Sharpening the Dirac inequality

We explain an idea towards a possible proof of a conjecture of Salamanca-Riba and Vogan. This conjecture, also called the Convex hull conjecture, sharpens the well known Dirac inequality of Partahasarathy, which has been useful in several partial classifications of unitary representations of real reductive groups. The idea we present originates from collaboration with David Renard

Dirac inequality for highest weight Harish-Chandra modules I

Let $G$ be a connected simply connected noncompact classical simple Lie group of Hermitian type. Then $G$ has unitary highest weight representations. The proof of the classification of unitary highest weight representations of $G$ given by Enright, Howe and Wallach is based on the Dirac inequality of Parthasarathy, Jantzen's formula and Howe's theory of dual pairs where one group in the pair is compact. In this paper we focus on the Dirac inequality which can be used to prove the classification in a more direct way.Comment: 28 page

Effectiveness of the E-Permit System in the Procedure for Obtaining Building Permits in the Republic of Croatia

Cilj je rada analizirati upotrebu i učinkovitost sustava eDozvola u postupku ishođenja građevinskih dozvola u Republici Hrvatskoj, a u kontekstu razvoja e-uprave u Republici Hrvatskoj i Europskoj uniji. Za teorijski dio rada, koristila se relevantna znanstvena i stručna literatura te odgovarajuće znanstvene metode. U radu su prikazani rezultati provedenog empirijskog istraživanja putem online upitnika, koji je upućen na 116 dostupnih e-adresa pročelnika ili voditelja ispostava nadležnih županijskih i gradskih upravnih odjela ili pripadajućih ispostava koji izdaju građevinske dozvole te na načelnika Sektora građevinskih i uporabnih dozvola Ministarstva prostornog uređenja, graditeljstva i državne imovine. Na temelju rezultata istraživanja, uspoređenih s rezultatima dvaju prijašnjih istraživanja ove tematike te u odnosu na prikazana izvješća, normativni i strateški okvir Europske unije i Republike Hrvatske, može se zaključiti da je sustav eDozvola ubrzao i poboljšao postupak ishođenja građevinskih dozvola u Republici Hrvatskoj.The aim of the paper is to analyse the use and effectiveness of the ePermit system in the process of obtaining building permits in the Republic of Croatia, and in the context of the development of e-government in the Republic of Croatia and the European Union. For the theoretical part of the work, a relevant scientific and professional literature and appropriate scientific methods are used. The paper presents the results of the conducted empirical research through an online questionnaire, that was sent to 116 available e-mail addresses of heads or branch managers of jurisdiction county and city administrative departments or related branches that issue building permits to the head of the Department of Building and User Permits of the Ministry of Spatial Planning, Construction and State Property. Based on the results of this research, compared with the results of two previous studies on this topic, and in relation to the presented reports, the normative and strategic framework of the European Union and the Republic of Croatia, it can be concluded that the ePermit system has accelerated and improved the process of obtaining building permits in the Republic of Croatia

Povratak u prošlost: bakreno doba u sjevernoj Hrvatskoj

Knjiga Povratak u prošlost. Bakreno doba u sjevernoj Hrvatskoj nastala je u sklopu istoimene izložbe postavljene u Arheološkom muzeju u Zagrebu u suradnji s Odsjekom za arheologiju Filozofskog fakulteta u Zagrebu i Arheološkim muzejom u Osijeku. Publikacija sadrži 16 tekstova koje pokrivaju različite bakrenodobne teme kroz razdoblje od približno 2000 godina – od načina života i organizacije naselja, izrade i upotrebe predmeta od različitih materijala, iskorištavanja različitih sirovina do zagrobnog života. Osim područja sjeverne Hrvatske u tekstovima je naglašena i međuovisnsot i komunikacija s ostalim dijelovima europskog kontinenta.Knjiga Povratak u prošlost. Bakreno doba u sjevernoj Hrvatskoj nastala je u sklopu istoimene izložbe postavljene u Arheološkom muzeju u Zagrebu u suradnji s Odsjekom za arheologiju Filozofskog fakulteta u Zagrebu i Arheološkim muzejom u Osijeku. Publikacija sadrži 16 tekstova koje pokrivaju različite bakrenodobne teme kroz razdoblje od približno 2000 godina – od načina života i organizacije naselja, izrade i upotrebe predmeta od različitih materijala, iskorištavanja različitih sirovina do zagrobnog života. Osim područja sjeverne Hrvatske u tekstovima je naglašena i međuovisnsot i komunikacija s ostalim dijelovima europskog kontinenta

Sustainability of Serbian Villages in COVID-19 Pandemic Conditions

The subject of this paper is to determine how the COVID-19 virus pandemic affected the situation in Serbian villages. The task of the paper is to show the positive and negative consequences that resulted from the pandemic. This would indicate that some of them may represent a new idea, a chance, or would work in favor of the sustainability of the villages of Serbia. In support of objectivity, research was carried out among the population that inhabits the rural areas of Serbia. It examined the extent to which internationally recognized phenomena and consequences of the COVID-19 virus pandemic were present in the study area and considered the nature of their impact on sustainability. The results of the semi-structured questionnaire were processed using descriptive statistics, t-test, and analysis of variance (ANOVA). Respondents contributed to the conception of possible solutions with their comments. The obtained differences in the answers resulted from different socio-demographic characteristics of the respondents, but also from the fact that the villages of Serbia differ in natural and social characteristics. Respondents’ responses are in favor of economic and sociodemographic sustainability, but they do not think in terms of environmental sustainability. The paper reveals several development opportunities, which complement each other and contribute to different methods for sustainability of rural villages in Serbia