Search results for "tematiikka"
showing 10 items of 350 documents
Matemaatikon kaksi vapautta : säännön seuraamisen ongelma ja vahva konventionalismi matematiikan filosofiassa
2006
Torus computed tomography
2020
We present a new computed tomography (CT) method for inverting the Radon transform in 2D. The idea relies on the geometry of the flat torus, hence we call the new method Torus CT. We prove new inversion formulas for integrable functions, solve a minimization problem associated to Tikhonov regularization in Sobolev spaces and prove that the solution operator provides an admissible regularization strategy with a quantitative stability estimate. This regularization is a simple post-processing low-pass filter for the Fourier series of a phantom. We also study the adjoint and the normal operator of the X-ray transform on the flat torus. The X-ray transform is unitary on the flat torus. We have i…
A classification of C-Fuchsian subgroups of Picard modular groups
2017
Myosporidium ladogensis n. comb. in burbot Lota lota from Finland: fine structure and microsporidian taxonomy.
2020
Infections with microsporidian parasites are described in skeletal muscle of burbot Lota lota from Lake Haukivesi, Finland. Infected myocytes contained spores within sporophorous vesicles (SPVs) in contact with host cell cytoplasm, similar to Pleistophora ladogensis in L. lota and smelt Osmerus eperlanus in western Russia and northern Germany. Analysis of small subunit ribosomal RNA (SSU rRNA) gene sequences indicated identity with Myosporidium spraguei in burbot and pike-perch from this lake. The latter is considered a junior synonym of P. ladogensis. Phylogenetic analysis of SSU rRNA sequences resolved the burbot parasite apart from a clade containing the type species P. typicalis, but to…
Poisson-prosessit
2015
Tämän tutkielman tarkoituksena on tutustua erilaisiin Poisson-prosesseihin, joita käytetään muun muassa vakuutusmatematiikassa, jonotusteoriassa, rahoituksessa sekä kun mallinnetaan aikaa, kunnes jotakin tapahtuu. Tutkielmassa tutustutaan Poisson-prosessien tärkeimpiin jakauman tunnuslukuihin ja ominaisuuksiin todistuksineen sekä esimerkkien muodossa nähdään mitä hyötyä ominaisuuksista käytännössä on. Ensimmäisenä tutustutaan homogeeniseen ja epähomogeeniseen Poisson-prosessiin sekä niiden ominaisuuksiin. Esimerkeissä lasketaan eri käytännön ongelmia ja lisäksi lasketaan tunnettu odottamiseen liittyvä paradoksi, joka tunnetaan muun muassa nimellä liftarin paradoksi ja josta tässä käytetään …
Ongelmanratkaisun opettaminen todennäköisyystehtävissä
2017
Mitä enemmän oppilas tai opiskelija oivaltaa itse, sitä enemmän hän oppii ja nauttii ongelmanratkaisusta. Tämä ajatus toimii lähtökohtana tutkielmassa. Käsiteltävät tehtävät ovat tasoltaan yläkouluun ja / tai lukioon soveltuvia. Tutkielma antaa opettajalle käytännönläheisiä esimerkkejä opetustilanteessa hyödynnettävistä todennäköisyysongelmista. Tehtävistä esitetään useita ratkaisuvaihtoehtoja, jotta opettajan on helpompi samaistua erilaisiin ajattelutapoihin. Mikä tärkeintä, tutkielmaan on kehitetty kysymyksiä, joilla oppijaa voi ohjata hienovaraisesti eteenpäin ratkaisussaan. Tavoitteena on, että ratkoja keksii kysymysten avulla itse ratkaisun kuhunkin ongelmaan. Ongelmanratkaisutaitojen …
Disciplinary contextualisation of transversal competence in Finnish local curricula : the case of multiliteracy, mathematics, and social studies
2020
Competence-based education is a widely implemented educational approach, but more research is needed into the relationship between transversal competences and individual disciplines. In this article, we present the results of a study focusing on how the transversal competence of multiliteracy is contextually defined in Finnish local curricula in the disciplines of mathematics and social studies. The article offers new insights into the discussion between content- and competence-based educations by introducing the concept of disciplinary contextualisation. Based on the qualitatively analysed data, four different types of disciplinary contextualisation are presented and further discussed. The…
Robustness of the Gaussian concentration inequality and the Brunn–Minkowski inequality
2016
We provide a sharp quantitative version of the Gaussian concentration inequality: for every $r>0$, the difference between the measure of the $r$-enlargement of a given set and the $r$-enlargement of a half-space controls the square of the measure of the symmetric difference between the set and a suitable half-space. We also prove a similar estimate in the Euclidean setting for the enlargement with a general convex set. This is equivalent to the stability of the Brunn-Minkowski inequality for the Minkowski sum between a convex set and a generic one.
On the interior regularity of weak solutions to the 2-D incompressible Euler equations
2016
We study whether some of the non-physical properties observed for weak solutions of the incompressible Euler equations can be ruled out by studying the vorticity formulation. Our main contribution is in developing an interior regularity method in the spirit of De Giorgi–Nash–Moser, showing that local weak solutions are exponentially integrable, uniformly in time, under minimal integrability conditions. This is a Serrin-type interior regularity result $$\begin{aligned} u \in L_\mathrm{loc}^{2+\varepsilon }(\Omega _T) \implies \mathrm{local\ regularity} \end{aligned}$$ for weak solutions in the energy space $$L_t^\infty L_x^2$$ , satisfying appropriate vorticity estimates. We also obtain impr…
Abstract and concrete tangent modules on Lipschitz differentiability spaces
2020
We construct an isometric embedding from Gigli's abstract tangent module into the concrete tangent module of a space admitting a (weak) Lipschitz differentiable structure, and give two equivalent conditions which characterize when the embedding is an isomorphism. Together with arguments from a recent article by Bate--Kangasniemi--Orponen, this equivalence is used to show that the ${\rm Lip}-{\rm lip}$ -type condition ${\rm lip} f\le C|Df|$ implies the existence of a Lipschitz differentiable structure, and moreover self-improves to ${\rm lip} f =|Df|$. We also provide a direct proof of a result by Gigli and the second author that, for a space with a strongly rectifiable decomposition, Gigli'…