A decomposition result for a class of polling models

Boxma and Groenendijk have shown that the workload in polling models decomposes into two independent variables. This paper demonstrates a different type of decomposition that has an explicit multi-dimensional form. This decomposition does not apply to all polling models, but does, for example, apply to models with constant switch-over times and either exhaustive or gated service disciplines. For such models, we show that the population of customers present in the system (represented by a vector indicating the number of customers at each queue) at key time points breaks into two independent subpopulations: (1) the population of customers present in the related model with zero switch-over times; (2) another population, which is particularly easy to analyze. This result has a number of theoretical and applied implications.     

Direct fission versus sequential evaporation mechanism of sputtered caesium iodide cluster ions

A triple stage hybrid mass spectrometer was scanned for the trapping of the reaction intermediates of the over-all loss of two CsI-moieties from size-selected caesium iodide cluster ions of the general formula Cs (CsI)⁺ _n . In addition to appropriate MS/MS/MS-methods an electrically floated collision cell has been applied to trap intermediates of unimolecular and collision-induced evaporations. In comparison with other experimental findings the features of the evaporation mechanism are discussed.     

Krichever-Novikov-like bases on punctured Riemann surfaces

Bases of holomorphic -differentials on N-punctured Riemann surfaces of arbitrary genus are constructed. The resulting extension of the Virasoro algebra on N-punctured spheres is displayed explicitly.     

Decomposition of EuPdIn and EuPtIn at high temperature and high pressure—formation of the hexagonal Laves phases EuPd0.72In1.28 and EuPt0.56In1.44

EuPd_0.72In_1.28 and EuPt_0.56In_1.44 were prepared under multianvil high-pressure (10.5 GPa) high-temperature (1500 and 1400 K) conditions from the precursor compounds EuPdIn and EuPtIn. They were investigated by X-ray diffraction on both powders and single crystals: MgZn₂-type, space group P6₃/mmc, a=578.7(1) pm, c=944.9(3) pm, wR2=0.0734, 263 F² values for EuPd_0.72In_1.28 and a=591.1(2) pm, c=933.8(2) pm, wR2=0.0853, 151 F² values for EuPt_0.56In_1.44 with 13 variable parameters per refinement. Both structures are built up from face- and corner-sharing tetrahedra of palladium (platinum) and indium atoms. The europium cations are located in cavities within the three-dimensional [Pd_0.72In_1.28] and [Pt_0.56In_1.44] networks. The 2a and 6 h positions of the tetrahedral networks show mixed Pd/In and Pt/In occupancy in EuPd_0.72In_1.28 and EuPt_0.56In_1.44, respectively. The crystal chemistry of these indides is briefly discussed.     

Structure and Magnetic Properties of Ce3Ge0.66In4.34 and Ce11Ge4.74In5.26

New indides Ce₃Ge_0.66In_4.34 and Ce₁₁Ge_4.74In_5.26 were synthesized from the elements by arc‐melting and subsequent annealing at 870 K. Single crystals were grown through special annealing procedures in sealed tantalum tubes in a high‐frequency furnace. Both compounds were investigated on the basis of X‐ray powder and single crystal data: I4/mcm, La₃GeIn₄ type, a = 848.8(1), c = 1192.0(2) pm, Z = 4, wR2 = 0.0453, 499 F² values, 17 variables for Ce₃Ge_0.66In_4.34 and I4/mmm, Sm₁₁Ge₄In₆ type (ordered version of the Ho₁₁Ge₁₀ type), a = 1199.3(2), c = 1662.0(3) pm, wR2 = 0.0507, 1217 F² values, 41 variables for Ce₁₁Ge_4.74In_5.26. The Ce₃Ge_0.66In_4.34 structure shows a mixed Ge/In occupancy on the 4c Wyckoff position. This site is octahedrally coordinated by cerium atoms. These octahedra share all edges, leading to a three‐dimensional network. The latter is penetrated by a two‐dimensional indium substructure which consists of flattened tetrahedra at In–In distances of 291 and 300 pm. The Ce₁₁Ge_4.74In_5.26 structure contains three crystallographically independent germanium sites. The latter are coordinated by eight or nine cerium neighbors. These CN8 and CN9 polyhedra are condensed to a complex network which is penetrated by a three‐dimensional indium network with In–In distances of 301–314 pm. The 16m site shows a mixed In/Ge occupancy. Chemical bonding in both compounds is dominated by the p elements. Both ternaries studied exhibit localized magnetism due to the presence of Ce³⁺ ions. The compound Ce₃GeIn₄ remains paramagnetic down to 1.72 K, whereas Ce₁₁Ge₄In₆ orders ferromagnetically at T_C = 7.5 K.     

