Retail facility location under changing market conditions

In this paper we investigate the location of retail facilitiesunder changing market conditions when market conditions areexpected to change during the planning horizon. Three modelsare presented: (1) the minimax regret model where the objectivefunction is to minimize the maximum possible loss under differentmarket scenarios, (2) the Stackelberg equilibrium model wherebya future competitor enters the market and one wishes to maximizethe market share captured throughout the planning horizon incorporatingthe market share loss to the competitor, and (3) the thresholdmodel in which we consider a minimum threshold level such thatif the market share captured by the new facility fails to reachthat threshold, the facility will not survive. Our objectiveis to minimize the probability of failure.     

The stereochemical dependence of unimolecular dissociation of monosaccharide-glycolaldehyde anions in the gas phase: a basis for assignment of the stereochemistry and anomeric configuration of monosaccharides in oligosaccharides by mass spectrometry via a key discriminatory product ion of disaccharide fragmentation, m/z 221

Mass spectrometry of hexose-containing disaccharides often yields product ions of m/z 221 in the negative ion mode. Using a Paul trap, isolation and collision-induced dissociation of the m/z 221 anions yielded mass spectra that easily differentiated their stereochemistry and anomeric configuration, for all 16 stereochemical variants. The ions were shown to be glycopyranosyl-glycolaldehydes through chemical synthesis of their standards. The stereochemistry dramatically affected fragmentation which was dependent on four relative stereochemical arrangements: (1) the relationship between the hydroxyl group at position 2 and the anomeric configuration, (2) a cis relationship of the anomeric position and positions 2 and 3 (1,2,3-cis), (3) a 1,2 trans-2,3 cis relationship, and (4) the relationship between the hydroxyl group at position 4 and the anomeric configuration. After labeling the reducing carbonyl oxygen of a series of disaccharides with 18O to mass-discriminate between their monosaccharide components, it was demonstrated that m/z 221 anions are comprised of an intact nonreducing sugar glycosidically linked to a 2-carbon aglycon derived from the reducing sugar, irrespective of the linkage position between monosaccharides. This enabled the location of the intact sugar to be assigned to the nonreducing side of a glycosidic linkage. Detailed studies of experimental factors necessary for reproducibility demonstrated that the unique mass spectrum for each m/z 221 anion could be obtained from month-to-month through the use of an internal energy-input calibrant ion that ensured reproducible energy deposition into the ions. The counterparts to these ions for the 2-acetamido-2-deoxyhexoses were m/z 262 anions, and the anomeric configuration and stereochemistry of these anions could also be reproducibly discriminated for N-acetylglucosamine and N-acetylgalactosamine. The fragmentation patterns of m/z 221 anions provide a firm reproducible basis for assignment of sugar stereochemistries in the gas phase.     

Imaginaries in Hilbert spaces

We characterise imaginaries (up to interdefinability) in Hilbert spaces using a Galois theory for compact unitary groups.The authors would like to thank Frank Wagner and the CIRM for their hospitality during the Simpleton 2002 meeting during which the discussions that led to this paper took place.The first author would like to thank Ilan Hirshberg for a few important hintsAt the time of the writing of this paper, the first author was a graduate student with the Équipe de logique mathématique of Université Paris VIIMathematics Subject Classification (2000): 03C45, 03C95     

A dynamic benchmarking system for assessing the recovery of inpatients: Evidence from the neurorehabilitation process

The shortage of medical resources (mainly beds) is a critical and increasingly prevalent problem affecting hospitals. Of the factors that contribute to these shortages, the ambiguity and insufficiency of the criteria used to identify whether an inpatient should be discharged are among the most detrimental. To address this issue, this study applies data envelopment analysis (DEA) on existing inpatient data from the Neurorehabilitation Center at Toronto’s Bridgepoint Hospital to create a dynamic benchmarking system to evaluate the health stage of an inpatient ready to be discharged. Unlike the more traditional parametric techniques, DEA provides non-subjective benchmarking that does not require any prior specification of the production function making it a more desirable choice for this application. The dynamic model categorizes the inpatient’s discharge status as rejected, under observation, or approved. This new approach not only allows managers to gain insight into the potential causes of medical resource shortages, but also allows clinicians to treat inpatients more effectively based on their discharge categories. For validation, the results of the dynamic model were compared with actual inpatient discharge assessments provided by the Bridgepoint Hospital.     

Location with acceleration–deceleration distance

In this paper we investigate a model where travel time is not necessarily proportional to the distance. Every trip starts at speed zero, then the vehicle accelerates to a cruising speed, stays at the cruising speed for a portion of the trip and then decelerates back to a speed of zero. We define a time equivalent distance which is equal to the travel time multiplied by the cruising speed. This time equivalent distance is referred to as the acceleration–deceleration (A–D) distance. We prove that every demand point is a local minimum for the Weber problem defined by travel time rather than distance. We propose a heuristic approach employing the generalized Weiszfeld algorithm and an optimal approach applying the Big Triangle Small Triangle global optimization method. These two approaches are very efficient and problems of 10,000 demand points are solved in about 0.015 seconds by the generalized Weiszfeld algorithm and in about 1 minute by the BTST technique. When the generalized Weiszfeld algorithm was repeated 1000 times, the optimal solution was found at least once for all test problems.     

