Effect of sample pre-cracking method and notch geometry in plane strain fracture toughness tests as applied to a PMMA resin

The influence of test method factors (notch shape, square or angular, and pre-cracking method, by tapping onto or pressing a razor blade) on the results obtained in plane strain fracture toughness test according to standard ASTM D5045 using SENB specimens made of a commercial PMMA resin were investigated. Results were analyzed quantitatively by comparing the obtained K-IC values and qualitatively by observing their effect on the Moire fringes observed using photoelasticity, showing that, at 95% significance level, the K-IC values are affected by the pre-cracking method, with the most conservative value being obtained when natural pre-cracks were introduced by tapping onto a razor blade (K-IC = 1.15 +/- 0.11 MPa.m(0.5)). This correlates with a perturbation in the stress field close to the pre-crack tip observed in the photoelasticity test sample when it was introduced by pressing the razor blade. Surprisingly, notch geometry only slightly affects the results. (C) 2012 Elsevier Ltd. All rights reserved.

Differential calculus and integration of generalized functions over membranes

In this paper we continue the development of the differential calculus started in Aragona et al. (Monatsh. Math. 144: 13-29, 2005). Guided by the so-called sharp topology and the interpretation of Colombeau generalized functions as point functions on generalized point sets, we introduce the notion of membranes and extend the definition of integrals, given in Aragona et al. (Monatsh. Math. 144: 13-29, 2005), to integrals defined on membranes. We use this to prove a generalized version of the Cauchy formula and to obtain the Goursat Theorem for generalized holomorphic functions. A number of results from classical differential and integral calculus, like the inverse and implicit function theorems and Green's theorem, are transferred to the generalized setting. Further, we indicate that solution formulas for transport and wave equations with generalized initial data can be obtained as well.

Riemannian Submersions with Discrete Spectrum

We prove some estimates on the spectrum of the Laplacian of the total space of a Riemannian submersion in terms of the spectrum of the Laplacian of the base and the geometry of the fibers. When the fibers of the submersions are compact and minimal, we prove that the spectrum of the Laplacian of the total space is discrete if and only if the spectrum of the Laplacian of the base is discrete. When the fibers are not minimal, we prove a discreteness criterion for the total space in terms of the relative growth of the mean curvature of the fibers and the mean curvature of the geodesic spheres in the base. We discuss in particular the case of warped products.

Combinatorial-topological framework for the analysis of global dynamics

We discuss an algorithmic framework based on efficient graph algorithms and algebraic-topological computational tools. The framework is aimed at automatic computation of a database of global dynamics of a given m-parameter semidynamical system with discrete time on a bounded subset of the n-dimensional phase space. We introduce the mathematical background, which is based upon Conley's topological approach to dynamics, describe the algorithms for the analysis of the dynamics using rectangular grids both in phase space and parameter space, and show two sample applications. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4767672]

Sildenafil vs. Sodium Nitroprusside for the Pulmonary Hypertension Reversibility Test Before Cardiac Transplantation

Background: Pulmonary hypertension is associated with a worse prognosis after cardiac transplantation. The pulmonary hypertension reversibility test with sodium nitroprusside (SNP) is associated with a high rate of systemic arterial hypotension, ventricular dysfunction of the transplanted graft and high rates of disqualification from transplantation. Objective: This study was aimed at comparing the effects of sildenafil (SIL) and SNP on hemodynamic, neurohormonal and echocardiographic variables during the pulmonary reversibility test. Methods: The patients underwent simultaneously right cardiac catheterization, echocardiography, BNP measurement, and venous blood gas analysis before and after receiving either SNP (1 - 2 mu g/kg/min) or SIL (100 mg, single dose). Results: Both drugs reduced pulmonary hypertension, but SNP caused a significant systemic hypotension (mean blood pressure - MBP: 85.2 vs. 69.8 mm Hg; p < 0.001). Both drugs reduced cardiac dimensions and improved left cardiac function (SNP: 23.5 vs. 24.8%, p = 0.02; SIL: 23.8 vs. 26%, p < 0.001) and right cardiac function (SIL: 6.57 +/- 2.08 vs. 8.11 +/- 1.81 cm/s, p = 0.002; SNP: 6.64 +/- 1.51 vs. 7.72 +/- 1.44 cm/s, p = 0.003), measured through left ventricular ejection fraction and tissue Doppler, respectively. Sildenafil, contrary to SNP, improved venous oxygen saturation, measured on venous blood gas analysis. Conclusion: Sildenafil and SNP are vasodilators that significantly reduce pulmonary hypertension and cardiac geometry, in addition to improving biventricular function. Sodium nitroprusside, contrary to SIL, was associated with systemic arterial hypotension and worsening of venous oxygen saturation. (Arq Bras Cardiol 2012;99(3):848-856)

Differential geometry of grassmannians and the Plucker map

Using the Plucker map between grassmannians, we study basic aspects of classic grassmannian geometries. For 'hyperbolic' grassmannian geometries, we prove some facts (for instance, that the Plucker map is a minimal isometric embedding) that were previously known in the 'elliptic' case.