At the roots of Europe: post-Synodal Apostolic Exhortation Ecclesia in Europe and the role of Ecclesiastical Archives

Between 1994 and 1999 the Catholic church promoted five special synods, one for each Continent of the Earth: Africa, America, Asia, Oceania and Europe. On June, 28, 2003, Pope John Paul II promulgated the post-synodal apostolic exhortation Ecclesia in Europa, addressed to the whole European Community in order to illustrate the results of the Synod of European Churches held in 1999. The document wanted to be a way for taking in consideration one’s own past and the Christian roots looking to provide the governance of the new Europe, especially in the perspective of the largest enlargement of the European Union planned between 2004 and 2007. Those cultural and Christian roots are readily available within the ecclesiastical archives of all European countries, a priceless patrimony which, after the Second Vatican Council, the Catholic church aimed to enhance more and more. The present work illustrates the main documents that led the Church to highlight the importance of the ecclesiastical archives in the European history by a brief analysis of the apostolic exhortation Ecclesia in Europa.Entre 1994 y 1999, la Iglesia Católica promovió cinco sínodos especiales, uno para cada Continente de la Tierra: África, América, Asia, Oceanía y Europa. El 28 de junio de 2003, el Papa Juan Pablo II promulgó la exhortación apostólica post-sinodal Ecclesia in Europa, dirigida a toda la Comunidad Europea, a instituciones y ciudadanos, para ilustrar los resultados del Sínodo de las Iglesias europeas. El documento quería ser una invitación a considerar su pasado, sus raíces cristianas, en el gobierno de la nueva Europa, especialmente en vista de la mayor ampliación de la Unión Europea planeada entre 2004 y 2007. Esas raíces culturales y cristianas están fácilmente disponibles en los archivos eclesiásticos de todos los países europeos, un patrimonio único y que, después del Concilio Vaticano II, la Iglesia católica ha mejorado mucho. La comunicación investiga los principales documentos que llevaron a la Iglesia a este importante camino de conocimiento de los archivos, también a la luz de un breve análisis del texto de la exhortación apostólica Ecclesia in Europa, con el fin de que la gente entienda el papel de los archivos eclesiásticos en la historia europea

Integrability of the sub-Riemannian mean curvature at degenerate characteristic points in the Heisenberg group

We address the problem of integrability of the sub-Riemannian mean curvature of an embedded hypersurface around isolated characteristic points. The main contribution of this note is the introduction of a concept of mildly degenerate characteristic point for a smooth surface of the Heisenberg group, in a neighborhood of which the sub-Riemannian mean curvature is integrable (with respect to the perimeter measure induced by the Euclidean structure). As a consequence we partially answer to a question posed by Danielli-Garofalo-Nhieu in [Danielli D., Garofalo N., Nhieu D.M., Proc. Amer. Math. Soc., 2012], proving that the mean curvature of a real-analytic surface with discrete characteristic set is locally integrable.Comment: 12 page

The Pilgrimage to the Holy Face of Lucca in 1896: Documents and News from the Archive of the Congregation of the Holy Face

100 records and many other documentary testimonies regarding the Congregation of the Holy Face of Lucca are stored within the funds of the Historical Diocesan Archive of Lucca. The Chapters of the Society of the Holy Face are present within the same Archive; this document is dated back to 1306-1308 and it is brought up together with the minutes of the meetings in a paper register of 16th-17th century, the only one remained concerning the renewed Society of the Holy Sacrament and the Holy Face. The brotherhood recovered importance during the 19th century mostly thanks to some priests of Lucca, including the Abbot Pietro Pera (the future Archbishop between 1845 and 1846). Specifically, two important moments regarding the renewed interest for the relics of Lucca can be registered after the Napoleonic Era. First, a competition for the construction of a golden lamp for the chapel of the Holy Face was carried out between 1835 and 1836, and Abbot Pera was charged to supervise the enterprise. Related documentaries as well as the various drawings presented for the competition are stored in the Archives of the Congregation of the Holy Face. Moreover, a pilgrimage to the simulacrum of Lucca took place during 1896. This event was very successful: the City and the entire Diocese accurately organized the arrival of about 132,000 pilgrims by controlling pilgrims’ overnighting and daily meals, and developing a visiting route concerning the shrines of the City.

