A linear time algorithm for restricted bin packing and scheduling problems

In this paper we are concerned with the subproblem of bin packing, where the set of possible weights of elements is finite. In [5] it was mentioned that this problem could be solved by an exhaustive search procedure in polynomial time, but the degree of the polynomial is high and increases as the cardinality of the set of weights increases. However, we will show that a more careful analysis of the problem leads to a linear time algorithm. The impact of this result on task scheduling is discussed.     

On the Distribution and Scaling of Convective Wavespeeds in the Shear Layers of Heated Supersonic Jets

The noise generated by supersonic plumes is of growing concern given the enormous peak noise intensity radiated by tactical aircraft engines. A key component of this noise is the enhanced radiation of mixing noise caused by large scale eddies convecting supersonically relative to the surrounding quiescent medium. As very little data exist for eddy convection in high Reynolds number, supersonic plumes, our current ability to develop concepts that alter compressible eddy convection is limited. Herein we present new experimental data of eddy convective wavespeeds in the developing shear layer of supersonic heated jets. A new scaling of the wavespeed in radial similarity coordinates is proposed which takes into account the influence of the ratio of static densities between the jet and ambient streams. In particular, we observe a structural change in wavespeed spectra at the end of the potential core—in addition to high turbulence levels, the potential core breakdown region can have enhanced eddy wavespeeds, increasing noise radiation efficiency. The results provide a first examination of the interplay of density ratio effects and the dynamic breakdown process of the potential core in supersonic jets—physics integral to the noise generation process.     

A Method for the Synthesis of 2,3-Disubstituted 2,3-Dihydrobenzofurans

Summary.  The synthesis of 2,3-disubstituted 2,3-dihydrobenzofuran diastereomers is described. The key step in the reaction sequence is the chemoselective reduction of a tert. alcohole with tert.-butylamine-borane/AlCl₃. The relative configuration of the substituents on the dihydrofurane moiety was assigned via NMR spectroscopy. Received September 7, 1999. Accepted November 9, 1999     

Analysis of horizontal symmetries in a minimal SU(2)L×SU(2)R×U(1) gauge theory

A left-right symmetric gauge theory of electroweak interactions is considered in which only one Higgs field and its charge conjugate couple to quarks. Among all possible parity transformations those allowing for phenomenologically acceptable mass matrices are singled out. In such a theory arbitrary horizontal symmetry groups with unitary representations are investigated. Both for two and three quark generations essentially only one model emerges which is compatible with empirical constraints on quark masses and mixing angles.     

Parabolic methods for the construction of spacelike slices of prescribed mean curvature in cosmological spacetimes

Spacelike hypersurfaces of prescribed mean curvature in cosmological spacetimes are constructed as asymptotic limits of a geometric evolution equation. In particular, an alternative, constructive proof is given for the existence of maximal and constant mean curvature slices.     

Mean values and fluctuations in the fragmentation of mesoscopic systems using an exactly solvable model with strict particle conservation and quantum symmetry

A detailed discussion of self-similarities in fragment-size distributions and fluctuations is presented using an exactly solvable model of fragmentation (the “chain model”). The effects of particle-number conservation and quantum symmetry can rigorously be considered in systems ranging from microscopic to macroscopic. Due to the analyticity of the model the various scalings can be studied free of any statistical noise. Using a tuning parameter we can generate self-similar distributions with realistic power-laws and/or fluctuations which show intermittency. Finite-size effects neither destroy nor cause intermittency. The relation of self-similarity in both the averages and the fluctuations can be studied analytically. It is found that they are unlinked - there are cases where the size-distribution is a power-law with realistic exponents τ between ?2 and ?3 but no intermittency. Two cases will even be shown which have indistinguishable fragment distributions but very different factorial moments. We also discuss the interpretation of both the size and slope of the factorial moments in terms of multiplicity and bin mixing. We show that while either is sufficient to produce large moments, one must have bin mixing to produce large slopes. The two types of mixing are necessarily linked in constrained systems such as described by our model.     

The short vacuum arc. II. Model and theoretical aspects

For pt.I see ibid., vol.16, no.3, p.342-7, June 1988. A physical model is presented of the development of a short cathode-anode vacuum arc, from the moment of electrode separation to the final state, a cathode-autonomous vacuum arc. Although the highly nonstationary initial phase is accessible only to qualitative reasoning, the analysis of the stationary arc is treated quantitatively, accounting for anode influence using an existence diagram. The cathode-autonomous phase is previously known in the literature. Results for the phase transitions, arc appearance, and arc motion agree qualitatively with previous observations (reported in Part I)     

A unique left-right symmetric model from general horizontal symmetry

Invariance under a general horizontal symmetry of a left-right symmetric six flavour model with minimal Higgs structure leads to definite phenomenological predictions. Stringent bounds on the Cabibbo angle are obtained and CP violation is naturally small for light hadrons.