Fourier transform spectroscopy of CrO: Rotational analysis of the A5Σ-X5Π (0,0) band near 8000 cm−1

The emission spectrum of CrO has been investigated by Fourier transform spectroscopy in the near infrared. New weak electronic bands have been found in the 6000- to 10 000-cm^?1 region, the strongest of which, near 8000 cm^?1, is shown to be the (0,0) band of a ⁵Σ-⁵Π transition where the ⁵Π lower state is the ground state. Fifty branches have been assigned in this band, which have permitted the first detailed characterizations of quintet electronic states in the gas phase. Accurate values have now been obtained for the spin-orbit coupling and Λ-doubling intervals in the ground state (which could only be estimated in the previous laser-induced fluorescence work in the visible region by Hocking et al. [Canad. J. Phys.58, 516–533 (1980)]). The relative branch intensities are not consistent with those calculated for a pure ⁵Σ-⁵Π(a) transition, and indicate considerable spin-orbit contamination such that there are interference effects between two or more competing transition moments. It is not known whether the ⁵Σ excited state is ⁵Σ⁺ or ⁵Σ^?.     

Scheduling Vehicles for Refuse Collection

This paper reports an application of vehicle-scheduling algorithms in the collection of refuse. The problem differs from classical vehicle-scheduling applications in that the tipping site and the place where the vehicles are garaged are at different locations. Several algorithms are tested in terms of total route mileage and computational loads. An improvement over the manual method of the order of 8% was obtained using average figures for refuse volume over a period of time. The results appear to be more useful in obtaining a good solution when the main problem parameters change rather than in the day-to-day routeing of vehicles.     

New measurement of the rare decay K+ --> pi(+)&mgr;(+)&mgr;(-)

More than 400 K+-->pi(+)&mgr;(+)&mgr;(-) events were observed in a rare K+ decay experiment at the Brookhaven Alternating Gradient Synchrotron. Normalized to the K+-->pi(+)pi(+)pi(-) decay, the branching ratio is determined to be [9.22+/-0.60(stat)+/-0. 49(syst)]x10(-8). This branching ratio and the &mgr;&mgr; mass spectrum is in very good agreement with the measurement of the K+-->pi(+)e(+)e(-) decay, but deviates significantly from the previous measurement.     

Stability-indicating high-performance liquid chromatographic assay and analysis of decomposition products of 2-[4-[(7-chloro-2-quinoxalinyl)oxy]phenoxy]propanoic acid

A stability-indicating HPLC assay has been developed for 2-{4-[(7-chloro-2-quinoxalinyl)oxy]phenoxy}propanoic acid (XK469). XK-469 is the 7-chloro analog of herbicide Quizalofop and is currently under development as an antineoplastic agent. HPLC separation of XK469 is achieved with an ODS column using isocratic elution of an aqueous MeOH mobile phase. The assay is reproducible (RSD=0.9%), linear (r²=0.999), accurate (error=1.2%) and sensitive (LDL=1.2 ng). The HPLC separates XK469 from its forced decomposition products. Identities of the decomposition products have been elucidated.     

Capturing coalescence and break-up processes in vertical gas–liquid flows: Assessment of population balance methods

Gas–liquid flows are commonly encountered in industrial flow systems. Numerical studies have been performed to assess the performances of different population balance approaches – direct quadrature method of moments (DQMOMs), average bubble number density (ABND) model and homogeneous MUlti-SIze-Group (MUSIG) model – in tracking the changes of gas void fraction and bubble size distribution under complex flow conditions and to validate the model predictions against experimental measurements from medium- and large-sized vertical pipes. Subject to different gas injection method and flow conditions, bubble size evolution exhibited a coalescence dominant trend in the medium-sized pipe; while bubble break-up was found to be dominant in large-sized pipe. The two experiments were therefore strategically selected for carrying out a thorough examination of existing population balance models in capturing the complicated behaviour of bubble coalescence and break-up. In general, predictions of all the different population balance approaches were in reasonable agreement with experimental data. More importantly, encouraging results have been obtained in adequately capturing the dynamical changes of bubbles size due to bubble interactions and transition from wall peak to core peak gas void fraction profiles. As a compromise between numerical accuracy and computational time, DQMOM has performed rather well in capturing the essential two-phase flow structures within the medium- and large-sized vertical pipes when compared to those of ABND and homogeneous MUSIG models. From a practical perspective, the ABND model may still be considered as a more viable approach for industrial applications of gas–liquid flow systems.     

Moments of discounted aggregate claim costs until ruin in a Sparre Andersen risk model with general interclaim times

In the context of a Sparre Andersen risk model with arbitrary interclaim time distribution, the moments of discounted aggregate claim costs until ruin are studied. Our analysis relies on a novel generalization of the so-called discounted density which further involves a moment-based component. More specifically, while the usual discounted density contains a discount factor with respect to the time of ruin, we propose to incorporate powers of the sum until ruin of the discounted (and possibly transformed) claims into the density. Probabilistic arguments are applied to derive defective renewal equations satisfied by the moments of discounted aggregate claim costs until ruin. Detailed examples concerning the discounted aggregate claims and the number of claims until ruin are studied upon assumption on the claim severities. Numerical illustrations are also given at the end.     

Characterizations of counter-monotonicity and upper comonotonicity by (tail) convex order

In this paper, we characterize counter-monotonic and upper comonotonic random vectors by the optimality of the sum of their components in the senses of the convex order and tail convex order respectively. In the first part, we extend the characterization of comonotonicity by  Cheung (2010) and show that the sum of two random variables is minimal with respect to the convex order if and only if they are counter-monotonic. Three simple and illuminating proofs are provided. In the second part, we investigate upper comonotonicity by means of the tail convex order. By establishing some useful properties of this relatively new stochastic order, we prove that an upper comonotonic random vector must give rise to the maximal tail convex sum, thereby completing the gap in  Nam et al. (2011)’s characterization. The relationship between the tail convex order and risk measures along with conditions under which the additivity of risk measures is sufficient for upper comonotonicity is also explored.