Function spaces and pseudo-differential operators on vector bundles
The objective of this Master thesis is to give coordinate-free definitions of certain concepts in modern analysis on vector bundles and to apply these tools to elliptic partial differential equations. Topics that we cover are distribution theory, Sobolev spaces and pseudo-differential operators.
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Generalized finite difference schemes with higher order Whitney forms
Kettunen, Lauri; Lohi, Jonni; Räbinä, Jukka; Mönkölä, Sanna; Rossi, Tuomo (EDP Sciences, 2021)Finite difference kind of schemes are popular in approximating wave propagation problems in finite dimensional spaces. While Yee’s original paper on the finite difference method is already from the sixties, mathematically ... -
Ricci-flow based conformal mapping of the proximal femur to identify exercise loading effects
Narra, Nathaniel; Abe, Shinya; Dimitrov, Vassil; Nikander, Riku; Kouhia, Reijo; Sievänen, Harri; Hyttinen, Jari (Nature Publishing Group, 2018)The causal relationship between habitual loading and adaptive response in bone morphology is commonly explored by analysing the spatial distribution of mechanically relevant features. In this study, 3D distribution of ... -
Quasi-Continuous Vector Fields on RCD Spaces
Debin, Clément; Gigli, Nicola; Pasqualetto, Enrico (Springer, 2021)In the existing language for tensor calculus on RCD spaces, tensor fields are only defined m-a.e.. In this paper we introduce the concept of tensor field defined ‘2-capacity-a.e.’ and discuss in which sense Sobolev vector ... -
Open-source QCD analysis of nuclear parton distribution functions at NLO and NNLO
Walt, Marina; Helenius, Ilkka; Vogelsang, Werner (American Physical Society, 2019)We present new sets of nuclear parton distribution functions (nPDFs) at next-to-leading order and next-to-next-to-leading order. Our analyses are based on deeply inelastic scattering data with charged-lepton and neutrino ... -
A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries
Le Donne, Enrico (De Gruyter Open, 2017)Carnot groups are distinguished spaces that are rich of structure: they are those Lie groups equipped with a path distance that is invariant by left-translations of the group and admit automorphisms that are dilations with ...
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