Zeta function regularization for a scalar field in a compact domain

We express the zeta function associated to the Laplacian operator on $S^1_r\times M$ in terms of the zeta function associated to the Laplacian on $M$, where $M$ is a compact connected Riemannian manifold. This gives formulas for the partition function of the associated physical model at low and high temperature for any compact domain $M$. Furthermore, we provide an exact formula for the zeta function at any value of $r$ when $M$ is a $D$-dimensional box or a $D$-dimensional torus; this allows a rigorous calculation of the zeta invariants and the analysis of the main thermodynamic functions associated to the physical models at finite temperature.Comment: 19 pages, no figures, to appear in J. Phys.

Spectral analysis and zeta determinant on the deformed spheres

We consider a class of singular Riemannian manifolds, the deformed spheres $S^N_k$, defined as the classical spheres with a one parameter family $g[k]$ of singular Riemannian structures, that reduces for $k=1$ to the classical metric. After giving explicit formulas for the eigenvalues and eigenfunctions of the metric Laplacian $\Delta_{S^N_k}$, we study the associated zeta functions $\zeta(s,\Delta_{S^N_k})$. We introduce a general method to deal with some classes of simple and double abstract zeta functions, generalizing the ones appearing in $\zeta(s,\Delta_{S^N_k})$. An application of this method allows to obtain the main zeta invariants for these zeta functions in all dimensions, and in particular $\zeta(0,\Delta_{S^N_k})$ and $\zeta'(0,\Delta_{S^N_k})$. We give explicit formulas for the zeta regularized determinant in the low dimensional cases, $N=2,3$, thus generalizing a result of Dowker \cite{Dow1}, and we compute the first coefficients in the expansion of these determinants in powers of the deformation parameter $k$.Comment: 1 figur

Productivity growth of the cities of Jiangsu province, China: a Kaldorian approach

© 2017 Informa UK Limited, trading as Taylor & Francis Group This paper considers the determinants of economic growth of the cities of Jiangsu province, China, adopting a Kaldorian approach. It is found that there is a close correlation between the growth of non-industry and industry (Kaldor’s first law) that provides indirect evidence for the export-base theory. The paper discusses two competing explanations of the foundations of the Verdoorn law (Kaldor’s second law), which, in its simplest form, is the relationship between industrial productivity and output growth. It also considers the static–dynamic Verdoorn law paradox. This arises from the fact that estimating the Verdoorn law in log-levels often gives statistically insignificant estimates of the Verdoorn coefficient while the use of growth rates gives significant values of around one half. The results show that this does not occur when data for the cities are used. A plausible explanation for the paradox is that it results from spatial aggregation bias. It is also found that inter-province urban productivity disparities first increase, but subsequently decrease over the period considered

Laboratorio di Restauro architettonico

Nell'a.a. 2013-14 la didattica del Laboratorio di restauro (Scuola di Architettura Urbanistica Ingegneria delle cstruzioni del Politecnico di Milano) è stata coinvolta in una esperienza di sinergia con l'attività educativa promossa dalla Provincia a sostegno di un gruppo di studenti di scuole lecchesi, a rischio di abbandono scolastico. Tema comune di lavoro è stato la vicenda della fabbrica Faini di Lecco, che produceva materiali metallici, da decenni dismessa. Il tema del 'recupero' è stato quindi affrontato su due fronti: da una parte il gruppo lecchese di allievi delle scuole di secondo grado è stato guidato dagli insegnanti attraverso un'esperienza di laboratorio teatrale; dall'altra parte,gli studenti del Laboratorio di restauro si sono occupati, come previsto dal programma didattico, del progetto di 'recupero' degli edifici del complesso, divenuto testimonianza di archeologia industriale e in attesa di riutilizzazione. L'argomento di lavoro, affrontato da angolazioni e da soggetti evidentemente differenti - anche per età anagrafica - ha visto occasioni comuni di scambio di informazioni, di notizie storiche e di visite dell'area della ex fabbrica. Gli esiti dell'iniziativa sono stati positivi sia per gli allievi delle scuole, sia pe rgli studenti universitari. I primi hanno progettato e messo in scena uno spettacolo, rappresentato in due repliche, al termine del loro percorso di 'recupero', che ha portato anche benefici diretti sul piano scolastico. Gli studenti del Politecnico hanno svolto regolarmente le attività laboratoriali previste e ad alcuni di essi, più particolarmente interessati, è stata offerta l'occasione di seguire da vicino alcuni aspetti tecnici dell'allestimento scenografico e della regia. Inoltre, in concomitanza con le date dello spettacolo, è stata esposta una selezione di elaborati prodotti nell'ambito del Laboratorio di restauro

On the sample size dependence of the critical current density in MgB2_2 superconductors

Sample size dependent critical current density has been observed in magnesium diboride superconductors. At high fields, larger samples provide higher critical current densities, while at low fields, larger samples give rise to lower critical current densities. The explanation for this surprising result is proposed in this study based on the electric field generated in the superconductors. The dependence of the current density on the sample size has been derived as a power law $j\propto R^{1/n}$ ($n$ is the $n$ factor characterizing $E-j$ curve $E=E_c(j/j_c)^n$). This dependence provides one with a new method to derive the $n$ factor and can also be used to determine the dependence of the activation energy on the current density.Comment: Revtex, 4 pages, 5 figure

INCOME INEQUALITY AND GROWTH: PROBLEMS WITH THE ORTHODOX APPROACH

Abstract. This paper discusses the main issues about increasing inequality, whether it matters and its impact on economic activity and growth. It starts by briefly considering the empirical evidence of the share of income going to the top one percent since 1945 in the advanced countries. It then considers whether this represents an increase in the productivity of the top one percent or merely an extraction of economic rent. The empirical evidence suggests the latter is generally the case and, as a consequence, there is not likely to be a trade-off between greater income equality and efficiency (the latter being reflected in a lower economic growth rate). This is reinforced by considering the mainstream explanation of the distribution of income and by a consideration of the argument as to whether labor is paid its marginal product, which is found to be problematic. Hence, some reservations about the use of the aggregate production function are raised. The paper turns next to the question of whether or not a greater degree of inequality causes a slower economic growth, both for the advanced and the developing countries. It next considers if the increasing gap between the top one percent and the rest of the income distribution has been either responsible for, or exacerbated, the Great Recession. It concludes that the degree of inequality is an important factor in determining economic activity and one that has been ignored for too long in macroeconomics

Effect of eye lateralization on contralateral suppression of transient evoked otoacoustic emissions

Several studies have previously demonstrated that postural changes modify evoked otoacoustic emission. In order to evaluate a possible interaction between eye muscles and ciliated cells in the inner ear, we studied the effects of eye lateralization on the contralateral suppression of transient evoked otoacoustic emissions (TEOAEs). Thirty-eight normal hearing subjects with TEOAEs were recruited. Their TEAOEs at threshold level were recorded with contralateral suppression (white noise) via straight ahead fixation and right or left lateral fixation. Eye lateralization in the same direction of the white noise significantly decreased the suppression at 4 kHz (p = 0.003). The signal-to-noise ratio in the suppression condition with straight ahead was 1.54 (± 4.610) dB, while the ratio was 3.48 (± 4.631) dB in the suppression condition with gaze toward the white noise. Eye lateralization seems to reduce the contralateral suppression effect of TEOAEs at 4 kHz. However, further studies are necessary to investigate the possible mechanisms of this phenomenon