Comparing the Morse index and the first Betti number of minimal hypersurfaces

By extending and generalizing previous work by Ros and Savo, we describe a method to show that in certain positively curved ambient manifolds the Morse index of every closed minimal hypersurface is bounded from below by a linear function of its first Betti number. The technique is flexible enough to prove that such a relation between the index and the topology of minimal hypersurfaces holds, for example, on all compact rank one symmetric spaces, on products of the circle with spheres of arbitrary dimension and on suitably pinched submanifolds of the Euclidean spaces. These results confirm a general conjecture due to Schoen and Marques–Neves for a wide class of ambient spaces

Index estimates for free boundary minimal hypersurfaces

We show that the Morse index of a properly embedded free boundary minimal hypersurface in a strictly mean convex domain of the Euclidean space grows linearly with the dimension of its first relative homology group (which is at least as big as the number of its boundary components, minus one). In ambient dimension three, this implies a lower bound for the index of a free boundary minimal surface which is linear both with respect to the genus and the number of boundary components. Thereby, the compactness theorem by Fraser and Li implies a strong compactness theorem for the space of free boundary minimal surfaces with uniformly bounded Morse index inside a convex domain. Our estimates also imply that the examples constructed, in the unit ball, by Fraser–Schoen and Folha–Pacard–Zolotareva have arbitrarily large index. Extensions of our results to more general settings (including various classes of positively curved Riemannian manifolds and other convexity assumptions) are discussed

Effect of Systemic Hypertension With Versus Without Left Ventricular Hypertrophy on the Progression of Atrial Fibrillation (from the Euro Heart Survey).

Hypertension is a risk factor for both progression of atrial fibrillation (AF) and development of AF-related complications, that is major adverse cardiac and cerebrovascular events (MACCE). It is unknown whether left ventricular hypertrophy (LVH) as a consequence of hypertension is also a risk factor for both these end points. We aimed to assess this in low-risk AF patients, also assessing gender-related differences. We included 799 patients from the Euro Heart Survey with nonvalvular AF and a baseline echocardiogram. Patients with and without hypertension were included. End points after 1 year were occurrence of AF progression, that is paroxysmal AF becoming persistent and/or permanent AF, and MACCE. Echocardiographic LVH was present in 33% of 379 hypertensive patients. AF progression after 1 year occurred in 10.2% of 373 patients with rhythm follow-up. In hypertensive patients with LVH, AF progression occurred more frequently as compared with hypertensive patients without LVH (23.3% vs 8.8%, p = 0.011). In hypertensive AF patients, LVH was the most important multivariably adjusted determinant of AF progression on multivariable logistic regression (odds ratio 4.84, 95% confidence interval 1.70 to 13.78, p = 0.003). This effect was only seen in male patients (27.5% vs 5.8%, p = 0.002), while in female hypertensive patients, no differences were found in AF progression rates regarding the presence or absence of LVH (15.2% vs 15.0%, p = 0.999). No differences were seen in MACCE for hypertensive patients with and without LVH. In conclusion, in men with hypertension, LVH is associated with AF progression. This association seems to be absent in hypertensive women

Progression From Paroxysmal to Persistent Atrial Fibrillation. Clinical Correlates and Prognosis

Objectives: We investigated clinical correlates of atrial fibrillation (AF) progression and evaluated the prognosis of patients demonstrating AF progression in a large population. Background: Progression of paroxysmal AF to more sustained forms is frequently seen. However, not all patients will progress to persistent AF. Methods: We included 1,219 patients with paroxysmal AF who participated in the Euro Heart Survey on AF and had a known rhythm status at follow-up. Patients who experienced AF progression after 1 year of follow-up were identified. Results: Progression of AF occurred in 178 (15%) patients. Multivariate analysis showed that heart failure, age, previous transient ischemic attack or stroke, chronic obstructive pulmonary disease, and hypertension were the only independent predictors of AF progression. Using the regression coefficient as a benchmark, we calculated the HATCH score. Nearly 50% of the patients with a HATCH score >5 progressed to persistent AF compared with only 6% of the patients with a HATCH score of 0. During follow-up, patients with AF progression were more often admitted to the hospital and had more major adverse cardiovascular events. Conclusions: A substantial number of patients progress to sustained AF within 1 year. The clinical outcome of these patients regarding hospital admissions and major adverse cardiovascular events was worse compared with patients demonstrating no AF progression. Factors known to cause atrial structural remodeling (age and underlying heart disease) were independent predictors of AF progression. The HATCH score may help to identify patients who are likely to progress to sustained forms of AF in the near future. \ua9 2010 American College of Cardiology Foundation

