Splitting fields and general differential Galois theory

An algebraic technique is presented that does not use results of model theory and makes it possible to construct a general Galois theory of arbitrary nonlinear systems of partial differential equations. The algebraic technique is based on the search for prime differential ideals of special form in tensor products of differential rings. The main results demonstrating the work of the technique obtained are the theorem on the constructedness of the differential closure and the general theorem on the Galois correspondence for normal extensions..Comment: 33 pages, this version coincides with the published on

Models for Chronology Selection

In this paper, we derive an expression for the grand canonical partition function for a fluid of hot, rotating massless scalar field particles in the Einstein universe. We consider the number of states with a given energy as one increases the angular momentum so that the fluid rotates with an increasing angular velocity. We find that at the critical value when the velocity of the particles furthest from the origin reaches the speed of light, the number of states tends to zero. We illustrate how one can also interpret this partition function as the effective action for a boosted scalar field configuration in the product of three dimensional de Sitter space and $S^1$. In this case, we consider the number of states with a fixed linear momentum around the $S^1$ as the particles are given more and more boost momentum. At the critical point when the spacetime is about to develop closed timelike curves, the number of states again tends to zero. Thus it seems that quantum mechanics naturally enforces the chronology protection conjecture by superselecting the causality violating field configurations from the quantum mechanical phase space.Comment: 20 pages, Late

Chronology Protection in Generalized Godel Spacetime

The effective action of a free scalar field propagating in the generalized Godel spacetime is evaluated by the zeta-function regularization method. From the result we show that the renormalized stress energy tensor may be divergent at the chronology horizon. This gives a support to the chronology protection conjecture.Comment: Latex 6 pages, typos correcte

Rotation and the AdS/CFT correspondence

In asymptotically flat space a rotating black hole cannot be in thermodynamic equilibrium because the thermal radiation would have to be co-rotating faster than light far from the black hole. However in asymptotically anti-de Sitter space such equilibrium is possible for certain ranges of the parameters. We examine the relationship between conformal field theory in rotating Einstein universes of dimensions two to four and Kerr anti-de Sitter black holes in dimensions three to five. The five dimensional solution is new. We find similar divergences in the partition function of the conformal field theory and the action of the black hole at the critical angular velocity at which the Einstein rotates at the speed of light. This should be an interesting limit in which to study large $N$ Yang-Mills.Comment: 24 pages, RevTeX, 1 figure, references adde

Divergences in the Effective Action for Acausal Spacetimes

The 1--loop effective Lagrangian for a massive scalar field on an arbitrary causality violating spacetime is calculated using the methods of Euclidean quantum field theory in curved spacetime. Fields of spin 1/2, spin 1 and twisted field configurations are also considered. In general, we find that the Lagrangian diverges to minus infinity at each of the nth polarised hypersurfaces of the spacetime with a structure governed by a DeWitt-Schwinger type expansion.Comment: 17 pages, Late

Is the Broad-Line Region Clumped or Smooth? Constraints from the H alpha Profile in NGC 4395, the Least Luminous Seyfert 1 Galaxy

The origin and configuration of the gas which emits broad lines in Type I active galactic nuclei is not established yet. The lack of small-scale structure in the broad emission-line profiles is consistent with a smooth gas flow, or a clumped flow with many small clouds. An attractive possibility for the origin of many small clouds is the atmospheres of bloated stars, an origin which also provides a natural mechanism for the cloud confinement. Earlier studies of the broad-line profiles have already put strong lower limits on the minimum number of such stars, but these limits are sensitive to the assumed width of the lines produced by each cloud. Here we revisit this problem using high-resolution Keck spectra of the H alpha line in NGC 4395, which has the smallest known broad-line region (~10^14 cm). Only a handful of the required bloated stars (each having r~10^14 cm) could fit into the broad-line region of NGC 4395, yet the observed smoothness of the H alpha line implies a lower limit of ~10^4-10^5 on the number of discrete clouds. This rules out conclusively the bloated-stars scenario, regardless of any plausible line-broadening mechanisms. The upper limit on the size of the clouds is ~10^12 cm, which is comparable to the size implied by photoionization models. This strongly suggests that gas in the broad-line region is structured as a smooth rather than a clumped flow, most likely in a rotationally dominated thick disk-like configuration. However, it remains to be clarified why such a smooth, gravity-dominated flow generates double-peaked emission lines only in a small fraction of active galactic nuclei.Comment: 12 pages, including 3 figures, accepted for publication in The Astrophysical Journa

