A constrained matching problem

We show that certain manpower scheduling problems can be modeled as the following constrained matching problem. Given an undirected graphG = (V,E) with edge weights and a digraphD = (V,A). AMaster/Slave-matching (MS-matching) ofG with respect toD is a matching ofG such that for each arc (u, v) A for which the nodeu is matched, the nodev is matched, too. TheMS-Matching Problem is the problem of finding a maximum-weight MS-matching. Letk(D) be the maximum size of a (weakly) connected component ofD. We prove that MS-matching is an NP-hard problem even ifG is bipartite andk(D) 3. Moreover, we show that in the relevant special case wherek(D) 2, the MS-Matching Problem can be transformed to the ordinary Matching Problem.This research was supported by Grant 03-KL7PAS-6 of the German Federal Ministry of Research and Technology.     

Backscattering enhancements associated with subsonic Rayleigh waves on polymer spheres in water: observation and modeling for acrylic spheres

Unlike most common solids, "plastic" polymer solids typically have shear and Rayleigh wave phase velocities less than the speed of sound in water. Subsonic Rayleigh waves on smooth objects in water are not classified as leakey waves and it is necessary to reexamine backscattering mechanisms. Also the intrinsic material dissipation of the Rayleigh wave can be significant. Backscattering by acrylic or polymethlmethacrylate (PMMA) spheres in water is analyzed and measured in the region ka = 1.5-7 and it is found that prominent low-lying resonance peaks of the form function f exist. The peaks can be modeled with quantitative ray theory as the result of coupling of subsonic Rayleigh waves with sound through acoustic tunneling. The most prominent maximum of f=5.63 occurs at ka = 1.73 and is associated with the quadrupole (or n=2) partial wave. In addition to explaining the scattering, the target strength is found to be sufficiently large that such spheres may be useful for passive low frequency targets.     

Synthesis of sterically encumbered and functionalized diaryl-diazenes by formal [3+3] cyclization of 2-aryldiazenyl-3-silyloxy-2-en-1-ones with 1,3-bis(silyloxy)-1,3-butadienes

Functionalized diaryl-diazenes (azo-dyes) were regioselectively prepared by formal [3+3] cyclization of 1,3-bis(silyloxy)-1,3-butadienes with 2-aryldiazenyl-3-silyloxy-2-en-1-ones.     

A spiral wave front beacon for underwater navigation: transducer prototypes and testing

Transducers for acoustic beacons which can produce outgoing signals with wave fronts whose horizontal cross sections are circular or spiral are studied experimentally. A remote hydrophone is used to determine its aspect relative to the transducers by comparing the phase of the circular signal to the phase of the spiral signal. The transducers for a "physical-spiral" beacon are made by forming a strip of 1-3 piezocomposite transducer material around either a circular or spiral backing. A "phased-spiral" beacon is made from an array of transducer elements which can be driven either in phase or staggered out of phase so as to produce signals with either a circular or spiral wave front. Measurements are made to study outgoing signals and their usefulness in determining aspect angle. Vertical beam width is also examined and phase corrections applied when the hydrophone is out of the horizontal plane of the beacon. While numerical simulations indicate that the discontinuity in the physical-spiral beacon introduces errors into the measured phase, damping observed at the ends of the piezocomposite material is a more significant source of error. This damping is also reflected in laser Doppler vibrometer measurements of the transducer's surface velocity.     

Evolution of structure and properties of a liquid crystalline epoxy during curing

The evolution of structure, and thermal and dynamic mechanical properties of a liquid crystalline epoxy during curing has been studied with differential scanning calorimetry (DSC), polarized optical microscopy, x-ray scattering, and dynamic mechanical analysis. The liquid crystalline epoxy was the diglycidyl ether of 4,4′-dihydroxy-α-methylstilbene (DGEDHMS). Two curing agents were used in this study: a di-functional amine, the aniline adduct of DGEDHMS, and a tetra-functional sulfonamido amine, sulfanilamide. The effects of curing agent, cure time, and cure temperature have been investigated. Isothermal curing of the liquid crystalline epoxy with the di-functional amine and the tetra-functional sulfonamido amine causes an increase in the mesophase stability of the liquid crystalline epoxy resin. The curing also leads to various liquid crystalline textures, depending on the curing agent and cure temperature. These textures coarsen during the isothermal curing. Moreover, curing with both curing agents results in a layered structure with mesogenic units aligned perpendicular to the layer surfaces. The layer thickness decreases with cure temperature for the systems cured with the tetra-functional curing agent. The glass transition temperature of the cured networks rises with increasing cure temperature due to the increased crosslink density. The shear modulus of the cured networks shows a strong temperature dependence. However, it does not change appreciably with cure temperature. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 2363–2378, 1997     

Influence of grain structure on processing of EVA-modified PVC

Two grades of VC-graft copolymers, a nonporous grade A and a porous grade B, both modified with 6% ethylene-vinyl acetate copolymer (EVA), are compared with respect to their processing behavior. It is shown that the porous material B can be processed under milder conditions than grade A to molded articles of great toughness.     

Some trimethyl phosphine and trimethyl phosphite complexes of tungsten(IV)

Direct reduction of WCl₆ with PMe₃ in toluene at 120°C in a sealed tube affords the complexes [WCl₄(PMe₃)_x] (x = 2, 3). [WCl₄(PMe₃)₃] abstracts oxygen from equimolar amounts of water in wet acetone or tetrahydrofuran to give [WOCl₂(PMe₃)₃] in very high yields. This procedure has been successfully applied to the high yield synthesis of other known oxotungsten(IV) complexes, [WOCl₂(PR₃)₃] (PR₃ = PMe₂Ph and PMePh₂). Metathesis reactions of [WOCl₂(PMe₃)₃] with NaX give [WOX₂(PMe₃)₃] (X = NCO, NCS) and [WOX₂(PMe₃)] (X = Me₂NCS₂). The synthesis of the trimethylphosphite analogue, [WOCl₂(P(OMe)₃)₃], is also described and the structures of the new complexes assigned on the basis of IR and ¹H and ³¹P NMR spectroscopy.     

Acoustic propagation from a spiral wave front source in an ocean environment

A spiral wave front source generates a pressure field that has a phase that depends linearly on the azimuthal angle at which it is measured. This differs from a point source that has a phase that is constant with direction. The spiral wave front source has been developed for use in navigation; however, very little work has been done to model this source in an ocean environment. To this end, the spiral wave front analogue of the acoustic point source is developed and is shown to be related to the point source through a simple transformation. This makes it possible to transform the point source solution in a particular ocean environment into the solution for a spiral source in the same environment. Applications of this transformation are presented for a spiral source near the ocean surface and seafloor as well as for the more general case of propagation in a horizontally stratified waveguide.     

Modeling interface roughness scattering in a layered seabed for normal-incident chirp sonar signals

Downward looking sonar, such as the chirp sonar, is widely used as a sediment survey tool in shallow water environments. Inversion of geo-acoustic parameters from such sonar data precedes the availability of forward models. An exact numerical model is developed to initiate the simulation of the acoustic field produced by such a sonar in the presence of multiple rough interfaces. The sediment layers are assumed to be fluid layers with non-intercepting rough interfaces.     

Chelation control in the [3+3] annulation reaction of alkoxy-substituted 1,1-diacylcyclopropanes with 1,3-bis(trimethylsilyloxy)-1,3-butadienes

Functionalized arenes were prepared by chelation-controlled ‘[3+3] cyclization/homo-Michael’ reactions of 1,3-bis(trimethylsilyloxy)-1,3-butadienes with benzyloxy- or methoxy-substituted 1,1-diacylcyclopropanes.