On the temporal analysis of special GERT networks using a modified Markov renewal process

In this paper we show how to represent a STEOR network (GERT network with only nodes of the stochastic exclusive-or Type) by a modified Markov renewal process. The computation of the renewal kernel of this process yields the temporal analysis of the network.

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Zusammenfassung Es wird gezeigt, wie ein STEOR-Netzplan (GERT-Netzplan, der nur Knoten vom Typ stochastisch exklusiv-oder enthält) durch einen modifizierten Markowschen Erneuerungsprozeß beschrieben werden kann. Die Bestimmung der Erneuerungsfunktionen dieses Prozesses liefert die Auswertung des STEOR-Netzplans (im Sinne der Zeitplanung).

     

The complexification and degree of a semi-algebraic set

The complexification of a semi-algebraic set is the smallest complex algebraic set containing S. Let S be defined by s polynomials of degrees less than d. We prove that the geometric degree of the complexification is less than . Received: 9 January 1997; in final form: 11 August 2000 / Published online: 17 May 2001     

A Readily Accessible Class of Chiral Cp Ligands and their Application in RuII‐Catalyzed Enantioselective Syntheses of Dihydrobenzoindoles

Chiral cyclopentadienyl (Cp^x) ligands have a large application potential in enantioselective transition‐metal catalysis. However, the development of concise and practical routes to such ligands remains in its infancy. We present a convenient and efficient two‐step synthesis of a novel class of chiral Cp^x ligands with tunable steric properties that can be readily used for complexation, giving Cp^xRh^I, Cp^xIr^I, and Cp^xRu^II complexes. The potential of this ligand class is demonstrated with the latter in the enantioselective cyclization of azabenzonorbornadienes with alkynes, affording dihydrobenzoindoles in up to 98:2 e.r., significantly outperforming existing binaphthyl‐derived Cp^x ligands.     

Reduction pathway of end-on terminally coordinated dinitrogen. V. N-N bond cleavage in Mo/W hydrazidium complexes with diphosphine coligands. Comparison with triamidoamine systems

N-N cleavage of the dialkylhydrazido complex [W(dppe)2(NNC5H10)] (B(W)) upon treatment with acid, leading to the nitrido/imido complex and piperidine, is investigated experimentally and theoretically. In acetonitrile and at room temperature, B(W) reacts orders of magnitude more rapidly with HNEt3BPh4 than its Mo analogue, [Mo(dppe)2(NNC5H10)] (B(Mo)). A stopped-flow experiment performed for the reaction of B(W) with HNEt3BPh4 in propionitrile at -70 degrees C indicates that protonation of B(W) is completed within the dead time of the stopped-flow apparatus, leading to the primary protonated intermediate B(W)H+. Propionitrile coordination to this species proceeds with a rate constant k(obs(1)) of 1.5 +/- 0.4 s(-1), generating intermediate RCN-B(W)H+ (R = Et) that rapidly adds a further proton at Nbeta and then mediates N-N bond splitting in a slower reaction (k(obs(2)) = 0.35 +/- 0.08 s(-1), 6 equiv of acid). k(obs(1)) and k(obs(2)) are found to be independent of the acid concentration. The experimentally observed reactivities of B(Mo) or B(W) with acids in nitrile solvents are reproduced by DFT calculations. In particular, geometry optimization of models of solvent-coordinated, Nbeta-protonated intermediates is found to lead spontaneously to separation into the nitrido/imido complexes and piperidine/piperidinium, corresponding to activationless heterolytic N-N bond cleavage processes. Moreover, DFT indicates a spontaneous cleavage of nonsolvated B(W) protonated at Nbeta. In the second part of this article, a theoretical analysis of the N-N cleavage reaction in the Mo(III) triamidoamine complex [HIPTN3N]Mo(N2) is presented (HIPTN3N = hexaisopropylterphenyltriamidoamine). To this end, DFT calculations of the Mo(III)N2)triamidoamine complex and its protonated and reduced derivatives are performed. Calculated structural and spectroscopic parameters are compared to available experimental data. N-N cleavage most likely proceeds by one-electron reduction of the Mo(V) hydrazidium intermediate [HIPTN3N]Mo(NNH3)+, which is predicted to have an extremely elongated N-N bond. From an electronic-structure point of view, this reaction is analogous to that of Mo/W hydrazidium complexes with diphos coligands. The general implications of these results with respect to synthetic N2 fixation are discussed.     

Optimization of STEOR networks via Markov renewal programming

We show how to treat the problems of time optimization and cost optimization of STEOR networks (GERT networks with only nodes of the stochastic exclusive-or type) within the scope of Markov decision processes and present the related dynamic programming techniques.

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Zusammenfassung Es wird gezeigt, wie das Problem der Zeit- und Kostenoptimierung von STEOR-Netzplänen (GERT-Netzplänen, die nur Knoten vom Typ stochastisch exklusiv-oder enthalten) als Markowscher Entscheidungsprozeß formuliert werden kann, und es werden die entsprechenden Verfahren der dynamischen Optimierung angegeben.

     

Utilization of microwave heating in the McMurry reaction for facile coupling of aldehydes and ketones to give alkenes

Microwave heating was applied in high-yield syntheses of alkenes by McMurry coupling of aldehydes and ketones with low-valent titanium. All aldehydes and ketones including sulfur end-capped analogues gave alkenes in isolated yields above 80% without detectable amounts of pinacols.     

