Archimedean ϕ ‐tolerance graphs

Let ? be a symmetric binary function, positive valued on positive arguments. A graph G = (V,E) is a ?‐tolerance graph if each vertex υ ∈ V can be assigned a closed interval I_υ and a positive tolerance t_υ so that xy ∈ E ? | I_x ∩ I_y|≥ ? (t_x,t_y). An Archimedean function has the property of tending to infinity whenever one of its arguments tends to infinity. Generalizing a known result of [15] for trees, we prove that every graph in a large class (which includes all chordless suns and cacti and the complete bipartite graphs K_2,k) is a ?‐tolerance graph for all Archimedean functions ?. This property does not hold for most graphs. Next, we present the result that every graph G can be represented as a ?_G‐tolerance graph for some Archimedean polynomial ?_G. Finally, we prove that there is a ?universal”? Archimedean function ? ^* such that every graph G is a ?^*‐tolerance graph. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 179–194, 2002     

A Helly theorem for convexity in graphs

It is shown that for chordless path convexity in any graph, the Helly number equals the size of a maximum clique.     

A parallel colorimetric method for the rapid discovery and optimization of heterogeneous hydrodesulfurization catalysts

A spectrophotometric based, parallel approach to screen heterogeneous catalysts for hydrodesulfurization has been developed. The method utilizes optical changes resulting from the hydrodesulfurization of 1,1'-binaphthothiophene to 1,1'-binaphthyl to determine catalyst activity. Hydrodesulfurization of 1,1'-binaphthothiophene to 1,1'-binaphthyl results in a loss of conjugation in the binaphthyl ring system. This results in a blue shift of more than 60 nm in the UV-vis spectrum. Since only small amounts of the HDS catalyst and 1,1'-binaphthothiophene are required, a large number of catalysts may be screened simultaneously. The synthesis of the 1,1'-binaphthothiophene and conditions for HDS catalyst screening are described.     

Enantioselective synthesis of (-)-terpestacin and structural revision of siccanol using catalytic stereoselective fragment couplings and macrocyclizations

(-)-Terpestacin (1, naturally occurring enantiomer) and (+)-11-epi-terpestacin (2) were prepared using catalyst-controlled, stereoselective, intermolecular reductive coupling reactions of alkyne 9 and aldehyde 10, affording allylic alcohols 42 or 11-epi-42 in a 3:1 ratio (or 1:3 depending on the enantiomer of ligand 41a used). These stereoselective fragment couplings were instrumental in confirming that "siccanol" is not 11-epi-terpestacin but, in fact, is (-)-terpestacin itself. Several intramolecular alkyne-aldehyde reductive coupling approaches to 1 and 2 were also investigated and are discussed herein.     

SmI2-promoted Reformatsky-type coupling reactions in exceptionally hindered contexts

Highly substituted, very hindered enones were synthesized using a two-step procedure that utilizes a diiodosamarium-promoted Reformatsky-type coupling and dehydration using Martin sulfurane. Both alpha-chloro- and alpha-bromoketones were coupled with a variety of carbonyl nucleophiles to form the intermediate beta-hydroxyketones, occurring with excellent diastereoselectivity, favoring the syn isomer (R1=Me). This technique complements other methods and enables the preparation of enones outside of the scope of current olefination methodology.     

anti-1,2-Diols via Ni-catalyzed reductive coupling of alkynes and alpha-oxyaldehydes

[reaction: see text] Ni-catalyzed reductive coupling of aryl alkynes (1) and enantiomerically enriched alpha-oxyaldehydes (2) afford differentiated anti-1,2-diols (3) with high diastereoselectivity and regioselectivity, despite the fact that the methoxymethyl (MOM) and para-methoxybenzyl (PMB) protective groups typically favor syn-1,2-diol formation in carbonyl addition reactions of this family of aldehydes.     

A velocity matching car-following model on a closed ring in which overtaking is allowed

Car-following models seek to describe the behaviour of a group of vehicles as they move along a stretch of road. In such models the behaviour of each vehicle is taken to be dependant on the motion of the vehicle in front and overtaking is not permitted. In this paper the effect of removing this ‘no-overtaking’ restriction is investigated. The resulting model is described in terms of a set of coupled time delay differential equations and these are solved numerically to analyse their post-transient behaviour under a periodic perturbation. For certain parameter choices this behaviour is found to be chaotic, and the degree of chaos is estimated using the Grassberger–Procaccia dimension.     

The Cumulative and Residual Impact of a Systemic Reform Program on Teacher Change and Student Learning of Science

This longitudinal, five‐year study of teachers and students who had participated in a systemic reform program in science explored if (1) teacher change in practice realized during a three‐year program is sustained one, two, and three years following the program, (2) student performance on state science assessments two years following studying with teachers at this school still demonstrated significant differences from students who attended the control school, and (3) student performance continued to be enhanced for both White and Minority students. Student achievement was assessed using the Discovery Inquiry Test in Science during sixth through eighth grades and the Ohio Graduation Test was used in 10th grade. The same students completed the test in grades 6–8 and 10th grade. Students from the Program school significantly outperformed students who attended the control school on the 10th grade state assessment in science. Findings in this study revealed the ability for sustained, whole‐school, professional development programs to have a cumulative and residual impact on teacher change and student learning of science.