A Dynamic location problem for graphs

We introduce a class of optimization problems, calleddynamic location problems, involving the processing of requests that occur sequentially at the nodes of a graphG. This leads to the definition of a new parameter of graphs, called the window indexWX(G), that measures how large a window into the future is needed to solve every instance of the dynamic location problem onG optimally on-line. We completely characterize this parameter:WX(G)k if and only ifG is a weak retract of a product of complete graphs of size at mostk. As a byproduct, we obtain two (polynomially recognizable) structural characterizations of such graphs, extending a result of Bandelt.     

Graphs whose every transitive orientation contains almost every relation

Given a graphG onn vertices and a total ordering ≺ ofV(G), the transitive orientation ofG associated with ≺, denotedP(G; ≺), is the partial order onV(G) defined by settingx<y inP(G; ≺) if there is a pathx=x ₁ x ₂…x _r=y inG such thatx ₁ ≺x _j for 1≦i<j≦r. We investigate graphsG such that every transitive orientation ofG contains ₂ ⁿ −o(n ²) relations. We prove that almost everyG _n,p satisfies this requirement if , but almost noG _n,p satisfies the condition if (pn log log logn)/(logn log logn) is bounded. We also show that every graphG withn vertices and at mostcn logn edges has some transitive orientation with fewer than ₂ ⁿ −δ(c)n ² relations. Partially supported by MCS Grant 8104854.     

A study of mesoamerican obsidian sources using activation analysis

An extensive study of Mesoamerican obsidian source samples from 37 sites has been begun to better differentiate and define the trace element content at known Mesoamerican obsidian quarries, with particular emphasis on those in Mexico. This paper reports on the first results in that study as well as studies of sample contamination by grinding and results for the new National Bureau of Standards No. 278 Obsidian SRM.     

Student-Designed Multistep Synthesis Projects in Organic Chemistry

The incorporation of research projects into undergraduate chemistry courses provides a perspective that is fundamentally unavailable in most laboratory experiences. While independent, multistep synthesis projects in organic chemistry have been reported previously, most efforts have been directed at relatively restricted, closely guided research plans with modest student participation in the experimental design. We have implemented a more open-ended synthesis project, limited principally by cost, safety and availability of materials. In the second semester of the sophomore organic sequence, students develop multiple drafts of a plan for a three-to-four-step synthesis. Subsequently, students obtain their own literature protocols for the individual steps. The synthesis is performed over three four-hour laboratory periods. The students conclude this project with a poster presentation of the results at the end of the semester. Evaluation of the students work focuses not only on the successful synthesis of the target but also on planning, troubleshooting, purification, and spectral analysis.     

Mediated amperometric biosensors for d-galactose,glycolate and l-amino acids based on a ferrocene-modified carbon paste electrode

Direct-current cyclic voltammetry is used to investigate the suitability of a ferrocene derivative as a mediator with galactose, glycolate and l-amino acid oxidases. The three enzymes coupled catalytically to ferrocene monocarboxylic acid exhibiting homogeneous second-order rate constants in the range 0.4 × 10⁵ to 8.5 × 10⁵ l mol^?1 s^?1. Enzyme electrodes which responded to d-galactose, glycolate or l-amino acids were constructed. The appropriate oxidase was retained behind a dialysis membrane at a carbon paste electrode containing the poorly soluble derivative 1,1′-dimethylferrocene. All the electrodes responded rapidly to millimolar concentrations of their respective substrates producing 95% of the steady-state current response in <2 min. This general method of biosensor construction should be widely applicable to oxidases and other oxidoreductase enzymes.