Markovian network processes: Congestion-dependent routing and processing

A Markovian network process describes the movement of discrete units among a set of nodes that process the units. There is considerable knowledge of such networks, often called queueing networks, in which the nodes operate independently and the routes of the units are independent. The focus of this study, in contrast, is on networks with dependent nodes and routings. Examples of dependencies are parallel processing across several nodes, blocking of transitions because of capacity constraints on nodes, alternate routing of units to avoid congestion, and accelerating or decelerating the processing rate at a node depending on downstream congestion. We introduce a general network process representing the numbers of units at the nodes and derive its equilibrium distribution. This distribution takes the form of a product of functions of vectors in which the arguments of the functions satisfy an interchangeability property. This new type of distribution may apply to other multi-variate processes as well. A basic idea in our approach is a linking of certain micro-level balance properties of the network routing to the processing rates at the nodes. The link is via routing-balance partitions of nodes that are inherent in any network. A byproduct of this approach is a general characterization of blocking of transitions without the restriction that the process is reversible, which had been a standard assumption. We also give necessary and sufficient conditions under which a unit moving in the network sees a time average for the unmoved units (called the MUSTA property). Finally, we discuss when certain flows between nodes in an open network are Poisson processes.This research was sponsored in part by Air Force Office of Scientific Research contract 84-0367.     

Replacement-Policy Development: A Case Study of Glove Replacement at a Nuclear Processing Facility

Individual/group replacement models were used to identify the minimum-cost policy for replacing protective gloves that are utilized in product fabrication at a nuclear processing facility. Since historical data on glove longevity were not available to determine the failure-rate distribution, the classical replacement model for items that fail was modified to consider glove life as a normally distributed variable. Moreover, the absence of replacement-cost required that the classical model be transformed to incorporate the ratio of single to unit-group replacement cost. Sensitivity analysis on these two input parameter values provided guidance for the development of an appropriate replacement policy.     

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Few-Body Systems — News Section

Announcement     

The global structure of simple space-times

According to a standard definition of Penrose, a space-time admitting well-defined future and past null infinitiesI ⁺ andI ^– is asymptotically simple if it has no closed timelike curves, and all its endless null geodesics originate fromI ^– and terminate atI ⁺. The global structure of such space-times has previously been successfully investigated only in the presence of additional constraints. The present paper deals with the general case. It is shown thatI ⁺ is diffeomorphic to the complement of a point in some contractible open 3-manifold, the strongly causal regionI ₀ ⁺ ofI ⁺ is diffeomorphic to , and every compact connected spacelike 2-surface inI ⁺ is contained inI ₀ ⁺ and is a strong deformation retract of bothI ₀ ⁺ andI ⁺. Moreover the space-time must be globally hyperbolic with Cauchy surfaces which, subject to the truth of the Poincaré conjecture, are diffeomorphic to ³.     

New theoretical insight into the interactions and properties of formic acid: development of a quantum-based pair potential for formic acid

We performed ab initio quantum-chemical studies for the development of intra- and intermolecular interaction potentials for formic acid for use in molecular-dynamics simulations of formic acid molecular crystal. The formic acid structures considered in the ab initio studies include both the cis and trans monomers which are the conformers that have been postulated as part of chains constituting liquid and crystal phases under extreme conditions. Although the cis to trans transformation is not energetically favored, the trans isomer was found as a component of stable gas-phase species. Our decomposition scheme for the interaction energy indicates that the hydrogen-bonded complexes are dominated by the Hartree-Fock forces while parallel clusters are stabilized by the electron correlation energy. The calculated three-body and higher interactions are found to be negligible, thus rationalizing the development of an atom-atom pair potential for formic acid based on high-level ab initio calculations of small formic acid clusters. Here we present an atom-atom pair potential that includes both intra- and inter molecular degrees of freedom for formic acid. The newly developed pair potential is used to examine formic acid in the condensed phase via molecular-dynamics simulations. The isothermal compression under hydrostatic pressure obtained from molecular-dynamics simulations is in good agreement with experiment. Further, the calculated equilibrium melting temperature is found to be in good agreement with experiment.     

