On second order degree of graphs

Given a vertex v of a graph G the second order degree of v denoted as d 2(v) is defined as the number of vertices at distance 2 from v.In this paper we address the following question:What are the sufficient conditions for a graph to have a vertex v such that d2(v) ≥ d(v),where d(v) denotes the degree of v? Among other results,every graph of minimum degree exactly 2,except four graphs,is shown to have a vertex of second order degree as large as its own degree.Moreover,every K-4-free graph or every maximal planar graph is shown to have a vertex v such that d2(v) ≥ d(v).Other sufficient conditions on graphs for guaranteeing this property are also proved.     

Untersuchung von Fetten und ?len.

Ohne Zusammenfassung     

Die quantitative Verfolgung des Sulfurierungsprozesses

Ohne Zusammenfassung     

Apparate

Ohne Zusammenfassung     

Preparation and Evaluation of [18F]AlF-NOTA-NOC for PET Imaging of Neuroendocrine Tumors: Comparison to [68Ga]Ga-DOTA/NOTA-NOC

Background: The somatostatin receptors 1–5 are overexpressed on neuroendocrine neoplasms and, as such, represent a favorable target for molecular imaging. This study investigates the potential of [¹⁸F]AlF-NOTA-[1-Nal³]-Octreotide and compares it in vivo to DOTA- and NOTA-[1-Nal³]-Octreotide radiolabeled with gallium-68. Methods: DOTA- and NOTA-NOC were radiolabeled with gallium-68 and NOTA-NOC with [¹⁸F]AlF. Biodistributions of the three radioligands were evaluated in AR42J xenografted mice at 1 h p.i and for [¹⁸F]AlF at 3 h p.i. Preclinical PET/CT was applied to confirm the general uptake pattern. Results: Gallium-68 was incorporated into DOTA- and NOTA-NOC in yields and radiochemical purities greater than 96.5%. NOTA-NOC was radiolabeled with [¹⁸F]AlF in yields of 38 ± 8% and radiochemical purity above 99% after purification. The biodistribution in tumor-bearing mice showed a high uptake in tumors of 26.4 ± 10.8 %ID/g for [⁶⁸Ga]Ga-DOTA-NOC and 25.7 ± 5.8 %ID/g for [⁶⁸Ga]Ga-NOTA-NOC. Additionally, [¹⁸F]AlF-NOTA-NOC exhibited a tumor uptake of 37.3 ± 10.5 %ID/g for [¹⁸F]AlF-NOTA-NOC, which further increased to 42.1 ± 5.3 %ID/g at 3 h p.i. Conclusions: The high tumor uptake of all radioligands was observed. However, [¹⁸F]AlF-NOTA-NOC surpassed the other clinically well-established radiotracers in vivo, especially at 3 h p.i. The tumor-to-blood and -liver ratios increased significantly over three hours for [¹⁸F]AlF-NOTA-NOC, making it possible to detect liver metastases. Therefore, [¹⁸F]AlF demonstrates promise as a surrogate pseudo-radiometal to gallium-68.     

Influence of post-deposition annealing on the structural,optical and electrical properties of Li and Mg co-doped ZnO thin films deposited by sol–gel technique

Lithium (Li) and magnesium (Mg) co-doped zinc oxide (ZnO) thin films were deposited by sol–gel method using spin coating technique. The films were deposited on glass substrates and annealed at different temperatures. The effects of annealing temperature on the structural, optical and electrical properties of the deposited films were investigated using X-ray diffraction (XRD), Ultraviolet–Visible absorption spectra (UV–VIS), photoluminescence spectra (PL), X-ray photo electron spectroscopy (XPS) and Hall measurements. XRD patterns indicated that the deposited films had a polycrystalline hexagonal wurtzite structure with preferred (0 0 0 2) orientation. All films were found to exhibit a good transparency in the visible range. Analysis of the absorption edge revealed that the optical band gap energies of the films annealed at different temperatures varies between 3.49 eV and 3.69 eV. Room temperature PL spectra of the deposited films annealed at various temperatures consist of a near band edge emission and visible emission due to the electronic defects, which are related to deep level emissions, such as oxide antisite (O_Zn), interstitial zinc (Zn_i), interstitial oxygen (O_i) and zinc vacancy (V_Zn) which are generated during annealing process. The influence of annealing temperature on the chemical state of the dopants in the film was analysed by XPS spectra. Ion beam analysis (Rutherford back scattering) experiments were performed to evaluate the content of Li and Mg in the films. Hall measurements confirmed the p-type nature of the deposited films.     

Transverse energy distributions in Si-nucleus collisions at 10 GeV/nucleon

Transverse energy distributions have been measured for collisions of 10 GeV/nucleon Si with targets of Al, Cu and Pb using a combination of a NaI wall and a uranium based sampling calorimeter. The measured cross sectionsdσ/dE _T anddE _T /dη are consistent with full stopping and an increase, with increasing values ofE _T , of energy flow into large angles.     

A new family of noncommutative 2-spheres

We give new examples of noncommutative manifolds. In particular we construct a “strong” deformation of C(S²), consisting of a family of noncommutative 2-spheres, and study their analytic and topological properties.