On the Aharonov-Casher formula for different self-adjoint extensions of the Pauli operator with singular magnetic field

Two different self-adjoint Pauli extensions describing a spin-1/2 two-dimensional quantum system with singular magnetic field are studied. An Aharonov-Casher type formula is proved for the maximal Pauli extension and it is also checked that this extension can be approximated by operators corresponding to more regular magnetic fields

Spectral properties of higher order anharmonic oscillators

We discuss spectral properties of the self-adjoint operator $$-d^2/dt^2 + (t^{k+1}/(k+1)-\alpha)^2$$ in $L^2(\mathbb{R})$ for odd integers $k$. We prove that the minimum over $\alpha$ of the ground state energy of this operator is attained at a unique point which tends to zero as $k$ tends to infinity. Moreover, we show that the minimum is non-degenerate. These questions arise naturally in the spectral analysis of Schr\"{o}dinger operators with magnetic field. This extends or clarifies previous results by Pan-Kwek, Helffer-Morame, Aramaki, Helffer-Kordyukov and Helffer.Comment: 15 pages, 2 figure

Lack of diamagnetism and the Little-Parks effect

When a superconducting sample is submitted to a sufficiently strong external magnetic field, the superconductivity of the material is lost. In this paper we prove that this effect does not, in general, take place at a unique value of the external magnetic field strength. Indeed, for a sample in the shape of a narrow annulus the set of magnetic field strengths for which the sample is superconducting is not an interval. This is a rigorous justification of the Little-Parks effect. We also show that the same oscillation effect can happen for disc-shaped samples if the external magnetic field is non-uniform. In this case the oscillations can even occur repeatedly along arbitrarily large values of the Ginzburg--Landau parameter $\kappa$. The analysis is based on an understanding of the underlying spectral theory for a magnetic Schr\"{o}dinger operator. It is shown that the ground state energy of such an operator is not in general a monotone function of the intensity of the field, even in the limit of strong fields

Eigenvalue asymptotics of the even-dimensional exterior Landau-Neumann Hamiltonian

We study the Schroedinger operator with a constant magnetic field in the exterior of a compact domain in $\mathbb{R}^{2d}$, $d\geq 1$. The spectrum of this operator consists of clusters of eigenvalues around the Landau levels. We give asymptotic formulas for the rate of accumulation of eigenvalues in these clusters. When the compact is a Reinhart domain we are able to show a more precise asymptotic formula

UWB in medical diagnostics and treatment

Advances in neuro diagnostics based on microwave antenna system in terms of a helmet including a set of broad band patch antennas is presented. It is shown that classification algorithms can be used to detect internal bleeding in stroke patients. The present presentation paper also address the challenges to deliver uniform target levels of hyperthermia under strict spatial and temporal parameters

Challenges of implementing decision support systems: Joining the views of consultant and customer

In today's business environment, organizations rely on information systems to store and process the information constantly gathered. These systems are used to support the everyday needs of the organization. It is apparent that many of these systems has limited or no analytical capabilities, can the introduction of a decision support system could enable practitioners to benefit from this can thus increase their productivity by executing excellent decisions. This thesis choose to focus on expertise necessary for implementing the system, and challenges accompanied with this process. In order to find the answers regarding these topics, a theoretical framework on the topic of decision support systems and the approaches necessary to implement the system. The framework is composed by four themes; External expertise, Internal expertise, Human challenges, Conceptual challenges. The thesis support the arguments from the theoretical grounding by conducting a qualitative analysis with both consultants and the customer in a specific implementation environment. The use of semi-structured interviewing enables the thesis to benefit from the development of each interviewee and can thus get a rich description on the situation of the implementation. Each of the four themes will present the personal impressions of both consultant and customer by presenting each party separately and thus enabling every factor to be discussed from a provider perspective as well as buyer. The findings of this thesis contribute to the body of knowledge by presenting each theme in context to the implementation setting of the project