The Historical Diocesan Archive of Lucca, Unesco Heritage (Italy)

The ecclesiastical archives contain the millennial memory of our past. Unlike the Italian State Archives and the European National Archives, they are the only institutions that can boast a history coming back much long before the year 1000 a.D. The activity of researcher therefore must be made easier as much as possible. A heritage of enormous importance is located in Lucca. The Historical Diocesan Archive of Lucca is one of the most important ecclesiastical archives in the world, with almost 1,500 linear meters of documentation and over 13,500 parchments. Its archival items cover around 15th centuries of history and the wealth of them is known worldwide to scholars and archival institutions. In 2011, the Early Middle Ages documents present in Lucca’s Archive were included in the Memory of the World Register by UNESCO. This recognition places the Archive in front of two important challenges for the future: the correct preservation of such a precious asset and the correct management of the assets and spaces in which the scrolls are stored. The present paper presents the documentary and library collections of the Archive, briefly focusing on some peculiarities, and analyzing more concretely those aspects that affect the life of the archive itself, for instance its physical location, its historical importance and the role that it plays as a memory of society

Failure of the curvature-dimension condition in sub-Finsler manifolds

The Lott-Sturm-Villani curvature-dimension condition $\mathsf{CD}(K,N)$ provides a synthetic notion for a metric measure space to have curvature bounded from below by $K$ and dimension bounded from above by $N$. It has been recently proved that this condition does not hold in sub-Riemannian geometry for every choice of the parameters $K$ and $N$. In this paper, we extend this result to the context sub-Finsler geometry, showing that the $\mathsf{CD}(K,N)$ condition is not well-suited to characterize curvature in this setting. Firstly, we show that this condition fails in (strict) sub-Finsler manifolds equipped with a smooth strongly convex norm and with a positive smooth measure. Secondly, we focus on the sub-Finsler Heisenberg group, proving that curvature-dimension bounds can not hold also when the reference norm is less regular, in particular when it is of class $C^{1,1}$. The strategy for proving these results is a non-trivial adaptation of the work of Juillet [Rev. Mat. Iberoam., 37(1):177-188, 2021], and it requires the introduction of new tools and ideas of independent interest. Finally, we demonstrate the failure of the (weaker) measure contraction property $\mathsf{MCP}(K,N)$ in the sub-Finsler Heisenberg group, equipped with a singular strictly convex norm and with a positive smooth measure. This result contrasts with what happens in the \sr Heisenberg group, which instead satisfies $\mathsf{MCP}(0,5)$.Comment: 55 pages, 12 figures. Fixed minor issue in Theorem 1.5 and added section 2.

Heat content asymptotics for sub-Riemannian manifolds

We study the small-time asymptotics of the heat content of smooth non-characteristic domains of a general rank-varying sub-Riemannian structure, equipped with an arbitrary smooth measure. By adapting to the sub-Riemannian case a technique due to Savo, we establish the existence of the full asymptotic series: \begin{equation} Q_\Omega(t) = \sum_{k=0}^{\infty} a_k t^{k/2}, \qquad \text{as } t\to 0. \end{equation} We compute explicitly the coefficients up to order $k=5$, in terms of sub-Riemannian invariants of the domain and its boundary. Furthermore, we prove that every coefficient can be obtained as the limit of the corresponding one for a suitable Riemannian extension. As a particular case we recover, using non-probabilistic techniques, the order $2$ formula due to Tyson and Wang in the first Heisenberg group [J. Tyson, J. Wang, Comm. PDE, 2018]. An intriguing byproduct of our fifth-order analysis is the evidence for new phenomena in presence of characteristic points. In particular, we prove that the higher order coefficients in the expansion can blow-up in their presence. A key tool for this last result is an exact formula for the sub-Riemannian distance from a specific surface with an isolated characteristic point in the first Heisenberg group, which is of independent interest.Comment: 45 pages, 4 figures. (v2) Simplified proof of Thm. 3.1, removed appendix A; (v3) several minor improvements and clarifications. Final version to appear on J. Math. Pures App

First-order heat content asymptotics on RCD(K,N){\sf RCD}(K,N) spaces

In this paper, we prove first-order asymptotics on a bounded open set of the heat content when the ambient space is an ${\sf RCD}(K,N)$ space, under a regularity condition for the boundary that we call measured interior geodesic condition of size $\epsilon$. We carefully study such a condition, relating it to the properties of the disintegration of the signed distance function from $\partial \Omega$ studied by Cavalletti and Mondino.Comment: 46 pages, 2 figure

Dendrometer and intra-annual tree growth : what kind of information can be inferred?

