Local Optima Avoidance in Depot Location

The locating of a set of depots to serve a given set of customers is complicated by the existence of local optima of the cost function. It is shown that the strategic siting of hazards (conventionally used to model natural obstacles) can lead to the avoidance of such local optima. A set of heuristics for hazard-siting is given and some examples are considered.     

3.508 μ-HeXe-laser line absorption by CH3COOCH3, CH3, and NO2 and infrared emission at 6.89 μ by CH3COOCH3 and CH3 at elevated temperatures

Shock-tube HeXe-laser absorption data at ω_L=2850.633 cm^-1 for CH₃COOCH₃ at 757≤T, °K≤1344, NO₂at 412≤T, °K≤1859, andCH₃at 1283≤T, °K≤1562 are presented. Approximate models are used for the effective spectral absorption coefficient of vibration-rotation lines for analytical representations of the results around atmospheric pressures. For CH₃COOCH₃, an equivalent Voigt-profile for an isolated line was adopted in order to account for a dependence on total pressure of the laser absorption coefficient. Shock-tube emission data at λ=6.890 μ(Δλ=0.197μ) forCH₃COOCH₃at 814≤T, °K≤1651 and for CH₃at 1377≤T, °K≤1562 in the v₄-fundamental of the H-bond bending mode of the CH₃-group are well described at atmospheric pressures by approximations of just-overlapping-line models for polyatomic molecules. The adopted models are useful for concentration-time history measurements of methyl acetate, nitrogen dioxide, and methyl radicals behind shock waves.     

Octupole vibrations in the even mercury and lead isotopes

Prominent groups are observed corresponding to excited states in the region of 2.6 MeV in the scattering of 24 and 27 MeV α-particles from ^{198, 200, 202, 204}Hg and ^{204, 206, 208}Pb. For each of the Pb isotopes the state concerned is identified with the known 3^? octupole vibration. Angular distribution measurements for scattering to the Pb and ²⁰⁴Hg states are in agreement with octupole-vibration coupled-channels predictions, and systematic trends suggest that the states observed in the isotopes ^{198, 200, 202}Hg can also be attributed to octupole vibrations.     

Static quadrupole moments of the first excited states of 200Hg and 202Hg

The static quadrupole moments Q_2⁺ and B(E2; 0⁺ → 2⁺) values of the 2⁺ first excited states of ²⁰⁰Hg and ²⁰²Hg have been determined using the reorientation effect in Coulomb excitation. An annular silicon surface-barrier detector was used to detect backscattered ⁴He, ¹²C and ¹⁶O projectiles. It is found that for ²⁰⁰Hg, Q_2⁺ = +1.07 ± 0.19 e · b(+0.98 ± 0.19 e · b) for destructive (constructive) interference from the 2^+′ state, and B(E2; 0⁺ → 2⁺) = 0.853 ± 0.007 e² · b². For ²⁰²Hg, we find Q_2⁺ = +1.01 ± 0.13 e · b (+0.87 ± 0.13 e · b) and B(E2; 0⁺ → 2⁺) = 0.605 ± 0.005 e² · b². The Q_2⁺ value obtained for ²⁰⁰Hg is in agreement with previous work, but that for ²⁰²Hg is not. The results obtained are compared with the predictions of various nuclear models, and the mass dependence of Q_2⁺ in the region 182 ≦ A ≦ 206 is examined.     

On Zamolodchikov's solution of the tetrahedron equations

The tetrahedron equations arise in field theory as the condition for theS-matrix in 2+1-dimensions to be factorizable, and in statistical mechanics as the condition that the transfer matrices of three-dimensional models commute. Zamolodchikov has proposed what appear (from numerical evidence and special cases) to be non-trivial particular solutions of these equations, but has not fully verified them. Here it is proved that they are indeed solutions.     

Spontaneous staggered polarization of theF-model

The order parameter of the two-dimensionalF-model, namely the spontaneous staggered polarizationP ₀, is derived exactly. At the critical temperatureP ₀ has an essential singularity, bothP ₀ and all its derivatives with respect to temperature vanishing.     

Compressible laminar boundary layer behavior studied by a finite difference method

Zusammenfassung Die L?sung des Systems der nichtlinearen partiellen Differentialgleichungen der laminaren kompressiblen Grenzschicht bereitet erhebliche mathematische Schwierigkeiten. In dieser Arbeit wird ein Differenzenverfahren benutzt, um die Str?mung entlang einer gekrümmten Wand zu untersuchen. Analytische Bedingungen für seine Stabilit?t sind angegeben, und die Konvergenz der L?sung gegen die L?sung des Differentialgleichungssystems ist durch Vergleichsrechnungen mit verschiedener Schrittweite erprobt. Der Einfluss von beliebigen Druck- und Temperaturverteilungen ist an einer Reihe von Beispielen untersucht. Da das Verfahren Energiedissipation und Ver?nderlichkeit der Dichte und der Z?higkeit vollst?ndig berücksichtigt, sind seine Ergebnisse benutzt, um die Vereinfachungen kritisch zu diskutieren, die so oft angewendet werden, um die analytische L?sung des Problems zu erleichtern.

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This research was supported by the Air Force Office of Scientific Research of the Air Research and Development Command under Contract AF 18(600)-1488.     

Electroproduction of π0 mesons in the resonance region at q2=1.0 (GeV/c)2

Data are presented for the reaction ep → epπ⁰ at a nominal momentum transfer squared of 1.0 (GeV/c)². The data were obtained using an extracted electron beam from NINA and two magnetic spectrometers for coincidence detection of the electron and proton. Differential cross sections have been measured for isobar masses in the range 1.19–1.73 GeV/c².