A Backlog Inventory Model During Restricted Sale Periods

Optimal purchasing policies are derived for a continuous review inventory system in which backlogs are permissible and temporary price discounts are available. This paper derives such policies assuming that the sale price is not available at the regularly-scheduled replenishment time. Results indicate that, under specific conditions, maximum positive cost savings are generated when a special order is placed at the end of the sale period.     

Substituent-controlled reactivity in the Nazarov cyclisation of allenyl vinyl ketones

Alkyl substitution α to the ketone of an allenyl vinyl ketone enhances Nazarov reactivity by inhibiting alternative pathways involving the allene moiety and through electron donation and/or steric hindrance. This substitution pattern also accelerates Nazarov cyclisation by increasing the population of the reactive conformer and by stabilising the oxyallyl cation intermediate. Furthermore, α substitution by an alkyl group does not alter the regioselectivity of interrupted Nazarov reactions when the oxyallyl cation intermediate is intercepted by addition of an oxygen nucleophile, or by [4+3] cyclisation with acyclic dienes. The regioselectivity of the Nazarov process for allenyl vinyl ketones was determined to be a result of an electronic bias in the oxyallyl cation intermediate. Computational data are consistent with this observation.     

Quasi-Affinity in certain Classes of Operators

The family of operators S + V (, C, Re > 0), where V isan injective S-Volterra operator (that is, [S, V[ = V²) and— A — V^–1 generates a uniformly bounded C₀-semigroup,is studied in the context of similarity and of the weaker quasi-affinityrelation. It is shown that S is similar to S + V for all , C,Re > 1, and is a quasi-affine transform of S + tV for allt 0 and 0 < < 1.     

Continuous dependence on modeling for nonlinear ill-posed problems

The nonlinear ill-posed Cauchy problem , where A is a positive self-adjoint operator on a Hilbert space H, χ∈H, and h:[0,T)×H→H is a uniformly Lipschitz function, is studied in order to establish continuous dependence results for solutions to approximate well-posed problems. The authors show here that solutions of the problem, if they exist, depend continuously on solutions to corresponding approximate well-posed problems, if certain stabilizing conditions are imposed. The approximate problem is given by , v(0)=χ, for suitable functions f. The main result is that , where C and M are computable constants independent of β and 0<β<1. This work extends to the nonlinear case earlier results by the authors and by Ames and Hughes.     

Indicators of middle school students' mathematics enjoyment and confidence

A study involving 916 students spanning grades 5–8 was conducted to investigate indicators that may contribute to enjoyment and confidence in mathematics. For this group of middle school students, mathematics enjoyment, mathematics confidence, and attitudes toward school were found to generally decline across grade levels. Mathematics enjoyment and confidence were also found to differ significantly based upon student preferences for future careers. Gender differences as well as similarities regarding predictors of mathematics enjoyment and confidence were identified. Specifically, the best predictor for end of year mathematics enjoyment for males was beginning of year attitude toward school, while the most significant predictor of end of year enjoyment for females was beginning of year dispositions toward mathematics (semantic perception). A strong relationship between mathematics enjoyment and confidence overall was found, with indications that activities that increase mathematics enjoyment contribute to increased confidence, and also that activities that increase mathematics confidence contribute to increased enjoyment.     

Adaptive cross-correlation algorithm for extended scene Shack-Hartmann wavefront sensing

We present an adaptive cross-correlation algorithm for a large dynamic range extended-scene Shack-Hartmann wavefront sensor. We show that it accurately measures very fine image shifts over many pixels under a variety of practical imaging conditions.     

Measuring asymmetric temporal interdependencies in simulated and biological networks

We use a newly developed metric to characterize asymmetric temporal interdependencies in networks of coupled dynamical elements. We studied the formation of temporal ordering in a system of coupled Rossler oscillators for different connectivity ratios and network topologies and also applied the metric to investigate the functional structure of a biological network (cerebral ganglia of Helix snail). In the former example we show how the local ordering evolves to the global one as a function of structural parameters of the network, while in the latter we show spontaneous emergence of functional interdependence between two groups of electrodes.     

Cooperation in bike racing—When to work together and when to go it alone

We present an agent‐based model of bicycle racing that incorporates both physiology and the types of multiplayer scenarios that arise in real races. In these scenarios, riders can choose to share the workload with other riders (cooperate) or pursue their own self‐interests (defect). We compare the model's predictions to race situations and use it to investigate how different strategies can affect outcomes. We find that an individual player's best strategy depends on fitness level: below‐average riders fare better as defectors whereas above‐average riders perform better as cooperators. The strategies of stronger riders affect their teammates' results as well. The teammates of defecting strong riders fare worse overall than the teammates of cooperating strong riders. These results reproduce a dynamic that played out in the 2009 Tour de France. The winner, Alberto Contador, pursued a strategy perceived by many to be unusually uncooperative by repeatedly defecting on his teammates. The strategy worked to his advantage but may have negatively affected his teammates' placements. © 2011 Wiley Periodicals, Inc. Complexity, 17,39–44, 2011     

Scheduling in Multiclass Networks with Deterministic Service Times

We consider general feed-forward networks of queues with deterministic service times and arbitrary arrival processes. There are holding costs at each queue, idling may or may not be permitted, and servers may fail. We partially characterize the optimal policy and give conditions under which lower priority should be given to jobs that would be delayed later in the network if they were processed now.     

Spectral representations for unbounded operators with real spectrum

The author would like to thank Prof. S. Shatz and the University of Pennsylvania for their hospitality