Asymptotic and exact series representations for the incomplete Gamma function

Using a variational approach, two new series representations for the incomplete Gamma function are derived: the first is an asymptotic series, which contains and improves over the standard asymptotic expansion; the second is a uniformly convergent series, completely analytical, which can be used to obtain arbitrarily accurate estimates of $\Gamma(a,x)$ for any value of $a$ or $x$. Applications of these formulas are discussed.Comment: 8 pages, 4 figure

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

Non perturbative regularization of one loop integrals at finite temperature

A method devised by the author is used to calculate analytical expressions for one loop integrals at finite temperature. A non-perturbative regularization of the integrals is performed, yielding expressions of non-polynomial nature. A comparison with previuosly published results is presented and the advantages of the present technique are discussed.Comment: 7 pages, 2 figures, 2 tables; corrected some typos and simplified eq. (8

Inversion of perturbation series

We investigate the inversion of perturbation series and its resummation, and prove that it is related to a recently developed parametric perturbation theory. Results for some illustrative examples show that in some cases series reversion may improve the accuracy of the results

Spectroscopy of annular drums and quantum rings: perturbative and nonperturbative results

We obtain systematic approximations to the states (energies and wave functions) of quantum rings (annular drums) of arbitrary shape by conformally mapping the annular domain to a simply connected domain. Extending the general results of Ref.\cite{Amore09} we obtain an analytical formula for the spectrum of quantum ring of arbirtrary shape: for the cases of a circular annulus and of a Robnik ring considered here this formula is remarkably simple and precise. We also obtain precise variational bounds for the ground state of different quantum rings. Finally we extend the Conformal Collocation Method of \cite{Amore08,Amore09} to the class of problems considered here and calculate precise numerical solutions for a large number of states ($\approx 2000$).Comment: 12 pages, 12 figures, 2 table

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

Variational collocation on finite intervals

In this paper we study a new family of sinc--like functions, defined on an interval of finite width. These functions, which we call ``little sinc'', are orthogonal and share many of the properties of the sinc functions. We show that the little sinc functions supplemented with a variational approach enable one to obtain accurate results for a variety of problems. We apply them to the interpolation of functions on finite domain and to the solution of the Schr\"odinger equation, and compare the performance of present approach with others.Comment: 12 pages, 8 figures, 1 tabl

Reply to "Comment on 'Quantization of FRW spacetimes in the presence of a cosmological constant and radiation'"

The Comment by Amore {\it et al.} [gr-qc/0611029] contains a valid criticism of the numerical precision of the results reported in a recent paper of ours [Phys. Rev. D {\bf 73}, 044022 (2006)], as well as fresh ideas on how to characterize a quantum cosmological singularity. However, we argue that, contrary to what is suggested in the Comment, the quantum cosmological models we studied show hardly any sign of singular behavior.Comment: 4 pages, accepted by Physical Review

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

Maximum temperature and solar radiation as predictors of bipolar patient admission in an emergency psychiatric ward

Environmental variables can regulate behavior in healthy subjects. Recently, some authors investigated the role of meteorological variables in bipolar patients with an impact on both the onset and course of bipolar disorder (BD). The aim of this study was to investigate the impact of meteorological variables and other indexes in bipolar hospitalized patients. We examined all patients admitted to the Psychiatric Inpatient Unit of San Luigi Gonzaga Hospital, Orbassano (Turin, Italy) from September 2013 to August 2015, collecting several socio-demographic and clinical characteristics. Seven hundred and thirty patients were included. Compared to the day of admission of control individuals, patients with BD were admitted on a day that presented higher minimum, medium, and maximum temperature, higher maximum humidity, higher solar radiation, and higher hours of sunshine. After logistic regression analysis, admissions to the emergency psychiatric ward due to a primary diagnosis of BD were associated with maximum temperature and solar radiation. The current study provides a novel perspective on the question surrounding seasonal mood patterns in patients with BD. A greater awareness of all possible precipitating factors is needed to inform self-management and psycho-educational programs as well as to improve resilience regarding affective recurrences in the clinical practice