In this thesis, we present a mathematical study of three problems arising in the kinetic theory of quantum gases. In the first part, we consider a Boltzmann equation that is used to describe the time evolution of the ...

The discovery of high-temperature superconductors in 1986 represented a major experimental breakthrough (Nobel Prize 1987), but their theoretical explanation is still a subject of much debate. These materials have many ...

Fire-spotting is often responsible for a dangerous flare up in the wildfire and causes secondary ignitions isolated from the primary fire zone leading to perilous situations. The main aim of the present research to provide ...

In the Fourier heat conduction equation, when the flux definition is expressed as the product of a constant diffusivity and the temperature gradient, the characteristic length scale evolves as the square root of time. ...

We consider an ensemble of Ornstein–Uhlenbeck processes featuring a population of relaxation times and a population of noise amplitudes that characterize the heterogeneity of the ensemble. We show that the centre-of-mass ...

The emerging diffusive dynamics in many complex systems shows a characteristic crossover behaviour from anomalous to normal diffusion which is otherwise fitted by two independent power-laws. A prominent example for a ...

Our goal is to convince the readers that the theory of complex normal surface singularities can be a powerful tool in the study of numerical semigroups, and, in the same time, a very rich source of interesting affine and ...

We study invariance of multiplicity of complex analytic germs and degree of complex affine sets under outer bi-Lipschitz transformations (outer bi-Lipschitz homeomorphims of germs in the first case and outer bi-Lipschitz ...

A polynomial counterpart of the Seiberg-Witten invariant associated with a negative definite plumbing 3-manifold has been proposed by earlier work of the authors. It is provided by a special decomposition of the zeta-function ...

In this paper it is presented some classes of homeomorphisms that preserve multiplicity and tangent cones of complex analytic sets. Moreover, we present a class of homeomorphisms that has the multiplicity as an invariant ...