Next‐Generation o‐Nitrobenzyl Photolabile Groups for Light‐Directed Chemistry and Microarray Synthesis

Light as an external trigger is a valuable and easily controllable tool for directing chemical reactions with high spatial and temporal accuracy. Two o‐nitrobenzyl derivatives, benzoyl‐ and thiophenyl‐NPPOC, undergo photo‐deprotection with significantly improved efficiency over that of the commonly used NPPOC group. The two‐ and twelvefold increase in photo‐deprotection efficiency was proven using photolithograph synthesis of microarrays.     

Elliptic curve cryptography: The serpentine course of a paradigm shift

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Over a period of sixteen years elliptic curve cryptography went from being an approach that many people mistrusted or misunderstood to being a public key technology that enjoys almost unquestioned acceptance. We describe the sometimes surprising twists and turns in this paradigm shift, and compare this story with the commonly accepted Ideal Model of how research and development function in cryptography. We also discuss to what extent the ideas in the literature on “social construction of technology” can contribute to a better understanding of this history.

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For a video summary of this paper, please visit http://www.youtube.com/watch?v=HHFFvfDoTK4.     

A Mixed‐Method Study: Assessing the BAR Model's Impact on Preservice Teachers' Efficacy Beliefs

This study took place at a mid‐sized, Midwestern university located in a mid‐sized town. The researchers developed the BAR model to teach mathematics methods both in the classroom and in the field. The preservice teachers took Enochs, Smith, and Huinker's Mathematics Teaching Efficacy Beliefs Instrument (MTEBI) on the first and last day of class. A total of 297 responses were collected from the pre‐ and posttests, with 280 matching responses, which were then used for data analysis. Mixed methods were used to analyze qualitative and quantitative data. The researchers sought to determine if the specific teaching methods from the BAR model led to positive changes in preservice teacher efficacy beliefs. They also explored if efficacy beliefs changed as a result of field experiences. Preservice teachers' efficacy scores changed positively on every item on the MTEBI. The researchers also determined that there was an increase in preservice teachers' outputs as a result of their field experiences.     

Counting lattice chains and Delannoy paths in higher dimensions

Lattice chains and Delannoy paths represent two different ways to progress through a lattice. We use elementary combinatorial arguments to derive new expressions for the number of chains and the number of Delannoy paths in a lattice of arbitrary finite dimension. Specifically, fix nonnegative integers n₁,…,n_d, and let L denote the lattice of points (a₁,…,a_d)∈Z^d that satisfy 0≤a_i≤n_i for 1≤i≤d. We prove that the number of chains in L is given by where . We also show that the number of Delannoy paths in L equals Setting n_i=n (for all i) in these expressions yields a new proof of a recent result of Duchi and Sulanke [9] relating the total number of chains to the central Delannoy numbers. We also give a novel derivation of the generating functions for these numbers in arbitrary dimension.     

The circular chromatic numbers of planar digraphs

The circular chromatic number is a refinement of the chromatic number of a graph. It has been established in [3,6,7] that there exists planar graphs with circular chromatic number r if and only if r is a rational in the set {1} ∪ [2,4]. Recently, Mohar, in [1,2] has extended the concept of the circular chromatic number to digraphs and it is interesting to ask what the corresponding result is for digraphs. In this article, we shall prove the new result that there exist planar digraphs with circular chromatic number r if and only if r is a rational in the interval [1,4]. © 2006 Wiley Periodicals, Inc. J Graph Theory 55: 14–26, 2007     

Evaluation of long‐term performance of antioxidants using prooxidants instead of thermal acceleration

Evaluation of stabilization efficiencies of different antioxidants in polymers at low temperature and relatively short time was performed using incorporation of a prooxidant for catalytic oxidation. Comparisons were made between polypropylene films stabilized with primary antioxidants (Irganox 1076, Irganox 1010, and α‐tocopherol), with or without the prooxidant manganese stearate at different temperatures. A faster degradation was obtained in the presence of a prooxidant than without it. The relative efficiency of the antioxidants at prooxidant acceleration correlated better to low temperature long‐term test than at the thermal acceleration. The results were affected by initial differences in the amounts of the antioxidants present after the processing of the films. These differences were corrected for by a recalculation using microwave‐assisted extraction (MAE) and high performance liquid chromatography analysis from the exponential decrease in the amount of antioxidant in the films. The fastest comparison of the antioxidants efficiency was obtained from oxidation induction times, using total luminescence intensity measurements, but reliable results could also be obtained from the time to apparent failure. © 2005 Wiley Periodicals,Inc. J Polym Sci Part A: Polym Chem 43: 4537–4546, 2005