breaks Lorentz symmetry. So there emerges a new principle of symmetry in the space-time at the subatomic level for very low energies close to the background frame ($v\approx V$), providing a fundamental understanding for the uncertainty principle, i.e., the uncertainty relations should emerge from the space-time with an invariant minimum speed.Comment: 10 pages, 8 figures, Correlated paper in: http://www.worldscientific.com/worldscinet/ijmpd?journalTabs=read. arXiv admin note: substantial text overlap with arXiv:physics/0702095, arXiv:0705.4315, arXiv:0709.1727, arXiv:0805.120

CCRS proposal for evaluating LANDSAT-4 MSS and TM data

The measurement of registration errors in LANDSAT MSS data is discussed as well as the development of a revised algorithm for the radiometric calibration of TM data and the production of a geocoded TM image

Stochastic transitions: Paths over higher energy barriers can dominate in the early stages

The time evolution of many physical, chemical, and biological systems can be modelled by stochastic transitions between the minima of the potential energy surface describing the system of interest. We show that in cases where there are two (or more) possible pathways that the system can take, the time available for the transition to occur is crucially important. The well-known results of reaction rate theory for determining the rates of the transitions apply in the long-time limit. However, at short times, the system can instead choose to pass over higher energy barriers with much higher probability, as long as the distance to travel in phase space is shorter. We construct two simple models to illustrate this general phenomenon. We also present an extension of the gMAM algorithm of Vanden-Eijnden and Heymann [J. Chem. Phys. {\bf 128}, 061103 (2008)] to determine the most likely path at both short and long times.Comment: 7 pages, 5 Figure