Cohomologie de fibrés en droite sur le fibré cotangent de variétés grassmanniennes généralisées

Cette thèse s'intéresse à la cohomologie de fibrés en droite sur le fibré cotangent de variétés projectives. Plus précisément, pour $G$ un groupe algébrique simple, connexe et simplement connexe, $P$ un sous-groupe maximal de $G$ et $\omega$ un générateur dominant du groupe de caractères de $P$, on cherche à comprendre les groupes de cohomologie $H^i(T^*(G/P),\mathcal{L})$ où $\mathcal{L}$ est le faisceau des sections d'un fibré en droite sur $T^*(G/P)$. Sous certaines conditions, nous allons montrer qu'il existe un isomorphisme, à graduation près, entre $H^i(T^*(G/P),\mathcal{L})$ et $H^i(T^*(G/P),\mathcal{L}^{\vee})$ Après avoir travaillé dans un contexte théorique, nous nous intéresserons à certains sous-groupes paraboliques en lien avec les orbites nilpotentes. Dans ce cas, l'algèbre de Lie du radical unipotent de $P$, que nous noterons $\nLie$, a une structure d'espace vectoriel préhomogène. Nous pourrons alors déterminer quels cas vérifient les hypothèses nécessaires à la preuve de l'isomorphisme en montrant l'existence d'un $P$-covariant $f$ dans $\comp[\nLie]$ et en étudiant ses propriétés. Nous nous intéresserons ensuite aux singularités de la variété affine $V(f)$. Nous serons en mesure de montrer que sa normalisation est à singularités rationnelles.

On Parabolic Subgroups and Hecke Algebras of some Fractal Groups

* The authors thank the “Swiss National Science Foundation” for its support.

Variétés de drapeaux et opérateurs différentiels

Soit G un groupe algébrique semi-simple sur un corps de caractéristique 0. Ce mémoire discute d'un théorème d'annulation de la cohomologie supérieure du faisceau D des opérateurs différentiels sur une variété de drapeaux de G. On démontre que si P est un sous-groupe parabolique de G, alors H^i(G/P,D)=0 pour tout i>0. On donne en fait trois preuves indépendantes de ce théorème. La première preuve est de Hesselink et n'est valide que dans le cas où le sous-groupe parabolique est un sous-groupe de Borel. Elle utilise un argument de suites spectrales et le théorème de Borel-Weil-Bott. La seconde preuve est de Kempf et n'est valide que dans le cas où le radical unipotent de P agit trivialement sur son algèbre de Lie. Elle n'utilise que le théorème de Borel-Weil-Bott. Enfin, la troisième preuve est attribuée à Elkik. Elle est valide pour tout sous-groupe parabolique mais utilise le théorème de Grauert-Riemenschneider. On présente aussi une construction détaillée du faisceau des opérateurs différentiels sur une variété.

An Oka principle for equivariant isomorphisms

Let G be a reductive complex Lie group acting holomorphically on normal Stein spaces X and Y, which are locally G-biholomorphic over a common categorical quotient Q. When is there a global G-biholomorphism X → Y? If the actions of G on X and Y are what we, with justification, call generic, we prove that the obstruction to solving this local-to-global problem is topological and provide sufficient conditions for it to vanish. Our main tool is the equivariant version of Grauert's Oka principle due to Heinzner and Kutzschebauch. We prove that X and Y are G-biholomorphic if X is K-contractible, where K is a maximal compact subgroup of G, or if X and Y are smooth and there is a G-diffeomorphism ψ : X → Y over Q, which is holomorphic when restricted to each fibre of the quotient map X → Q. We prove a similar theorem when ψ is only a G-homeomorphism, but with an assumption about its action on G-finite functions. When G is abelian, we obtain stronger theorems. Our results can be interpreted as instances of the Oka principle for sections of the sheaf of G-biholomorphisms from X to Y over Q. This sheaf can be badly singular, even for a low-dimensional representation of SL2(ℂ). Our work is in part motivated by the linearisation problem for actions on ℂn. It follows from one of our main results that a holomorphic G-action on ℂn, which is locally G-biholomorphic over a common quotient to a generic linear action, is linearisable.

