Two-root Riemannian Manifolds

Osserman manifolds are a generalization of locally two-point homogeneous spaces. We introduce $k$-root manifolds in which the reduced Jacobi operator has exactly $k$ eigenvalues. We investigate one-root and two-root manifolds as another generalization of locally two-point homogeneous spaces. There is no connected one-root or two-root Riemannian manifold of dimension $n\geq 3$ other than those that are globally Osserman, unless $n$ is divisible by four

Control of high frequency electromagnetic radiation

Mössbauer nuclei in thin film nanostructures are an established platform for X-ray quantum optics, and provide novel methods for the narrowband control of hard X-rays. However, quantum optical models for these nanostructures have so far only considered grazing incidence geometry, in a regime of idealized plane wave propagation, and homogeneous nuclear hyper-fine environments. We develop a theoretical description for the interaction of X-rays with Mössbauer nuclei in arbitrary geometries, including dispersive effects, using macroscopic quantum electrodynamics to derive Maxwell-Bloch equations. We use this formalism to study: 1. the effects of beam divergence and inhomogeneous hyper-fine distributions on energy spectra at grazing incidence. In particular, we demonstrate that the collective Lamb shift and broadening of single mode super-radiance can be used to overcome the effects of inhomogeneous broadening, and result in a single line spectrum in the large collective coupling limit. 2. the equations of motion for guided modes coupled to Mössbauer nuclei. We show that these modes obey equations of motion analogous to nuclear forward scattering. We study the interference of multiple modes coupled to a longitudinally structured layer of nuclei, and demonstrate selective super and sub radiant emission. This demonstrates that front coupling to thin film nanostructures opens the door for a vast new space of techniques for the control of hard X-rays

Uticaj galektina-3 na remodelovanje miokarda i rani klinički ishod kod pacijenata sa akutnim infarktom miokarda

Our study investigated association between galectin-3 levels and adverse left ventricular remodelling at six months. Eighty-six patients following first AMI and stable angina (control group) were enrolled in this study and blood samples collected on day 1 from the femoral vein and artery, the right atrium near the coronary sinus and the aortic root; on day 5 from cubital vein and radial artery; on day 30 from the cubital vein. Patients with LVESV ≥ 20% at six months, were included in the LVR group. In patients with acute myocardial infarction, on day 1, Galectin-3 plasma levels in the femoral vein (10.34 ng/ml ± 3.81 vs 8.22 ng/ml ± 2.34, p=0.01), and coronary sinus (10.7 ng/ml ± 3.97 vs 8.41 ng/ml ± 2.56, p=0.007) were higher in the LVR group. Positive correlations between galectin-3 levels from aortic root and coronary sinus, aortic root and femoral vein, and coronary sinus and femoral vein were observed in both groups. On day 30, galectin-3 concentration in the cubital vein was an independent risk factor of LVR six months post-AMI, demonstrating 1.5-fold increased risk. Day-30 galectin-3 showed positive correlations with echocardiography parameters indicative of diastolic and systolic dysfunction. On day one galectin-3 levels in aortic root are significantly higher in patients with fatal outcome six months later. Determining galectin-3 plasma concentration on day 30 following AMI could have beneficial prognostic value in predicting LVR

PROCUREMENT OPTIMIZATION BY SELECTING EFFICIENT SUPPLIERS USING DEA-FUCOM-COCOSO APPROACH AND SOLVING ORDER ALLOCATION PROBLEM

Procurement logistics is one of the most important segments of the supply chain and one of the key factors of a company’s competitiveness. For that reason, many companies strive for constant optimization of this segment of the supply chain, both in terms of costs and in terms of time, reliability, etc. The aim of this paper is to develop a new approach based on DEA-FUCOM-CoCoSo methods that aim to select efficient suppliers. The developed model was tested on the data of one trading company. The DEA method was used in order to select only efficient ones from 29 observed in this paper. The FUCOM method was used to determine the weights of the 9 observed criteria used in the CoCoSo method for evaluation of 6 efficient suppliers. The results of the application of this method determined the final rank of suppliers, after which only the first 3 suppliers were considered. At the very end, a model for solving the problem of order allocation is defined in order to determine from which supplier it is necessary to order goods and in what quantity. By applying the defined model, the quantities that need to be ordered from certain suppliers in order to meet the demand on the market are obtained. Based on the results, the developed approach showed the possibility of large application not only on the observed example but also on a larger problem