Stationary remaining service time conditional on queue length

In Mandelbaum and Yechiali [The conditional residual service time in the M/G/1 queue, http://www.math.tau.ac.il/∼uriy/publications (No. 30a), 1979] and in Fakinos [The expected remaining service time in a single-server queue, Oper. Res. 30 (1982) 1014-1018] a simple formula is derived for the (stationary) expected remaining service time in a M/G/1 queue, conditional on the number of customers in the system. We give a short new proof of the formula using Rate Conservation Law, and generalize to handle higher moments.     

The renaissance of palladium(II)-catalyzed oxidation chemistry

Palladium(II)-catalyzed oxidations constitute a paramount reaction class but have remained immature over the past few decades. Recently, this field has reappeared at the forefront of organometallic catalysis. This emerging area article outlines recent developments in palladium(II)-catalyzed oxidation chemistry with discussion of potential future growth.     

Origin of enantioselection in chiral alcohol oxidation catalyzed by Pd[(-)-sparteine]Cl2

A kinetic investigation into the origin of enantioselectivity for the Pd[(-)-sparteine]Cl(2)-catalyzed aerobic oxidative kinetic resolution (OKR) is reported. A mechanism to account for a newly discovered chloride dissociation from Pd[(-)-sparteine]Cl(2) prior to alcohol binding is proposed. The mechanism includes (1) chloride dissociation from Pd[(-)-sparteine]Cl(2) to form cationic Pd(-)-sparteine]Cl, (2) alcohol binding, (3) deprotonation of Pd-bound alcohol to form a Pd-alkoxide, and (4) beta-hydride elimination of Pd-alkoxide to form ketone product and a Pd-hydride. Utilizing the addition of (-)-sparteine HCl to control the [Cl(-)] and [H(+)] and the resulting derived rate law, the key microscopic kinetic and thermodynamic constants were extracted for each enantiomer of sec-phenethyl alcohol. These constants allow for the successful simulation of the oxidation rate in the presence of exogenous (-)-sparteine HCl. A rate law for oxidation of the racemic alcohol was derived that allows for the successful prediction of the experimentally measured k(rel) values when using the extracted constants. Besides a factor of 10 difference between the relative rates of beta-hydride elimination for the enantiomers, the main enhancement in enantiodetermination results from a concentration effect of (-)-sparteine HCl and the relative rates of reprotonation of the diastereomeric Pd-alkoxides.     

Dual role of (-)-sparteine in the palladium-catalyzed aerobic oxidative kinetic resolution of secondary alcohols

The mechanistic details of the palladium-catalyzed aerobic oxidative kinetic resolution of secondary alcohols have been elucidated. (-)-Sparteine was found to have a dual role as a chiral ligand and an exogenous base. Saturation kinetics were observed for the dependence on (-)-sparteine concentration. A first-order dependence on [alcohol] and [catalyst] as well as inhibition by addition of (-)-sparteine HCl were observed. These results are consistent with rate-limiting deprotonation under low (-)-sparteine concentrations and rate-limiting beta-hydride elimination using saturating (-)-sparteine concentrations. This conclusion is further supported by a kinetic isotope effect of 1.31 +/- 0.04 under saturation. The enantioselectivity events are also controlled by addition of (-)-sparteine in which high concentrations afford a more selective kinetic resolution.     

Light traffic for workload in queues

General exact light traffic limit theorems are given for the distribution of steadystate workloadV, in open queueing networks having as input a general stationary ergodic marked point process {(t _n ,K _n )n0 (where t_n denotes the arrival time and K_n the routing and service times of the nth customer). No independence assumptions of any kind are required of the input. As the light traffic regime, it is only required that the Palm distribution for the exogenous interarrival time converges weakly to infinity (while the service mechanism is not allowed to change much). As is already known in the context of a single-server queue, work is much easier to deal with mathematically in light traffic than is customer delayD, and consequently, our results are far more general than existing results forD. We obtain analogous results for multi-channel and infinite-channel queues. In the context of open queueing networks, we handle both the total workload in the network as well as the workload at isolated nodes.Research supported in part by the Japan Society for the Promotion of Science during the author's fellowship in Tokyo, and by NSF Grant DDM 895 7825.     