Motivic Decomposition of Projective Pseudo-Homogeneous Varieties

Let G be a semi-simple algebraic group over a field k. Projective G-homogeneous varieties are projective varieties over which G acts transitively. The stabilizer or the isotropy subgroup at a point on such a variety is a parabolic subgroup which is always smooth when the characteristic of k is zero. However, when k has positive characteristic, we encounter projective varieties with transitive G-action where the isotropy subgroup need not be smooth. We call these varieties projective pseudo-homogeneous varieties. To every such variety, we can associate a corresponding projective homogeneous variety. In this thesis, we extensively study the Chow motives (with coefficients from a finite connected ring) of projective pseudo-homogeneous varieties for G inner type over k and compare them to the Chow motives of the corresponding projective homogeneous varieties. This is done by proving a generic criterion for the motive of a variety to be isomorphic to the motive of a projective homogeneous variety which works for any characteristic of k. As a corollary, we give some applications and examples of Chow motives that exhibit an interesting phenomenon. We also show that the motives of projective pseudo-homogeneous varieties satisfy properties such as Rost Nilpotence and Krull-Schmidt.

Should Koos grade I vestibular schwannomas be treated early with gamma knife surgery? A subgroup analysis in a series of 190 consecutive patients.

INTRODUCTION: Gamma knife surgery (GKS) for vestibular schwannomas (VS) has a long-term clinical and scientific track record. After a period of de-escalation of dose prescription, results show a high rate of tumor control with improvement of clinical outcome (less than 1% facial palsy, 50-70% hearing preservation). Régis et al. (J Neurosurg 2013;119 Suppl.:105-11) suggested recently that proactive GKS management in intracanalicular tumors is better than a « wait and see » strategy when hearing is still useful at the time of diagnosis. MATERIALS AND METHODS: Based on these previous findings, we prospectively analyzed 190 vestibular schwannomas (VS), treated with GKS as first intention over a period of 4 years (2010-2014). We concentrated on patient, tumor and dosimetric characteristics. Special attention was given on the dose to the cochlea and its impact in maintaining serviceable hearing. RESULTS: The mean follow-up period was 1.3years (range 0.6-3.6). Preoperative serviceable hearing was present in 63.11% patients. The mean maximal diameter was 15.1mm (range 5-29.5). The size and volume of the tumor corresponded to Koos grade I, II, III and IV in 15.9%, 34.8%, 45.4% and 3.8% of the cases, respectively. The mean target volume was 1.24cm(3) (0.017-7.8). The mean prescription isodose volume was 1.6 cc (0.032-8.5). The mean marginal dose was 12Gy (11-12). The mean maximal dose received by the cochlea in patients with GR class 1 and 2 was 4.1Gy (1.5-7.6). Our preliminary neuroradiological follow-up shows 97% tumor control, with 45% shrinkage. Patients presenting with GR class 1 and class 2 at baseline retained serviceable hearing in 85% of cases. Among the patients with a follow-up of at least one year, those with Koos I tumors had the highest probability to maintain identical level of hearing after GKS. CONCLUSION: Our preliminary data suggest that Koos I patients should be treated early with GKS, before tumor growth and/or hearing deterioration, as they have the highest probability of hearing preservation.

Hemodynamic mechanisms of the attenuated blood pressure response to mental stress after a single bout of maximal dynamic exercise in healthy subjects

To determine the hemodynamic mechanisms responsible for the attenuated blood pressure response to mental stress after exercise, 26 healthy sedentary individuals (age 29 ± 8 years) underwent the Stroop color-word test before and 60 min after a bout of maximal dynamic exercise on a treadmill. A subgroup (N = 11) underwent a time-control experiment without exercise. Blood pressure was continuously and noninvasively recorded by infrared finger photoplethysmography. Stroke volume was derived from pressure signals, and cardiac output and peripheral vascular resistance were calculated. Perceived mental stress scores were comparable between mental stress tests both in the exercise (P = 0.96) and control (P = 0.24) experiments. After exercise, the blood pressure response to mental stress was attenuated (pre: 10 ± 13 vs post: 6 ± 7 mmHg; P < 0.01) along with lower values of systolic blood pressure (pre: 129 ± 3 vs post: 125 ± 3 mmHg; P < 0.05), stroke volume (pre: 89.4 ± 3.5 vs post: 76.8 ± 3.8 mL; P < 0.05), and cardiac output (pre: 7.00 ± 0.30 vs post: 6.51 ± 0.36 L/min; P < 0.05). Except for heart rate, the hemodynamic responses and the mean values during the two mental stress tests in the control experiment were similar (P > 0.05). In conclusion, a single bout of maximal dynamic exercise attenuates the blood pressure response to mental stress in healthy subjects, along with lower stroke volume and cardiac output, denoting an acute modulatory action of exercise on the central hemodynamic response to mental stress.

