On the recursive sequence x(n+1)=xn-(k+1)/1+xnxn-1...xn-k

In this paper a solution of the one difference equation was investigated

The Schrodinger equation with Hulthen potential plus ring-shaped potential

We present the solutions of the Schr$\ddot{o}$dinger equation with the Hulth$\acute{e}$n potential plus ring-shape potential for $\ell\neq 0$ states within the framework of an exponential approximation of the centrifugal potential.Solutions to the corresponding angular and radial equations are obtained in terms of special functions using the conventional Nikiforov-Uvarov method. The normalization constant for the Hulth$\acute{e}$n potential is also computed.Comment: Typed with LateX,12 Pages, Typos correcte

Special Functions Related to Dedekind Type DC-Sums and their Applications

In this paper we construct trigonometric functions of the sum T_{p}(h,k), which is called Dedekind type DC-(Dahee and Changhee) sums. We establish analytic properties of this sum. We find trigonometric representations of this sum. We prove reciprocity theorem of this sums. Furthermore, we obtain relations between the Clausen functions, Polylogarithm function, Hurwitz zeta function, generalized Lambert series (G-series), Hardy-Berndt sums and the sum T_{p}(h,k). We also give some applications related to these sums and functions

Comparison between the STENTYS self-apposing bare metal and paclitaxel-eluting coronary stents for the treatment of saphenous vein grafts (ADEPT trial)

Aims To describe the safety and performance of STENTYS self-expandable bare metal stents (BMS) versus paclitaxel-eluting stents (PES) in saphenous vein grafts (SVGs). Methods and Results A randomised controlled trial was performed in four hospitals in three European countries between December 2011 and December 2013. Patients with de novo lesions (>50% stenosis) in an SVG with a diameter between 2.5–6 mm were included. Primary endpoint was late lumen loss at 6 months. Secondary endpoints included procedural success and the occurrence of major adverse cardiac events (MACE) at 12 months. A total of 57 patients were randomised to STENTYS self-apposing BMS (n = 27) or PES (n = 30). Procedural success was obtained in 89.5%. No significant differences in late lumen loss were found between BMS and PES at 6 months (0.53 mm vs 0.47; p = 0.86). MACE rates at 12 months were comparable in both groups (BMS 22.2% vs. PES 26.7%; p = 0.70). Conclusions Treatment of SVGs with STENTYS self-expandable stents is safe and effective. No significant differences were found in late lumen loss and MACE between BMS and PES

Magnetic and superconducting anisotropy in Ni-doped RbEuFe4_4As4_4 single crystals

We investigate the effect of Ni doping on the Fe-site in single crystals of the magnetic superconductor RbEuFe$_4$As$_4$ for doping concentrations of up to 4%. A clear suppression in the superconducting transition temperature is observed in specific heat, resistivity and magnetization measurements. Upon Ni-doping, the resistivity curves shift up in a parallel fashion indicating a strong increase of the residual resistivity due to scattering by charged dopand atoms while the shape of the curve and thus the electronic structure appears largely unchanged. The observed step $\Delta C/T_c$ at the superconducting transition decreases strongly for increasing Ni doping in agreement with expectations based on a model of multi-band superconductivity and strong inter-band pairing. The upper critical field slopes are reduced upon Ni doping for in- as well as out-of-plane fields leading to a small reduction in the superconducting anisotropy. The specific heat measurements of the magnetic transition reveal the same BKT behavior close to the transition temperature $T_m$ for all doping levels. The transition temperature is essentially unchanged upon doping. The in to out-of-plane anisotropy of Eu-magnetism observed at small magnetic fields is unaltered as compared to the undoped compound. All of these observations indicate a decoupling of the Eu magnetism from superconductivity and essentially no influence of Ni doping on the Eu magnetism in this compound

Point defect segregation and its role in the detrimental nature of Frank partials in Cu(In,Ga)Se2 thin-film absorbers

The interaction of point defects with extrinsic Frank loops in the photovoltaic absorber material Cu(In,Ga)Se₂ was studied by aberration-corrected scanning transmission electron microscopy in combination with electron energy-loss spectroscopy and calculations based on density-functional theory. We find that Cu accumulation occurs outside of the dislocation cores bounding the stacking fault due to strain-induced preferential formation of Cu‾²In, which can be considered a harmful hole trap in Cu(In,Ga)Se₂. In the core region of the cation-containing α-core, Cu is found in excess. The calculations reveal that this is because Cu on In-sites is lowering the energy of this dislocation core. Within the Se-containing β-core, in contrast, only a small excess of Cu is observed, which is explained by the fact that Cu¡ⁿ and Cu¡ are the preferred defects inside this core, but their formation energies are positive. The decoration of both cores induces deep defect states, which enhance nonradiative recombination. Thus, the annihilation of Frank loops during the Cu(In,Ga)Se₂ growth is essential in order to obtain absorbers with high conversion efficiencies