Arsenic Speciation Analysis in Solutions Treated with Zeolites

Experiments have been carried out to study the behaviour of organoarsenicals treated with zeolites by means of speciation analysis. IC-ICP-MS was applied to identify and quantify arsenite, arsenate and the following organoarsenicals: monomethylarsonic acid (MMA), dimethylarsinic acid (DMA), trimethylarsine oxide (TMAO), tetramethylarsonium bromide (TMA⁺), arsenobetaine (AsB) and arsenocholine (AsC). Zeolites loaded with ferrous ions did not significantly increase the retention of inorganic arsenic species compared to the native zeolites, while there was a ten-fold removal of arsenate relating to arsenite. The formation of As(V) and DMA in the leachates containing clinoptilolites and mordenites was confirmed in the presence of natural and synthetic zeolites. Arsenobetaine and arsenocholine yielded higher levels of arsenate than the methylated species.     

Determination of (R)- and (S)-phenprocoumon in human plasma by enantioselective liquid chromatography/electrospray ionisation tandem mass spectrometry

Phenprocoumon is a commonly used oral anticoagulant of the coumarin type, and has found extensive clinical use in the treatment of thrombophlebitis, pulmonary embolism and atrial fibrillation. In the course of a clinical study to investigate the influence of genetic polymorphisms of the CYP2C9 enzyme on phenprocoumon metabolism, we developed a new enantioselective liquid chromatography/electrospray ionisation tandem mass spectrometry (LC/MS/MS) method to quantify (R)- and (S)-phenprocoumon in human plasma. HPLC separation of the enantiomers was achieved on a Chira-Grom-2 column under isocratic conditions using a water/acetonitrile/formic acid eluent. For detection and quantification a triple-quadrupole MS system was used in the selected reaction monitoring (SRM) mode. As an internal standard the structurally homologous compound warfarin was chosen. The detector response was linear with a correlation coefficient of 0.988-0.999 for (R)-phenprocoumon and 0.989-0.999 for (S)-phenprocoumon in the investigated concentration range between 62.5 and 1000 ng/mL (per enantiomer). The limit of detection (LOD) was 12.5 ng/mL.     

Synthesis of pyrimidines from 3-trifluoromethylsulfonyl-oxypropeniminium triflates and nitriles; molecular and crystal structure of the 1:1 and 1:2 Adducts of a 4-(2-diethylaminovinyl)pyrimidine with triflic acid

The 3-trifluoromethylsulfonyloxy-1-hexeniminium triflate 1 reacts with two equivalents of an aliphatic nitrile or of benzonitrile to give the 4-(2-diethylaminovinyl)pyrimidinediium bis(triflates) 4 , which can be deprotonated to give the monoprotonated or neutral pyrimidines 5 and 6 , respectively. When the related 1-phenyl-substituted iminium salt 7 is heated in acetonitrile at 140°, 1,5-cyclization of the cation leading to indane derivative 8 competes with formation of the pyrimidinium salt 9 . X-ray crystal structure determination reveals significant differences in the bond lengths of mono-and diprotonated 4-(2-diethylaminovinyl)pyrimidines 5a and 4a .     

Deprotonierte Dithiocarbaminsäureester als Thiolat-S-Donor-Liganden. Strukturen von Ph(H)NC(S)SMe,Co(PhNC(S)SMe)3 und Cu6(PhNC(S)SMe)6

Deprotonated Dithiocarbamic Acid Esters as Thiolate S-Donor Ligands. Structures of Ph(H)NC(S)SMe, Co(PhNC(S)SMe)₃, and Cu₆(PhNC(S)SMe)₆ The reaction of N-phenyl-S-methyldithiocarbamate, PhN(H)C(?S)SMe, ( 1 ) with cobalt(II) and copper(II) salts yields the monomeric compound Co^III(PhNC(S)SMe)₃ ( 2 ) and the hexameric compound Cu₆^I(PhNC(S)SMe)₆ ( 3 ). These complexes contain the negatively charged imino-thiolate ligand PhN?C(? S)SMe, which has been formed by deprotonation of 1 . The crystal structures of 1 – 3 have been determined. 1 forms centrosymmetrical dimers through N? H …? S bridge bonds, the conformation in the solid state and in solution is Z,E′. Co^III shows in 2 a trigonal-antiprismatic coordination, with the ligands acting as N,S-chelates. 3 contains an octahedral Cu₆-core with Cu …? Cu-distances ranging from 276.3(5) to 305.7(4) pm. Each copper center is trigonally coordinated to one nitrogen and two sulfur atoms of three different ligands. Crystal data: 1 , triclinic, space group P1 , a = 590.5(6), b = 869.0(1), c = 968.5(9) pm, α = 67.29(8), β = 78.44(8), γ = 81.64(9)°, Z = 2, 1 775 reflections, R(R_w) = 0.0317(0.032). 2 , orthorhombic, space group Pbca, a = 978.0(2), b = 1 842.9(4), c = 3 059.7(6) pm, Z = 8, 1 129 reflections, R(R_w) = 0.0997(0.0886). 3 , monoclinic, space group P2₁/c, a = 1 363.1(3), b = 1 342.8(3), c = 1 671.9(3) pm, β = 103.48°, Z = 2, 1 374 reflections, R(R_w) = 0.0708(0.0617).