Job selection and sequencing on a single machine in a random environment

We examine a single machine scheduling problem with random processing times and deadline. Given a set of independent jobs having specified initiation costs and terminal revenues, the objective is to select a subset of the jobs and sequence the selected jobs such that the expected profit is maximized. The job selection aspect considered by us marks a clear departure from the pure sequencing focus found in the traditional scheduling literature. In this paper, we assume an exponentially distributed deadline and do not allow preemption. Even under these conditions, the selection and sequencing problem remains quite difficult (unlike its pure sequencing counterpart); we in fact conjecture that the problem is NP-hard. However, we show that the problem can be efficiently solved as long as the cost parameter is agreeable or an approximate solution is acceptable. To this end, we describe several solution properties, present dynamic programming algorithms (one of which exhibits a pseudo-polynomial time worst-case complexity), and propose a fully-polynomial time approximation scheme. In addition, we study a number of special cases which can be solved in polynomial time. Finally, we summarize our work and discuss an extension where the jobs are precedence related.     

On labeled vertex-transitive digraphs with a prime number of vertices

We enumerate, up to isomorphism, several classes of labeled vertex-transitive digraphs with a prime number of vertices.     

Backward production of the B meson in K−p interactions at 4.2 GeVc

The backward production of the B(1235) meson is studied in the reaction K^?p→Σ^?π⁺ω. This reaction is observed in the final state Σ^?π⁺π⁺π^?π⁰. A π⁺ω mass enhancement is visible in the region of the B meson for events with small |u|K^? →Σ^?) squared four-momentum transfer. The properties of the enhancement agree with those of the B meson. The cross section for K^?p→Σ^?B⁺ at $\text{4.15}\text{GeV}\text{c}$ incident K^? momentum is (3.2 ± 0.5) μb. The backward production of the B meson is compared with similar baryon exchange productions of the A₁ and C(Q₁) axial vector mesons observed in the same experiment.     

Ω− produced in K−p reactions at 4.2 GeV/c

Forty $\text{Ω}{}^{\mathrm{?}}$ events have been observed in a large (133 events/βb) experiment at 4.2 GeV/c incident K^? momentum. Thirty nine of the events come from the three-body reaction $\text{K}{}^{\mathrm{?}}\text{p}\text{→Ω}{}^{\mathrm{?}}\text{K}{}^{\mathrm{+}}\text{K}{}^0$. The $\text{Ω}{}^{\mathrm{?}}$ is mainly produced in the forward hemisphere (direction of the incident K^?). The lifetime is measured to be τ = (0.75 _+0.14?0.11 × 10^?10 sec substantially less than the Particle Data Group value of (1.3 _?0.3^+0.2) × 10^?10 sec. The mass is determined to be 1671.7 ± 0.6 MeV, in good agreement with other determinations. The decay asymmetry parameter α (for the decay mode $\text{Ω}{}^{\mathrm{?}}\text{→ Λ}\text{K}{}^{\mathrm{?}}$) is found to be ?0.2 ± 0.4.     

Charged multiplicities in K−p interactions at 100 GeV/c

The charged multiplicity distribution is presented for K^?p interactions produced in the hydrogen bubble chamber, BEBC, using an r.f. separated, tagged K^? beam of 110 GeV/c momentum. A comparison with K⁺p, πp and pp data at lower energies shows that the main features of the multiplicity distributions depend on energy and charge of the incident particles, but not on their strangeness. At high energies, only the energy is important.     

Silicon in organic synthesis. 14. Five ring annulation processes based upon thermal rearrangement of (1-trimethylsilylcyclopropyl)ethylenes

Pyrolysis of (1-trimethylsilylcyclopropyl)ethylenes affords silyl substituted cyclopentenes in high yield. Subsequent reaction of these products with varied electrophiles forms the basis of a new and versatile five-ring annulation sequence.     

Ratiometric comparison of intense field ionization of atoms and diatomic molecules

Intense-laser ionization rates for rare gas atoms and diatomic molecules have been precisely compared by making simultaneous measurements of ionization yield vs laser intensity for mixed atomic and molecular targets. At a given laser intensity, the N (2) and F (2) ionization yields are slightly greater than that of Ar. Conversely, comparison of O (2) and S (2) with Xe indicates significant ionization suppression in these molecules. Recent molecular ionization models that successfully describe ionization suppression in O (2) and its absence in N (2) fail to explain our observations in F (2) and S (2).     

New Molybdenyl Iodates: Hydrothermal Preparation and Structures of Molecular K2MoO2(IO3)4 and Two-Dimensional β-KMoO3(IO3)

Two new molybdenyl iodates, K₂MoO₂(IO₃)₄ (1) and β-KMoO₃(IO₃) (2), have been prepared from the reactions of MoO₃ with KIO₄ and NH₄Cl at 180°C in aqueous media. The structure of 1 consists of molecular [MoO₂(IO₃)₄]²⁻ anions separated by K⁺ cations. The Mo(VI) centers are ligated by two cis-oxo ligands and four monodentate iodate anions. Both terminal and bridging oxygen atoms of the iodate anions form long ionic contacts with the K⁺ cations. β-KMoO₃(IO₃) (2) displays a two-dimensional layered structure constructed from ²_∞[(MoO₃(IO₃)]¹⁻ anionic sheets separated by K⁺ cations. These sheets are built from one-dimensional chains formed from corner-sharing MoO₆ octahedra that run along the b-axis that are linked together through bridging iodate groups. K⁺ cations separate the layers from one another and form long contacts with oxygen atoms from both the iodate anions and molybdenyl moieties. Crystallographic data: 1, monoclinic, space group C2/c, a=12.8973(9) Å, b=6.0587(4) Å, c=17.694(1) Å, β=102.451(1)°, Z=4, MoKα, λ=0.71073, R(F)=2.64% for 97 parameters with 1584 reflections with I>2σ(I); 2, monoclinic, space group P2₁/n, a=7.4999(6) Å, b=7.4737(6) Å, c=10.5269(8) Å, β=109.023(1)°, Z=4, MoKα, λ=0.71073, R(F)=2.73% for 83 parameters with 1334 reflections with I>2σ(I).