Black hole topology in f(R) gravity

Hawking's topology theorem in general relativity restricts the cross-section of the event horizon of a black hole in 3+1 dimension to be either spherical or toroidal. The toroidal case is ruled out by the topology censorship theorems. In this article, we discuss the generalization of this result to black holes in f(R) gravity in 3+1 and higher dimensions. We obtain a sufficient differential condition on the function f'(R), which restricts the topology of the horizon cross-section of a black hole in f(R) gravity in 3+1 dimension to be either S^2 or S^1× S^1. We also extend the result to higher dimensional black holes and show that the same sufficient condition also restricts the sign of the Yamabe invariant of the horizon cross-section.by Akash K Mishra, Mostafizur Rahman and Sudipta Sarka

Transverse rupture strength of a PM tool steel

Powder Metallurgy has been reported as a suitable alternate processing route for the manufacture of tool steels. The advantage of this technique is in being able to obtain a refined and more uniform microstructure that improves properties such high wear resistance and toughness. A molybdenum containing AISI M3:2 tool steel, (trade name Sinter 23), manufactured from spherical gas-atomized powders by hot isostatic pressing followed by hot working was tested in three-point bending tests after various heat treatments. Transverse rupture strength (TRS) samples were cut and heat treated at four distinct austenitizing temperatures. Each austenitizing temperature was combined with three tempering temperatures, giving a total of twelve different hardening conditions. Hardness tests were carried out to establish correlations among the effectiveness of heat treatment, the hardness values and the TRS results. At least five parallel samples were tested in each heat treatment condition

17 beta-Estradiol and steady-state concentrations of H2O2: antiapoptotic effect in endometrial cells from patients with endometriosis

Increased levels of hydrogen peroxide (H2O2) can initiate protective responses to limit or repair oxidative damage. However, H2O2 signals also fine-tune responses to growth factors and cytokines controlling cell division, differentiation, and proliferation. Because 17 beta-estradiol (E-2) also plays important roles in these processes, and is considered a major risk factor in the development and progression of endometriosis, this study evaluated whether E-2 has an antiapoptotic effect on oxidative stress in endometrial cells in combination with steady-state H2O2 levels ([H2O2]ss). Endometrial stromal cells were prepared from the eutopic endometrium of 18 women with and without endometriosis to produce primary cells. These cells were stimulated with E-2 for 20 h, exposed to [H2O2]ss, and examined for cell viability, proliferation, and apoptosis. the endometrial cells from women with endometriosis maintained the steady state for 120 min at high H2O2 concentrations. When they were pretreated with E-2 and exposed to [H2O2]ss, a decrease in apoptosis level was observed compared to the control cells (p < 0.01). the endometrial cells from patients with endometriosis subjected to both E-2 and [H2O2]ss showed increased ERK phosphorylation. These findings suggested that H2O2 is a signaling molecule that downregulates apoptosis in endometrial cells, supporting the fact that endometriosis, albeit a benign disease, shares some features with cancer such as decreased catalase levels. These results link the E-2 effects on [H2O2]ss to resistance to apoptosis and progression of endometriosis. (C) 2013 Elsevier Inc. All rights reserved.Associacao Beneficente de Coleta de SangueFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Universidade Federal de São Paulo, Dept Gynecol, BR-04044 São Paulo, BrazilCharitable Assoc Blood Collect, São Paulo, BrazilUniversidade Federal de São Paulo, Dept Biochem, BR-04044 São Paulo, BrazilUniversidade Federal de São Paulo, Dept Biophys, BR-04044 São Paulo, BrazilUniversidade Federal de São Paulo, Dept Gynecol, BR-04044 São Paulo, BrazilUniversidade Federal de São Paulo, Dept Biochem, BR-04044 São Paulo, BrazilUniversidade Federal de São Paulo, Dept Biophys, BR-04044 São Paulo, BrazilWeb of Scienc

Letter from Jean-Pierre Olivier to Emmett L. Bennett Jr., Bennett, Emmett L., Jr.

Jean-Pierre Olivier strongly asserts that he is all for the reordering of the Linear B tablets in a manner that is logical rather than numerical, as well as touching briefly on his various work projects.Classic