Divisibilidad de números combinatorios. El teorema de Lucas

El objeto de la presente nota es analizar el problema de divisibilidad de un número combinatorio (n-k) por un número primo p. La respuesta de esta pregunta no trivial resulta ser muy elegante y su demostración elemental. Este resultado, debido al matemático francés Edouard Lucas, apareció por primera vez en un texto de Teoría de Números de este autor. La demostración que daremos es debida a Fine (American Math. Monhly 1947). Antes de abordar el resultado general consideraremos el caso en que p = 2, y daremos una prueba independiente en este caso

Evaluation of Native Grasses for Sustainable Turfgrass in the Bioclimatic Mediterranean Region

This study reports the results of a research project (Mi.T.E.A.Med) funded by the Italian Ministry of Agriculture. The research was organised in two phases: the first one involved the screening of the study area (Southern Italy) to find suitable turfgrass species and the second one focused on ex situ cultivation to test the ecotypes with salinity resistance. During the first step of the research, 11 sites from 6 regions of Southern and Central Italy were identified. In these sites, 24 ecotypes of Cynodon dactylon (L.) Pers. were collected and their habitus, phenology, and some biometric parameters have been determined. During the 2 years of research, both botanic and agronomic characterisation of the collected C. dactylon ecotypes was carried out. Some native accessions showed a behaviour similar to commercial cultivars, while an ecotype from the Abruzzo Region showed better results compared to the commercial cultivars for several quality indices. The results of this project showed that Mediterranean-adapted native grass species (e.g. Cynodon dactylon (L.) Pers.) are worth investigating for turfgrass, making for their performance and low resource requirement (especially water). This species can be used as promising alternatives to conventional non-native turfgrasses

INTESTINAL AND PULMONARY INFECTION BY Cryptosporidium parvum IN TWO PATIENTS WITH HIV/AIDS

We describe two patients with HIV/AIDS who presented pulmonary and intestinal infection caused by Cryptosporidium parvum, with a fatal outcome. The lack of available description of changes in clinical signs and radiographic characteristics of this disease when it is located in the extra-intestinal region causes low prevalence of early diagnosis and a subsequent lack of treatment

evaluation of native grasses for sustainable turfgrass in the bioclimatic mediterranean region

This study reports the results of a research project (Mi.T.E.A.Med) funded by the Italian Ministry of Agriculture. The research was organised in two phases: the first one involved the screening of the study area (Southern Italy) to find suitable turfgrass species and the second one focused on ex situ cultivation to test the ecotypes with salinity resistance. During the first step of the research, 11 sites from 6 regions of Southern and Central Italy were identified. In these sites, 24 ecotypes of Cynodon dactylon (L.) Pers. were collected and their habitus, phenology, and some biometric parameters have been determined. During the 2 years of research, both botanic and agronomic characterisation of the collected C. dactylon ecotypes was carried out. Some native accessions showed a behaviour similar to commercial cultivars, while an ecotype from the Abruzzo Region showed better results compared to the commercial cultivars for several quality indices. The results of this project showed that Mediterranean-adapted native grass species (e.g. Cynodon dactylon (L.) Pers.) are worth investigating for turfgrass, making for their performance and low resource requirement (especially water). This species can be used as promising alternatives to conventional non-native turfgrasses

A importância dos espaços públicos e áreas verdes pós-pandemia na cidade de São Paulo (SP)

