Computing the link center of a simple polygon

The link center of a simple polygonP is the set of pointsx insideP at which the maximal link-distance fromx to any other point inP is minimized. Here the link distance between two pointsx, y insideP is defined to be the smallest number of straight edges in a polygonal path insideP connectingx toy. We prove several geometric properties of the link center and present an algorithm that calculates this set in timeO(n ²), wheren is the number of sides ofP. We also give anO(n logn) algorithm for finding an approximate link center, that is, a pointx such that the maximal link distance fromx to any point inP is at most one more than the value attained from the true link center.Work on this paper by the second author has been supported by National Science Foundation Grant DMS-8501947. Work by the third author has been supported by the Canadian National Science and Engineering Research Council, Grant A0332. Work by the fifth author has been supported by Office of Naval Research Grant N00014-82-K-0381, National Science Foundation Grant DCR-83-20085, and by grants from the Digital Equipment Corporation, and the IBM Corporation. Work by the seventh author has been supported by a Killam Senior Research Fellowship from the Canada Council, and work by the ninth author has been supported by the National Science Foundation Grants DCR-84-01898 and DCR-84-01633. Part of the work on this paper has been carried out at the Workshop on Movable Separability of Sets at the Bellairs Research Institute of McGill University, Barbados, February 1986. Further acknowledgments can be obtained from the tenth author upon request.     

A technique for on-line sensitivity analysis of flexible manufacturing systems

The recent perturbation analysis approach to discrete event systems is applied to flexible manufacturing systems (FMS). While analytic (queueing) models are useful in preliminary design of such systems, they are not accurate enough at the detailed design/operation stage. Thus, experimentation on detailed simulations or on the actual system has been the way to optimize system performance. Perturbation analysis allows us to derive the sensitivity of system performance, with respect to several design/operating parameters, by observing a single experiment (and without having to actually alter the parameters — often a costly operation). Thus, observation of one experiment can give accurate directions for the improvement of several parameter values. Here we give a simulation example illustrating how perturbation analysis could be used on-line on an FMS to improve its performance, including reducing its operating cost. Experimental results are also presented validating the estimates obtained from this technique.Work supported by U.S. Office of Naval Research Contracts N00014-75-C-0648 and N00014-79-C-0776, and NSF Grant ENG78-15231, at Harvard University.A preliminary version of this paper appeared in the Proc. 1st ORSA/TIMS Conf. on Flexible Manufacturing Systems, August 1984. This version includes two appendices, which relate to implementation of the technique described in the main body of the paper.     

Observation of autoionization resonances in uranium by step-wise laser photoionization

A large number of autoionization resonances have been observed in uranium in the energy range 50,590–51,560cm^–1 by two-step three-photon ionization technique, using two copper vapor laser pumped dye lasers. A Rydberg series converging to the ionization limit of UII at 1749cm^–1 (⁶ L _13/2) has been identified. Some of these resonances are very narrow with a fwhm of 0.1cm^–1. Possible origins of these are discussed.     

Morpholine complexes of copper(II) alkanoates and chloroacetates

Summary Morpholine complexes of copper(II) alkanoates and chloroacetates of formula Cu(O₂CR)₂(Morph)_n (where R = H, Me, Et, n-Pr, i-Pr, n-Bu, i-Bu, CH₂Cl, CHCl₂ and CCl₃; Morph = Morpholine and n=1 and/or 2) have been isolated by the direct interaction of morpholine with the respective copper(II) carboxylates in a suitable organic medium and characterized by elemental analyses and various physicochemical techniques. Molecular weight determinations show that 11 complexes are dimeric whereas 21 complexes are monomeric in solution. Electronic spectra and magnetic moments suggest that 11 complexes are dinuclear carboxylate bridged species while 21 addition complexes have atrans-octahedral configuration. The i.r. spectra indicate that morpholine behaves as a monodentate ligand and coordinates through its nitrogen atom.     

Analysis by phase-titration of three-component systems containing two mutually immiscible or partially miscible components

A method, based on phase titration, for the analysis of ternary mixtures containing two mutually immiscible or partially miscible components is described. The method involves titrating a measured amount of the sample at constant temperature with one of the immiscible components to a turbidimetric end-point. The refractive index of the resultant solution (clarified by addition of the mutually miscible component) is determined and from the results the composition of the ternary mixture is estimated. The method is illustrated for the system consisting of benzene, cyclohexane and nitromethane.     

Ferrofluid catalyzed water gas shift reaction to give carbon-dioxide and hydrogen

A ferrofluid consisting of colloidally dispersed magnetite particles in water was found to be an efficient selective catalyst for water gas shift reaction at 15–25 atmosphere of CO pressure in the temperature range of 423–553 K where the products obtained were only CO₂ and H₂. The reaction was studied as a function of variation of the concentration of catalyst, pressure of CO gas and temperature. Kinetic parameters suggested a mechanism involving first order dependence in CO and catalyst concentrations.     

Interactions in aqueous nonelectrolyte systems. Gibbs energy of interaction of the ether group with the hydroxyl group and the amide group

Freezing temperatures of dilute aqueous solutions of equimolar mixtures of 1,3,5-trioxane with myo-inositol, d-mannitol, cyclohexanol, formamide, and acetamide, and 1,4-dioxane with myo-inositol, d-mannitol, formamide, and acetamide have been measured. These data yield pairwise Gibbs energies of interactions between the molecules in an aqueous solution. Using the group additivity principle, the results also yield the pairwise functional group Gibbs energies of interaction for the ether group with the hydroxyl and amide group. These results have been combined with all available data from the literature to yield the Gibbs energy and enthalpy of interaction of amides, ethers, alcohols, and saccharides in aqueous solution.To whom correspondence should be addressed.     

Design and synthesis of dimeric heparinoid mimetics

Synthetic oligosaccharide constructs exhibiting tailored and well-defined heparan sulfate (HS) like sequences offer the potential to modulate dynamic HS-dependent biomolecular recognition processes. We report an efficient strategy for the generation of HS-like fragments [GlcA-beta-(1,4)-GlcNAc] and related dimerized (gemini) disaccharides (4a and 4b) via n-pentenyl glycoside formation. When a convergent synthetic approach was utilized, construction of target molecules was achieved through a combination of chemoselective protection/deprotection protocols, imidate and n-pentenyl glycosylations, and functional group manipulations followed by ozonolysis and reductive amination. For example, glycosylation of a 2-azido glycoside (25) with a trichloroacetimidate glucuronic acid donor (13), using a catalytic amount of TMSOTf, furnished heparin-like disaccharides (28a and 28b) that were equipped with an n-pentenyl tether at the anomeric end. In turn, heparinoid-like gemini disaccharides (4a and 4b) were produced by selective transformation of the olefinic unit in the n-pentenyl glycoside to the four-carbon aldehyde followed by reductive amination with ethylenediamine. The described synthetic approach provides access to structural variants of small heparinoid oligomers as versatile building blocks for generating novel HS mimetic pharmacotherapeutics, diagnostic reagents, and biomaterials.