The period of a classical oscillator

We develop a simple method to obtain approximate analytical expressions for the period of a particle moving in a given potential. The method is inspired to the Linear Delta Expansion (LDE) and it is applied to a large class of potentials. Precise formulas for the period are obtained.Comment: 5 pages, 4 figure

Variational collocation for systems of coupled anharmonic oscillators

We have applied a collocation approach to obtain the numerical solution to the stationary Schr\"odinger equation for systems of coupled oscillators. The dependence of the discretized Hamiltonian on scale and angle parameters is exploited to obtain optimal convergence to the exact results. A careful comparison with results taken from the literature is performed, showing the advantages of the present approach.Comment: 14 pages, 10 table

A new representation for non--local operators and path integrals

We derive an alternative representation for the relativistic non--local kinetic energy operator and we apply it to solve the relativistic Salpeter equation using the variational sinc collocation method. Our representation is analytical and does not depend on an expansion in terms of local operators. We have used the relativistic harmonic oscillator problem to test our formula and we have found that arbitrarily precise results are obtained, simply increasing the number of grid points. More difficult problems have also been considered, observing in all cases the convergence of the numerical results. Using these results we have also derived a new representation for the quantum mechanical Green's function and for the corresponding path integral. We have tested this representation for a free particle in a box, recovering the exact result after taking the proper limits, and we have also found that the application of the Feynman--Kac formula to our Green's function yields the correct ground state energy. Our path integral representation allows to treat hamiltonians containing non--local operators and it could provide to the community a new tool to deal with such class of problems.Comment: 9 pages ; 1 figure ; refs added ; title modifie

THE 'MASSERIA ROTA' IN NAPLES (ITALY). A VERNACULAR HERITAGE TO PRESERVE

Abstract. The 'Masseria Rota' in Cercola, near Naples, is one of the best-preserved examples of the important vernacular architectural heritage of the Vesuvian area. Built in the 17th century upon more ancient pre-existences, the farm is an extraordinary example of the construction capabilities typical of the Neapolitan area and the dual vocation, productive and residential of the Vesuvian 'masserie'. The production area for slaughter and winemaking – located on the basement floor and still in good condition – coexists with the residential part with a sober decorative apparatus, enriched by the nineteenth-century transformations. Its planimetric U-shaped layout denounces a development for subsequent integrations that is also evident from the mensiochronological analysis of the walls. Unfortunately, despite the its indisputable historical, architectural and documentary value, the 'Masseria Rota' is in a serious state of abandonment, suffocated by contemporary buildings often devoid of specific values. The contribution to be presented illustrates the results of a teaching experiment that aims to propose methodological guidelines for the drafting of a restoration project aware and respectful of the identity of the aforementioned 'Masseria', and intends to provide a contribution of knowledge for the preservation and enhancement of a vernacular building heritage present on the slopes of Vesuvius, guiltily forgotten and abandoned in recent decades, which, instead, represents one of the most interesting and important of the settlement and construction modes of a territory inhabited since antiquity – despite the cyclical destructions caused by the volcanic activity of Vesuvius – for its environmental and landscape characteristics

MATERIAL/HISTORIC REALITY: CATCHING THE TRANSFORMATION. FROM A CASE OF APPLIED RESEARCH TO THE TRANS-DISCIPLINARY APPROACH TO PRESERVE ARCHITECTURE

The present paper aims at dealing with some issues of knowledge of the architectural heritage. Given the increasing use of the innovative technologies in the field of the cultural heritage it is important to focus on their usefulness and potentialities in order to the conservation project management. The role of the new survey techniques and the accurate representations of the dimensional, structural and material consistency of the historic buildings and their context is mandatory and can influence the restoration choices. Starting from a recent applied research concerning a significant and symbolic monument of Naples, Castel Nuovo, the paper intends to highlight not only the importance of the integration of the specialist surveys, but also the role of the critical interpretation. The results of the different disciplines involved in the knowledge process have to be evaluated critically in view of the conservation of the tangible and intangible values. Furthermore, catching the complexity of architecture of the past depends on the capacity to maintain a close and constant contactwith the building physicality and also on a complex methodology which is inclusive of new interpretative instruments which could increase a virtuous hermeneutic circle

Systematic perturbation calculation of integrals with applications to physics

In this paper we generalize and improve a method for calculating the period of a classical oscillator and other integrals of physical interest, which was recently developed by some of the authors. We derive analytical expressions that prove to be more accurate than those commonly found in the literature, and test the convergence of the series produced by the approach.Comment: 11 pages, 5 figure

Acetate intolerance is mediated by enhanced synthesis of nitric oxide by endothelial cells.

The clinical picture of acetate intolerance strictly mimics the nitric oxide (NO) effect, including smooth muscle relaxation and extreme vasodilation. Because acetate induces production of cAMP, which is a powerful stimulus of NO synthase (NOS), we evaluated the effect of different dialysate solutions with and without acetate on NOS activity in endothelial cells (EC). NOS activity of EC, evaluated as H3-citrulline produced from H3-arginine, was modulated by the dialysate composition (e.g., 38 mmol/L acetate produced an increase of 3.2 +/- 0.39-fold compared with basal values (P < 0.0005), and the small amount of acetate (4 mmol/L) in 35 mmol/L bicarbonate solution increased the NOS activity by 2 +/- 0.49-fold (P < 0.05). Conversely, the acetate-free solution produced no effect on NOS activity. The mRNA encoding for inducible NOS was highly expressed in EC incubated with acetate buffer and also with acetate in bicarbonate dialysis buffer. The EC proliferative index was depressed by acetate (P < 0.0005), and tumor necrosis factor synthesis was increased (P < 0.0005) compared with acetate-free buffer. This study suggests that dialytic "acetate intolerance" can be induced by the activation, through cAMP and tumor necrosis factor release, of NOS. The small amount of acetate in bicarbonate dialysate, although capable of inducing in vitro NOS activation, is likely to be rapidly metabolized, whereas the large amounts of this anion in acetate fluids overwhelm metabolism by the liver. Acetate-free dialysate is the only solution that provides an acceptable level of biocompatibility both in vivo and in vitro