Order statistics applications to queueing and scheduling problems

We prove several basic combinatorial identities and use them in two applications: the queue inference engine (QIE) and earliest due date rule (EDD) scheduling. Larson (1990) introduced the QIE. His objective was to deduce the behavior of a multiserver queueing system without observing the queue. With only a Poisson arrival assumption, he analyzed the performance during a busy period. Such a period starts once all servers are busy with the queue empty, and it ends as soon as a server becomes idle. We generalize the standard order statistics result for Poisson processes, and show how to sample a busy period in the M/M/c system. We derive simple expressions for the variance of the total waiting time in the M/M/c and M/D/1 queues given that n Poisson arrivals and departures occur during a busy period. We also perform a probabilistic analysis of the EDD for a one-machine scheduling problem with earliness and tardiness penalties. The schedule is without preemption and with no inserted idle time. The jobs are independent and each may have a different due date. For large n, we show that the variance of the total penalty costs of the EDD is linear in n. The mean of the total penalty costs of the EDD is known to be proportional to the square root of n (see Harel (1993)). This revised version was published online in June 2006 with corrections to the Cover Date.     

Application of an air stable Pd oxazoline complex for Heck, Suzuki, Sonogashira and related C-C bond-forming reactions

The novel complex trans-[PdCl₂(η¹-N-2-ethyl-2-oxazoline)₂] is shown to be an active and oxidatively robust catalyst for C-C bond-forming reactions (Heck, Sonogashira, Ullman, Suzuki), which can be carried out in air without rigorous solvent/substrate purification and in the absence of additional free ligand.     

The electron-impact induced loss of CHNO from 1,3-bis-(3-m-tolyl-1,2,4-oxadiazol-5-yl)hexafluoropropane

High resolution mass measurement established that the m/e 425 peak in the mass spectrum of 1,3-bis-(3-m-tolyl-1, 2,4-oxadiazol-5-yl)hexafluoropropane corresponds to [M ? CHNO]. This peak is absent from the mass spectrum of the para isomer.     

Characterisation of putative pentose-containing conjugates as minor metabolites of 4-bromoaniline present in the urine of rats following intraperitoneal administration

The metabolic fate of 4-bromoaniline (4-BrA) was investigated following intraperitoneal administration to the rat at 50 mg kg(-1), using high-performance liquid chromatography/time-of-flight tandem mass spectrometry (HPLC/TOF-MS/MS). Up to five metabolites were detected in urine that correspond to isomeric pentose conjugates (possibly ribosides) of a hydroxysulphate of 4-BrA. This identification is supported by further studies where the water used in the reversed-phase solvent system was replaced with deuterated water in order to confirm that the number of exchangeable protons present in the metabolites was consistent with the proposed structures.     

Qualification of automated low-field NMR relaxometry for quality control of polymers in a production setting

Implementation of a low-field time-domain nuclear magnetic resonance (NMR) scanner as a diagnostic tool in the production of new polymer components is described in the context of qualification of a new QA/QC device. A study to determine the optimal experimental parameters was performed and a robotic autosampler was built to enable scanning of multiple pads. Relationships between T₂ values and physical properties of DC745 slabs were investigated, and the appropriate sampling parameters for the production setting were determined. Two versions of a robotic autosampler were built and, for the component described here, a fourth radial axis was required in addition to traditional X, Y, and Z movement to eliminate the large variability in T₂ due to inconsistent sample coverage caused by the complex rib geometry of the component. Data show that with appropriate choice of experimental conditions of the NMR detector and the detection geometry of the robotic autosampler, sufficient resolution of variations in cross-link density on the millimeter scale could be determined. All data to date demonstrate that low-field NMR devices are a feasible tool for use in production settings for non-destructive quality control of polymer components.     

Persistent metal bis(hexafluoroacetylacetonato) complexes featuring a 2,2'-bipyridine substituted triarylamminium radical cation

Herein, we describe the preparation of a 2,2'-bipyridine derivative containing a redox-active N,N'-(4,4'-dimethoxydiphenylamino) substituent (1), which readily coordinates M(hfac)(2) salts [M = Mn (2), Ni (3), Cu (4)] to generate stable, neutral, and pseudo-octahedral coordination complexes, which have been fully characterized. Cyclic voltammetry and spectroelectrochemical measurements on complexes 2-4 indicate stable one-electron oxidation processes, and the formation of persistent radical cation complexes. The neutral complexes (M = Mn or Ni) were subject to one-electron oxidation with NOPF(6) in acetonitrile, and magnetic moments of the resulting solutions were obtained using the Evans method at different temperatures. Our experimental results suggest that the first reported ferromagnetically coupled metal-triarylamminum radical cation complex is obtained when M = Mn(2+), and antiferromagnetic coupling results when M = Ni(2+). These results are supported by results from density functional theory calculations, which indicate that a π spin polarization mechanism for magnetic exchange coupling is operative in singly oxidized complexes, 2-4.     

Structure of organic and metal-organic networks based on a bifunctional m-terphenyl carboxylic acid

A series of metal-organic frameworks (MOFs) based upon the ligand 2,6-diphenyl-1,4-dibenzoic acid [Ph2C6H2(CO2H)2]infinity have been prepared and characterized by X-ray crystallography. The networks exhibit a variety of topologies and coordination modes at the metal center. The reaction of the ligand with cobalt(II) nitrate or zinc(II) nitrate in methanol/pyridine results in the formation of isostructural 1-D chains [(Ph2C6H2(CO2)2)M(py)2(MeOH)]infinity, where M = Zn, Co; however, in the presence of ethanol and triethylamine, Zn(NO3)2 reacts to form a 2-D clay-like network, [(Ph2C6H2(CO2)2)Zn(EtOH)2]infinity. 2-D networks are also formed in similar reactions with copper(II) nitrate or silver(I) nitrate to give [(Ph2C6H2(CO2)(CO2H))2Cu(py)2]infinity, [(Ph2C6H2(CO2)CO2H))2Cu(py)4.2H2O](infinity), and [(Ph2C6H2(CO2)2)Ag2]infinity, respectively. The hydrogen-bonded chains formed by the ligand alone and with 4,4'-dipyridyl are also described.     

Genetics teaching for non-geneticist health care professionals in the UK

OBJECTIVES: It was the aim of this study to describe the structure and content of training in genetics for non-genetics specialist health care professionals in the UK. METHODS: Data were collected by assessment of published syllabi and curricula and through contact with educational leads at responsible organisations. RESULTS: Twenty-six universities, 7 Royal Colleges and various intercollegiate boards and committees are involved in the provision of medical education at various levels, in addition to institutions offering nursing and/or midwifery training. Genetics is taught in variable formats, quantities and contents, and although some institutions are moving to adopt minimum competencies in genetics, this is by no means widespread. CONCLUSIONS: Given the wide number of stakeholders in the field, consensus competencies seem most likely to advance practice, and thus, phase II of the GenEd project will survey professionals to ascertain their priorities for genetic education.