885 research outputs found

    F. John's stability conditions vs. A. Carasso's SECB constraint for backward parabolic problems

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    In order to solve backward parabolic problems F. John [{\it Comm. Pure. Appl. Math.} (1960)] introduced the two constraints "∄u(T)∄≀M\|u(T)\|\le M" and ∄u(0)−g∄≀Ύ\|u(0) - g \| \le \delta where u(t)u(t) satisfies the backward heat equation for t∈(0,T)t\in(0,T) with the initial data u(0).u(0). The {\it slow-evolution-from-the-continuation-boundary} (SECB) constraint has been introduced by A. Carasso in [{\it SIAM J. Numer. Anal.} (1994)] to attain continuous dependence on data for backward parabolic problems even at the continuation boundary t=Tt=T. The additional "SECB constraint" guarantees a significant improvement in stability up to t=T.t=T. In this paper we prove that the same type of stability can be obtained by using only two constraints among the three. More precisely, we show that the a priori boundedness condition ∄u(T)∄≀M\|u(T)\|\le M is redundant. This implies that the Carasso's SECB condition can be used to replace the a priori boundedness condition of F. John with an improved stability estimate. Also a new class of regularized solutions is introduced for backward parabolic problems with an SECB constraint. The new regularized solutions are optimally stable and we also provide a constructive scheme to compute. Finally numerical examples are provided.Comment: 15 pages. To appear in Inverse Problem

    Vertical flow in the Southern Ocean estimated from individual moorings

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    In this study, we demonstrate that oceanic vertical velocities can be estimated from individual mooring measurements, even for non-stationary flow. This result is obtained under three assumptions: i. weak diffusion (PĂ©clet number ≫1), ii. weak friction (Reynolds number ≫1), and iii. small inertial terms (Rossby number â‰Ș1). The theoretical framework is applied to a set of 4 moorings located in the Southern Ocean. For this site, the diagnosed vertical velocities are highly variable in time, their standard deviation being one-to-two orders of magnitude greater than their mean. We demonstrate that the time-averaged vertical velocities are largely induced by geostrophic flow, and can be estimated from the time-averaged density and horizontal velocities. This suggests that local time-mean vertical velocities are primarily forced by the time-mean ocean dynamics, rather than by e.g. transient eddies or internal waves. We also show that, in the context of these four moorings, the time-mean vertical flow is consistent with stratified Taylor column dynamics in the presence of a topographic obstacle

    Discussion of Recent Decisions

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    Evolution of the AO Spine Sacral and Pelvic Classification System: a systematic review.

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    OBJECTIVE The purpose of this study was to describe the genesis of the AO Spine Sacral and Pelvic Classification System in the context of historical sacral and pelvic grading systems. METHODS A systematic search of MEDLINE, EMBASE, Google Scholar, and Cochrane databases was performed consistent with the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines to identify all existing sacral and pelvic fracture classification systems. RESULTS A total of 49 articles were included in this review, comprising 23 pelvic classification systems and 17 sacral grading schemes. The AO Spine Sacral and Pelvic Classification System represents both the evolutionary product of these historical systems and a reinvention of classic concepts in 5 ways. First, the classification introduces fracture types in a graduated order of biomechanical stability while also taking into consideration the neurological status of patients. Second, the traditional belief that Denis central zone III fractures have the highest rate of neurological deficit is not supported because this subgroup often includes a broad spectrum of injuries ranging from a benign sagittally oriented undisplaced fracture to an unstable "U-type" fracture. Third, the 1990 Isler lumbosacral system is adopted in its original format to divide injuries based on their likelihood of affecting posterior pelvic or spinopelvic stability. Fourth, new discrete fracture subtypes are introduced and the importance of bilateral injuries is acknowledged. Last, this is the first integrated sacral and pelvic classification to date. CONCLUSIONS The AO Spine Sacral and Pelvic Classification is a universally applicable system that redefines and reorders historical fracture morphologies into a rational hierarchy. This is the first classification to simultaneously address the biomechanical stability of the posterior pelvic complex and spinopelvic stability, while also taking into consideration neurological status. Further high-quality controlled trials are required prior to the inclusion of this novel classification within a validated scoring system to guide the management of sacral and pelvic injuries

