The Casas-Alvero conjecture for infinitely many degrees

Over a field of characteristic zero, it is clear that a polynomial of the form (X-a)^d has a non-trivial common factor with each of its d-1 first derivatives. The converse has been conjectured by Casas-Alvero. Up to now there have only been some computational verifications for small degrees d. In this paper the conjecture is proved in the case where the degree of the polynomial is a power of a prime number, or twice such a power. Moreover, for each positive characteristic p, we give an example of a polynomial of degree d which is not a dth power but which has a common factor with each of its first d-1 derivatives. This shows that the assumption of characteristic zero is essential for the converse statement to hold.Comment: 7 pages; v2: corrected some typos and references, and added section on computational aspect

Prelog Chow rings and degenerations

For a simple normal crossing variety X, we introduce the concepts of prelog Chow ring, saturated prelog Chow group, as well as their counterparts for numerical equivalence. Thinking of X as the central fibre in a (strictly) semistable degeneration, these objects can intuitively be thought of as consisting of cycle classes on X for which some initial obstruction to arise as specializations of cycle classes on the generic fibre is absent. Cycle classes in the generic fibre specialize to their prelog counterparts in the central fibre, thus extending to Chow rings the method of studying smooth varieties via strictly semistable degenerations. After proving basic properties for prelog Chow rings and groups, we explain how they can be used in an envisaged further development of the degeneration method by Voisin et al. to prove stable irrationality of very general fibres of certain families of varieties; this extension would allow for much more singular degenerations, such as toric degenerations as occur in the Gross-Siebert programme, to be usable. We illustrate that by looking at the "baby example" of degenerations of elliptic curves, and we compute the saturated prelog Chow group of degenerations of cubic surfaces.Comment: 33 pages, 14 figure

Prelog Chow groups of self-products of degenerations of cubic threefolds

It is unknown whether smooth cubic threefolds have an (integral Chow-theoretic) decomposition of the diagonal, or whether they are stably rational or not in general. As a first step towards making progress on these questions, we compute the (saturated numerical) prelog Chow group of the self-product of a certain degeneration of cubic threefolds.Comment: 20 pages, 1 figur

Acute effects of acetyl-L-carnitine on sodium cyanide-induced behavioral and biochemical deficits

In the present study we investigated the effects of acute treatment with acetyl-L-carnitine (50 mg/kg, i.v. 90 min before the sodium cyanide injection) on a sodium cyanide-induced behavioral deficit in the Morris water escape task. In a first experiment the spatial discrimination performance of the rats was found to be dose-dependently impaired after an i.c.v. injection of sodium cyanide (2.5 and 5.0 mu g). Acute treatment with acetyl-L-carnitine was found to increase the behavioral deficit after sodium cyanide, these findings were replicated in a second experiment. Based on these results it can be argued that an acute administration of acetyl-L-carnitine appears to potentiate a sodium cyanide-induced behavioral deficit. An additional in vitro experiment with rat brain synaptosomes showed clear effects of administered sodium cyanide on the energy-dependent incorporation of inositol into phosphoinositides and on the ATP concentration. In vitro acetyl-L-carnitine administration had no effect on the sodium cyanide-induced energy depletion. The negative behavioral findings are in contrast with our previously found protective effect of chronic treatment with acetyl-L-carnitine (via drinking water) on the sodium cyanide-induced behavioral deficit. Since chronic acetyl-L-carnitine treatment has no effect on the phosphoinositide metabolism it was suggested that acetyl-L-carnitine may act via the formation of an ATP-independent reservoir of activated acyl groups. Thus, fatty acids as acylated derivatives can be used for reacylation processes during an acute period of energy depletion. However, we have no clear explanation for the discrepancy in behavioral results between the chronic vs acute treatment of acetyl-L-carnitine at present. Further research is needed to characterize the mechanism of action of acetyl-L-carnitine in relation to sodium cyanide. (C) 1998 Elsevier Science Ltd. All rights reserved

Partially-erupting prominences: a comparison between observations and model-predicted observables

