Natural Connection with Totally Skew-Symmetric Torsion on Riemannian Almost Product Manifolds

On a Riemannian almost product manifold $(M,P,g)$ we consider a linear connection preserving the almost product structure $P$ and the Riemannian metric $g$ and having a totally skew-symmetric torsion. We determine the class of the manifolds $(M,P,g)$ admitting such a connection and prove that this connection is unique in terms of the covariant derivative of $P$ with respect to the Levi-Civita connection. We find a necessary and sufficient condition the curvature tensor of the considered connection to have similar properties like the ones of the K\"ahler tensor in Hermitian geometry. We pay attention to the case when the torsion of the connection is parallel. We consider this connection on a Riemannian almost product manifold $(G,P,g)$ constructed by a Lie group $G$.Comment: 14 pages, a revised edition, an example is adde

Canonical connection on a class of Riemannian almost product manifolds

The canonical connection on a Riemannian almost product manifold is an analogue to the Hermitian connection on an almost Hermitian manifold. In this paper we consider the canonical connection on a class of Riemannian almost product manifolds with non-integrable almost product structure. We construct and characterize an example by a Lie group.Comment: 19 pages, some corrections in the example; J. Geom. (2012

A classification of the torsion tensors on almost contact manifolds with B-metric

The space of the torsion (0,3)-tensors of the linear connections on almost contact manifolds with B-metric is decomposed in 15 orthogonal and invariant subspaces with respect to the action of the structure group. Three known connections, preserving the structure, are characterized regarding this classification.Comment: 17 pages, exposition clarified, references adde

Bright light therapy versus physical exercise to prevent co-morbid depression and obesity in adolescents and young adults with attention-deficit/hyperactivity disorder: study protocol for a randomized controlled trial

Background: The risk for major depression and obesity is increased in adolescents and adults with attention-deficit / hyperactivity disorder (ADHD) and adolescent ADHD predicts adult depression and obesity. Non-pharmacological interventions to treat and prevent these co-morbidities are urgently needed. Bright light therapy (BLT) improves day– night rhythm and is an emerging therapy for major depression. Exercise intervention (EI) reduces obesity and improves depressive symptoms. To date, no randomized controlled trial (RCT) has been performed to establish feasibility and efficacy of these interventions targeting the prevention of co-morbid depression and obesity in ADHD. We hypothesize that the two manualized interventions in combination with mobile health-based monitoring and reinforcement will result in less depressive symptoms and obesity compared to treatment as usual in adolescents and young adults with ADHD. Methods: This trial is a prospective, pilot phase-IIa, parallel-group RCT with three arms (two add-on treatment groups [BLT, EI] and one treatment as usual [TAU] control group). The primary outcome variable is change in the Inventory of Depressive Symptomatology total score (observer-blinded assessment) between baseline and ten weeks of intervention. This variable is analyzed with a mixed model for repeated measures approach investigating the treatment effect with respect to all three groups. A total of 330 participants with ADHD, aged 14 – < 30 years, will be screened at the four study centers. To establish effect sizes, the sample size was planned at the liberal significance level of α = 0.10 (two-sided) and the power of 1-β = 80% in order to find medium effects. Secondary outcomes measures including change in obesity, ADHD symptoms, general psychopathology, health-related quality of life, neurocognitive function, chronotype, and physical fitness are explored after the end of the intervention and at the 12-week follow-up. This is the first pilot RCT on the use of BLT and EI in combination with mobile health-based monitoring and reinforcement targeting the prevention of co-morbid depression and obesity in adolescents and young adults with ADHD. If at least medium effects can be established with regard to the prevention of depressive symptoms and obesity, a larger scale confirmatory phase-III trial may be warranted.The trial is funded by the EU Framework Programme for Research and Innovation, Horizon 2020 (Project no. 667302). Funding period: January 2016–December 2020. This funding source had no role in the design of this study and will not have any role during its execution, analyses, interpretation of the data, or decision to submit results. Some local funds additionally contributed to carry out this study, especially for the preparation of the interventions: FBO research activity is by the Spanish Ministry of Economy and Competitiveness – MINECO (RYC-2011-09011) and by the University of Granada, Plan Propio de Investigación 2016, Excellence actions: Unit of Excellence on Exercise and Health (UCEES)

Ab initio investigation of the hyperfine structure in the 12^2Πu_u(X2^2A1_1, A2^2B1_1 system of BH2_2)

No abstract availabl

Ab initio calculation of the vibronically averaged hyperfine coupling constants in the two lowest electronic states of H2_2O+^+

No abstract availabl

Ab initio Investigation of the Structure of the X2^2A', A2^2A'' (12^2Π) Spectral System of HCO: Investigation of the Magnetic Hyperfine Effects

Results ofan ab initio study ofthe hyperfine structure of the X$^2$A', A$^2$ A" ( 1$^2 \Pi$) system ofthe formyl radical are presented. Special attention is paid to the analysis of the interplay between the vibronic and magnetic hyperfine etfects. The results of computations are in very good agreement with the available experimental findings. The values for the hyperfine coupling constants in lower bending Ievels of both electronic species are predicted

REVISITED VIBRONIC MODEL FOR LI+ ION AND FA(LI) CENTER IN ALKALI-HALIDES

The controversial far-infrared optical absorption in Li-doped alkali halides is now attributed to transitions between the low-lying energy levels of an anharmonic oscillator composed of three halogen-ion pairs centred at the cation site which vibrate in the T1u ungerade mode. This oscillator is electronically coupled to the impurity dragging it into rotation over sites. Several experimental features derive simply from our model such as the absence of any clear-cut lithium-isotope effect and the low-frequency range. The capital effect of an F centre at a nearest-neighbour (nn) site is to reduce the dimensionality of vibration forcing the impurity to rotate in the perpendicular (001)-plane. This upgrades the optical frequency in proportion to (3/2)1/2 and shrinks the off-centre displacement. We finally show that recent computer-simulation data on Li-doped alkali halides provide a solid ground for regarding the Li off-centredness as a pseudo-Jahn-Teller phenomenon