Inequalities for moments of tails of random variables,with a queueing application

Summary For a non-negative random variable X and 1 such that EX<, E(X-Y) ⁺ /{E(X-y) ₊}⁺ is monotonic-decreasing in y, and hence no smaller than EX . Inequalities for E(X-Y) ₊ E(, 1, y, z0) are also given. This relation enables an inequality of Kingman for the mean waiting time in a stationary GI/G/1 queue to be sharpened.Work done as Visiting Fellow, Department of Statistics, University of Melbourne     

Novel metal complexes containing a chiral trinitrogen isoindoline-based pincer ligand: in situ synthesis and structural characterization

The first synthesis and characterization of metal coordinated complexes containing in situ prepared chiral trinitrogen 1,3-bis(4,5-dihydrooxazol-2-ylimino)isoindoline-based pincer ligands are reported. Two zinc complexes, isolated as Zn(L)(2), where L = 1,3-bis(4,5-dihydro-4-(R)-phenyloxazol-2-ylimino)isoindoline ((R,R)-5) or 1,3-bis(4,5-dihydro-4-(S)-iso-propyloxazol-2-ylimino)isoindoline ((S,S)-6), respectively, are reported. Complexes Zn((R,R)-5)(2) and Zn((S,S)-6)(2) were prepared in situ through the condensation of phthalonitrile with enantiopure 2-amino-4-(R)-phenyloxazoline ((R)-3) or 2-amino-4-(S)-iso-propyloxazoline ((S)-4) in the presence of ZnCl(2) at 80 °C in dry toluene over 3-4 days. The characterizations of Zn((R,R)-5)(2) and Zn((S,S)-6)(2) in both the solid (X-ray crystallography) and solution (multinuclear NMR spectroscopy) states are reported.     

Factors influencing hydride formation in a Pd/TiO2 catalyst

A sample containing Pd nanoparticles deposited on TiO(2) was subjected to a series of different thermal pretreatments. The range of these treatments was selected to provide a palladium surface in a number of different states, including a form where TiO(x) overlayers had been formed. Experiments were conducted to determine how the state of the Pd surface influenced the formation of Pd hydride. The amount of hydrogen released during a temperature-programmed experiment was used to quantify the extent of Pd beta-hydride formation following room-temperature exposure to hydrogen. Samples were characterized by HAADF (high-angle annular dark-field) electron microscopy with EDX (energy-dispersive X-ray) analysis and CO pulse chemisorption and FTIR (Fourier transform infrared spectroscopy) of adsorbed CO. The amount and the ease with which Pd beta-hydride was formed was found to be dependent on the metal surface area, the presence of titania overlayers, and the Pd surface roughness/defect concentration.     

A shock tube study of cyclopentane and cyclohexane ignition at elevated pressures

Ignition delay times for cyclopentane/air and cyclohexane/air mixtures were measured in a shock tube at temperatures of 847–1379 K, pressures of 11–61 atm, and equivalence ratios of ? = 1.0, 0.5, and 0.25. Ignition times were determined using electronically excited OH emission monitored through the shock tube endwall and piezoelectric pressure measurements made in the shock tube sidewall. The dependence of ignition time on pressure, temperature, and equivalence ratio is quantified and correlations for ignition time formulated. Measured ignition times are compared to kinetic modeling predictions from four recently published mechanisms. The data presented provide a database for the validation of cycloalkane kinetic mechanisms at the elevated pressures found in practical combustion engines. © 2008 Wiley Periodicals, Inc. Int J Chem Kinet 40: 624–634, 2008     

Phosphine‐Directed CH Borylation Reactions: Facile and Selective Access to Ambiphilic Phosphine Boronate Esters

Ambiphilic ligands have received considerable attention over the last two decades due to their unique reactivity as organocatalysts and ligands. The iridium‐catalyzed C? H borylation of phosphines is described in which the phosphine is used as a directing group to provide selective formation of arylboronate esters with unique scaffolds of ambiphilic compounds. A variety of aryl and benzylic phosphines were subjected to the reaction conditions, selectively providing stable, isolable boronate esters upon protection of the phosphine as the borane complex. After purification, the phosphine‐substituted boronate esters could be deprotected and isolated in pure form.     

Revisiting queueing output processes: a point process viewpoint

After some historical notes concerning queueing output processes N _dep??, the paper discusses methods for establishing asymptotic linear relations for var??N _dep??(0,t], whether in the crude form B ₁ t or the more detailed form B ₁ t+B ₀+o(1) for t→∞. The crude form holds whenever the process N _adm of customers admitted to service has a linear asymptote, and then (var??N _dep??(0,t])/t and (var??N _adm(0,t])/t share a common limit (that may be infinite) in stationary G/G/k/K systems. A standard integral formula for the variance of a stationary orderly point process shows that, if N _dep?? is a renewal process whose generic lifetime X has finite second moment, then B ₁=(var??X)/([E(X)]²), and the more detailed linear asymptote holds when E(X ³) is finite. Geometric ergodicity of the queue size process Q(?) in stationary M/M/k/K systems establishes that the more detailed linear asymptote is true for them. It is conjectured that var??N(0,t]～B ₁ t for any stationary point process N possessing an embedded regenerative structure.     

Accessing Ambiphilic Phosphine Boronates through C−H Borylation by an Unforeseen Cationic Iridium Complex

Ambiphilic molecules, which contain a Lewis base and Lewis acid, are of great interest based on their unique ability to activate small molecules. Phosphine boronates are one class of these substrates that have interesting catalytic activity. Direct access to these phosphine boronates is described through the iridium‐catalyzed C?H borylation of phosphines. An unconventional cationic iridium catalyst was identified as optimal for a range of phosphines, providing good yields and selectivity across a diverse class of phosphine boronates (isolated as the borane‐protected phosphine). A complimentary catalyst system (quinoline‐based silane ligand with [(COD)IrOMe]₂) was optimal for biphenyl‐based phosphines. Selective polyborylation was also shown providing bis‐ and tris‐borylated phosphines. Deprotection of the phosphine boronate provided free ambiphilic phosphine boronates, which do not have detectable interactions between the phosphorus and boron atoms in solution or the solid state.