Cooperative Strategies for Solving the Bicriteria Sparse Multiple Knapsack Problem

For hard optimization problems, it is difficult to design heuristic algorithms which exhibit uniformly superior performance for all problem instances. As a result it becomes necessary to tailor the algorithms based on the problem instance. In this paper, we introduce the use of a cooperative problem solving team of heuristics that evolves algorithms for a given problem instance. The efficacy of this method is examined by solving six difficult instances of a bicriteria sparse multiple knapsack problem. Results indicate that such tailored algorithms uniformly improve solutions as compared to using predesigned heuristic algorithms.     

THE ENERGY ASPECT OF THE RECIPROCAL INTERACTIONS OF PAIRS OF TWO DIFFERENT VIBRATION MODES OF A CLAMPED ANNULAR PLATE

The standardized mutual active and reactive sound power of a clamped plate, representing the energy aspect of the reciprocal interactions of two different in vacuo modes, has been computed. It was assumed that the vibrations are axisymmetric, elastic and time harmonic, the plate's transverse deflection is small as compared with the plate's size, and that the vibration velocity is small as compared with the acoustic wavenumber generated. The Kirchhoff-Love theory of a perfectly elastic plate was used. The integral formulae for the mutual sound power were transformed into their Hankel representations which made possible their subsequent computation. A closed path integral was used to express the integral in its Hankel representation to compute the mutual active sound power. The asymptotic stationary phase method was used to compute the two magnitudes, i.e., the mutual active and reactive sound power. The results obtained are the asymptotic formulae valid for the acoustically fast waves. The oscillating as well as the non-oscillating terms have been identified in the formulae to make possible their further separate analysis. The availability of the asymptotic formulae makes possible some fast numerical computations of the mutual sound power. Moreover, the formulae presented herein, together with those for the individual modes known from the literature, make a complete basis for further computations of the total sound power of the plate's damped and forced vibrations in fluid.     

Chlorine nitrate photolysis by a new technique: very low pressure photolysis

Very low pressure photolysis (VLPØ) of chlorine nitrate was performed in a quartz Knudsen cell. The light source was a 2500 W high-pressure xenon lamp, and a modulated molecular-beam mass spectrometer was used to monitor the concentration of ClONO₂ and photolysis products. Because of the low pressures used (? 10^?3 torr) and the short residence time in the cell (≈1 s), secondary reactions were unimportant and the primary products could be directly identified. The primary photolysis products (λ ≈ 2700 Å) are atomic chlorine and NO₃ free radical. Chlorine atoms were identified both by the appearance of Cl₂ (wall recombination product; the walls were not poisoned) and by HCl produced when C₂H₆ was added to the cell. Nitrate free radical was directly identified as a mass peak at m/e = 62, as well as by chemical titration with nitric oxide: NO₃ + NO → 2NO₂. It was verified by direct tests that the peak at m/e = 62 did not arise from possible HNO₃ contamination or from N₂O₅, a possible secondary product. This titration reaction was used to measure quantitatively a lower limit to the primary quantum yield, φ ? 0.5 ± 0.3. This represents a lower limit because of the unknown extent of the secondary photolysis of NO₃ under our conditions. We believe this to be the first observation using mass spectrometry of the NO₃ free radical. The quantum yield for atomic chlorine is φ = 1.0 ± 0.2. N₂O was used to test for O(¹D) according to the reaction, O(¹D) + N₂O → products; none was observed. Triplet oxygen, O(³P) was observed to the extent of ≈ 10% by the reaction O(³P) + NO₂ → NO + O₂, but this yield can also be due to the photolysis of NO₃ free radical produced in the primary step. We conclude that the predominant reaction pathway is

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Calculation of angular dependence of photoemission for the Al(100) + O system using a simple molecular orbital cluster model

The angular dependence of photoemission from oxygen chemisorbed on the (100) face of aluminum is calculated using a molecular cluster model. The cluster contains five aluminum atoms with one oxygen atom located in the four-fold site; two A1O distances are considered. The calculations employed the Xα scattered wave formalism and are the first results to be obtained for a chemisorption problem in which both initial and final states are based on a cluster model.