    Movement disorder and neuronal migration disorder due to ARFGEF2 mutation

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    We report a child with a severe choreadystonic movement disorder, bilateral periventricular nodular heterotopia (BPNH), and secondary microcephaly based on compound heterozygosity for two new ARFGEF2 mutations (c.2031_2038dup and c.3798_3802del), changing the limited knowledge about the phenotype. The brain MRI shows bilateral hyperintensity of the putamen, BPNH, and generalized atrophy. Loss of ARFGEF2 function affects vesicle trafficking, proliferation/apoptosis, and neurotransmitter receptor function. This can explain BPNH and microcephaly. We hypothesize that the movement disorder and the preferential damage to the basal ganglia, specifically to the putamen, may be caused by an increased sensitivity to degeneration, a dynamic dysfunction due to neurotransmitter receptor mislocalization or a combination of both

    Particles at oil–air surfaces : powdered oil, liquid oil marbles, and oil foam

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    The type of material stabilized by four kinds of fluorinated particles (sericite and bentonite platelet clays and spherical zinc oxide) in air–oil mixtures has been investigated. It depends on the particle wettability and the degree of shear. Upon vigorous agitation, oil dispersions are formed in all the oils containing relatively large bentonite particles and in oils of relatively low surface tension (Îłla < 26 mN m⁻Âč) like dodecane, 20 cS silicone, and cyclomethicone containing the other fluorinated particles. Particle-stabilized oil foams were obtained in oils having Îłla > 26 mN m⁻Âč where the advancing air–oil–solid contact angle Ξ lies between ca. 90° and 120°. Gentle shaking, however, gives oil-in-air liquid marbles with all the oil–particle systems except for cases where Ξ is <60°. For oils of tension >24 mN m⁻Âč with omniphobic zinc oxide and sericite particles for which advancing Ξ ≄ 90°, dry oil powders consisting of oil drops in air which do not leak oil could be made upon gentle agitation up to a critical oil:particle ratio (COPR). Above the COPR, catastrophic phase inversion of the dry oil powders to air-in-oil foams was observed. When sheared on a substrate, the dry oil powders containing at least 60 wt % of oil release the encapsulated oil, making these materials attractive formulations in the cosmetic and food industries

    The Look-back Time Evolution of Far-Ultraviolet Flux from the Brightest Cluster Elliptical Galaxies at z < 0.2

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    We present the GALEX UV photometry of the elliptical galaxies in Abell clusters at moderate redshifts (z < 0.2) for the study of the look-back time evolution of the UV upturn phenomenon. The brightest elliptical galaxies (M_r < -22) in 12 remote clusters are compared with the nearby giant elliptical galaxies of comparable optical luminosity in the Fornax and Virgo clusters. The sample galaxies presented here appear to be quiescent without signs of massive star formation or strong nuclear activity, and show smooth, extended profiles in their UV images indicating that the far-UV (FUV) light is mostly produced by hot stars in the underlying old stellar population. Compared to their counterparts in nearby clusters, the FUV flux of cluster giant elliptical galaxies at moderate redshifts fades rapidly with ~ 2 Gyrs of look-back time, and the observed pace in FUV - V color evolution agrees reasonably well with the prediction from the population synthesis models where the dominant FUV source is hot horizontal-branch stars and their progeny. A similar amount of color spread (~ 1 mag) in FUV - V exists among the brightest cluster elliptical galaxies at z ~ 0.1, as observed among the nearby giant elliptical galaxies of comparable optical luminosity.Comment: Accepted for publication in the Special GALEX ApJ Supplement, December 200
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