Detecting interfaces in a parabolic-elliptic problem from surface measurements

Assuming that the heat capacity of a body is negligible outside certain inclusions the heat equation degenerates to a parabolic-elliptic interface problem. In this work we aim to detect these interfaces from thermal measurements on the surface of the body. We deduce an equivalent variational formulation for the parabolic-elliptic problem and give a new proof of the unique solvability based on Lions’s projection lemma. For the case that the heat conductivity is higher inside the inclusions, we develop an adaptation of the factorization method to this time-dependent problem. In particular this shows that the locations of the interfaces are uniquely determined by boundary measurements. The method also yields to a numerical algorithm to recover the inclusions and thus the interfaces. We demonstrate how measurement data can be simulated numerically by a coupling of a finite element method with a boundary element method, and finally we present some numerical results for the inverse problem.

Il moto browniano in finanza

In questo lavoro si presenta il fenomeno fisico nominato moto browniano, s’illustra il modello matematico atto a descriverlo e si analizza come questo abbia avuto notevole importanza in ambito finanziario, in particolare nell’elaborazione del modello di Black, Scholes e Merton per la valutazione dei derivati.

La congettura di Collatz

Presentazione dei risultati più importanti e famosi che riguardano la congettura di Collatz. Analisi empiriche e nuovi risultati riguardanti la congettura e le sue generalizzazioni.

Trasformata e antitrasformata di Fourier per funzioni sommabili e applicazioni

In questa tesi viene trattata la trasformata di Fourier per funzioni sommabili, con particolare riguardo per il cosiddetto teorema di inversione, che permette il calcolo di sofisticati integrali reali. Viene inoltre fornito un capitolo di premesse di analisi complessa, utili al calcolo esplicito di trasformate di Fourier.

Sulla decomposizione di misure

Questa tesi illustra il teorema di decomposizione delle misure e come questo viene applicato alle trasformazioni che conservano la misura. Dopo aver dato le definizioni di σ-algebra e di misura ed aver enunciato alcuni teoremi di teoria della misura, si introducono due differenti concetti di separabilità: quello di separabilità stretta e quello di separabilità, collegati mediante un lemma. Si descrivono poi la funzione di densità relativa e le relative proprietà e, dopo aver definito il concetto di somma diretta di spazi di misura, si dimostra il teorema di decomposizione delle misure, che permette sotto certe ipotesi di esprimere uno spazio di misura come somma diretta di spazi di misura. Infine, dopo aver spiegato cosa significa che una trasformazione conserva la misura e che è ergodica, si dimostra il teorema di Von Neumann, per il quale le trasformazioni che conservano la misura risultano decomponibili in parti ergodiche.

Coordinate isoterme

Questa tesi si propone di verificare l'esistenza di coordinate isoterme su una superficie. Le coordinate isoterme danno localmente una mappa conforme da una varietà riemanniana bidimensionale al piano Euclideo. Se la superficie è orientabile, allora si può dare un atlante di carte isoterme, cioè le cui coordinate associate siano isoterme. Queste coordinate esistono a patto che vengano soddisfatte certe condizioni. Il risultato nelle classi di Holder è dovuto a Korn e Lichtensten. Chern ha notevolmente semplificato la loro dimostrazione.

Nuclear cysteine cathepsin variants in thyroid carcinoma cells

The cysteine peptidase cathepsin B is important in thyroid physiology by being involved in thyroid prohormone processing initiated in the follicular lumen and completed in endo-lysosomal compartments. However, cathepsin B has also been localized to the extrafollicular space and is therefore suggested to promote invasiveness and metastasis in thyroid carcinomas through, e.g., ECM degradation. In this study, immunofluorescence and biochemical data from subcellular fractionation revealed that cathepsin B, in its single- and two-chain forms, is localized to endo-lysosomes in the papillary thyroid carcinoma cell line KTC-1 and in the anaplastic thyroid carcinoma cell lines HTh7 and HTh74. This distribution is not affected by thyroid stimulating hormone (TSH) incubation of HTh74, the only cell line that expresses a functional TSH-receptor. Immunofluorescence data disclosed an additional nuclear localization of cathepsin B immunoreactivity. This was supported by biochemical data showing a proteolytically active variant slightly smaller than the cathepsin B proform in nuclear fractions. We also demonstrate that immunoreactions specific for cathepsin V, but not cathepsin L, are localized to the nucleus in HTh74 in peri-nucleolar patterns. As deduced from co-localization studies and in vitro degradation assays, we suggest that nuclear variants of cathepsins are involved in the development of thyroid malignancies through modification of DNA-associated proteins.

Learning for sustainability - LforS: Simulation games - a creative tool for interactive learning

Description of simulation and training games as tool for awareness and capacity development in multi steakeholder processes

Self-help extension: Farmer-to-farmer extension

As staff and mobility cost have the lion share of the costs of extension work, there have been many alternatives to assign farmers the job of facilitators, trainers and advisors. The arguments behind are that they are geopraphically closer to the clients, but also mentally and culturally, because they are members of the client group themselves, speak their language and share their experience and daily life. The article starts with the origins of the larger movement in Latin-America, and then discusses potentials and limitations, and finally experience from elsewhere.

Learning for Sustainability - LforS: Training modules and workshop guidelines

Description of LforS training modules and guidelines for moderators.

Learning for Sustainability - LforS: Stakeholder dialogue

Description of the role fo stakeholder dialogue in rural extension and development. Tools and methods for stakeholder dialogues.

Learning for Sustainability - LforS: An extension approach in small scale farming

Description of LforS as a integrativ and learning oriented extension approach

Promoting local innovation - a tool for sustainable rural development

Change, be it socio-cultural, political, institutional, technological, economic or ecological motivates local communities and farming families to mobilise and increase their innovation potential in order to create ways of life and production that match their own visions and priorities. In spite of the growing recognition of the potential of local innovations, they are hardly being integrated into development plans and projects; as a consequence, their diffusion within and between communities is limited. therefore interactive and participatory methods for supporting and strengthening the innovative potential of local actors are valuable inputs for sustainable rural development. the article presents an approach to promote local innovations.