Operational Research and Regulation: Theory and Practice

In this Blackett Lecture, Professor Littlechild, Director General of Electricity Supply in the UK's Office of Electricity Regulation, renews acquaintance with some models he has developed over the years, introduces some models he has recently met, and discusses models that it would seem to be worthwhile developing. He concludes that for all concerned in the electricity industry, success depends on ever improving decision-making, in which OR has a vital role.     

Characterization of isolated homogeneous hypersurface singularities in ℂ4

Let V be a hypersurface with an isolated singularity at the origin in ? ⁿ⁺¹. It is a natural question to ask when V is defined by weighted homogeneous polynomial or homogeneous polynomial up to biholomorphic change of coordinates. In 1971, a beautiful theorem of Saito gives a necessary and sufficient condition for V to be defined by a weighted homogeneous polynomial. For a two-dimensional isolated hypersurface signularity V, Xu and Yau found a coordinate free characterization for V to be defined by a homogeneous polynomial. Recently Lin and Yau gave necessary and sufficient conditions for a 3-dimensional isolated hypersurface singularity with geometric genus bigger than zero to be defined by a homogeneous polynomial. The purpose of this paper is to prove that Lin-Yau’s theorem remains true for singularities with geometric genus equal to zero.     

(2 + 1) Resonance enhanced multiphoton ionization of hydrogen chloride in a pulsed supersonic jet: Vacuum wavenumbers of rotational lines with detailed band analysis for excited electronic states of HCl

A comprehensive study of the excited electronic states of HCl is reported. Using resonance enhanced multiphoton ionization ((2 + 1) REMPI) and time-of-flight mass spectrometry (TOFMS) over 120 band systems are analyzed. Supersonic jet techniques are used to prepare rotationally cold species for laser spectroscopy in the 77 000 to 96 000 cm⁻¹ region. At least 50 new electronic states are characterized as well as several features only tentatively assigned previously. A long vibrational progression consisting of 29 vibrational levels of the deeply bound V¹Σ⁺(0⁺) valence/ion-pair state is studied. We also extend the identification and analysis to high vibrational levels of low-lying Rydberg states. The assignments of [²Π_i] Rydberg state complexes are evaluated in terms of spin-orbit coupling and united-atom calculations. In several band systems, the spectra exhibit anomalous rotational line intensities and broadened linewidths which are consistent with predissociation. Multiphoton ionization with mass spectrometry permits the investigation of isotope effects as well as the appearance of fragment species associated with repulsive potential curves.     

Wechselnde Bindungen in einem Zweikörpersystem mit trockener Reibung

Übersicht Betrachtet wird ein zwangserregtes Zweikörpersystem mit wechselnden Bindungen infolge trockener Reibung. Stationäre Bewegungen werden als Grenzfall instationärer Einschwingvorgänge berechnet. Abhängig von den Systemparametern ergeben sich drei typische Bewegungsformen. Ihnen entsprechen dauernde Haftzustände, wechselnde Haft-Gleitzustände oder dauernde Gleitzustände an der Berührfläche beider Körper.

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Intermittant constraints in a two-body-system with dry friction

Summary An externally excited two-body-system with intermittant constraints due to dry friction is considered. Stationary motions are calculated as limit cases of instationary transients. Depending on the parameters of the system, three typical modes are of interest. These correspond to permanent sticking, slipstick behaviour, or to permanent slipping in the contact surface of the bodies, respectively.

     

Convergent route to the purpuromycin bisphenolic spiroketal: hydrogen bonding control of spiroketalization stereochemistry

A mild and efficient [3+2] nitrile oxide/olefin cycloaddition provided a rapid and convergent entry into precursors of bisphenolic spiroketals, a structural type unique to the rubromycin family of natural products. In addition, implementation of the premise that a hydrogen bond from the C4-OH controls the stereochemistry of the purpuromycin core resulted in moderate diastereocontrol in the spiroketalization. Spectroscopic and X-ray data of these systems have provided the first assignment of the relative configuration of purpuromycin.     

Dielectric properties of a hydrated sulfonated poly(styrene-ethylene/butylenes-styrene) triblock copolymer

The present study showed that sulfonated poly(styrene-ethylene/butylenes-styrene) (S-SEBS) triblock copolymer ionomers can be made to exhibit dielectric constants on the order of a hundreds thousand. Although they are too lossy at this point to use as dielectric materials in capacitors or as electrostrictive Maxwell effect transducer materials because of their high hydrogen ion conductivity, the results of these initial dielectric studies as a function of ion content were used to try to understand the effects of a polar plasticizer, water, on dielectric properties of the acid form of this ionomer. This was done before moving on to more tightly bound ions (rather than the hydrogen ions of the sulfonic acid groups used here) and to other polar, less mobile plasticizers (which also interact strongly with the ionic dipoles). The discovery of such high dielectric constants suggested the possibility that low dielectric loss versions of this type of polymer, as well as other members of the class known as ionomers, might find future applications as extremely high dielectric constant materials in capacitors or transducers. Experimental results for films with degrees of sulfonation on the order of 10% or more showed dielectric constants on the order of ?′ ∼ 100,000 but dielectric loss tangents near D = tan δ ∼ 0.3, when the materials were exposed to high humidity conditions. Experiments to determine the effects of water content on the material's dielectric response showed that water can easily move into and out of the films studied and that this transport behavior is strongly correlated to the relative humidity of the environment and to the degree of sulfonation. Water content, in this case, was thus the primary consideration when attempting to understand the observed high dielectric constants in films with degree of sulfonation greater than 5.5%. However, vacuum-dried films were, also, examined and observed to exhibit a dielectric constant on the order of 2 until the degree of sulfonation was greater than 11%. Above this value, the dielectric constant increased by approximately 100% to a value on the order of 4.     

Two-dimensional Anhydrous Cadmium(II) Phthalate

The in situ hydrolysis of phthalyl-γ-glutaminyl-histidine with Cd(ClO₄)₂·6H₂O in the presence of water and methanol affords a novel two-dimensional cadmium coordination polymer, a new phase, anhydrous cadmium(II) phthalate, ( 1 ). The structure was determined by single crystal X-ray diffraction. Crystal data: P2₁/c, a = 13.8168(14), b = 7.0351(7), c = 8.2054(8) Å, β = 105.540(2)°, V = 768.43(13) ų, Z = 4, R₁ = 0.0380, wR₂ = 0.1111.