A gate to organokrypton chemistry: HKrCCH

An organic molecule containing krypton, HKrCCH, is reported. The preparation of HKrCCH includes 193-nm photolysis of H2C2/Kr solid mixtures at 8 K and subsequent thermal mobilization of hydrogen atoms at >/=30 K. The identification is based on infrared absorption spectroscopy and supported by ab initio calculations which show ionic and covalent contributions to the bonding. We believe that a series of similar organokrypton molecules can be prepared as computationally demonstrated for HKrC4H and HKrC3H3. These results feature a generally novel way for activating chemically the H-CC- group, which can find practical applications of the krypton catalysis.     

Synthesis and characterisation of HRuRh3(CO)12. Crystal structures of HRuRh3(CO)12, HRuRh3(CO)10(PPh3)2 and HRuCo3(CO)10(PPh3)2

A new ruthenium-rhodium mixed-metal cluster HRuRh₃(CO)₁₂ and its derivatives HRuRh₃(CO)₁₀(PPh₃)₂ and HRuCo₃(CO)₁₀(PPh₃)₂ have been synthesized and characterized. The following crystal and molecular structures are reported: HRuRh₃(CO)₁₂: monoclinic, space group P2₁/c, a 9.230(4), b 11.790(5), c 17.124(9) Å, β 91.29(4)°, Z = 4; HRuRh₃(CO)₁₀(PPh₃)₂·C₆H₁₄: triclinic, space group P$\text{1}$, a 11.777(2), b 14.079(2), c 17.010(2) Å, α 86.99(1), β 76.91(1), γ 72.49(1)°, Z = 2; HRuCo₃(CO)₁₀(PPh₃)₂·CH₂Cl₂: triclinic, space group P$\text{1}$, a 11.577(7), b 13.729(7), c 16.777(10) Å, α 81.39(4), β 77.84(5), γ 65.56°, Z = 2. The reaction between Rh(CO)₄^? and (Ru(CO)₃Cl₂)₂ tetrahydrofuran followed by acid treatment yields HRuRh₃(CO)₁₂ in high yield. Its structural analysis was complicated by a 80–20% packing disorder. More detailed structural data were obtained from the fully ordered structure of HRuRh₃(CO)₁₀(PPh₃)₂, which is closely related to HRuCo₃(CO)₁₀(PPh₃)₂ and HFeCo₃(CO)₁₀(PPh₃)₂. The phosphines are axially coordinated.     

The extended supporting hyperplane algorithm for convex mixed-integer nonlinear programming

A new deterministic algorithm for solving convex mixed-integer nonlinear programming (MINLP) problems is presented in this paper: The extended supporting hyperplane (ESH) algorithm uses supporting hyperplanes to generate a tight overestimated polyhedral set of the feasible set defined by linear and nonlinear constraints. A sequence of linear or quadratic integer-relaxed subproblems are first solved to rapidly generate a tight linear relaxation of the original MINLP problem. After an initial overestimated set has been obtained the algorithm solves a sequence of mixed-integer linear programming or mixed-integer quadratic programming subproblems and refines the overestimated set by generating more supporting hyperplanes in each iteration. Compared to the extended cutting plane algorithm ESH generates a tighter overestimated set and unlike outer approximation the generation point for the supporting hyperplanes is found by a simple line search procedure. In this paper it is proven that the ESH algorithm converges to a global optimum for convex MINLP problems. The ESH algorithm is implemented as the supporting hyperplane optimization toolkit (SHOT) solver, and an extensive numerical comparison of its performance against other state-of-the-art MINLP solvers is presented.     

Chordal graphs and join spaces

A join space is an abstract model for partially ordered linear, spherical and projective geometries. A characterization for chordal graphs which are join spaces is given: a chordal graph is a join space if and only if it does not contain one of the two forbidden graphs as an induced subgraph.     

Nachweis und Bestimmung des Eisens, sowie seine Trennung von anderen Elementen

Ohne Zusammenfassung     

Nachweis und Bestimmung des Fluors

Ohne Zusammenfassung     

Nachweis und Bestimmung des Berylliums und seine Trennung von anderen Elementen

Ohne Zusammenfassung     

Nickel und Kobalt

Ohne Zusammenfassung