<p><b>Aims:</b> We investigate several partially-erupting prominences to study their relationship with other CME-associated phenomena and compare these observations with observables predicted by a model of partially-expelled-flux-ropes (Gibson & Fan 2006a, ApJ, 637, L65; 2006b, J. Geophys. Res., 111, 12103).</p> <p><b>Methods:</b> We studied 6 selected events with partially-erupting prominences using multi-wavelength observations recorded by the Extreme-ultraviolet Imaging Telescope (EIT), Transition Region and Coronal Explorer (TRACE), Mauna Loa Solar Observatory (MLSO), Big Bear Solar Observatory (BBSO), and Soft X-ray Telescope (SXT). The observational features associated with partially-erupting prominences were then compared with the predicted observables from the model.</p> <p><b>Results:</b> The partially-expelled-flux-rope (PEFR) model can explain the partial eruption of these prominences, and in addition predicts a variety of other CME-related observables that provide evidence of internal reconnection during eruption. We find that all of the partially-erupting prominences studied in this paper exhibit indirect evidence of internal reconnection. Moreover, all cases showed evidence of at least one observable unique to the PEFR model, e.g., dimmings external to the source region and/or a soft X-ray cusp overlying a reformed sigmoid.</p> <p><b>Conclusions:</b> The PEFR model provides a plausible mechanism to explain the observed evolution of partially-erupting-prominence-associated CMEs in our study.</p&gt

A case study of speculative financial bubbles in the South African stock market 2003-2006

We tested 45 indices and common stocks traded in the South African stock market for the possible existence of a bubble over the period from Jan. 2003 to May 2006. A bubble is defined by a faster-than-exponential acceleration with significant log-periodic oscillations. The faster-than-exponential acceleration characteristics are tested with several different metrics, including nonlinearity on the logarithm of the price and power law fits. The log-periodic properties are investigated in detail using the first-order log-periodic power-law (LPPL) formula, the parametric detrending method, the $(H,q)$-analysis, and the second-order Weierstrass-type model, resulting in a consistent and robust estimation of the fundamental angular log-frequency $\omega_1 =7\pm 2$, in reasonable agreement with previous estimations on many other bubbles in developed and developing markets. Sensitivity tests of the estimated critical times and of the angular log-frequency are performed by varying the first date and the last date of the stock price time series. These tests show that the estimated parameters are robust. With the insight of 6 additional month of data since the analysis was performed, we observe that many of the stocks on the South Africa market experienced an abrupt drop mid-June 2006, which is compatible with the predicted $t_c$ for several of the stocks, but not all. This suggests that the mini-crash that occurred around mid-June of 2006 was only a partial correction, which has resumed into a renewed bubbly acceleration bound to end some times in 2007, similarly to what happened on the S&P500 US market from Oct. 1997 to Aug. 1998.Comment: 20 Latex pages including 10 figures + an appendix (1 table, 10 figures

A Stable and Robust Calibration Scheme of the Log-Periodic Power Law Model

We present a simple transformation of the formulation of the log-periodic power law formula of the Johansen-Ledoit-Sornette model of financial bubbles that reduces it to a function of only three nonlinear parameters. The transformation significantly decreases the complexity of the fitting procedure and improves its stability tremendously because the modified cost function is now characterized by good smooth properties with in general a single minimum in the case where the model is appropriate to the empirical data. We complement the approach with an additional subordination procedure that slaves two of the nonlinear parameters to what can be considered to be the most crucial nonlinear parameter, the critical time $t_c$ defined as the end of the bubble and the most probably time for a crash to occur. This further decreases the complexity of the search and provides an intuitive representation of the results of the calibration. With our proposed methodology, metaheuristic searches are not longer necessary and one can resort solely to rigorous controlled local search algorithms, leading to dramatic increase in efficiency. Empirical tests on the Shanghai Composite index (SSE) from January 2007 to March 2008 illustrate our findings

Analysis and interpretation of a fast limb CME with eruptive prominence, C-flare and EUV dimming