Quantification of copper and zinc species fractions in legume seeds extracts by SEC/ICP-MS: validation and uncertainty estimation

Fractions of Cu and Zn species in legume samples (common white bean, pea, chick pea and lentil seeds and defatted soybean flour) were analysed by on-line hyphenation of size exclusion chromatography and inductively coupled plasma-mass spectrometry. Samples were extracted by 0.02 mol l⁻¹ Tris–HCl buffer solution, pH 7.5. The extraction efficiency lay in the region 60–90 and 60–80% for Cu and Zn, respectively. Quantification of elements in the individual chromatographic fractions was carried out by isotope dilution (ID) and external calibration (EC) techniques. For ID analysis the chromatographic effluent was mixed with the flow of ⁶⁵Cu and ⁶⁸Zn isotope enriched solution and the isotope ratio values ⁶³Cu/⁶⁵Cu and (⁶⁴Zn+⁶⁶Zn)/⁶⁸Zn were measured. In the case of EC technique calibration solutions of elements were injected to the flow of mobile phase by the second injector. Prior entering detector the effluent was mixed with the flow of internal standard solution (In, 50 μg l⁻¹). Both methods have similar precision, however the behaviour of both studied elements was not the same. The chromatographic analysis itself was the main source of variability in the case of Cu. For Zn species analysis, the extraction process and the manipulation with the extract, played the significant role too. It was probably caused by lower stability of the present zinc chelates. The total amounts of Zn found in all chromatographic fractions represented 85–95% of Zn in sampled extract whereas those of Cu approached 100%. In case of small peaks the results of ID and EC were not the same. The EC results were lower then ID results. The great deal of results uncertainty accounts for the precision.     

BIOLOGICAL ACTIVITIES OF PHTHALOCYANINES-X. SYNTHESES AND ANALYSES OF SULFONATED PHTHALOCYANINES

Abstract— Synthetic methods to obtain selectively sulfonated metallo phthalocyanines are compared. Both condensation and direct sulfonation procedures lead to mixtures of mono- to tetrasulfonated products which are resolved by reverse phase liquid chromatography in buffered aqueous-methanol. The proportion of sulfonated derivatives is examined as a function of the starting reagents in the case of the condensation method, and as a function of the temperature and reaction time in the case of the direct sulfonation procedure. The number of sulfonate groups per phthalocyanine molecule is determined by oxidative degradation of the phthalocyanine ring followed by quantitative chromatographic analysis of the sulfophthalamide and phthalamide fragments.     

The synthesis of 1,4-diazacycl[3,2,2]azine

The diazaanalog of “cycl[3,2,2]azine”, “1,4-diazacycl[3,2,2]azine” (1,4,7b-triazacyclopent-[cd]indene) and its 2-methyl derivative were prepared. These compounds are subject to facile acid-catalyzed hydrolysis affording substituted imidazo[1,2-a]pyridines.     

Evaluation of gas chromatography-tandem quadrupole mass spectrometry for the determination of organochlorine pesticides in fats and oils

A gas chromatography-tandem quadrupole mass spectrometry multi-residue method for the analysis of 19 organochlorine pesticides in fats and oils has been developed. Gel permeation chromatography was employed to remove lipid material prior to GC-MS/MS analysis. Average recoveries of the pesticides spiked at 10 and 50 microg kg(-1) into fish oil, pork fat, olive oil and hydrogenated vegetable oil were typically in the range 70-110% with relative standard deviations generally less than 10%. Calculated limits of detection are between 0.1 and 2.0 microg kg(-1) and results obtained for the analysis of proficiency test materials are in good agreement with assigned values. The higher selectivity of the GC-MS/MS compared to electron capture detection and GC-MS in selective ion monitoring mode allowed unambiguous identification and confirmation of all the target pesticides at low microg kg(-1) levels in fats and oils in a single analysis.