A family of stadium-like billiards with parabolic boundaries under scaling analysis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Maximal Subgroups of Compact Lie Groups

This report aims at giving a general overview on the classification of the maximal subgroups of compact Lie groups (not necessarily connected). In the first part, it is shown that these fall naturally into three types: (1) those of trivial type, which are simply defined as inverse images of maximal subgroups of the corresponding component group under the canonical projection and whose classification constitutes a problem in finite group theory, (2) those of normal type, whose connected one-component is a normal subgroup, and (3) those of normalizer type, which are the normalizers of their own connected one-component. It is also shown how to reduce the classification of maximal subgroups of the last two types to: (2) the classification of the finite maximal Sigma-invariant subgroups of centerfree connected compact simple Lie groups and (3) the classification of the Sigma-primitive subalgebras of compact simple Lie algebras, where Sigma is a subgroup of the corresponding outer automorphism group. In the second part, we explicitly compute the normalizers of the primitive subalgebras of the compact classical Lie algebras (in the corresponding classical groups), thus arriving at the complete classification of all (non-discrete) maximal subgroups of the compact classical Lie groups.

The effect of acute magnesium loading on the maximal exercise performance of stable chronic obstructive pulmonary disease patients

OBJECTIVE: The potential influence of magnesium on exercise performance is a subject of increasing interest. Magnesium has been shown to have bronchodilatatory properties in asthma and chronic obstructive pulmonary disease patients. The aim of this study was to investigate the effects of acute magnesium IV loading on the aerobic exercise performance of stable chronic obstructive pulmonary disease patients. METHODS: Twenty male chronic obstructive pulmonary disease patients (66.2 +/- 8.3 years old, FEV1: 49.3 +/- 19.8%) received an IV infusion of 2 g of either magnesium sulfate or saline on two randomly assigned occasions approximately two days apart. Spirometry was performed both before and 45 minutes after the infusions. A symptom-limited incremental maximal cardiopulmonary test was performed on a cycle ergometer at approximately 100 minutes after the end of the infusion. ClinicalTrials.gov: NCT00500864 RESULTS: Magnesium infusion was associated with significant reductions in the functional residual capacity (-0.41 l) and residual volume (-0.47 l), the mean arterial blood pressure (-5.6 mmHg) and the cardiac double product (734.8 mmHg.bpm) at rest. Magnesium treatment led to significant increases in the maximal load reached (+8 w) and the respiratory exchange ratio (0.06) at peak exercise. The subgroup of patients who showed increases in the work load equal to or greater than 5 w also exhibited significantly greater improvements in inspiratory capacity (0.29 l). CONCLUSIONS: The acute IV loading of magnesium promotes a reduction in static lung hyperinflation and improves the exercise performance in stable chronic obstructive pulmonary disease patients. Improvements in respiratory mechanics appear to be responsible for the latter finding.

Absolutely Continuous Spectrum for Parabolic Flows/Maps

This work is devoted to creating an abstract framework for the study of certain spectral properties of parabolic systems. Specifically, we determine under which general conditions to expect the presence of absolutely continuous spectral measures. We use these general conditions to derive results for spectral properties of time-changes of unipotent flows on homogeneous spaces of semisimple groups regarding absolutely continuous spectrum as well as maximal spectral type; the time-changes of the horocycle flow are special cases of this general category of flows. In addition we use the general conditions to derive spectral results for twisted horocycle flows and to rederive spectral results for skew products over translations and Furstenberg transformations.

Undulatory Physical Resistance Training Program Increases Maximal Strength In Elderly Type 2 Diabetics.

