An Upper Bound for List T-Colourings

Erds, Rubin and Taylor showed in 1979 that for any connectedgraph G which is not a complete graph or an odd cycle, ch(G) , where is the maximum degree of a vertex in G and ch(G) isthe choice number of the graph (also proved by Vizing in 1976).They also gave a characterisation of D-choosability. A graphG is D-choosable if, when we assign to each vertex v of G alist containing d(v) elements, where d(v) is the degree of vertexv, we can always choose a proper vertex colouring from theselists, however the lists were chosen. In this paper we shallgeneralise their results on the choice number of G and D-choosabilityto the case where we have T-colourings.     

Synthesis of diastereomeric ketoconazole analogs

Syntheses of trans-isomers of ketoconazole, and the corresponding des-acetyl, 1-methyl-, 1-formyl and 1-methanesulfonyl analogs were investigated. These isomers, along with the corresponding cis-diastereomers were characterized by their carbon-13 nmr spectra.     

Synthesis of 3,5-difluorotyrosine-containing peptides: application in substrate profiling of protein tyrosine phosphatases

Fully protected 3,5-difluorotyrosine (F2Y), Fmoc-F2Y(tBu)-OH, is efficiently prepared by a chemoenzymatic process and incorporated into individual peptides and combinatorial peptide libraries. The F2Y-containing peptides display kinetic properties toward protein tyrosine phosphatases (PTPs) similar to their corresponding tyrosine-containing counterparts but are resistant to tyrosinase action. These properties make F2Y a useful tyrosine surrogate during peptide library screening for optimal PTP substrates.     

Estimating a retailer's base stock level: an optimal distribution center order forecast policy

Errors in order forecasts are a salient source of inefficiencies in retail supply chains. Many operational decisions made by suppliers hinge on order forecasts, which typically are based solely on either order or point-of-sale (POS) history. Using a discrete-time formulation, this research demonstrates that if a supplier knows that a retailer is using a base stock policy, it should use that knowledge to forecast the retailer's orders, even if the supplier does not know the base stock level and/or have access to POS data.     

New bounds on the condition number of the Hessian of the preconditioned variational data assimilation problem

Data assimilation algorithms combine prior and observational information, weighted by their respective uncertainties, to obtain the most likely posterior of a dynamical system. In variational data assimilation the posterior is computed by solving a nonlinear least squares problem. Many numerical weather prediction (NWP) centers use full observation error covariance (OEC) weighting matrices, which can slow convergence of the data assimilation procedure. Previous work revealed the importance of the minimum eigenvalue of the OEC matrix for conditioning and convergence of the unpreconditioned data assimilation problem. In this article we examine the use of correlated OEC matrices in the preconditioned data assimilation problem for the first time. We consider the case where there are more state variables than observations, which is typical for applications with sparse measurements, for example, NWP and remote sensing. We find that similarly to the unpreconditioned problem, the minimum eigenvalue of the OEC matrix appears in new bounds on the condition number of the Hessian of the preconditioned objective function. Numerical experiments reveal that the condition number of the Hessian is minimized when the background and observation lengthscales are equal. This contrasts with the unpreconditioned case, where decreasing the observation error lengthscale always improves conditioning. Conjugate gradient experiments show that in this framework the condition number of the Hessian is a good proxy for convergence. Eigenvalue clustering explains cases where convergence is faster than expected.     

Predicting retailer orders with POS and order data: The inventory balance effect

Despite advances in retail point-of-sale (POS) data sharing, retailers’ suppliers struggle to effectively use POS data to improve their fulfillment planning processes. The challenge lies in predicting retailer orders. We present evidence that retail echelon inventory processes translate into a long-run balance or equilibrium between orders and POS, which we refer to as the inventory balance effect, allowing for more accurate order forecasting. Based on the inventory balance effect, this research prescribes a forecasting approach which simultaneously uses both sources of information (retailer order history and POS data) to predict retailer orders to suppliers. Using data from a consumable product category, this approach is shown to outperform approaches based singularly on order or POS data, by up to 125%. The strength of this novel approach – significantly improved forecast accuracy with minimal additional analysis – make it a candidate for widespread adoption in retail supply chain collaborative planning and forecasting initiatives with corresponding impact on fulfillment performance and related operating costs.     

The development of a thermal neutron activation (TNA) system as a confirmatory non-metallic land mine detector

In order to detect and locate buried landmines for peacekeeping, the Canadian Department of National Defence (DND), under the Improved Landmine Detection Project, is developing a vehicle-mounted, two-phase mine detection system. The first phase constitutes a suite of detectors used to indicate the possibility of a mine at a particular location (to ±30 cm in accuracy). In the second phase a Thermal Neutron Activation (TNA) system is used to confirm the presence of explosives via detection of the 10.83 MeV gamma-ray associated with nitrogen decay. The TNA system developed for this uses a 100 μg²⁵²Cf neutron source surrounded by four 3″×3″ NaI(Tl) detectors. Combining the use of state-of-the art radiation transport codes for design, judicious choice of specialized shielding materials and development of high-rate, fast-pulse processing electronics, has led to a system which can; (i) confirm the presence of all surface- or lightly-buried anti-tank mines in a few seconds to a minute (depending on mass of explosive), (ii) confirm the presence of anti-tank mines down to 20 cm depth in less than 5 minutes, (iii) confirm the presence of large (>100 g nitrogen) anti-personnel mines in less than five minutes, (iv) operate in adverse climatic conditions. These results have been verified in field trials and the system is due to be fielded in 1999.     

Recent advances in molecular diversity

Molecular Diversity -     

A small molecule that induces assembly of a four way DNA junction at low temperature

Small molecules that induce the formation of higher order DNA structures have potential therapeutic and nanotechnology applications. Screening of a click library has identified the first compound to induce the formation of a Holliday junction structure at room temperature without the need for a high temperature annealing step.     

Structures of trimetallic molybdenum and tungsten suboxide cluster anions

Anion photoelectron spectra of Mo(3)O(y)(-) and W(3)O(y)(-) (y = 3-6) are reported and analyzed using density functional theory results in an attempt to determine whether electronic and structural trends in the less oxidized clusters (y = 3, 4) could elucidate the disparate chemical properties of the M(3)O(y)(-) (M = Mo, W, y = 5, 6) species. In general, cyclic structures are calculated to be more stable by at least 1 eV than extended structures, and the lowest energy structures calculated for the most reduced species favor M = O terminal bonds. While the numerous low-energy structures found for Mo(3)O(y)(-)/Mo(3)O(y) and W(3)O(y)(-)/W(3)O(y) were, in general, similar, various structures of W(3)O(y)(-)/W(3)O(y) were found to be energetically closer lying than analogous structures of Mo(3)O(y)(-)/Mo(3)O(y). Additionally, the Mo-O-Mo bridge bond was found to be a more stabilizing structural motif than the W-O-W bridge bond, with the oxygen center in the former having the highest negative charge. Based on this, the observation of trapped intermediates in reactions between Mo(3)O(y)(-) and water or CO(2) that are not observed in analogous W(3)O(y)(-) reactivity studies may be partially attributed to the role of bridge bond fluxionality.