There is a growing European policy interest in small and medium-sized towns’ (SMSTs) potential to contribute to a more balanced territorial development. National policy in Denmark has only recently ...begun to address SMSTs directly. Often, SMSTs’ development is reduced to either being part of bigger functional urban regions or, in the case of rural areas, hidden behind larger regional development agendas. A key research question is therefore which development paths can we see beyond the growth-decline dichotomy. On the backdrop of this, the ESPON TOWN DENMARK project (2022) juxtaposed general trends of growth and decline in population and employment in Danish SMSTs to other aspects as demography, education, industry, service provision as well as regional position. We develop and apply an analytical typology adding more nuances to SMST’s development pathways.
We prove a generalized version of Evans and Griffith's Improved New Intersection Theorem: Let I be an ideal in a local ring R. If a finite free R-complex, concentrated in nonnegative degrees, has ...I-torsion homology in positive degrees, and the homology in degree 0 has an I-torsion minimal generator, then the length of the complex is at least dim R - dim R/I. This improves the bound ht I obtained by Avramov, Iyengar, and Neeman in 2018.
We expand on two existing characterizations of rings of Gorenstein (weak) global dimension zero and give two new characterizations of rings of finite Gorenstein (weak) global dimension. We also ...include the answer to a question of Y.~Xiang on Gorenstein weak global dimension of group rings.
A test complex for Gorensteinness Christensen, Lars Winther; Veliche, Oana
Proceedings of the American Mathematical Society,
02/2008, Letnik:
136, Številka:
2
Journal Article
Recenzirano
Odprti dostop
Let R be a commutative noetherian ring with a dualizing complex. By recent work of Iyengar and Krause (2006), the difference between the category of acyclic complexes and its subcategory of totally ...acyclic complexes measures how far R is from being Gorenstein. In particular, R is Gorenstein if and only if every acyclic complex is totally acyclic. In this note we exhibit a specific acyclic complex with the property that it is totally acyclic if and only if R is Gorenstein.
Pure-minimal chain complexes Christensen, Lars Winther; Thompson, Peder
Rendiconti - Seminario matematico della Università di Padova,
01/2019, Letnik:
142
Journal Article
Recenzirano
Odprti dostop
We introduce a notion of pure-minimality for chain complexes of modules and show that it coincides with (homotopic) minimality in standard settings, while being a more useful notion for complexes of ...flat modules. As applications, we characterize von Neumann regular rings and left perfect rings.
Artiklen analyserer omstruktureringen af befolkning, erhverv og beskæftigelse i de mellemstore byer i land- og yderkommunerne i Danmark. Artiklen undersøger, om den afmatning, som er kendt fra de ...mindste byer uden for storbyregionerne, har ramt de mellemstore byer, eller om disse følger deres egne udviklingsveje. Til analysen har vi opdelt de mellemstore byer på baggrund af deres befolknings- og beskæftigelsesvækst i perioden 2012-2019 i fire bytyper, som vi undersøger nærmere. Vi inkluderer human kapital i analysen for at undersøge konsekvenserne af vidensøkonomien. Der er tydelige forskelle mellem de fire bytyper og stor variation inden for typerne med fokus på befolkning, erhverv og beskæftigelse, mens der er mindre forskelle i forhold til human kapital. Dette studie viser, at de mindste byer af de mellemstore byer har klaret sig bedst. Dette peger på, at udviklingsvejene adskiller fra de mindste byer, men også at der er forskelle mellem de mellemstore byer.
Distinctive characteristics of Iwanaga--Gorenstein rings are typically understood through their intrinsic symmetry. We show that several of those that pertain to the Gorenstein global dimensions ...carry over to the one-sided situation, even without the noetherian hypothesis. Our results yield new relations among homological invariants related to the Gorenstein property, not only Gorenstein global dimensions but also the suprema of projective/injective dimensions of injective/projective modules and finitistic dimensions.
Copenhagen today appears to be a resurgent city and city region. It came back to life in the mid‐1990s and, until recently, has shown marked growth in key variables such as jobs, income and ...inhabitants, primarily as a result of the rise and spatial dynamics of its service‐ and knowledge‐based economy. Its resurgence is also evident in the central municipalities that 20 years ago struggled with the repercussions of a long‐term urban crisis. Financially, the central city was almost doomed in the late 1980s and early 1990s, and the city of Copenhagen was close to bankruptcy. Central‐city development was characterized by a set of eroding processes that included de‐industrialization, suburbanization, high unemployment rates, high welfare costs, an outdated housing market, strong segregation and various other factors. Copenhagen city and its city region have now been revitalized and today are a strong national centre of economic growth. Although one can catch glimpses of the crisis in key variables, urban turn remains strong; for instance, up to now, rising unemployment has been seen mainly outside the large urban areas in Denmark. However, the housing‐market bubble has burst and other signs of crisis have been appearing since as early as 2006. Nevertheless, the city is far removed from the gloomy days of the late 1980s and early 1990s.
Résumé
Copenhague apparaît aujourd'hui comme une ville et une région métropolitaine en résurgence. Après sa résurrection au milieu des années 1990, elle a affiché, jusqu'à dernièrement, des variables clés en nette croissance (dont emplois, revenus et habitants), principalement grâce à l'essor et à la dynamique spatiale de son économie fondée sur les services et le savoir. Sa résurgence se manifeste également dans les municipalités du centre qui luttaient vingt ans plus tôt contre les répercussions d'une longue crise urbaine. Sur le plan financier, le centre‐ville était quasiment condamnéà la fin des années 1980 et au début des années 1990, et la ville de Copenhague frôlait la faillite. L'aménagement du centre‐ville se caractérisait par un ensemble de mécanismes destructeurs comprenant désindustrialisation, mouvement de suburbanisation, taux de chômage importants, coûts sociaux élevés, marché du logement dépassé, forte ségrégation, ainsi que plusieurs autres facteurs. À présent, la ville de Copenhague et sa région métropolitaine ont repris vie et constituent un pôle national solide de croissance économique. Même si on peut entrevoir quelques incidences de la crise sur les variables clés, le revirement se maintient; par exemple, jusqu'à maintenant, l'augmentation du chômage se constate surtout hors des grandes zones urbaines danoises. Toutefois, la bulle du marché du logement a éclaté et d'autres signes de crise ont fait leur apparition dès 2006. Néanmoins, la ville est loin de la période sombre de la fin des années 1980 et du début des années 1990.
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