As cidades estão sofrendo profundas transformações no campo da saúde, cultura, relações sociais, e principalmente na vida urbana, provocando inúmeras reflexões e questionamentos ao modelo de cidade que poderá ser desfrutada pós-pandemia da COVID-19, destacando a importância e o papel dos espaços públicos e das áreas verdes em períodos excepcionais como no caso da pandemia e para o futuro da vida urbana. Diante da atual situação, este artigo tem por objetivo recomendar diretrizes de convivência e de uso adequado para as áreas verdes e espaços públicos, compatíveis com as exigências da saúde pública para o período da pandemia, até que se tenha uma vacina eficiente, e ao mesmo tempo, colaborar com diretrizes para uma qualidade de vida urbana com maior valorização das áreas verdes, vencida a pandemia. Esse estudo foi baseado na Pesquisa Emoções Momentâneas: Comportamentos e Hábitos Cotidianos Pós-Pandemia (XIMENES et al., 2020), nas revisões de literatura técnica e científica, nas análises das informações disponíveis e no mapeamento das áreas verdes do município de São Paulo. A ressignificação das cidades pós-pandemia deverá abordar a implementação de novas políticas públicas, e meios de apropriação e convivência dos espaços públicos, parques e áreas verdes da cidade de São Paulo, tornando-os mais humanizados, seguros e inclusivos; trabalhando estratégias integradas ao desenvolvimento urbano sustentável na retomada das atividades de lazer, cultura, gastronomia e entretenimento.Cities are undergoing profound transformations in the fields of health, culture, social relations, and especially in urban life, causing numerous reflections and questions to the city model that can be enjoyed after the pandemic of COVID-19, highlighting the importance and the role of public spaces and green areas in exceptional periods as in the case of the pandemic and for the future of urban life. In view of the situation, this article aims to recommend guidelines for coexistence and proper use of green areas and public spaces, compatible with public health requirements for the pandemic period, until an efficient vaccine is obtained, and, at the same time, collaborate with guidelines for the quality of urban life with greater appreciation of green areas after the pandemic is over. This study was based on the Momentary Emotions Research: Post-Pandemic Behaviors and Daily Habits (XIMENES et al., 2020), on the reviews of technical and scientific literature, on the analysis of the available information and on the mapping of the green areas in the city of São Paulo. The resignification of post-pandemic cities should address the implementation of new public policies, and means of appropriation and coexistence of public spaces, parks and green areas in the city of São Paulo. This will make them more humanized, safe and inclusive; development strategies integraded to sustainable urban development in the return of leisure, culture, gastronomy and entertainment activities

INTESTINAL AND PULMONARY INFECTION BY Cryptosporidium parvum IN TWO PATIENTS WITH HIV/AIDS

We describe two patients with HIV/AIDS who presented pulmonary and intestinal infection caused by Cryptosporidium parvum, with a fatal outcome. The lack of available description of changes in clinical signs and radiographic characteristics of this disease when it is located in the extra-intestinal region causes low prevalence of early diagnosis and a subsequent lack of treatment

Interactive management control via analytic hierarchy process : an empirical study in a public university hospital

This paper describes an application of analytic hierarchy process (AHP) to enhance interactive budgeting in one of the biggest public university hospitals in Italy. AHP improved budget allocation facilitating elicitation and formalisation of units' needs. Furthermore, AHP facilitated vertical communication among managers and stakeholders, as it allowed multilevel hierarchical representation of hospital needs, and horizontal communication among staff of the same hospital, as it allowed units' need prioritisation and standardisation, with a scientific multi-criteria approach, without using complex mathematics. Finally, AHP allowed traceability of a complex decision-making process (as budget allocation), this aspect being of paramount importance in public sectors, where managers are called to respond to many different stakeholders about their choices

Agronomic behaviour of some Cynodon dactylon ecotypes for turfgrass use in the Mediterranean climate

In Italy, the expansion of turfgrasses is limited by the lack of suitable species for cultivation in the Mediterranean climate. With this view, Mi.Te.A.Med. (Turfgrass improvement in the Mediterranean climate) research project was developed with the main purpose to find out and agronomically characterise native turfgrass species of Southern and Central Italy and to compare them with some commercial cultivars. During the first step of the research, 11 sites from 6 regions of Southern and Central Italy were identified. In these sites 24 ecotypes of Cynodon dactylon L. (Pers.) were collected and their habitus, phenology plus some biometric parameters have been determined. During the two years of research both botanic and agronomic characterisation of the collected C. dactylon ecotypes and their comparison with 3 commercial cultivars (Panama, Transcontinental and Yukon) was carried out. In the first year the colour loss interval was assessed. In the second year, colour index was measured by an electronic colorimeter, weekly growth rate was measured by a turfmeter, turf quality and ground cover percentage were assessed by visual estimate. Some native accessions showed behaviour similar to commercial cultivars while an ecotype from the Abruzzo region showed better results compared to the commercial cultivars for several quality indices