Improved convexity cuts for lattice point problems

The generalized lattice point (GLP) problem provides a formulation that accommodates a variety of discrete alternative problems. In this paper, we show how to substantially strengthen the convexity cuts for the GLP problem. The new cuts are based on the identification ofsynthesized lattice point conditions to replace those that ordinarily define the cut. The synthesized conditions give an alternative set of hyperplanes that enlarge the convex set, thus allowing the cut to be shifted deeper into the solution space. A convenient feature of the strengthened cuts is the evidence of linking relationships by which they may be constructively generated from the original cuts. Geometric examples are given in the last section to show how the new cuts improve upon those previously proposed for the GLP problem.     

Crystal structures and properties of mutagenic N-acyloxy-N-alkoxyamides--"most pyramidal" acyclic amides

X-Ray data for two N-acyloxy-N-alkoxyamides, a class of direct-acting mutagens, indicate extreme pyramidalisation at the amide nitrogen in keeping with spectroscopic and theoretically determined properties of amides with bisoxosubstitution at nitrogen. The combined electronegativity of two oxygens leads to average angles at nitrogen of 107.8 and 108.1 degrees and [chiN] of 66 degrees and 65 degrees. The sp3 nature of nitrogen results in negligible amide resonance as evidenced by long N-C(O) bonds, high IR carbonyl stretch frequencies, carbonyl 13C NMR data and very low amide isomerisation barriers. In addition, conformations in the solid state support a strong n(O)-sigma*(NOAc), anomeric interaction as predicted by molecular orbital theory. HF/6-31G* calculations on formamide, N-methoxyformamide and N-formyloxy-N-methoxyformamide support these findings.     

The pressure-volume-temperature relationship and the heat of fusion of polyoxymethylene

The pressure-volume-temperature relation of polyoxymethylene was measured at pressures from 100 to 2000 kg/cm² and from room temperature to 200°C. The dependence of the melting and crystallation temperatures on pressure was also determined. The unit cell parameters were measured up to 170°C by x-ray diffraction. These data were combined through the use of the Clapeyron equation to compute a heat of fusion of 92.9 cal/g. This value is considerably higher than those previously reported. The weight fraction crystallinity of an injection molded sample was 48% by calorimetry and 66% by interpolation between the specific volumes of the crystal and the amorphous phase. It is suggested that a simple two-phase model is inadequate to describe this polymer.     

Simple but powerful goal programming models for discriminant problems

Conventional statistical analysis includes the capacity to systematically assign individuals to groups. We suggest alternative assignment procedures, utilizing a set of interrelated goal programming formulations. We further demonstrate via simple illustration the potential of these procedures to play a significant part in addressing the discriminant problem, and indicate fundamental ideas that lay the foundation for other more sophisticated approaches.     

Evaluation of thermal analysis equipment for the determination of vapor pressure and heat of vaporization

A rapid, relatively simple method for determining vapor pressure and heat of vaporization on small amounts of organic compounds is described. A DuPont 900 differential thermal analyzer (DTA), a Perkin—Elmer Model DSC-1B differential scanning calorimeter (DSC), and a Thomas—Hoover (TH) melting point apparatus were evaluated in this work. Vapor pressure data for a wide variety of organic liquids were obtained by measuring the boiling points of the liquids at pressures ranging from 20 to 735 torr. A computer was used to rapidly plot the experimental data. The average deviations of boiling points from the literature values were 2.3°C for the DTA 1.2°C for the DSC, and 1.5°C for the TH. The vapor pressure data were used to solve the Haggenmacher equation for heat of vaporization (ΔH_v). The deviations of the experimental values for ΔH_v. from the literature values were 5.5%, 8.3%. and 3.3% for the DTA, DSC, and TH methods, respectively.     

Extensions of the Petal Method for Vehicle Routeing

The petal method for vehicle routeing imposes special structure on the form of a feasible route. In this paper we show that by extending the definition of a petal route, more general forms of vehicle route can be generated without invalidating the important underlying property that optimal petal solutions can be produced very easily. It will also be shown that the optimal generalized petal solution can be produced efficiently by multiple applications of a shortest path algorithm.     

Markov processes with identical last exit distributions

Summary LetX andY be two transient locally Hunt Markov processes. IfX andY enjoy the same last exit distributions from compact sets, thenY is equivalent to a time change ofX by the inverse of a strictly increasing continuous additive functional. This result can also be interpreted (with natural auxiliary hypotheses) as a statement in potential theory involving equilibrium measures.Research supported in part by NSF grant MCS-8002659 and an CNRS Fellowship while the author was visiting I.M.S.S., Universite de Grenoble II     

Oxidation reactions of azines.

Condensation of 2-([2.2]paracyclophan-4-yl)propene with formaldehyde and amines gave 4-paracyclophanyl substituted -piperidols which were readily dehydrated to the corresponding tetrahydropyridines. N-Methyl substituted 4-paracyclophanyltetrahydropyridine has been oxidized to the corresponding piperidin-2-one.For communication 2, see [1]. This article is also communication 4 in the series Synthesis, structure and biological activity of [2.2]paracyclophanes (for communication 3, see [2]).Russian University of National Friendship, Moscow 117198. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 5, pp. 653–658, May, 1997,     

Generating Cuts from Surrogate Constraint Analysis for Zero-One and Multiple Choice Programming

This paper presents a new surrogate constraint analysis that givesrise to a family of strong valid inequalities calledsurrogate-knapsack (S-K) cuts. The analytical procedure presentedprovides a strong S-K cut subject to constraining the values ofselected cut coefficients, including the right-hand side. Ourapproach is applicable to both zero-one integer problems and problemshaving multiple choice (generalized upper bound) constraints. We alsodevelop a strengthening process that further tightens the S-K cutobtained via the surrogate analysis. Building on this, we develop apolynomial-time separation procedure that successfully generates anS-K cut that renders a given non-integer extreme point infeasible. Weshow how sequential lifting processes can be viewed in our framework,and demonstrate that our approach can obtain facets that are notavailable to standard lifting methods. We also provide a relatedanalysis for generating fast cuts. Finally, we presentcomputational results of the new S-K cuts for solving 0-1 integerprogramming problems. Our outcomes disclose that the new cuts arecapable of reducing the duality gap between optimal continuous andinteger feasible solutions more effectively than standard liftedcover inequalities, as used in modern codes such as the CPLEX mixed0-1 integer programming solver.