The disengage deficit in hemispatial neglect is restricted to between-object shifts and is abolished by prism adaptation

We sought to determine the effects of prism adaptation on peripherally cued visual attention shifting in patients with spatial neglect, using a task devised by Egly et al. (J Exp Psychol Gen 123:161–177, 1994) based on the classic Posner paradigm. This task allowed a comparison of “within-object” versus “between-object” attention shifts. A display was presented containing two parallel outline rectangles, and subjects were asked to make rapid responses to a target, which would appear at one end of one of the rectangles. The target location was pre-cued with 75% validity: on invalid trials attention was directed either to the other end of the same rectangle, or to the other rectangle. Healthy subjects and right-hemisphere patients without neglect showed a left-right symmetrical pattern, with a larger validity effect when required to shift attention between rectangles, thus indicating a greater difficulty of attention-shifting between than within the respective shapes. The neglect patients showed the typical leftward “disengage deficit” previously observed in neglect, but only for attention shifts between objects, indicating that the effect is object-based rather than purely spatial. A comparison of vertical and horizontal shift costs showed that this attention-shifting deficit for left-hemifield target stimuli was directional rather than hemifield-based: it was absent for vertical shifts of attention within the left hemifield. Finally, we found that prism adaptation abolished the disengage deficit. We found no effects of prism adaptation in the control subjects. We argue that prism adaptation has a powerful effect on one of the fundamental manifestations of the neglect syndrome

Resolved Mid-IR Emission in the Narrow Line Region of NGC 4151

We present subarcsecond resolution mid infrared images of NGC 4151 at 10.8 micron and 18.2 micron. These images were taken with the University of Florida mid-IR camera/spectrometer OSCIR at the Gemini North 8-m telescope. We resolve emission at both 10.8 micron and 18.2 micron extending ~ 3.5" across at a P.A. of ~ 60 degrees. This coincides with the the narrow line region of NGC 4151 as observed in [OIII] by the Hubble Space Telescope. The most likely explanation for this extended mid-IR emission is dust in the narrow line region heated by a central engine. We find no extended emission associated with the proposed torus and place an upper limit on its mid-IR size of less than or equal to ~ 35 pc.Comment: accepted for publication in the Astrophysical Journal, 19 pages including 5 figure

Experimental Induction of Odontoblast Differentiation and Stimulation During Preparative Processes

In vivo implantation experiments have shown that ethylenediaminetetraaceticacid(EDTA)-soluble frac tions of dentin stimulate reparative dentinogenesis . When isolated embryonic dental papillae were cultured in the presence of these dentin constituents, odontoblast cytological and functional differentiation could be initiated and maintained in the absence of an enamel organ. These effects were attributed to the presence of TGF-/1- related molecules [TGF-/11 or bone morphogenetic protein -2a (BMP-2a)] which had to be used in combination with an EDT A-soluble fraction of dentin in order to specifically affect competent preodontoblasts . These EDT A-soluble constituents present in dentin could be replaced by heparin or fibronectin which both have been reported to interact with TGF-/1. The association of such defined matrix components with a TGF-/1-related molecule represents a biologically active complex triggering odontoblast functional differentiation. In response to caries, odontoblasts modulate their secretory activity and are stimulated to elaborate reactionary dentin. This might be induced by active molecules such as IGF, TGF-6 or BMP which are liberated from dentin consecutively to the demineralization process. Reparative dentinogenesis is distinct from reactionary dentinogenesis and more complex since it implicates the differentiation of precursor cells present in the dental papilla. The developmental history of these cells is different from that of the physiological predontoblasts in developing teeth. The nature of these stem cells and the mechanism of their induction still remain open questions

Threshold for Chaos and Thermalization in One-Dimensional Mean-Field Bose-Hubbard Model

We study the threshold for chaos and its relation to thermalization in the 1D mean-field Bose-Hubbard model, which in particular describes atoms in optical lattices. We identify the threshold for chaos, which is finite in the thermodynamic limit, and show that it is indeed a precursor of thermalization. Far above the threshold, the state of the system after relaxation is governed by the usual laws of statistical mechanics.Comment: 4 pages, 3 figures, published versio