Neither even nor odd: Sixth grade students’ dilemmas regarding the parity of zero

This study investigates two sixth grade students’ dilemmas regarding the parity of zero. Both students originally claimed that zero was neither even nor odd. Interviews revealed a conflict between students’ formal definitions of even numbers and their concept images of even numbers, zero, and division. These images were supported by practically based explanations relying on everyday contexts. By using mathematically based explanations that rely solely on mathematical notions, students were able to correctly conclude that zero is an even number. Extending the natural number system in elementary school to include zero can be used as springboard to encourage the use of mathematically based explanations.     

An efficient, PIFA mediated approach to benzo-, naphtho-, and heterocycle-fused pyrrolo[2,1-c][1,4]diazepines. An advantageous access to the antitumor antibiotic DC-81

[reaction: see text] The synthesis of a series of optically pure benzo-, naphtho-, and heterocycle-fused pyrrolo[2,1-c][1,4]-diazepin-5,11-dione derivatives starting from l-proline methyl ester is presented. The synthetic plan includes an aroylation step at the proline nitrogen followed by transformation of the ester residue into a N-methoxyamide group. The subsequent key cyclization step embraces the PIFA mediated formation of a N-acylnitrenium intermediate and its succeeding intramolecular trapping by the aromatic ring. The presented general approach solves the need of starting from not very accessible amino (or a related functionality) aromatic starting materials, and its effectiveness is demonstrated in the synthesis of the antitumor antibiotic DC-81.     

Why Does Pivalaldehyde (Trimethylacetaldehyde) Unexpectedly Seem More Basic Than 1‐Adamantanecarbaldehyde in the Gas Phase? FT‐ICR and High‐Level Ab Initio Studies

Fourier transform ion cyclotron resonance spectroscopy (FT ICR) techniques, including collision-induced dissociation (CID) methodology, were applied to the study of the gas-phase protonation of pivalaldehyde (1) and 1-adamantanecarbaldehyde (2). A new synthetic method for 2 was developed. The experiments, together with a thorough computational study involving ab initio and density functional theory (DFT) calculations of high level, conclusively show that upon monoprotonation in the gas phase, compound 1 yields monoprotonated methyl isopropyl ketone 3. The mechanism of this gas-phase acid-catalyzed isomerization is different from that reported by Olah and Suryah Prakash for the reaction in solution. In the latter case, isomerization takes place through the diprotonation of 1.     

Some results on construction of orthogonal Latin squares by the method of sum composition

A method of sum composition for construction of orthogona Latin squares was introduced by A. Hedayat and E. Seiden [1]. In this paper we exhibit procedures for constructing a pair of orthogonal Latin squares of size p^α + 4 for primes of the form 4m + 1 or p ≡ 1, 2, 4 mod 7. We also show that for any p > 2n and n even one can construct and orthogonal pair of Latin squares of size p^α + n using the method of sum composition. We observe that the restriction xy = 1 used by Hedayat and Seiden is sometimes necessary.     

Study of the nitric oxide system in the rat cerebellum during aging

Background  

The cerebellum is the neural structure with the highest levels of nitric oxide, a neurotransmitter that has been proposed to play a key role in the brain aging, although knowledge concerning its contribution to cerebellar senescence is still unclear, due mainly to absence of integrative studies that jointly evaluate the main factors involved in its cell production and function. Consequently, in the present study, we investigate the expression, location, and activity of nitric oxide synthase isoenzymes; the protein nitration; and the production of nitric oxide in the cerebellum of adult and old rats.     

Failure of Krull-Schmidt for invertible lattices over a discrete valuation ring

Let be a prime greater than , and let be the semi-direct product of a group of order by a cyclic group of order , which acts faithfully on . Let be the localization of at . We show that the Krull-Schmidt Theorem fails for the category of invertible -lattices.

     

Rapid method for the determination of polycyclic aromatic hydrocarbons in agricultural soils by sonication-assisted extraction in small columns

A rapid method has been developed for the determination of 16 polycyclic aromatic hydrocarbons (PAHs) in soil based on their sonication-assisted extraction in small columns (SAESC) with a low volume of ethyl acetate and subsequent quantitation and identification by GC with electron impact mass spectrometric detection in the SIM mode (GC-MS-SIM). Spiked blank soil extracts were used as standards to counteract the matrix effect observed in the chromatographic determination. PAHs were confirmed at trace level by their retention times, their qualifier and target ions, and their qualifier/target abundance ratios. Recovery studies were performed at 0.5, 1.0, 5.0, and 10 microg/kg fortification levels for each PAH, and the recoveries obtained ranged from 91.2 to 99.8% with RSDs between 0.4 and 9.3%. The detection limits of the method ranged from 0.03 to 0.3 microg/kg for the different PAHs studied. The developed method is linear over the range assayed, 1-100 microg/L with determination coefficients higher than 0.996. PAH levels were determined using this method in soil samples taken from different agricultural areas of Spain. In general, PAH concentrations were low and the most frequently occurring PAHs were naphthalene, pyrene, phenanthrene, and fluoranthene.     

Stable isotope-free quantitative shotgun proteomics combined with sample pattern recognition for rapid diagnostics

Mass spectrometry (MS) has become a powerful tool for the quantitative analysis of complex protein samples. A high-throughput strategy for the comparative analysis of multiple protein samples with high complexity becomes more and more important. Two strategies, spectral count and peak intensity, for label-free MS analysis of prefractionated complex mixtures have been described recently to be useful for quantitation. Here we compare both strategies for rapid and quantitative 1-D shotgun LC/MS/MS analyses of highly complex protein mixtures using silica-based monolithic columns. First, we validated linearity and sensitivity of these methods by spiking varying amounts of an internal standard protein in a complex plant protein extract. Secondly, quantitative data of proteins of Medicago truncatula nodules were visualized with independent components analysis using data either obtained from spectral count or peak integration performed with commercial software. Spectral count showed apparent advantages over peak integration because several peptides per protein are automatically averaged, the linear dynamic range of quantitation increases in complex matrices and the number of quantified proteins surpasses the number of proteins using peak integration. Thus, for the need of rapid comparative analysis of highly complex protein samples, spectral count enables sample pattern recognition and identification of biomarkers in nongel based proteomic studies.     

Comparison of Benzyl Celluloses Synthesized in Aqueous NaOH and Dimethyl Sulfoxide/Tetrabutylammonium Fluoride

Cellulose was benzylated starting from the dissolved polymer in dimethyl sulfoxide (DMSO)/tetrabutylammonium fluoride trihydrate (TBAF) and heterogeneously in aqueous NaOH as reaction media. Differences in the distribution of benzyl moieties within the anhydroglucose unit in dependence on the synthesis pathway couldn't be found. However, as revealed by means of ¹H-NMR spectroscopy, significant differences in the distribution of substituents along the cellulose chains occurred. Conventionally synthesized samples (in aqueous NaOH), even in the presence of a phase transfer catalyst, possess a block-wise distribution of substituents, while a dissolution of cellulose in DMSO/TBAF prior to the reaction gives products that are uniformly substituted along the cellulose chains.