The system HCl+InCl3+H2O from 5 to 55°C: Application of Harned's rule

Electromotive-force measurements of cells containing hydrochloric acid and indium chloride have been made to determine the variation of the log of the activity coefficient of hydrochloric acid with change in the amount of indium chloride in the solution. The simpler Harned equations have been used to fit the data. The quadratic terms in the Harned equations for the activity coefficients of HCl in the salt mixtures are required for a good fit of the 968 experimental emf data points at all the experimental ionic strengths and temperatures. The more convenient Pitzer ion-interaction treatment of the data will be reported in a separate publication which will include the values of the Pitzer parameters for pure InCl₃(aq), and mixing parameters for H⁺–In⁺³ and H⁺–In⁺³–Cl^–. A comprehensive investigation on the mixed electrolyte solutions at 11 different constant total ionic strengths ranging from 0.05 to 3.5 mol-kg^–1 was made at 11 temperatures from 5 to 55°C using the cell without liquid junction of the type: Pt,H₂(g, 1 atm)|HCl(m _A)+InCl₃(m _B)+H₂O|AgCl,AG (A).     

Photoactive Analogs of Farnesyl Pyrophosphate Containing Benzoylbenzoate Esters: Synthesis and Application to Photoaffinity Labeling of Yeast Protein Farnesyltransferase

Farnesyl pyrophosphate (FPP) is involved in a large number of cellular processes including the prenylation of transforming mutants of Ras proteins implicated in cancer. Photoactive analogs could provide useful information about enzyme active sites that bind farnesyl pyrophosphate; however, the availability of such compounds is extremely limited. Molecules that incorporate benzophenone moieties are attractive photoaffinity labeling reagents because of their useful photochemical properties. Here, the syntheses of two compounds, 3a and 3b, containing para- and meta-substituted benzoylbenzoates are described. Compounds 3a and 3b are competitive inhibitors (with respect to FPP) of yeast protein farnesyltransferase (PFTase) with K(i) values of 910 and 380 nM, respectively. Both compounds inactivate PFTase upon photolysis, resulting in as much as 44% inactivation of enzyme activity. Photolysis of PFTase in the presence of [(32)P]3a or of [(32)P]3b results in preferential labeling of the beta subunit, suggesting that this subunit is involved in prenyl group recognition. These compounds should be valuable tools for studying enzymes that utilize FPP as a substrate.     

Activity Coefficients of Individual Ions from Titration Data

It is shown that the activity coefficients of the anions resulting from the dissociation of a weak polyprotic acid can be obtained from titration data. Activity coefficients are determined in terms of the activity coefficient of the undissociated acid. The extracted activity coefficients are also dependent on the pH scale adopted in the titration process and are considered as operational coefficients. The computational procedure uses an exact equation representing the titration curve and a nonlinear least-squares fitting procedure. As an illustration, the activity coefficients of the anions of succinic acid are determined. The method also allows study of the variation of the activity coefficients with the ionic strength in a straightforward manner.     

Directional approach to gradual cover: a maximin objective

The objective of original cover location models is to cover demand within a given distance by facilities. Locating a given number of facilities to cover as much demand as possible is referred to as max-cover, and finding the minimum number of facilities required to cover all the demand is referred to as set covering. When the objective is to maximize the minimum cover of demand points, the maximin objective is equivalent to set covering because each demand point is either covered or not. The gradual (or partial) cover replaces abrupt drop from full cover to no cover by defining gradual decline in cover. Both maximizing total cover and maximizing the minimum cover are useful objectives using the gradual cover measure. In this paper we use a recently proposed rule for calculating the joint cover of a demand point by several facilities termed “directional gradual cover”. The objective is to maximize the minimum cover of demand points. The solution approaches were extensively tested on a case study of covering Orange County, California.

     

Palladium-catalyzed microwave-assisted amination of 1-bromonaphthalenes and 5- and 8-bromoquinolines

[reaction: see text] 1-Aminonaphthalenes and 5- and 8-aminoquinolines were rapidly prepared from the respective aryl bromides in good yields by Pd-catalyzed aryl amination under microwave conditions. Consistent improvements in yields over those obtained under standard conditions were seen with quinoline substrates. In the cases where 5-bromo-8-cyanoquinoline was used as a substrate, no desired products were obtained under standard conditions with a number of different primary and secondary amines. However, microwave conditions provided the desired products in good to excellent yields.