Stereoselective synthesis of cis-3,4-disubstituted piperidines through ring transformation of 2-(2-mesyloxyethyl)azetidines

The reactivity of 2-(2-mesyloxyethyl)azetidines, obtained through monochloroalane reduction and mesylation of the corresponding β-lactams, with regard to different nucleophiles was evaluated for the first time, resulting in the stereoselective preparation of a variety of new 4-acetoxy-, 4-hydroxy-, 4-bromo-, and 4-formyloxypiperidines. During these reactions, transient 1-azoniabicyclo[2.2.0]hexanes were prone to undergo an S(N)2-type ring opening to afford the final azaheterocycles, which was rationalized by means of a detailed computational analysis. This approach constitutes a convenient alternative for the known preparation of 3,4-disubstituted 5,5-dimethylpiperidines, providing an easy access to the 5,5-nor-dimethyl analogues as valuable templates in medicinal chemistry. Furthermore, cis-4-bromo-3-(phenoxy or benzyloxy)piperidines were elaborated into the piperidin-3-one framework via dehydrobromination followed by acid hydrolysis.     

Disordered spheres with extensive overlap in projection: image simulation and analysis

This article simulates highly overlapped projections of spherical particles that are distributed randomly in space. The size and number of the features in the projections are examined as well as how these features change with particle size and concentration. First, there are discernable features in projection even when particles overlap extensively, and the size of these discernable features is the expected size of an individual particle. Second, the number of features increases with specimen thickness at a rate of t(0.543) when the specimen thickness is below a critical value and becomes independent of specimen thickness at higher thicknesses. A criterion is established for the critical thickness based on particle size and particle volume fraction. When the specimen thickness is known and smaller than the critical thickness, a single representative transmission electron microscopy (TEM) (or scanning TEM) image exhibiting extensive particle overlap can be used to determine the size and number density of the spherical particles.     

Generalized covering designs and clique coverings

Inspired by the “generalized t‐designs” defined by Cameron [P. J. Cameron, Discrete Math 309 (2009), 4835–4842], we define a new class of combinatorial designs which simultaneously provide a generalization of both covering designs and covering arrays. We then obtain a number of bounds on the minimum sizes of these designs, and describe some methods of constructing them, which in some cases we prove are optimal. Many of our results are obtained from an interpretation of these designs in terms of clique coverings of graphs. © 2011 Wiley Periodicals, Inc. J Combin Designs 19:378‐406, 2011     

Expression of Hepatoma-derived growth factor family members in the adult central nervous system

Background  

Hepatoma-derived growth factor (HDGF) belongs to a polypeptide family containing five additional members called HDGF related proteins 1–4 (HRP-1 to -4) and Lens epithelial derived growth factor. Whereas some family members such as HDGF and HRP-2 are expressed in a wide range of tissues, the expression of others is very restricted. HRP-1 and -4 are only expressed in testis, HRP-3 only in the nervous system. Here we investigated the expression of HDGF, HRP-2 and HRP-3 in the central nervous system of adult mice on the cellular level by immunohistochemistry. In addition we performed Western blot analysis of various brain regions as well as neuronal and glial cell cultures.     

Cyclic triamines as potential high energy materials. Thermochemical properties of triaziridine and triazirine

As part of our survey of potential high-energy materials, we are considering molecules that have relatively high nitrogen content. Such molecules can decompose or combust to make very stable products. Here, we present calculated thermochemical properties of two molecules containing three nitrogen atoms in a ring: triaziridine and triazirine . Gaussian-2 and -3, CBS-APNO, and CBS-QB3 are the high-precision methods used in this study.     

Students' Retention of Mathematical Knowledge and Skills in Differential Equations

This study investigates students' retention of mathematical knowledge and skills in two differential equations classes. Posttests and delayed posttests after 1 year were administered to students in inquiry‐oriented and traditional classes. The results show that students in the inquiry‐oriented class retained conceptual knowledge, as seen by their performance on modeling problems, and retained equal proficiency in procedural problems, when compared with students in the traditionally taught classes. The results of this study add additional support to the claim that teaching for conceptual understanding can lead to longer retention of mathematical knowledge.