Mononuclear and binuclear copper(I) complexes ligated by bis(3,5-diisopropyl-1-pyrazolyl)methane: insight into the fundamental coordination chemistry of three-coordinate copper(I) complexes with a neutral coligand

By using the neutral bidentate nitrogen-containing ligand, bis(3,5-diisopropyl-1-pyrazolyl)methane (L1' '), the copper(I) complexes [Cu(L1' ')2](CuCl2) (1CuCl2), [Cu(L1' ')2](ClO4) (1ClO4), [Cu(L1' ')]2(ClO4)2 (2ClO4), [Cu(L1' ')]2(BF4)2 (2BF4), [Cu(L1' ')(NCMe)](PF6) (3PF6), [Cu(L1' ')(PPh3)](ClO4) (4ClO4), [Cu(L1' ')(PPh3)](PF6) (4PF6), [{Cu(L1' ')(CO)}2(mu-ClO4)](ClO4) (5ClO4), and the copper(II) complexes [{Cu(L1' ')}2(mu-OH)2(mu-ClO4)2] (6), and [Cu(L1' ')Cl2] (7) were systematically synthesized and fully characterized by X-ray crystallography and by IR and 1H NMR spectroscopy. In the case of copper(II), ESR spectroscopy was also applied. In comparison with the related neutral tridentate ligand L1', bis-chelated copper(I) complexes and binuclear linear-coordinated copper(I) complexes are easy to obtain with L1' ', like 1CuCl2, 1ClO4, 2ClO4, and 2BF4. Importantly, stronger and bulkier ligands such as acetonitrile (3PF6) and especially triphenylphosphine (4ClO4 and 4PF6) generate three-coordinate structures with a trigonal-planar geometry. Surprisingly, for the smaller ligand carbon monoxide, a mononuclear three-coordinate structure is very unstable, leading to the formation of a binuclear complex (5ClO4) with one bridging perchlorate anion, such that the copper(I) centers are four-coordinate. The same tendency is observed for the copper(II) bis(mu-hydroxo) compounds 6, which is additionally bridged by two perchlorate anions. Both copper(II) complexes 6 and 7 were obtained by molecular O2 oxidation of the corresponding copper(I) complexes. A comparison of the new copper(I) triphenylphosphine complexes 4ClO4 and 4PF6 with corresponding species obtained with the related tridentate ligands L1' and L1 (8ClO4 and 9, respectively) reveals surprisingly small differences in their spectroscopic properties. Density functional theory (DFT) calculations are used to shed light on the differences in bonding in these compounds and the spectral assignments. Finally, the reactivity of the different bis(pyrazolyl)methane complexes obtained here toward PPh3, CO, and O2 is discussed.     

Synthesis of new functionalized 3,7-diazabicyclo[3.3.1]nonanes by aminomethylation of the Guareschi imides

The aminomethylation of 4,4-dialkyl-2,6-dioxopiperidine-3,5-dicarbonitriles (Guareschi imides) was studied for the first time. When the Guareschi imides were treated with primary aliphatic amines and an excess of formaldehyde, 2,4-dioxo-3,7-diazabicyclo[3.3.1]nonane-1,5-dicarbonitriles were obtained in varying yields (15–67%). The structure of 9,9-dimethyl-7-(2-methylpropyl)-2,4-dioxo-3,7-diazabicyclo[3.3.1]nonane-1,5-dicarbonitrile was studied by X-ray diffraction analysis.     

Capillary electrophoresis and phenylboronic acid solid phase extraction for the determination of S‐adenosylmethionine/S‐adenosylhomocysteine ratio in human urine

An approach that allows direct analysis of the ratio of S‐adenosylmethionine (SAM) and S‐adenosylhomocysteine (SAH) by using CE is presented. The analytes were extracted on phenylboronic acid phase and eluted with 100 mmol/L HCl. CE separation of the analytes took place in the transient isotachophoresis mode with addition of NaCl and meglumine to the samples. The sensitivity (S/N = 3) and quantification limit (S/N = 10) of the method were 0.07 and 0.2 μmol/L, respectively, using a silica capillary with 50 μm internal diameter and 30.5 cm total length. The BGE was 0.02 mol/L Tris with 1 mol/L HCOOH (pH 2.2), and the separation voltage was 15–17 kV. Accuracy of SAM and SAH analysis in urine was 96 and 105%, respectively; interday precision for the SAM/SAH ratio was within 6%. The theoretical plate number exceeded a million. Total analysis time was 8.5 min.     

Characterization of major and minor alk(en)ylresorcinols from mango (Mangifera indica L.) peels by high-performance liquid chromatography/atmospheric pressure chemical ionization mass spectrometry

5-Alkyl- and 5-alkenylresorcinols, as well as their hydroxylated derivatives, were extracted from mango (Mangifera indica L.) peels, purified on polyamide and characterized by high-performance liquid chromatography/atmospheric pressure chemical ionization mass spectrometry (HPLC/APcI-MS) for the first time. Among the 15 compounds analyzed, 3 major and 12 minor C(15)-, C(17)-, and C(19)-substituted resorcinols and related analogues, showing varying degrees of unsaturation, were characterized by their specific fragmentation patterns in collision-induced dissociation experiments. This marks the first report on the occurrence of mono-, di-, and triunsaturated C(15)-homologues, saturated and triunsaturated C(17)-homologues, and mono- and diunsaturated C(19)-homologues in mango peels. Additionally, several hydroxylated C(15)- and C(17)-homologues, also not yet described in mango, and a C(14)-monoene, unique because of its even-numbered side chain, were tentatively identified on the basis of their fragmentation patterns. The results obtained in the present study indicate that HPLC-DAD-APcI-MS(n), combined with the newly developed solid-phase extraction, is a powerful tool for the analysis of alk(en)ylresorcinols and could therefore be used for their determination in various matrices.