Model studies towards liquid crystalline dendrimers with mesogenic repeat units throughout the structure

Model studies towards liquid crystal dendrimers in which the mesogenic units are based on alkoxyalkylbiphenyls and repeat through the structure are described; the parent monomers show smectic mesophases demonstrating the suitability of the motifs.     

Lanthanide complexes as luminogenic probes to measure sulfide levels in industrial samples

A series of lanthanide-based, azide-appended complexes were investigated as hydrogen sulfide-sensitive probes. Europium complex 1 and Tb complex 3 both displayed a sulfide-dependent increase in luminescence, while Tb complex 2 displayed a decrease in luminescence upon exposure to NaHS. The utility of the complexes for monitoring sulfide levels in industrial oil and water samples was investigated. Complex 3 provided a sensitive measure of sulfide levels in petrochemical water samples (detection limit ∼ 250 nM), while complex 1 was capable of monitoring μM levels of sulfide in partially refined crude oil.     

Dollar vs. percentage markup pricing schemes under a dominant retailer

We investigate two very common pricing schemes for a Stackelberg-dominant retailer: percentage-markup and dollar-markup. We show that when a dominant retailer switches from dollar to percentage markup, the channel’s “overall pie” and the retailer’s “pie-piece” are both enlarged. In contrast, the manufacturer will be forced to levy a lower wholesale price, thus receiving a smaller pie-piece despite the larger pie. The preceding statements hold regardless of whether the demand is deterministic or stochastic. However, the effects of switching to percentage markup on the retail price and sales volume will depend not only on whether the demand is stochastic, but also on the assumed demand-curve shape and on whether demand stochasticity is “additive” or “multiplicative”. Besides presenting a comprehensive set of answers on the comparative performance of dollar- and percentagemarkups, our results also highlight the often overlooked importance of choosing between: (i) dollar- and percentage-markup; and (ii) the formats of the assumed stochasticity and demand curves.     

Convenient syntheses of the in vivo carbohydrate metabolites of mycophenolic acid: reactivity of the acyl glucuronide

Following in vivo use of mycophenolic acid, the O-aryl and O-acyl glucuronides, as well as the recently discovered O-aryl glucoside (Scheme 1), are all found as metabolites. We describe convenient preparations of all three derivatives. The phenolic glycosides are obtained by phase-transfer-catalysed alkylation of methyl mycophenolate in very high yield, as an excellent alternative to the Königs-Knorr reaction. We carefully optimised our earlier synthesis of the acyl glucuronide to give a highly pure product in a much improved yield. Finally, we describe the value of a synthetic acyl glucuronide in demonstrating its reactivity towards a known target protein with superior response to the naturally obtained material.     

Challenges students identified with a learning disability and as high-achieving experience when using diagrams as a visualization tool to solve mathematics word problems

This article addresses a much understudied topic and concern regarding how students of varying ability levels employ visualization as a strategy in mathematics learning. The importance of this topic can be found in its connection to students’ ability to solve mathematical word problems. Many students, particularly students with learning disabilities, often struggle to use visualization as a strategy and this impacts their mathematics performance. The purpose of this article is to present findings from a study that examined the challenges that students—those identified as learning disabled and high-achieving—displayed when using one visualization form, a diagram, to solve mathematics problems. Overall, nine challenges related to the use of diagram proficiency to solve problems were identified. Further, students with learning disabilities were found to be more likely than their high achieving peers to experience these challenges. Implications for practice are provided.     

Interassociates of Monogenic Semigroups

Given a monogenic semigroup, (S, ·) , we characterize all interassociates of (S, ·) . We determine necessary and sufficient conditions under which an interassociate of (S, ·) is isomorphic to (S, ·) . Finally, we find necessary and sufficient conditions under which two interassociates of (S, ·) are isomorphic.     

Optimal control of a high-volume assemble-to-order system with maximum leadtime quotation and expediting

For an assemble-to-order system with a high volume of prospective customers arriving per unit time, we show how to set nominal component production rates, quote prices and maximum leadtimes for products, and then, dynamically, sequence orders for assembly and expedite components. (Components must be expedited if necessary to fill an order within the maximum leadtime.) We allow for updating of the prices, maximum leadtimes, and nominal component production rates in response to periodic, random shifts in demand and supply conditions. Assuming expediting costs are large, we prove that our proposed policy maximizes infinite-horizon expected discounted profit in the high-volume limit. For a more general assemble-to-order system with arbitrary cost of expediting and the option to salvage excess components, we show how to solve an approximating Brownian control problem and translate its solution into an effective control policy.     

Left-to-right maxima in words and multiset permutations

We extend classical theorems of Rényi by finding the distributions of the numbers of both weak and strong left-to-right maxima (a.k.a. outstanding elements) in words over a given alphabet and in permutations of a given multiset.     

Teaching students with mathematics disabilities to solve multiplication and division word problems: the role of schema-based instruction

ZDM – Mathematics Education - Mathematical knowledge involving whole number multiplication and division is integral to understanding multiplicative structures such as ratios, slope, rate of...