Threshold strangeness production in pp interactions

During the actual lectures, features of the COSY-Jülich accelerator were presented, followed by a short summary of ongoing experiments at the COoler SYnchrotron COSY using internal as well as external beams in the range of 45 MeV to 2.5 GeV. Here the research of the COSY-11 collaboration is presented. This °⁰ facility studies the hidden and open strangeness production observing the ν and η′ as well the K⁺Y and K⁺K^? production in the proton—proton interactions at the respective thresholds.     

Electrochemical and Scalable Dehydrogenative C(sp3)−H Amination via Remote Hydrogen Atom Transfer in Batch and Continuous Flow

A hydrogen atom transfer-directed electrochemical intramolecular C−H amination has been developed in which the N-radical species are generated at the anode, and the base required for the reaction is generated at the cathode. A broad range of valuable pyrrolidines were prepared in good yields and with high chemoselectivity. The reaction was easily scaled up in both batch and continuous flow systems.     

Diphenylberyllium Reinvestigated: Structure,Properties, and Reactivity of BePh2, [(12-crown-4)BePh]+, and [BePh3]−

The first synthesis of BePh₂ was accomplished almost a century ago. However, its structure has remained unknown so far, while the corresponding aryls of the elements adjacent to beryllium in the periodic table are well investigated. Herein, we present an improved synthesis for diphenylberyllium and show by X-ray diffraction that it forms a trinuclear complex in the solid state. NMR spectroscopy revealed that this structure is also retained in solution but exhibits dynamic behavior. Its stability against heat and coordinating solvents is discussed and the possible obstacles to the synthesis of BePh₂ from BeCl₂ are examined. In the process of this study two ether adducts, BePh₂⋅Et₂O and Be₂Ph₄⋅Et₂O, have been characterized as well as the previously unknown triphenylberyllate anion. From the latter several single-crystal structures were obtained under various conditions, in which [BePh₃]⁻ is either isolated or acts as a ligand for Li⁺. Furthermore, the crown ether induced selfionization of BePh₂ is described and the resulting [(12-crown-4)BePh]⁺ cation was isolated, which shows an unusual 4+1 coordination around the Be atom.     

Path coupling without contraction

Path coupling is a useful technique for simplifying the analysis of a coupling of a Markov chain. Rather than defining and analysing the coupling on every pair in Ω×Ω, where Ω is the state space of the Markov chain, analysis is done on a smaller set SΩ×Ω. If the coefficient of contraction β is strictly less than one, no further analysis is needed in order to show rapid mixing. However, if β=1 then analysis (of the variance) is still required for all pairs in Ω×Ω. In this paper we present a new approach which shows rapid mixing in the case β=1 with a further condition which only needs to be checked for pairs in S, greatly simplifying the work involved. We also present a technique applicable when β=1 and our condition is not met.     

Entire functions with Julia sets of positive measure

Let f be a transcendental entire function for which the set of critical and asymptotic values is bounded. The Denjoy–Carleman–Ahlfors theorem implies that if the set of all z for which |f(z)| > R has N components for some R > 0, then the order of f is at least N/2. More precisely, we have log log M(r, f) ≥ (N/2) log r − O(1), where M(r, f) denotes the maximum modulus of f. We show that if f does not grow much faster than this, then the escaping set and the Julia set of f have positive Lebesgue measure. However, as soon as the order of f exceeds N/2, this need not be true. The proof requires a sharpened form of an estimate of Carleman and Tsuji related to the Denjoy–Carleman–Ahlfors theorem.     

Theoretical stability,thin film synthesis and transport properties of the Mon +1GaCn MAX phase

The phase stability of Mo_{n +1}GaC_n has been investigated using ab‐initio calculations. The results indicate stability for the Mo₂GaC phase only, with a formation enthalpy of –0.4 meV per atom. Subsequent thin film synthesis of Mo₂GaC was performed through magnetron sputtering from elemental targets onto Al₂O₃ [0001], 6H‐SiC [0001] and MgO [111] substrates within the temperature range of 500 °C and 750 °C. High structural quality films were obtained for synthesis on MgO [111] substrates at 590 ºC. Evaluation of transport properties showed a superconducting behavior with a critical temperature of approximately 7 K, reducing upon the application of an external magnetic field. The results point towards the first superconducting MAX phase in thin film form. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

The elliptic functions and integrals of the “{1 \mathord{\left/ {\vphantom {1 9}} \right. \kern-\nulldelimiterspace} 9}” problem

We describe the functions needed in the determination of the rate of convergence of best $L^\infty $ rational approximation to $\exp ( - x)$ on [0,∞) when the degree n of the approximation tends to ∞ (“1/9” problem).