The Geometry of Self-dual 2-forms

We show that self-dual 2-forms in 2n dimensional spaces determine a $n^2-n+1$ dimensional manifold ${\cal S}_{2n}$ and the dimension of the maximal linear subspaces of ${\cal S}_{2n}$ is equal to the (Radon-Hurwitz) number of linearly independent vector fields on the sphere $S^{2n-1}$. We provide a direct proof that for $n$ odd ${\cal S}_{2n}$ has only one-dimensional linear submanifolds. We exhibit $2^c-1$ dimensional subspaces in dimensions which are multiples of $2^c$, for $c=1,2,3$. In particular, we demonstrate that the seven dimensional linear subspaces of ${\cal S}_{8}$ also include among many other interesting classes of self-dual 2-forms, the self-dual 2-forms of Corrigan, Devchand, Fairlie and Nuyts and a representation of ${\cal C}l_7$ given by octonionic multiplication. We discuss the relation of the linear subspaces with the representations of Clifford algebras.Comment: Latex, 15 page

Monopole equations on 8-manifolds with Spin(7) holonomy

We construct a consistent set of monopole equations on eight-manifolds with Spin(7) holonomy. These equations are elliptic and admit non-trivial solutions including all the 4-dimensional Seiberg-Witten solutions as a special case.Comment: 14 pages, LATEX (No figures

Mental disorders frequency alternative and complementary medicine usage among patients with hypertension and type 2 diabetes mellitus

Objectives: Diabetes mellitus (DM) and hypertension (HT) are chronic disorders with which mental disorders may coexist and for which patients may resort to alternative medicine use. Alternative and complementary medicine is a treatment option that patients tend to use. This study is to determine the prevalence of mental disorders among patients diagnosed with DM and HT and their use of alternative medicine methods.Materials and Methods The study was conducted in a primary care setting. The data were collected from the Family Health Center No. 4 at Çankaya, Ankara, Turkey. It involved patients aged between 18 and 65, who were on follow‑up treatment for DM and HT. Patients accepted to participate in the study were administered the sociodemographic data form, the Primary Care Evaluation of Mental Disorders (PRIME‑MD) questionnaire and the alternative medicine inquiry form.Participants: One hundred and sixteen patients with HT and 119 patients with DM (type 2) were recruited for the study.Results: In this study, 47.4% of HT patients and 53.8% of the DM patients were diagnosed with a PRIME‑MD. The most commonly encountered disorder was mood disorders, in 37.1% of the HT patients and 45.4% of the DM patients. In this study, four HT patients (0.3%) and no DM patients stated that they resorted to complimentary medicine, which can use be used alongside conventional medical treatment and may help to feel better and cope better with any chronic condition. All four HT patients were using multivitamin combinations to support the treatment. As the alternative medicine usage was described as treatment used instead of conventional medical treatment we did not find any patient using alternative medicine.Conclusions: Mental disorders may coexist with HT and DM. Some of the HT and DM patients suffering from a mental disorder seek psychiatric support, while others do not. We believe that it is important to examine patients for mental disorders, while being followed‑up for a chronic disease.Keywords: Alternative medicine, diabetes mellitus, hypertension, mental disorde

Interstitialcy diffusion of oxygen in tetragonal La₂CoO_4+δ

We report on the mechanism and energy barrier for oxygen diffusion in tetragonal La2CoO4+δ. The first principles-based calculations in the Density Functional Theory (DFT) formalism were performed to precisely describe the dominant migration paths for the interstitial oxygen atom in La2CoO4+δ. Atomistic simulations using molecular dynamics (MD) were performed to quantify the temperature dependent collective diffusivity, and to enable a comparison of the diffusion barriers found from the force field-based simulations to those obtained from the first principles-based calculations. Both techniques consistently predict that oxygen migrates dominantly via an interstitialcy mechanism. The single interstitialcy migration path involves the removal of an apical lattice oxygen atom out from the LaO-plane and placing it into the nearest available interstitial site, whilst the original interstitial replaces the displaced apical oxygen on the LaO-plane. The facile migration of the interstitial oxygen in this path is enabled by the cooperative titling-untilting of the CoO6 octahedron. DFT calculations indicate that this process has an activation energy significantly lower than that of the direct interstitial site exchange mechanism. For 800-1000 K, the MD diffusivities are consistent with the available experimental data within one order of magnitude. The DFT- and the MD-predictions suggest that the diffusion barrier for the interstitialcy mechanism is within 0.31-0.80 eV. The identified migration path, activation energies and diffusivities, and the associated uncertainties are discussed in the context of the previous experimental and theoretical results from the related Ruddlesden-Popper structures