A proof of the Grothendieck-Serre conjecture on principal bundles over regular local rings containing infinite fields

Let R be a regular local ring, containing an infinite field. Let G be a reductive group scheme over R. We prove that a principal G-bundle over R is trivial, if it is trivial over the fraction field of R.Comment: Section "Formal loops and affine Grassmannians" is removed as this is now covered in arXiv:1308.3078. Exposition is improved and slightly restructured. Some minor correction

A new classification system for degenerative spondylolisthesis of the lumbar spine

This is the author accepted manuscript. The final version is available from Springer Verlag via the DOI in this record.PURPOSE: There is no consensus for a comprehensive analysis of degenerative spondylolisthesis of the lumbar spine (DSLS). A new classification system for DSLS based on sagittal alignment was proposed. Its clinical relevance was explored. METHODS: Health-related quality-of-life scales (HRQOLs) and clinical parameters were collected: SF-12, ODI, and low back and leg pain visual analog scales (BP-VAS, LP-VAS). Radiographic analysis included Meyerding grading and sagittal parameters: segmental lordosis (SL), L1-S1 lumbar lordosis (LL), T1-T12 thoracic kyphosis (TK), pelvic incidence (PI), pelvic tilt (PT), and sagittal vertical axis (SVA). Patients were classified according to three main types-1A: preserved LL and SL; 1B: preserved LL and reduced SL (≤5°); 2A: PI-LL ≥10° without pelvic compensation (PT < 25°); 2B: PI-LL ≥10° with pelvic compensation (PT ≥ 25°); type 3: global sagittal malalignment (SVA ≥40 mm). RESULTS: 166 patients (119 F: 47 M) suffering from DSLS were included. Mean age was 67.1 ± 11 years. DSLS demographics were, respectively: type 1A: 73 patients, type 1B: 3, type 2A: 8, type 2B: 22, and type 3: 60. Meyerding grading was: grade 1 (n = 124); grade 2 (n = 24). Affected levels were: L4-L5 (n = 121), L3-L4 (n = 34), L2-L3 (n = 6), and L5-S1 (n = 5). Mean sagittal parameter values were: PI: 59.3° ± 11.9°; PT: 24.3° ± 7.6°; SVA: 29.1 ± 42.2 mm; SL: 18.2° ± 8.1°. DSLS types were correlated with age, ODI and SF-12 PCS (ρ = 0.34, p < 0.05; ρ = 0.33, p < 0.05; ρ = -0.20, and p = 0.01, respectively). CONCLUSION: This classification was consistent with age and HRQOLs and could be a preoperative assessment tool. Its therapeutic impact has yet to be validated. LEVEL OF EVIDENCE: 4.No funds were received in support of this work. No benefits in any forms have been or will be received from a commercial party related directly or indirectly to the subject of this manuscript

Cyclotron resonance of the quasi-two-dimensional electron gas at Hg1-xCdxTe grain boundaries

The magnetotransmission of a p-type Hg0.766Cd0.234Te bicrystal containing a single grain boundary with an inversion layer has been investigated in the submillimetre wavelength range. For the first time the cyclotron resonance lines belonging to the various electric subbands of a quasi-two-dimensional carrier system at a grain boundary could be detected. The measured cyclotron masses and the subband densities determined from Shubnikov-de Haas experiments are compared with theoretical predictions and it is found that the data can be explained very well within the framework of a triangular well approximation model which allows for non-parabolic effects

The SPARC water vapour assessment II: comparison of stratospheric and lower mesospheric water vapour time series observed from satellites

Time series of stratospheric and lower mesospheric water vapour using 33 data sets from 15 different satellite instruments were compared in the framework of the second SPARC (Stratosphere-troposphere Processes And their Role in Climate) water vapour assessment (WAVAS-II). This comparison aimed to provide a comprehensive overview of the typical uncertainties in the observational database that can be considered in the future in observational and modelling studies, e.g addressing stratospheric water vapour trends. The time series comparisons are presented for the three latitude bands, the Antarctic (80°–70°S), the tropics (15°S–15°N) and the Northern Hemisphere mid-latitudes (50°–60°N) at four different altitudes (0.1, 3, 10 and 80hPa) covering the stratosphere and lower mesosphere. The combined temporal coverage of observations from the 15 satellite instruments allowed the consideration of the time period 1986–2014. In addition to the qualitative comparison of the time series, the agreement of the data sets is assessed quantitatively in the form of the spread (i.e. the difference between the maximum and minimum volume mixing ratios among the data sets), the (Pearson) correlation coefficient and the drift (i.e. linear changes of the difference between time series over time). Generally, good agreement between the time series was found in the middle stratosphere while larger differences were found in the lower mesosphere and near the tropopause. Concerning the latitude bands, the largest differences were found in the Antarctic while the best agreement was found for the tropics. From our assessment we find that most data sets can be considered in future observational and modelling studies, e.g. addressing stratospheric and lower mesospheric water vapour variability and trends, if data set specific characteristics (e.g. drift) and restrictions (e.g. temporal and spatial coverage) are taken into account

Sur la p-dimension des corps

Let A be an excellent integral henselian local noetherian ring, k its residue field of characteristic p>0 and K its fraction field. Using an algebraization technique introduced by the first named author, and the one-dimension case already proved by Kazuya KATO, we prove the following formula: cd_p(K) = dim(A) + p-rank(k), if k is separably closed and K of characteristic zero. A similar statement is valid without those assumptions on k and K

Open Problems on Central Simple Algebras

We provide a survey of past research and a list of open problems regarding central simple algebras and the Brauer group over a field, intended both for experts and for beginners.Comment: v2 has some small revisions to the text. Some items are re-numbered, compared to v

The management and survival outcomes of nasopharyngeal cancer in the Nordic countries

Peer reviewe

Lack of genotype-phenotype correlation in basal cell nevus syndrome:A Dutch multicenter retrospective cohort study

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