Rhenium-promoted diastereo- and enantioselective cyclopentannulation reactions: furans as 1,3-propene dipoles

The rhenium furan complexes TpRe(CO)(MeIm)(eta2-2-methylfuran) (1) and TpRe(CO)(MeIm)(eta2-2,5-dmethylfuran) (2) undergo Lewis acid-promoted cyclopentannulation reactions with enones and enals to generate 3-acetylcyclopentene complexes. During the reaction, a rearrangement occurs such that the alpha and beta carbons of the enone are incorporated into the new carbocycle. Treatment of these complexes with an oxidant (H2O2 or silver triflate) liberates the acetylcyclopentene. When a resolved form of the rhenium complex is used, the acetylcyclopentenes can be obtained enantioselectively.     

Linear dichroism study of retinoids

Linear dichroism spectra of several retinoids and related polyenes incorporated in stretched polyethylene films were determined. It is suggested that the retinoids are oriented with the plane of the ring parallel to the stretching direction of the film, the long polyene chain being displaced from that direction.     

Analysis of biologically active compounds in potatoes (Solanum tuberosum), tomatoes (Lycopersicon esculentum), and jimson weed (Datura stramonium) seeds

Potatoes and tomatoes, members of the Solanaceae plant family, serve as major, inexpensive low-fat food sources providing for energy, high-quality protein, fiber, vitamins, pigments, as well as other nutrients. These crops also produce biologically active secondary metabolites, which may have both adverse and beneficial effects in the diet. This limited overview, based largely on our studies with the aid of HPLC, TLC, ELISA, GC-MS, and UV spectroscopy, covers analytical aspects of two major potato trisaccharide glycoalkaloids, alpha-chaconine and alpha-solanine, and their hydrolysis products (metabolites) with two, one, and zero carbohydrate groups; the potato water-soluble nortropane alkaloids calystegine A3 and B2; the principal potato polyphenolic compound chlorogenic acid; potato inhibitors of digestive enzymes; the tomato tetrasaccharide glycoalkaloids dehydrotomatine and alpha-tomatine and hydrolysis products; the tomato pigments beta-carotene, lycopene, and chlorophyll; and the anticholinergic alkaloids atropine and scopolamine present in Datura stramonium (jimson weed) seeds that contaminate grain and animal feed. Related studies by other investigators are also mentioned. Accurate analytical methods for these food ingredients help assure the consumer of eating a good-quality and safe diet.     

Evaluation of matrix-assisted laser desorption ionization mass spectrometry for polymer characterization

A protocol for the preparation of polymeric samples for time-of-flight matrix-assisted laser desorption ionization mass spectrometry (TOF-MALDI-MS) analysis was developed. Dithranol was identified as a good matrix for polystyrene (PS), and the addition of silver for cationization of molecules was determined to be necessary. Based on this preparative method, low molecular weight samples of other polymers [polyisoprene, polybutadiene, poly(ethylene oxide), poly(methyl methacrylate), and polydimethylsiloxane] were analyzed with molecular weights up to 49 ku. The effects of laser intensity were determined to influence the molecular weight distribution of intact oligomers, most significantly for low molecular weight polymers. Linear and reflectron modes of analysis were evaluated; better signal intensity and resolution were obtained in the reflectron mode. The TOF-MALDI-MS measurements are compared with time-of-flight secondary ion mass spectrometry (TOF-SIMS) and gel permeation chromatography (GPC) for the same polymers. The M _n values calculated by TOF-MALDI-MS consistently are higher than values calculated by TOF-SIMS for all classes of polymers with molecular weights up to 8 ku. The molecular weights of the PS calculated from TOF-MALDI-MS are in good agreement with GPC (±10%). The composition of the terminal group on a polymer chain may affect the ion yields. The ion yields of intact oligomers were evaluated as a function of end group composition for both TOF-MALDI-MS and TOF-SIMS. The slight disparity of results between TOF-SIMS and TOF-MALDI-MS for the perfluoroalkyl-terminated PS suggests that the oligomers are desorbed preferentially from the surface in the TOF-SIMS analysis, rather than having an increased ionization probability.     

Cardinal characteristics at κ in a small u(κ) model

We provide a model where $\mathfrak{u}(\kappa )<2^{\kappa }$ for a supercompact cardinal κ. [10] provides a sketch of how to obtain such a model by modifying the construction in [6]. We provide here a complete proof using a different modification of [6] and further study the values of other natural generalizations of classical cardinal characteristics in our model. For this purpose we generalize some standard facts that hold in the countable case as well as some classical forcing notions and their properties.     

Mixing and sweeping out

A weakly mixing transformationT and a sequence (d _n) are constructed such thatT is uniformly mixing on (d _n),T is uniformly sweeping out on ([αd _n]) for allα∈(0, 1), and for all rationalα∈(0, 1)T is not mixing on ([αd _n]).     

Lower Bounds for the Lp-Norm in Terms of the Mellin Transform

Given a measurable function f on (0, ) with Mellin transformF(s), let |f|_p denote the L^p-norm of f with respect to the measuredx/x. We prove that under certain assumptions, for instanceif f is real and non-negative and F() converges for in an openinterval and F() 0, then wherec_p (2e)^–1. We derive similar inequalities for complex-valuedf, for the L^p-norm of the derivative of f, and for the supremumof real-valued f and of its derivative. The lower bounds areeminently applicable when f is a convolution product.     

Student Attitudes and Calculus Reform

This paper compares the attitudes about mathematics of students from traditionally taught calculus classes and those from a “reformed” calculus course. The paper is based on three studies, which together present a consistent picture of student attitudes about calculus reform. The reformed course appeared to violate students' deeply held beliefs about the nature of mathematics and how it should be learned. Although during their first months in the reformed course most students disliked it, their attitudes gradually changed. One and 2 years after, reform students felt significantly more than the traditionally taught students that they better understood how math was used and that they had been required to understand math rather than memorize formulas.