Dendrometer measurements provide time series composed of the rhythm of water storage fluctuations over the year and seasonal tree growth. For slow-growing trees, however, difficulties have been found in the identification of crucial events such as growth onset, stem growth period and cessation, rendering it necessary to define what can be measured and at which time scale. Time scale means the time interval (from one day to one month) at which stem radius variation is extracted. In this study, two conifer species were monitored by an automatic band dendrometer to assess several time scales and analysis approaches. Data were collected from 8 trees of Picea abies (L.) Karst and Larix decidua L., growing at 1020 and 2080 m a.s.l. in the eastern Italian Alps, from 2000 to 2003. Time series of stem radius variation were extracted with different approaches, such as the stem cycle, daily mean and daily maximum. Several approaches can be used, as very similar time series of stem radius variations were produced with high coefficients of correlation among the series. At lower altitude, the approximate onset was identified at the beginning of May with a 10-day time scale, when the distribution of stem radius variation differed from zero. The main growth period, from May to June-July, corresponded mainly with earlywood cell formation. At higher altitude, a time scale of at least 15 days facilitated identification of the main period of stem growth only, corresponding with earlywood cell formation. Even if latewood cells were produced in August at both altitudes, the variability in stem radius changes was higher than the amount of growth in terms of cell-wood production. For a slow-growing species in a cold environment, an understanding of the growth period, assessed with several time scales, is necessary when using time series of stem radius variation to assess growth and climate relationships. The period used for growth and climate analysis should correspond only with the main period of stem growth

An integrated model for designing and optimising an international logistics network

Supply-chain configuration has recently gained increasing attention both from the practitioner’s perspective and as a research area. This paper proposes an integrated model for designing and optimising international logistics networks. It consists of a mixed integer linear programming model and a data-mapping section (i.e. methodological guidelines for gathering and processing the data necessary to set up the model). It has been specifically developed for solving the configuration problem for supply chains characterised by a complexity level typical of real-life global logistics networks. Although this topic is well understood and well elaborated at a technical level in the extant literature, it still presents obstacles in practice especially in terms of dealing with real-life complexity, service-level constraints and data mapping. Thus, we developed our integrated approach with the aim to fill these gaps. We designed our model for dealing with multiple-layer, single location-layer, multiple-commodity and time-constrained logistics networks, to be implemented in a single period time horizon and in a deterministic environment. The proposed approach represents an innovative contribution to the existing body of scientific knowledge and facilitates the data gathering and processing activities, which are largely recognised as complex and time-consuming processes for the management of logistics activities

Applying an integrated logistics network design and optimisation model: the Pirelli Tyre case

The aim of the present paper is to provide an application to a real-life supply-chain context (i.e. the Pirelli Tyre European logistics network) of an integrated logistics network design and optimisation model. Starting from the analysis of supply chain under study and of the configuration problem to be solved, we identified the most suitable approach: a mixed integer linear programming optimisation model endowed with a series of guidelines for gathering and processing all the data necessary to set-up and run the model. The application of the selected integrated design and optimisation model to the Pirelli Tyre case led to significant cost savings related to three different service-level scenarios. Thus, the applied model could be profitably implemented by supply chain and logistics managers for optimising various operating contexts. Moreover, the exemplified data-mapping section represents a useful guideline, which can be applied by practitioners to gather and handle the high volume of data necessary for running the model in a real-life context. In conclusion, since the current state of the art is particularly lacking exhaustive supply-chain design models, the implemented integrated approach represents a significant contribution to the existing body of knowledge on supply chain configuration