Science,Engineering and Economics: OR at the Interface

Engineers designing submarine oil-pipeline systems for the Beaufort Sea need to know how deep to bury them. Scientists studying ice scour have a major input into this decision; so do the economics of burying and pipeline failures. An operational researcher was asked to examine the way these aspects can be treated and the way they can be fitted together. This paper describes the resulting study, to illustrate how operational research might help in other interfacing contexts.     

Observation of muon neutrino disappearance with the MINOS detectors in the NuMI neutrino beam

This Letter reports results from the MINOS experiment based on its initial exposure to neutrinos from the Fermilab NuMI beam. The rates and energy spectra of charged current nu(mu) interactions are compared in two detectors located along the beam axis at distances of 1 and 735 km. With 1.27 x 10(20) 120 GeV protons incident on the NuMI target, 215 events with energies below 30 GeV are observed at the Far Detector, compared to an expectation of 336+/-14 events. The data are consistent with nu(mu) disappearance via oscillations with |Delta(m)2/32|=2.74 +0.44/-0.26 x10(-3)eV(2) and sin(2)(2theta(23))>0.87 (68% C.L.).     

Probing the substrate specificity of the catalytically self-sufficient cytochrome P450 RhF from a Rhodococcus sp

Analysis of the substrate specificity of the self-sufficient cytochrome P450 RhF revealed that the enzyme tends to catalyse the dealkylation of substituted alkyl-aryl ethers with shorter alkyl moieties more readily than equivalent compounds with longer alkyl groups.     

Recursions associated to trapezoid,symmetric and rotation symmetric functions over Galois fields

Rotation symmetric Boolean functions are invariant under circular translation of indices. These functions have very rich cryptographic properties and have been used in different cryptosystems. Recently, Thomas Cusick proved that exponential sums of rotation symmetric Boolean functions satisfy homogeneous linear recurrences with integer coefficients. In this work, a generalization of this result is proved over any Galois field. That is, exponential sums over Galois fields of some rotation symmetric polynomials satisfy linear recurrences with integer coefficients. In the particular case of ${\mathbb{F}}_2$, an elementary method is used to obtain explicit recurrences for exponential sums of some of these functions. The concept of trapezoid Boolean function is also introduced and it is showed that the linear recurrences that exponential sums of trapezoid Boolean functions satisfy are the same as the ones satisfied by exponential sums of the corresponding rotations symmetric Boolean functions. Finally, it is proved that exponential sums of trapezoid and symmetric polynomials also satisfy linear recurrences with integer coefficients over any Galois field ${\mathbb{F}}_q$. Moreover, the Discrete Fourier Transform matrix and some Complex Hadamard matrices appear as examples in some of our explicit formulas of these recurrences.     

On the Delta set and catenary degree of Krull monoids with infinite cyclic divisor class group

Let M be a Krull monoid with divisor class group Z, and let S⊆Z denote the set of divisor classes of M which contain prime divisors. We find conditions on S equivalent to the finiteness of both Δ(M), the Delta set of M, and c(M), the catenary degree of M. In the finite case, we obtain explicit upper bounds on maxΔ(M) and c(M). Our methods generalize and complement a previous result concerning the elasticity of M.     

(7)Li NMR and two-dimensional exchange study of lithium dynamics in monoclinic Li(3)V(2)(PO(4))(3)

High-resolution solid-state (7)Li NMR was used to characterize the structure and dynamics of lithium ion transport in monoclinic Li(3)V(2)(PO(4))(3). Under fast magic-angle spinning (MAS) conditions (25 kHz), three resonances are clearly resolved and assigned to the three unique crystallographic sites. This assignment is based on the Fermi-contact delocalization interaction between the unpaired d-electrons at the vanadium centers and the lithium ions. One-dimensional variable-temperature NMR and two-dimensional exchange spectroscopy (EXSY) are used to probe Li mobility between the three sites. Very fast exchange, on the microsecond time scale, was observed for the Li hopping processes. Activation energies are determined and correlated to structural properties including interatomic Li distances and Li-O bottleneck sizes.