Search results for "ongelma"

Mathematical Fuzzy Logic in the Emerging Fields of Engineering, Finance, and Computer Sciences

2022

With more than 50 years of literature, fuzzy logic has gradually progressed from an emerging field to a developed research domain, incorporating the sub-domain of mathematical fuzzy logic (MFL) [...]

Jacobian of solutions to the conductivity equation in limited view

2022

Abstract The aim of hybrid inverse problems such as Acousto-Electric Tomography or Current Density Imaging is the reconstruction of the electrical conductivity in a domain that can only be accessed from its exterior. In the inversion procedure, the solutions to the conductivity equation play a central role. In particular, it is important that the Jacobian of the solutions is non-vanishing. In the present paper we address a two-dimensional limited view setting, where only a part of the boundary of the domain can be controlled by a non-zero Dirichlet condition, while on the remaining boundary there is a zero Dirichlet condition. For this setting, we propose sufficient conditions on the bounda…

The Calderón problem for the fractional Schrödinger equation

2020

We show global uniqueness in an inverse problem for the fractional Schr\"odinger equation: an unknown potential in a bounded domain is uniquely determined by exterior measurements of solutions. We also show global uniqueness in the partial data problem where the measurements are taken in arbitrary open, possibly disjoint, subsets of the exterior. The results apply in any dimension $\geq 2$ and are based on a strong approximation property of the fractional equation that extends earlier work. This special feature of the nonlocal equation renders the analysis of related inverse problems radically different from the traditional Calder\'on problem.

Mobiiliopetuksen käyttömahdollisuuksia : oppilaiden omien mobiililaitteiden käyttö peruskoulun alakoulun opetuksessa

2015

Muutaman viime vuoden aikana mobiililaitteiden käyttö kouluissa on yleistynyt. Tämä on osittain aiheuttanut ristiriitaista keskustelua laitteiden käytöstä opetuksessa. Osa opettajista on ottanut mobiililaitteet opetuskäyttöön innokkaasti. Mobiiliopetuksen mahdollisuuksia ei kuitenkaan ole vielä kovin paljon tutkittu. Tällä tutkimuksella oli tarkoitus selvittää, mitä mahdollisuuksia oppilaiden omat mobiililaitteet tarjoavat opetukseen. Aineiston analyysissa pyrittiin etsimään tietoa siitä, miten ongelma-perustaisen opetuksen menetelmä ja pelillisyys vaikuttavat opetus- ja oppimisprosessissa, kun opiskelumenetelmänä käytetään mobiilioppimista ja oppilaiden omia mobiililaitteita. Tutkimus teht…

Exponential instability in the fractional Calder\'on problem

2017

In this note we prove the exponential instability of the fractional Calder\'on problem and thus prove the optimality of the logarithmic stability estimate from \cite{RS17}. In order to infer this result, we follow the strategy introduced by Mandache in \cite{M01} for the standard Calder\'on problem. Here we exploit a close relation between the fractional Calder\'on problem and the classical Poisson operator. Moreover, using the construction of a suitable orthonormal basis, we also prove (almost) optimality of the Runge approximation result for the fractional Laplacian, which was derived in \cite{RS17}. Finally, in one dimension, we show a close relation between the fractional Calder\'on pro…

The linearized Calderón problem on complex manifolds

2019

International audience; In this note we show that on any compact subdomain of a Kähler manifold that admits sufficiently many global holomorphic functions , the products of harmonic functions form a complete set. This gives a positive answer to the linearized anisotropic Calderón problem on a class of complex manifolds that includes compact subdomains of Stein manifolds and sufficiently small subdomains of Kähler manifolds. Some of these manifolds do not admit limiting Carleman weights, and thus cannot by treated by standard methods for the Calderón problem in higher dimensions. The argument is based on constructing Morse holo-morphic functions with approximately prescribed critical points.…

Determining a Random Schrödinger Operator : Both Potential and Source are Random

2020

We study an inverse scattering problem associated with a Schr\"odinger system where both the potential and source terms are random and unknown. The well-posedness of the forward scattering problem is first established in a proper sense. We then derive two unique recovery results in determining the rough strengths of the random source and the random potential, by using the corresponding far-field data. The first recovery result shows that a single realization of the passive scattering measurements uniquely recovers the rough strength of the random source. The second one shows that, by a single realization of the backscattering data, the rough strength of the random potential can be recovered…

Environmental Problem-solving and Hands-on Geometry Learning through Storytelling inside a Geodesic Dome : Ice, Honey and Stardust

2019

In this workshop, we introduce a STEAM learning activity based on the construction of geodesic domes. This workshop will engage participants in various preliminary and exploratory constructions, while also applying the geometry of geodesic domes to approximate hemispheres. Various storytelling, role-playing, and environmental connections that can provide needed context for learners of all ages are explored. peerReviewed

Nuorten vankien lapsuuden väkivaltakokemukset ja heidän vanhempiensa parisuhdeongelmat

1999

The case of literacy motivation : Playful 3D immersive learning environments and problem-focused education for blended digital storytelling

2018

The University of Patras' Library Services designed and offered to primary and secondary schools the pilot educational program “From the Ancient to the Modern Tablets”, featuring immersive multimedia learning experiences about the book history. The pilot program consisted of three stages: a playful library tour, followed by an interactive game-based digital storytelling activity with game elements, and a collaborative creative reflective hands-on activity. Utilizing the avatar psychology power, the visualization and simulation affordances of 3D immersive learning environments and the appeal of storytelling and game-based learning, the “gamified” blended narrative on the book evolution enabl…