Renormalization group and triviality in noncompact lattice QED with light fermions

In the framework of noncompact lattice QED with light fermions, we derive the functional dependence of the average energy per plaquette on the bare parameters using block-spin Renormalization Group arguments and assuming that the renormalized coupling vanishes. Our numerical results for this quantity in $8^4$ and $10^4$ lattices show evidence for triviality in the weak coupling phase and point to a non vanishing value for the renormalized coupling constant in the strong coupling phase.Comment: 9 page

An approach to the teaching of music reading in the elementary grades

Thesis (Ed.M.)--Boston Universit

Global existence for reaction-diffusion evolution equations driven by the p-Laplacian on manifolds

We consider reaction-diffusion equations driven by the p-Laplacian on noncompact, infinite volume manifolds assumed to support the Sobolev inequality and, in some cases, to have L2 spectrum bounded away from zero, the main example we have in mind being the hyperbolic space of any dimension. It is shown that, under appropriate conditions on the parameters involved and smallness conditions on the initial data, global in time solutions exist and suitable smoothing effects, namely explicit bounds on the L∞ norm of solutions at all positive times, in terms of Lq norms of the data. The geometric setting discussed here requires significant modifications w.r.t. the Euclidean strategies

Blow-up versus global existence of solutions for reaction-diffusion equations on classes of Riemannian manifolds

It is well known from the work of Bandle et al. (J Differ Equ 251:2143-2163, 2011) that the Fujita phenomenon for reaction-diffusion evolution equations with power nonlinearities does not occur on the hyperbolic space H-N, thus marking a striking difference with the Euclidean situation. We show that, on classes of manifolds in which the bottom lambda of the L-2 spectrum of -delta is strictly positive (the hyperbolic space being thus included), a different version of the Fujita phenomenon occurs for other kinds of nonlinearities, in which the role of the critical Fujita exponent in the Euclidean case is taken by lambda. Such nonlinearities are time-independent, in contrast to the ones studied in Bandle et al. (2011). As a consequence of our results we show that, on a class of manifolds much larger than the case M = H-N considered in Bandle et al. (2011), solutions to (1.1) with power nonlinearity f(u) = u(p), p > 1, and corresponding to sufficiently small data, are global in time. Though qualitative similarities with similar problems in bounded, Euclidean domains can be seen in the results, the methods are significantly different because of noncompact setting dealt with

Diquark condensation in two colour QCD

Unquenched lattice SU(2) is studied at nonzero chemical potential in the strong coupling limit. The topic of diquark condensation is addressed analyzing the probability distribution function of the diquark condensate. We present results at zero external source without using any potentially dangerous extrapolation procedure. We find strong evidences for a (high density) second order phase transition where a diquark condensate appears, and show quantitative agreement of lattice calculations with low-energy effective Lagrangian calculations.Comment: 9 pages, 6 figures, to be published in the proceedings of the ``International Workshop on Non-Perturbative Methods and Lattice QCD'', Guangzhou, China, 15-21 May 200

Association between one-hour post-load plasma glucose levels and vascular stiffness in essential hypertension

Objectives: Pulse wave velocity (PWV) is a surrogate end-point for cardiovascular morbidity and mortality. A plasma glucose value $155 mg/dl for the 1-hour post-load plasma glucose during an oral glucose tolerance test (OGTT) is able to identify subjects with normal glucose tolerance (NGT) at high-risk for type-2 diabetes (T2D) and for subclinical organ damage. Thus, we addressed the question if 1-hour post-load plasma glucose levels, affects PWV and its central hemodynamic correlates, as augmentation pressure (AP) and augmentation index (AI). Methods: We enrolled 584 newly diagnosed hypertensives. All patients underwent OGTT and measurements of PWV, AP and AI. Insulin sensitivity was assessed by Matsuda-index. Results: Among participants, 424 were NGT and 160 had impaired glucose tolerance (IGT). Of 424 NGT, 278 had 1-h postload plasma glucose ,155 mg/dl (NGT,155) and 146 had 1-h post-load plasma glucose$155 mg/dl (NGT$155). NGT$155 had a worse insulin sensitivity and higher hs-CRP than NGT,155, similar to IGT subjects. In addition, NGT $155 in comparison with NGT,155 had higher central systolic blood pressure (134612 vs 131610 mmHg), as well as PWV (8.463.7 vs 6.761.7 m/s), AP (12.567.1 vs 9.865.7 mmHg) and AI (29.4611.9 vs 25.1612.4 regression analysis, 1-h post-load plasma glucose resulted the major determinant of all indices of vascular stiffness. Conclusion: Hypertensive NGT$155 subjects, compared with NGT,155, have higher PWV and its hemodynamic correlates that increase their cardiovascular risk profile