Browsing by Author "Petersson, Andreas"

Now showing 1 - 3 of 3

Introduktion till icke-standard analys - Ett bevis av transferprincipen och en explicit konstruktion av Brownsk rörelse
(2013-10-23) Anghammar, Oscar; Norder, Mikael; Petersson, Andreas; University of Gothenburg/Department of Mathematical Science; Göteborgs universitet/Institutionen för matematiska vetenskaper
I denna rapport konstrueras inledningsvis hyperreella tal från reella tal. Vi definierar aritmetik för skuggor av hyperreella tal och presenterar en icke-standard teori för serier och konvergens utifrån denna konstruktion. Förfarandet generaliseras sedan genom att skapa en icke-standard modell till matematisk analys utifrån en mängdteoretisk modell i ZF, som ett led i konstruktionen presenteras teori för filter och ultraprodukter. Vi visar sedan transferprincipen och bygger upp internalitetsbegreppet för att studera relationer mellan standard och icke-standard modellerna för att kunna härledda standardresultat från icke-standard resultat. Avslutningsvis tillämpas teorin för att skapa en explicit icke-standard konstruktion av Brownsk rörelse och vi ger ett bevis för att denna konstruktion är ekvivalent med standard formuleringen.
Stochastic Partial Differential Equations with Multiplicative Noise - Numerical simulations of strong and weak approximation errors
(2015-06-23) Petersson, Andreas; University of Gothenburg/Department of Mathematical Science; Göteborgs universitet/Institutionen för matematiska vetenskaper
A finite element Galerkin spatial discretization together with a backward Euler scheme is implemented to simulate strong error rates of the homogeneous stochastic heat equation with multiplicative trace class noise in one dimension. For the noise, two different operators displaying different degrees of regularity are considered, one of which is of Nemytskii type. The discretization scheme is extended to include discretization of the covariance operator of the Q-Wiener process driving the equation. The results agree with the theory. Furthermore, for exploratory reasons, weak error rates are also simulated using the classical Monte Carlo method and the multilevel Monte Carlo method.
”Strategies when facing a silver tsunami” -an explorative case study on the process of organizing a Village, in the Village-movement.
(2016-10-18) Petersson, Andreas; Göteborg University/Department of Social Work; Göteborgs universitet/Institutionen för socialt arbete
The aim of the study was to explore the organization of two Villages in the Village-to-Village network. The network consists of elder care organizations with the core principle of using older adults and volunteers to construct their organizations. A case study was made on two Villages in the USA. Data collections took place by visiting members, volunteers, staff and facilities but also through interviews with several people connected to the field. Data was later analyzed by applying a theoretical framework, based on the assumption that organizations are constructed entities, examining four stages in the process of organizing and finally comparing the cases. The findings suggest that in order to construct a Village one has to start with the need of the member. In an adapting process the organization work will benefit from finding a common identity and through the resources of the members themselves, and/or volunteers and staff create an environment where the possibility to engage socially will be promoted. The reason for this is that the social dimension of coming together seemed to, both create identities inside the network, and attract people to the network. The need for further research was identified to be: observation of the actual process, research in how to leverage the social dimension into practical use, research in how to adapt the Village model to other ethnicities and lower economic classes and research in how we tell the stories of our organizations.