Location on a One-Way Rectilinear Grid

This paper considers two basic location problems — the Weber problem and the minimax problem-on a regular grid of alternating one-way routes or streets. Both the facility to be located and the demand points are restricted to any point on the network. The one-way restriction is often used for efficiency in traffic flow, but complicates the distances in the system.     

Lower bounds based on linear programming for the quadratic assignment problem

In this paper we prove that the Classical Gilmore-Lawler lower bound for the quadratic assignment problem is equivalent to a solution of a certain linear programming problem. By adding additional constraints to this linear programming problem we derive a lower bound which is at least as good as the Gilmore-Lawler lower bound.Some of this research was done while the author was on sabbatical leave at the Department of Management, The Hong Kong University of Science and Technology, Kowloon, Hong Kong.     

An ion mobility spectrometry/mass spectrometry (IMS/MS) study of the site of protonation in anilines

Ion mobility spectrometry (IMS) and IMS/MS techniques were used to differentiate between nitrogenprotonated and carbon-protonated anilines, both of which coexist under the conditions of the IMS. Analysis of the results led to the conclusion that the former species had lower mobilities than the latter. This was attributed mainly to charge delocalization in the ring-protonated species, which results in a weaker interaction with the drift gas molecules. Furthermore,meta-alkyl substitution enhanced ring protonation, while in 2-chloroaniline the nitrogenprotonated species was predominant, as expected.     

Stereochemistry of the Vinylic S(RN)1 Reaction of Triarylvinyl Halides. The Structure of the Intermediate alpha-Arylvinyl Radical

Evidence for the intermediacy of a vinyl radical in the vinylic S(RN)1 reaction (S(RN)1(V)) of 2-anisyl-1,2-diphenylvinyl bromide 2 is obtained. The photostimulated S(RN)1(V) reaction of pinacolone enolate ion with (E)-2 and (Z)-2, which are used as stereoindicators, gives complete loss of the original stereochemistry of the two precursors in the substituted and hydrodehalogenated products; i.e., stereoconvergence is found. It is concluded that in the reaction of 2 a beta-substituted alpha-phenylvinyl radical is a reactive intermediate and that it has either a linear structure or an average linear structure due to a rapidly interconverting E,Z mixture of bent radicals. This conclusion is supported by comparing the stereochemical course of the S(RN)1(V) reaction with those of other reactions of the same precursor, which unambiguously give rise to the same alpha-phenylvinyl radical intermediate by alternative mechanisms. Among the reactions investigated, the hydrodehalogenation of precursor 2 by LAH appears to take place by an ET mechanism.     

Static and Dynamic Stereochemistry and Solvation of 2,2-Ditipylethenols(1)

The effect of increased bulk of the beta-aryl group in enols Ar(2)C=C(OH)R from Ar = mesityl = Mes (1) to Ar = 2,4,6-i-Pr(3)C(6)H(2) = Tip (2) was investigated. The solid-state structure when R = H (a) does not significantly differ for 1a and 2a. The dynamic behavior of 2a resembles that of 1a, but the rotational barriers for both the threshold one-ring flip process and the two-ring flip process are higher for 2a. The one-ring flip barrier for 2a is solvent-dependent. The threshold two-ring flip barriers when R = Me (2b) and t-Bu (2c) are higher than for the mesityl analogues, but that for 2c is higher than predicted. Solvations of 2a and 1a and their associations with DMSO are similar. The C=COH conformation is syn-planar with an OH.pi(Tip) association in non-hydrogen-bond-accepting solvents and is anti-clinal with OH.solvent association in hydrogen-bond-accepting solvents. In summary, the increased bulk associated with the change Mes --> Tip changes the structure and behavior in the expected direction but, except for the DeltaG(c)() values, not to a large extent.     

Wannier states of molecular impurity in a liquid rare gas

We have measured the vacuum ultraviolet absorption spectra of CH₃I in solid and in liquid krypton in the spectral region 2000–1450 Å. In both phases we have observed two Wannier series n(²E_{$\text{3}\text{2}$}) and n(²E_{$\text{1}\text{2}$}) up to n = 3. Information has been obtained concerning the features of the conduction band in a liquid rare gas.     

Enols of amides activated by the 2,2,2-trichloroethoxycarbonyl group

Reaction of isocyanates XNCO (X = Ar, i-Pr, t-Bu) with CH(2)(Y)CO(2)CH(2)CCl(3) (Y = CO(2)Me, CO(2)CH(2)CCl(3), CN) gave 15 amides XNHCOCH(Y)CO(2)CH(2)CCl(3) (6) or enols of amides XNHC(OH)=C(Y)CO(2)CH(2)CCl(3) (5) systems. The amide/enol ratios in solution depend strongly on the substituent Y and the solvent and mildly on the substituent X. The percentage of enol for group Y increases according to Y = CN > CO(2)CH(2)CCl(3) > CO(2)Me and decreases with the solvent according to CCl(4) > C(6)D(6) > CDCl(3) > THF-d(8) > CD(3)CN > DMSO-d(6). With the most acidic systems (Y = CN) amide/enol exchange is observed in moderately polar solvents and ionization to the conjugate base is observed in DMSO-d(6). The solid-state structure of the compound with Y = CN, X = i-Pr was found to be that of the enol. The reasons for the stability of the enols were discussed in terms of polar and resonance effects. Intramolecular hydrogen bonds result in a very low delta(OH) and contribute to the stability of the enols and are responsible for the higher percentage of the E-isomers when Y = CO(2)Me and the Z-isomers when Y = CN. The differences in delta(OH), delta(NH), K(enol), and E/Z enol ratios from the analogues with CF(3) instead of CCl(3) are discussed.     

Hybrid meta-heuristics with VNS and exact methods: alication to large unconditional and conditional vertex $$$$-centre roblems

Large-scale unconditional and conditional vertex \(p\)-centre problems are solved using two meta-heuristics. One is based on a three-stage approach whereas the other relies on a guided multi-start principle. Both methods incorporate Variable Neighbourhood Search, exact method, and aggregation techniques. The methods are assessed on the TSP dataset which consist of up to 71,009 demand points with \(p\) varying from 5 to 100. To the best of our knowledge, these are the largest instances solved for unconditional and conditional vertex \(p\)-centre problems. The two proposed meta-heuristics yield competitive results for both classes of problems.     

Oxa-ene reaction of enols of amides with 4-phenyl-1,2,4-triazoline-3,5-dione

The reaction of 16 enols of amides with 4-phenyl-1,2,4-triazoline-1,3-dione gave open chain adducts rather than the [2 + 2] cycloadducts with a hemiaminal moiety, both in solid state and in solution. This assignment is based on X-ray crystallography, (1)H and (13)C NMR data, and IR spectra. The suggested mechanism involves hydroxyl proton loss in a formal oxa-ene reaction. Mechanistic details and a possible alternative are discussed.