Quaternionic Hyperbolic Function Theory

We are studying hyperbolic function theory in the skew-field of quaternions. This theory is connected to k-hyperbolic harmonic functions that are harmonic with respect to the hyperbolic Riemannian metric (Formula Presented) in the upper half space (Formula Presented). In the case k = 2, the metric is the hyperbolic metric of the Poincaré upper half-space. Hempfling and Leutwiler started to study this case and noticed that the quaternionic power function xm(m ε Z), is a conjugate gradient of a 2-hyperbolic harmonic function. They researched polynomial solutions. We find fundamental k-hyperbolic harmonic functions depending only on the hyperbolic distance and x3. Using these functions we are able to verify a Cauchy type integral formula. Earlier these results have been verified for quaternionic functions depending only on reduced variables (x0, x1, x2). Our functions are depending on four variables. © Springer Nature Switzerland AG 2019.Peer reviewe

Universal distribution of magnetic anisotropy of impurities in ordered and disordered nano-grains

We examine the distribution of the magnetic anisotropy (MA) experienced by a magnetic impurity embedded in a metallic nano-grain. As an example of a generic magnetic impurity with partially filled $d$-shell, we study the case of $d^{1}$ impurities imbedded into ordered and disordered Au nano-grains, described in terms of a realistic band structure. Confinement of the electrons induces a magnetic anisotropy that is large, and can be characterized by 5 real parameters, coupling to the quadrupolar moments of the spin. In ordered (spherical) nano-grains, these parameters exhibit symmetrical structures and reflect the symmetry of the underlying lattice, while for disordered grains they are randomly distributed and, - for stronger disorder, - their distribution is found to be characterized by random matrix theory. As a result, the probability of having small magnetic anisotropies $K_L$ is suppressed below a characteristic scale $\Delta_E$, which we predict to scale with the number of atoms $N$ as $\Delta_E\sim 1/N^{3/2}$. This gives rise to anomalies in the specific heat and the susceptibility at temperatures $T\sim \Delta_E$ and produces distinct structures in the magnetic excitation spectrum of the clusters, that should be possible to detect experimentally

Replicating the Family: The Biopolitics of Involvement Discourses Concerning Relatives in Nursing Home Institutions

The aim of this study was to describe the biopolitics of involvement discourses articulated by nursing staff concerning relatives in nursing home institutions, using a Foucault-inspired discourse analytical approach. Previous research has described how relatives have not been involved in nursing homes on their own terms. This is partly due to a lack of communication and knowledge, but it is also a consequence of an unclear organizational structure. Results from a discourse analysis of six focus group interviews with nursing staff show that the “involvement discourse” in nursing homes can be described as a “new” vs “old” family rhetoric. This rhetoric can be said to uphold, legitimize and provide different subject positions for both nursing staff and relatives concerning the conditions for involvement in nursing homes. As part of a “project of possibility” in elderly care, it may be possible to adopt a critical pedagogical approach among nursing staff in order to educate, strengthen and support them in reflecting on their professional norming and how it conditions the involvement of relatives

Beyond viral suppression: the quality of life of people living with HIV in Sweden

Sweden has one of the best HIV treatment outcomes in the world and an estimated 95% of all diagnosed people living with HIV are virally suppressed, but the quality of life (QoL) is understudied. The aim of this study was to examine the associations between variables within sociodemographic, behavioural, clinical, psychological, sexual life, social support and personal resource component and the QoL of people living with HIV in Sweden. Data were derived from a cross-sectional, nation-wide survey completed by 15% (n = 1096) of all people living with HIV and collected at 15 infectious disease clinics and 2 needle exchange sites during 2014. Ordinal univariate and multivariate logistic regression analyses were used to examine associations between potential contributors and QoL. Respondents reported high QoL: 63% rated their QoL 7 or higher on a scale ranging from 0 to 10. QoL was independent of gender, age, mode of HIV transmission and country of origin. Lower QoL was associated with recent homelessness, hazardous alcohol consumption, comorbidities, treatment side-effects, HIV-related physical symptoms, hopelessness, negative self-image, sexual dissatisfaction, and negative changes in sex life after HIV. The QoL of people living with HIV in Sweden was high overall, but still significantly influenced by HIV

Conserved Matter Superenergy Currents for Orthogonally Transitive Abelian G2 Isometry Groups

In a previous paper we showed that the electromagnetic superenergy tensor, the Chevreton tensor, gives rise to a conserved current when there is a hypersurface orthogonal Killing vector present. In addition, the current is proportional to the Killing vector. The aim of this paper is to extend this result to the case when we have a two-parameter Abelian isometry group that acts orthogonally transitive on non-null surfaces. It is shown that for four-dimensional Einstein-Maxwell theory with a source-free electromagnetic field, the corresponding superenergy currents lie in the orbits of the group and are conserved. A similar result is also shown to hold for the trace of the Chevreton tensor and for the Bach tensor, and also in Einstein-Klein-Gordon theory for the superenergy of the scalar field. This links up well with the fact that the Bel tensor has these properties and the possibility of constructing conserved mixed currents between the gravitational field and the matter fields.Comment: 15 page

Microscopic origin of Heisenberg and non-Heisenberg exchange interactions in ferromagnetic bcc Fe

By means of first principles calculations we investigate the nature of exchange coupling in ferromagnetic bcc Fe on a microscopic level. Analyzing the basic electronic structure reveals a drastic difference between the $3d$ orbitals of $E_g$ and $T_{2g}$ symmetries. The latter ones define the shape of the Fermi surface, while the former ones form weakly-interacting impurity levels. We demonstrate that, as a result of this, in Fe the $T_{2g}$ orbitals participate in exchange interactions, which are only weakly dependent on the configuration of the spin moments and thus can be classified as Heisenberg-like. These couplings are shown to be driven by Fermi surface nesting. In contrast, for the $E_g$ states the Heisenberg picture breaks down, since the corresponding contribution to the exchange interactions is shown to strongly depend on the reference state they are extracted from. Our analysis of the nearest-neighbour coupling indicates that the interactions among $E_g$ states are mainly proportional to the corresponding hopping integral and thus can be attributed to be of double-exchange origin.Comment: 5 pages, 4 figure