Search results for "matriisit"

Neutriinojen ja kvarkkien sekoitusmatriisien välinen yhteys

2012

In this thesis relations between neutrino mixing matrix and quark mixing matrix are studied. The focus of the analysis is on two simple cases. In the first case it is assumed that the left matrix that diagonalizes the mass matrix of charged leptons and the corresponding matrix of down quarks are equal. In the second case it is likewise assumed that the corresponding diagonalizing matrices of neutrinos and up quarks are equal. First, theoretical concepts related to the mixing of quarks and especially to the mixing of neutrinos are presented. These are e.g. fermion mass generation in the Standard Model, Majorana masses of neutrinos and the so-called seesaw mechanism. Regarding experiments, ne…

Matriisin Hessenbergin muoto

2013

Spatial sign and rank based scatter matrices with applications

2007

The Radó–Kneser–Choquet theorem for $p$-harmonic mappings between Riemannian surfaces

2020

In the planar setting the Rad\'o-Kneser-Choquet theorem states that a harmonic map from the unit disk onto a Jordan domain bounded by a convex curve is a diffeomorphism provided that the boundary mapping is a homeomorphism. We prove the injectivity criterion of Rad\'o-Kneser-Choquet for $p$-harmonic mappings between Riemannian surfaces. In our proof of the injecticity criterion we approximate the $p$-harmonic map with auxiliary mappings that solve uniformly elliptic systems. We prove that each auxiliary mapping has a positive Jacobian by a homotopy argument. We keep the maps injective all the way through the homotopy with the help of the minimum principle for a certain subharmonic expressio…

Matriisinormeista

2015

Tässä tutkielmassa käsitellään vektori- ja matriisinormeja, niiden ominaisuuksia ja niihin liittyviä tuloksia. Matriisinormien tarkastelemiseksi on ensin mielekästä tietää, mikä on vektorinormi ja millaisia ominaisuuksia siltä vaaditaan. Vektorinormilla voidaan esimerkiksi laskea vektorin pituus. Matriisinormi taas mittaa esimerkiksi sitä, kuinka paljon maksimissaan vektori venyy matriisilla kerrottaessa. Vektorinormeille asetetaan kolme vaatimusta, joiden kaikkien tulee olla voimassa: positiivisuus, homogeenisuus ja kolmioepäyhtälö. Koska matriisit koostuvat vektoreista, siirtyvät vektorinormien vaatimukset suoraan matriisinormeille. Vektorinormien vaatimusten lisäksi matriisinormeille mää…