Coronal Mass ejections or CMEs are large dynamical solar-corona events. The mass balance and kinematics of a fast limb CME, including its prominence progenitor and the associated flare, will be compared with computed magnetic structures to look for their origin and effect. Multi-wavelength ground-based and space-borne observations are used to study a fast W-limb CME event of December 2, 2003, taking into account both on and off disk observations. Its erupting prominence is measured at high cadence with the Pic du Midi full H-alpha line-flux imaging coronagraph. EUV images from space instruments are processed including difference imaging. SOHO/LASCO images are used to study the mass excess and motions. A fast bright expanding coronal loop is identified in the region recorded slightly later by GOES as a C7.2 flare, followed by a brightening and an acceleration phase of the erupting material with both cool and hot components. The total coronal radiative flux dropped by 5 percent in the EUV channels, revealing a large dimming effect at and above the limb. The typical 3-part structure observed 1 hour later shows a core shaped similarly to the eruptive filament/prominence. The total measured mass of the escaping CME (1.5x10to16 g from C2 LASCO observations) definitely exceeds the estimated mass of the escaping cool prominence material although assumptions made to analyse the Ha erupting prominence, as well as the corresponding EUV darkening of the filament observed several days before, made this evaluation uncertain by a factor of 2. From the current free extrapolation we discuss the shape of the magnetic neutral surface and a possible scenario leading to an instability, including the small scale dynamics inside and around the filament.Comment: 11 pages, 9 figure

Interplanetary flux rope ejected from an X-ray bright point: The smallest magnetic cloud source-region ever observed

Using multi-instrument and multi-wavelength observations (SOHO/MDI and EIT, TRACE and Yohkoh/SXT), as well as computing the coronal magnetic field of a tiny bipole combined with modelling of Wind in situ data, we provide evidences for the smallest event ever observed which links a sigmoid eruption to an interplanetary magnetic cloud (MC). The tiny bipole, which was observed very close to the solar disc centre, had a factor one hundred less flux than a classical active region (AR). In the corona it had a sigmoidal structure, observed mainly in EUV, and we found a very high level of non-potentiality in the modelled magnetic field, 10 times higher than we have ever found in any AR. From May 11, 1998, and until its disappearance, the sigmoid underwent three intense impulsive events. The largest of these events had extended EUV dimmings and a cusp. The Wind spacecraft detected 4.5 days later one of the smallest MC ever identified (about a factor one hundred times less magnetic flux in the axial component than that of an average MC). The link between this last eruption and the interplanetary magnetic cloud is supported by several pieces of evidence: good timing, same coronal loop and MC orientation, same magnetic field direction and magnetic helicity sign in the coronal loops and in the MC. We further quantify this link by estimating the magnetic flux (measured in the dimming regions and in the MC) and the magnetic helicity (pre- to post-event change in the solar corona and helicity content of the MC). Within the uncertainties, both magnetic fluxes and helicities are in reasonable agreement, which brings further evidences of their link. These observations show that the ejections of tiny magnetic flux ropes are indeed possible and put new constraints on CME models.Fil: Mandrini, Cristina Hemilse. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; ArgentinaFil: Pohjolainen, S.. University of Turku; TurquíaFil: Dasso, Sergio Ricardo. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; ArgentinaFil: Green, L. M.. Cardiff University; Reino UnidoFil: Démoulin, Pascal. Centre National de la Recherche Scientifique. Observatoire de Paris; FranciaFil: van Driel Gesztelyi, Lidia. Centre National de la Recherche Scientifique. Observatoire de Paris; FranciaFil: Copperwheat, C.. Mullard Space Science Laboratory; Reino UnidoFil: Foley, C.. Mullard Space Science Laboratory; Reino Unid

Magnetic clouds in the solar wind: A numerical assessment study of analytical models

Magnetic clouds (MCs) are "magnetized plasma clouds" moving in the solar wind. MCs transport magnetic flux and helicity away from the Sun. These structures are not stationary but feature temporal evolution as they propagate in the solar wind. Simplified analytical models are frequently used for the description of MCs, and fit certain observational data well. The goal of the present study is to investigate numerically the validity of an analytical model which is widely used for the description of MCs, and to determine under which conditions this model's implied assumptions cease to be valid. A numerical approach is applied. Analytical solutions that have been derived in previous studies are implemented in a \textbf{3-D magnetohydrodynamic} simulation code as initial conditions. Initially, the analytical model represents the main observational features of the MCs. However, these characteristics prevail only if the structure moves with a velocity close to the velocity of the background flow. In this case an MC's evolution can quite accurately be described using an analytic, self-similar approach. The dynamics of the magnetic structures which move with a velocity significantly above or below that of the velocity of the solar wind is investigated in detail. Besides the standard case in which MCs only expand and propagate in the solar wind, the case of an MC rotating around its axis of symmetry is also considered, and the resulting influence on the MC's dynamics is studied