Prophet inequalities for parallel processes

Generalizations of prophet inequalities for single sequences are obtained for optimal stopping of several parallel sequences of independent random variables. For example, if {X_{i, j}, 1 ≤ i ≤ n, 1 ≤ j < ∞} are independent non-negative random variables, then

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and this bound is best possible. Applications are made to comparisons of the optimal expected returns of various alternative methods of stopping of parallel processes.     

Synthesis and molecular structure of [Al(CH3)2]2[C10H22N4] [Al(CH3)3]2: Condensation product of trimethylaluminum and a multidentate open-chain amine

The crystalline condensation product [Al(CH₃)₂]₂[C₁₀H₂₂N₄][Al(CH₃)₃]₂ is prepared from reaction of the multidentate open-chain amine 1,4-bis(3-aminopropyl)piperazine with trimethylaluminum in methylene chloride. The compound crystallized in the monoclinic space groupC2/c with unit cell parametersa=25.166(12),b=7.268(4),c=17.316(4) Å,=115.3(4)°, andD _c =1.06 g cm^–3 forZ=4. Least-squares refinement based on 1054 observed reflections with intensitiesI 3(I) in the range 2<2<45° led to a finalR factor of 0.053 (R _w =0.064). The title compound resides on a crystallographic center of symmetry with independent Al-N distances of 1.889(5), 2.058(5), and 2.030(5) Å.     

Stock Control and the Undershoot of the Re-order Level

Practical stock-control systems are frequently based on a policy of reviewing the stock balance and placing an order if this has fallen to or below a set level R. In order to facilitate the calculation of the control parameters, the assumption is generally made that the stock balance is exactly R when an order is placed, whereas in practice it may have fallen below R. This paper uses a steady-state analysis to evaluate some relatively simple adjustments which may be incorporated to handle this undershoot.     

Efficient synthesis of an imidazole-substituted delta-amino acid by the integration of chiral technologies

Two methods to produce (2S)-5-amino-2-(1-n-propyl-1H-imidazol-4-ylmethyl)-pentanoic acid were investigated. Diastereoisomeric salt resolution, using the quinidine salt, gave the desired intermediate in 98% ee and 33% yield. Asymmetric hydrogenation of various substrates gave high conversions, with up to 83% ee. Integration of these two approaches via asymmetric hydrogenation of a quinidine salt substrate followed by crystallization provided the desired intermediate in 94% ee and 76% yield.     

Polyfunctional pyridines from nitroacetamidine and β-diketones. A useful synthesis of substituted imidazo [4,5-b] pyridines and related compounds

Nitroacetamidine undergoes a useful cyclocondensation with β-diketones to produce substituted 2-amino-3-nitropyridines. Use of an acylpyruvate generates hitherto unreported 2-amino-3-nitropyridine-4-carboxylates. These may be converted easily to functionalized imidazo[4,5-b]pyridines and oxazolo-[5,4-b]pyridines.     

Evaluation of ion chromatography for determination of selected ions in geothermal well water

Ion chromatography is evaluated as a technique for the separation and determination of selected anions (fluoride, chloride, bromide, and sulfate) and cations (lithium. sodium, potassium and ammonium) in geothermal well water samples. The results achieved are compared with those obtained by other methods of analysis in a round-robin test.