Scenarios for the Origin of the Orbits of the Trans-Neptunian Objects 2000 CR105 and 2003 VB12

Explaining the origin of the orbit of 2000 CR105 (a ~ 230AU, q ~ 45AU) is a major test for our understanding of the primordial evolution of the outer Solar System. Gladman et al. (2001) showed that this objects could not have been a normal member of the scattered disk that had its perihelion distance increased by chaotic diffusion. In this paper we explore four seemingly promising mechanisms for explaining the origin of the orbit of this peculiar object: (i) the passage of Neptune through a high-eccentricity phase, (ii) the past existence of massive planetary embryos in the Kuiper belt or the scattered disk, (iii) the presence of a massive trans-Neptunian disk at early epochs which exerted tides on scattered disk objects, and (iv) encounters with other stars. Of all these mechanisms, the only one giving satisfactory results is the passage of a star. Indeed, our simulations show that the passage of a solar mass star at about 800 AU only perturbs objects with semi-major axes larger than roughly 200 AU to large perihelion distances. This is in good agreement with the fact that 2000 CR105 has a semi-major axis of 230AU and no other bodies with similar perihelion distances but smaller semi-major axes have yet been discovered. The discovery of 2003 VB12, (a=450AU, q=75AU) announced a few days before the submission of this paper, strengthen our conclusions.Comment: AJ submitted. 27 pages, 6 figure

Modeling galactic halos with predominantly quintessential matter

This paper discusses a new model for galactic dark matter by combining an anisotropic pressure field corresponding to normal matter and a quintessence dark energy field having a characteristic parameter $\omega_q$ such that $-1<\omega_q< -\frac{1}{3}$. Stable stellar orbits together with an attractive gravity exist only if $\omega_q$ is extremely close to $-\frac{1}{3}$, a result consistent with the special case studied by Guzman et al. (2003). Less exceptional forms of quintessence dark energy do not yield the desired stable orbits and are therefore unsuitable for modeling dark matter.Comment: 12 pages, 1 figur

Anisotropic interactions of a single spin and dark-spin spectroscopy in diamond

The nitrogen-vacancy (N-V) center in diamond is a promising atomic-scale system for solid-state quantum information processing. Its spin-dependent photoluminescence has enabled sensitive measurements on single N-V centers, such as: electron spin resonance, Rabi oscillations, single-shot spin readout and two-qubit operations with a nearby 13C nuclear spin. Furthermore, room temperature spin coherence times as long as 58 microseconds have been reported for N-V center ensembles. Here, we have developed an angle-resolved magneto-photoluminescence microscopy apparatus to investigate the anisotropic electron spin interactions of single N-V centers at room temperature. We observe negative peaks in the photoluminescence as a function of both magnetic field magnitude and angle that are explained by coherent spin precession and anisotropic relaxation at spin level anti-crossings. In addition, precise field alignment unmasks the resonant coupling to neighboring dark nitrogen spins that are not otherwise detected by photoluminescence. The latter results demonstrate a means of investigating small numbers of dark spins via a single bright spin under ambient conditions.Comment: 13 pages, 4 figure

Galois covers of the open p-adic disc

This paper investigates Galois branched covers of the open $p$-adic disc and their reductions to characteristic $p$. Using the field of norms functor of Fontaine and Wintenberger, we show that the special fiber of a Galois cover is determined by arithmetic and geometric properties of the generic fiber and its characteristic zero specializations. As applications, we derive a criterion for good reduction in the abelian case, and give an arithmetic reformulation of the local Oort Conjecture concerning the liftability of cyclic covers of germs of curves.Comment: 19 pages; substantial organizational and expository changes; this is the final version corresponding to the official publication in Manuscripta Mathematica; abstract update

Dark matter effects in vacuum spacetime

We analyze a toy model describing an empty spacetime in which the motion of a test mass (and the trajectories of photons) evidence the presence of a continuous and homogeneous distribution of matter; however, since the energy-momentum tensor vanishes, no real matter or energy distribution is present at all. Thus, a hypothetical observer will conclude that he is immersed in some sort of dark matter, even though he has no chance to directly detect it. This suggests yet another possibility of explaining the elusive dark matter as a purely dynamical effect due to the curvature of spacetime.Comment: 5 pages, 2 figures, expanded with comments about the exact motion and curvature invariant

The a-number of hyperelliptic curves

It is known that for a smooth hyperelliptic curve to have a large $a$-number, the genus must be small relative to the characteristic of the field, $p>0$, over which the curve is defined. It was proven by Elkin that for a genus $g$ hyperelliptic curve $C$ to have $a_C=g-1$, the genus is bounded by $g<\frac{3p}{2}$. In this paper, we show that this bound can be lowered to $g <p$. The method of proof is to force the Cartier-Manin matrix to have rank one and examine what restrictions that places on the affine equation defining the hyperelliptic curve. We then use this bound to summarize what is known about the existence of such curves when $p=3,5$ and $7$.Comment: 7 pages. v2: revised and improved the proof of the main theorem based on suggestions from the referee. To appear in the proceedings volume of Women in Numbers Europe-

Лекарственный анафилактический и псевдоаллергический шок: патогенез, клиника, дифференциальная диагностика, подходы к терапии

Представлены особенности патогенеза анафилактического и псевдоаллергического шока, обусловленного лекарственными средствами, сходства и различия в клиническом их течении, субъективные и объективные признаки дифференциальной диагностики, подходы к терапии.The peculiarities of the pathogenesis of anaphylactic and pseudoallergic shock caused by medications, similarity and differences of the clinical course, subjective and objective signs of differential diagnosis, approaches to therapy are presented

Tannakian approach to linear differential algebraic groups

Tannaka's Theorem states that a linear algebraic group G is determined by the category of finite dimensional G-modules and the forgetful functor. We extend this result to linear differential algebraic groups by introducing a category corresponding to their representations and show how this category determines such a group.Comment: 31 pages; corrected misprint

Local Surface Density of the Galactic Disk from a 3-D Stellar Velocity Sample

We have re-estimated the surface density of the Galactic disk in the solar neighborhood within $\pm$ 0.4 kpc of the Sun using parallaxes and proper motions of a kinematically and spatially unbiased sample of 1476 old bright red giant stars from the Hipparcos catalog with measured radial velocities from Barbier-Brossat & Figon (2000). We determine the vertical distribution of the red giants as well as the vertical velocity dispersion of the sample, (14.4 $\pm$ 0.26 km/sec), and combine these to derive the surface density of gravitating matter in the Galactic disk as a function of the galactic coordinate $z$. The surface density of the disk increases from 10.5 $\pm$ 0.5 $M_{\odot}$ / pc$^2$ within $\pm$ 50 pc to 42 $\pm$ 6 $M_{\odot}$ / pc$^2$ within $\pm$ 350 pc. The estimated volume density of the galactic disk within $\pm$ 50 pc is about 0.1 $M_{\odot}$ / pc$^3$ which is close to the volume density estimates of the observed baryonic matter in the solar neighborhood.Comment: 24 pages, 15 figures, AJ in pres