To investigate the effects of a specific protocol of undulatory physical resistance training on maximal strength gains in elderly type 2 diabetics. The study included 48 subjects, aged between 60 and 85 years, of both genders. They were divided into two groups: Untrained Diabetic Elderly (n=19) with those who were not subjected to physical training and Trained Diabetic Elderly (n=29), with those who were subjected to undulatory physical resistance training. The participants were evaluated with several types of resistance training's equipment before and after training protocol, by test of one maximal repetition. The subjects were trained on undulatory resistance three times per week for a period of 16 weeks. The overload used in undulatory resistance training was equivalent to 50% of one maximal repetition and 70% of one maximal repetition, alternating weekly. Statistical analysis revealed significant differences (p<0.05) between pre-test and post-test over a period of 16 weeks. The average gains in strength were 43.20% (knee extension), 65.00% (knee flexion), 27.80% (supine sitting machine), 31.00% (rowing sitting), 43.90% (biceps pulley), and 21.10% (triceps pulley). Undulatory resistance training used with weekly different overloads was effective to provide significant gains in maximum strength in elderly type 2 diabetic individuals.

Relationship Between Aerobic And Anaerobic Parameters From 3-minute All-out Tethered Swimming And 400-m Maximal Front Crawl Effort.

The main aim of this investigation was to verify the relationship of the variables measured during a 3-minute all-out test with aerobic (i.e., peak oxygen uptake [(Equation is included in full-text article.)] and intensity corresponding to the lactate minimum [LMI]) and anaerobic parameters (i.e., anaerobic work) measured during a 400-m maximal performance. To measure force continually and to avoid the possible influences caused by turns, the 3-minute all-out effort was performed in tethered swimming. Thirty swimmers performed the following tests: (a) a 3-minute all-out tethered swimming test to determine the final force (equivalent to critical force: CF3-MIN) and the work performed above CF3-MIN (W'3-MIN), (b) a LMI protocol to determine the LMI during front crawl swimming, and (c) a 400-m maximal test to determine the (Equation is included in full-text article.)and total anaerobic contribution (WANA). Correlations between the variables were tested using the Pearson's correlation test (p ≤ 0.05). CF3-MIN (73.9 ± 13.2 N) presented a high correlation with the LMI (1.33 ± 0.08 m·s; p = 0.01) and (Equation is included in full-text article.)(4.5 ± 1.2 L·min; p = 0.01). However, the W'3-MIN (1,943.2 ± 719.2 N·s) was only moderately correlated with LMI (p = 0.02) and (Equation is included in full-text article.)(p = 0.01). In summary, CF3-MIN determined during the 3-minute all-out effort is associated with oxidative metabolism and can be used to estimate the aerobic capacity of swimmers. In contrast, the anaerobic component of this model (W'3-MIN) is not correlated with WANA.

The Geometric Curvature Of The Spine Of Runners During Maximal Incremental Effort Test.

This study sought to analyse the behaviour of the average spinal posture using a novel investigative procedure in a maximal incremental effort test performed on a treadmill. Spine motion was collected via stereo-photogrammetric analysis in thirteen amateur athletes. At each time percentage of the gait cycle, the reconstructed spine points were projected onto the sagittal and frontal planes of the trunk. On each plane, a polynomial was fitted to the data, and the two-dimensional geometric curvature along the longitudinal axis of the trunk was calculated to quantify the geometric shape of the spine. The average posture presented at the gait cycle defined the spine Neutral Curve. This method enabled the lateral deviations, lordosis, and kyphosis of the spine to be quantified noninvasively and in detail. The similarity between each two volunteers was a maximum of 19% on the sagittal plane and 13% on the frontal (p<0.01). The data collected in this study can be considered preliminary evidence that there are subject-specific characteristics in spinal curvatures during running. Changes induced by increases in speed were not sufficient for the Neutral Curve to lose its individual characteristics, instead behaving like a postural signature. The data showed the descriptive capability of a new method to analyse spinal postures during locomotion; however, additional studies, and with larger sample sizes, are necessary for extracting more general information from this novel methodology.

Teste de banco : adequação da altura do ergometro a estatura, para individuos a partir de 09 anos de idade, de ambosos sexos, praticantes e não praticantes de atividade fisica

Universidade Estadual de Campinas. Faculdade de Educação Física