Solventless synthesis of monodisperse Cu2S nanorods, nanodisks, and nanoplatelets

Cu(2)S nanocrystals with disklike morphologies were synthesized by the solventless thermolysis of a copper alkylthiolate molecular precursor. The nanodisks ranged from circular to hexagonal prisms from 3 to 150 nm in diameter and 3 to 12 nm in thickness depending on the growth conditions. High resolution transmission electron microscopy (HRTEM) revealed the high chalcocite (hexagonal) crystal structure oriented with the c-axis ([001] direction) orthogonal to the favored growth direction. This disk morphology is thermodynamically favored as it allows the extension of the higher energy [100] and [110] surfaces with respect to the [001] planes. The hexagonal prism morphology also appears to relate to increased C-S bond cleavage of adsorbed dodecanethiol along the more energetic [100] facets relative to [001] facets. Monodisperse Cu(2)S nanodisks self-assemble into ribbons of stacked platelets. This solventless approach provides a new technique to synthesize anisotropic metal chalcogenide nanostructures with shapes that depend on both the face-sensitive thermodynamic surface energy and the surface reactivity.     

Palladium-Catalyzed Enantioselective Alkenylation of Enelactams Using a Relay Heck Strategy

In this report, a palladium-catalyzed redox-relay Heck process to access optically active alkenylated α,β-unsaturated lactams is described. Under mild reaction conditions, electron-deficient alkenyl triflates and electron-rich alkenyl iodonium salts undergo enantioselective and site-selective coupling with enelactams to deliver the products in high yields and excellent enantioselectivities. Furthermore, the products allow facile access to natural products such as (+)-calvine and (+)-2-epicalvine in addition to the bioactive molecule aza-goniothalamin.     

Enantioselective C2-Alkylation of Indoles through a Redox-Relay Heck Reaction of 2-Indole Triflates

A palladium-catalyzed enantioselective redox-relay Heck reaction of 2-indole triflates and disubstituted alkenes is reported. This process combines readily available indole triflates with a variety of alkenes to afford a range of indole derivatives bearing a stereocenter adjacent to C2. Enantioselectivity is achieved through use of a simple pyridine-oxazoline ligand. Tuning the electronics of the indole, through judicious choice of N-protecting group, is required to ensure selective β-hydride elimination away from the indole core. Utility of this method is highlighted in a modular formal synthesis of an S1P₁ agonist precursor developed by Merck.     

Development and Molecular Understanding of a Pd-Catalyzed Cyanation of Aryl Boronic Acids Enabled by High-Throughput Experimentation and Data Analysis

A synthetic method for the palladium-catalyzed cyanation of aryl boronic acids using bench stable and non-toxic N-cyanosuccinimide has been developed. High-throughput experimentation facilitated the screen of 90 different ligands and the resultant statistical data analysis identified that ligand σ-donation, π-acidity and sterics are key drivers that govern yield. Categorization into three ligand groups – monophosphines, bisphosphines and miscellaneous – was performed before the analysis. For the monophosphines, the yield of the reaction increases for strong σ-donating, weak π-accepting ligands, with flexible pendant substituents. For the bisphosphines, the yield predominantly correlates with ligand lability. The applicability of the designed reaction to a wider substrate scope was investigated, showing good functional group tolerance in particular with boronic acids bearing electron-withdrawing substituents. This work outlines the development of a novel reaction, coupled with a fast and efficient workflow to gain understanding of the optimal ligand properties for the design of improved palladium cross-coupling catalysts.     

Analysis of triacetone triperoxide by gas chromatography/mass spectrometry and gas chromatography/tandem mass spectrometry by electron and chemical ionization

The explosive triacetone triperoxide (TATP) has been analyzed by gas chromatography/mass spectrometry (GC/MS) and sub-nanogram detection limits are reported by ammonia positive ion chemical ionization (PICI), electron ionization (EI) and methane negative ion chemical ionization (NICI). Analysis by methane PICI and ammonia NICI gave detection limits in the low nanogram range. Analyses were carried out on (linear) quadrupole and ion trap instruments. Analysis of TATP by PICI using ammonia reagent gas is the preferred analytical method, producing low limits of detection as well as an abundant (greater than 60% of base peak) diagnostic adduct ion at m/z 240 corresponding to [TATP + NH4]+. Isolation of the [TATP + NH4]+ ion with subsequent collision-induced dissociation (CID) produces extremely low abundance product ions at m/z values greater than 60, and the m/z 223 ion corresponding to [TATP + H]+ was not observed. Density functional theory (DFT) calculations at the B88LYP/DVZP level indicate that dissociation of the complex to form NH4+ and TATP occurs at energies lower than peroxide bond dissociation, while protonation of TATP leads to cleavage of the ring structure. These results provide a method for pico-gram detection levels of TATP using commercial instrumentation commonly available in forensic laboratories. As a point of comparison, a detection limit of 15 ng was obtained by flame ionization detection.