A Note on Log-Convexity of q-Catalan Numbers

The q-Catalan numbers studied by Carlitz and Riordan are polynomials in q with nonnegative coefficients. They evaluate, at q = 1, to the Catalan numbers: 1, 1, 2, 5, 14,…, a log-convex sequence. We use a combinatorial interpretation of these polynomials to prove a q-log-convexity result. The sequence of q-Catalan numbers is not q-log-convex in the narrow sense used by other authors, so our work suggests a more flexible definition of q-log convex be adopted. Received January 2, 2007     

Mechanism of UV photoreactivity of alkylsiloxane self-assembled monolayers

A molecular level understanding of the photoreactivity of self-assembled monolayers (SAMs) becomes increasingly important as the spatial resolution starts to be limited by the size of the resist and the spatial extent of the photochemical reactions in photoresist micropatterning. To this end, a number of surface characterization techniques were combined to understand the reactive agents, reactive sites, kinetics, and reaction pathways in the UV photoreactivity of octadecylsiloxane (ODS) SAMs. Quantitative analysis of our results provides evidence that ground state atomic oxygen is the primary reactive agent for the UV degradation of ODS SAMs. UV degradation, which follows zero-order kinetics, results in the scission of alkyl chains instead of the siloxane headgroups. Our results suggest that the top of the ODS SAMs is the preferential reactive site. Using a novel, highly surface sensitive technique, fluorescence labeling of surface species, we identified the presence of submonolayer quantities chemical functional groups formed by the UV degradation. These groups are intermediates in a proposed mechanism based on hydrogen abstraction.     

Synthesis of 2,3,9,10,16,17,23,24-Octaalkynylphthalocyanines and the Effects of Concentration and Temperature on Their (1)H NMR Spectra

The syntheses of 3,4- and 4,5-diiodophthalonitriles are described. Coupling of the latter compound with Pd(PPh(3))(2)Cl(2) and 1-octyne, 1-heptyne, 1-hexyne, 1-pentyne, and 3,3-dimethyl-1-butyne gave a series of 4,5-dialkynylphthalonitriles. Hydrogenation of 4,5-bis(1-pentynyl)phthalonitrile and 4,5-bis(3,3-dimethyl-1-butynyl)phthalonitrile gave 4,5-dipentylphthalonitrile and 4,5-bis(3,3-dimethylbutyl)phthalonitriles. Condensation of the dialkynylphthalonitriles with lithium 1-pentoxide in 1-pentanol gave 2,3,9,10,16,17,23,24-octaalkynylphthalocyanines, while intervention of the intermediate dilithium phthalocyanines with zinc acetate gave the related zinc(II) phthalocyanines. (1)H NMR spectroscopy of these octaalkynylphthalocyanines exhibited large chemical shifts (1-2 ppm) of the internal and aromatic protons at concentrations ranging from 10(-)(2) to 10(-)(5) M and at temperatures from 27 to 147 degrees C. The effects of aggregation phenomena are discussed. The importance of reporting concentration and temperature values for NMR spectra of phthalocyanines is stressed.     

Catalytic asymmetric addition of alkylzinc and functionalized alkylzinc reagents to ketones

We describe our full report of the catalytic asymmetric addition of simple and functionalized dialkylzinc reagents to a broad range of saturated ketones and enones. The functionalized organozinc reagents contain esters, silyl ethers, alkyl chlorides, and alkyl bromides. In general, the resulting tertiary alcohol products are isolated with high ee's. With some substrates, yields are low as a result of the formation of aldol byproducts. Most substrates undergo additions with good yields reaching as high as 91%.     

Methods for generating protein molecular ions in ToF-SIMS

One of the greatest challenges in mass spectrometry lies in the generation and detection of molecular ions that can be used to directly identify the protein from the molecular weight of the molecular ion. Typically, proteins are large (MW > 1000), nonvolatile, and/or thermally labile, but the vaporization process produced by many mass spectrometry techniques including time-of-flight secondary ion mass spectrometry (ToF-SIMS) is inherently limited to generating ions from smaller compounds or fragments of the parent molecule, making the identification of proteins complex. The application of specific molecules to aid in the generation of high molecular weight ions in ToF-SIMS has been recognized for some time. In this study we have developed a matrix-SAM substrate preparation technique based on the self-assembly of a matrix-like molecule, mercaptonicotinic acid (MNA), on gold. We then compare this substrate with two existing ToF-SIMS sample preparation techniques, cationized alkane thiol and matrix-enhanced SIMS (MESIMS). The results of this study illustrate that while there is a range of methods that can be used to improve the molecular ion yield of proteins in ToF-SIMS, their efficacy and reproducibility vary considerably and crucially are linked to the sample preparation and/or protein application methods used. Critically, the MNA modified substrate was able to simultaneously induce molecular ions for each protein present in a multicomponent solution, suggesting that this sample preparation technique may have future application in proteomics and DNA analysis.     

Filling in the gaps: modelling incomplete CBL data using a graphing calculator

This article discusses the real-world problem-solving lesson that emerged when a high school math teacher used a motion detector with a CBL and graphing calculator to obtain the 'bounce' data of a ping-pong ball. While practising the 'bounce' data collection--a series of diminishing parabolas--the teacher accidentally pulled the motion detector away and then, realizing his mistake, pulled it back. The resulting data showed a series of parabolas, but one was missing. The teacher used this opportunity to create a lesson in which his students collect 'bad data' and then fill in the missing parabola using critical components of parabolas, such as the latus rectum and the vertex, and using matrices. The article provides all the necessary directions, formulas, and names of resources needed to replicate the lesson. The creation of this lesson demonstrates that a serendipitous error can create a genuine and authentic problem-solving activity for math students.     

Development of chiral heteroleptic magnesium amides; asymmetric deprotonations mediated by six-membered metallocyclic amidomagnesium naphtholates

A series of enantioenriched six-membered metallocyclic amidomagnesium naphtholates were prepared and used to probe the structure–reactivity/selectivity relationships of heteroleptic magnesium base complexes within asymmetric deprotonation reactions. An effective complex was identified and applied within enantioselective enolisation processes, delivering good levels of enantioselectivity and also revealing key structural requirements for achieving such selectivity.     

Sensory Response and Two-Photon-Fluorescence Study of Regioregular Polythiophene Nanoparticles

Nanoparticles of a regioregular and soluble polythiophene were fabricated by mini-emulsion technique. The fabricated nanoparticles were characterized by optical spectroscopy and dynamic light scattering. The fluorescence quenching of these fabricated nanoparticles with 2,4-dinitrotolune (DNT) in aqueous and organic solutions was investigated. Significant fluorescence quenching was observed. The Stern-Volmer constants were determined to be higher than that of the bulk polymer in solution, indicating that the nanoparticles provide better sensitivity in DNT sensing. Strong two-photon-induced fluorescence was measured from these nanoparticles.