High school students’ understanding of the function concept

This paper is a study of part of the Algebra Project's program for underrepresented high school students from the lowest quartile of academic achievement, social and economic status. The study focuses on students’ learning the concept of function. The curriculum and pedagogy are part of an innovative, experimental approach designed and implemented by the Algebra Project. The instructional treatment took place over 7 weeks during the Junior Year of 15 students from our target population. Immediately after instruction, a written instrument was administered followed, several weeks later, by in-depth interviews. The results are that many of our participants achieved a level of knowledge and understanding of functions on a par with beginning college students, including preservice teachers, as reported in the literature. Many conceptual difficulties that have been reported in the research literature were not as prevalent for our participants and some of them were capable of solving difficult problems involving composition of functions. We conclude that, with appropriate pedagogy, it is possible for students in the Algebra Project's target population to learn substantial and non-trivial mathematics at the high school level, and that the Algebra Project approach is one example of such a pedagogy.     

Model Identification in Exponential Smoothing

Model identification has traditionally been ignored in forecasting via exponential smoothing. The usual practice is to apply the same model to every time-series in a collection. This paper develops a procedure for model identification in large forecasting applications based on an examination of variances of differences of the time-series. The order of differencing yielding minimum variance suggests an appropriate model for the series. Empirical results show that this procedure selects models that give reasonable ex ante forecast accuracy.     

Tocochromanols composition in kernels recovered from different apricot varieties: RP-HPLC/FLD and RP-UPLC-ESI/MSn study

Composition of tocochromanols in kernels recovered from 16 different apricot varieties (Prunus armeniaca L.) was studied. Three tocopherol (T) homologues, namely α, γ and δ, were quantified in all tested samples by an RP-HPLC/FLD method. The γ-T was the main tocopherol homologue identified in apricot kernels and constituted approximately 93% of total detected tocopherols. The RP-UPLC-ESI/MSⁿ method detected trace amounts of two tocotrienol homologues α and γ in the apricot kernels. The concentration of individual tocopherol homologues in kernels of different apricots varieties, expressed in mg/100 g dwb, was in the following range: 1.38–4.41 (α-T), 42.48–73.27 (γ-T) and 0.77–2.09 (δ-T). Moreover, the ratio between individual tocopherol homologues α:γ:δ was nearly constant in all varieties and amounted to approximately 2:39:1.     

Molecular‐Weight‐Dependence on Domain Formation of Grafted Poly(ethylene‐co‐propylene) in a Poly(propylene) Matrix

Several novel poly(propylene)‐graft‐poly(ethylene‐co‐propylene) copolymers with isotactic poly(propylene) (PP) backbones and ethylene/propylene rubber (EPR) branches were synthesized. The thermomechanical properties of these samples were investigated using a dynamic mechanical analyzer. There appeared to be a critical EPR molecular weight above which a two‐phase system developed with EPR domains dispersed in a PP matrix. This domain formation gave an enhanced loss modulus compared to a commercial high impact PP product below 40°C.     

Reaction development and mechanistic study of a ruthenium catalyzed intramolecular asymmetric reductive amination en route to the dual Orexin inhibitor Suvorexant (MK-4305)

The first example of an intramolecular asymmetric reductive amination of a dialkyl ketone with an aliphatic amine has been developed for the synthesis of Suvorexant (MK-4305), a potent dual Orexin antagonist under development for the treatment of sleep disorders. This challenging transformation is mediated by a novel Ru-based transfer hydrogenation catalyst that provides the desired diazepane ring in 97% yield and 94.5% ee. Mechanistic studies have revealed that CO(2), produced as a necessary byproduct of this transfer hydrogenation reaction, has pronounced effects on the efficiency of the Ru catalyst, the form of the amine product, and the kinetics of the transformation. A simple kinetic model explains how product inhibition by CO(2) leads to overall first-order kinetics, but yields an apparent zero-order dependence on initial substrate concentration. The deleterious effects of CO(2) on reaction rates and product isolation can be overcome by purging CO(2) from the system. Moreover, the rate of ketone hydrogenation can be greatly accelerated by purging of CO(2) or trapping with nucleophilic secondary amines.     

Ultraviolet-C irradiation for prevention of central venous catheter-related infections: an in vitro study

Central venous catheters (CVC) are widely used in the United States and are associated with 250,000 to 500,000 CVC-related infections in hospitals annually. We used a catheter made from ultraviolet-C (UVC) transmissive material to test whether delivery of UVC from the lumen would allow inactivation of microorganisms on the outer surface of CVC. When the catheter was exposed to UVC irradiation from a cold cathode fluorescent lamp inside the catheter lumen at a radiant exposure of 3.6 mJ cm(-2) , more than 6-log(10) of drug-resistant Gram-positive bacteria adhered to the outer surface of the catheter were inactivated. Three to 7-log(10) of drug-resistant Gram-negative bacteria and 2.80-log(10) of fungi were inactivated at a radiant exposure of 11 mJ cm(-2).UVC irradiation also offered a highly selective inactivation of bacteria over keratinocytes under exactly comparable conditions. After 11 mJ cm(-2) UVC light had been delivered, over 6-log(10) of bacteria were inactivated while the viability loss of the keratinocytes was only about 57%.     

Hydrophilic interaction chromatography/electrospray mass spectrometry analysis of carbohydrate-related metabolites from Arabidopsis thaliana leaf tissue

This work describes the development and application of an on-line liquid chromatography/mass spectrometry (LC/MS) method using hydrophilic interaction chromatography (HILIC) coupled to negative ion mode electrospray ionisation ion trap mass spectrometry (ESI-MS) for the analysis of highly polar carbohydrate-related metabolites commonly found in plants, ranging from reducing and non-reducing sugars and sugar alcohols to sugar phosphates. Using this method, separation and detection of a mixture of eight authentic standard compounds containing glucose (Glc), sucrose (Suc), raffinose, verbascose, mannitol, maltitol, glucose-6-phosphate (Glc6P) and trehalose-6-phosphate (Tre6P) were achieved in less than 15 min. The method is rapid, robust, selective, and sensitive, with limits of detection (LODs) ranging from 0.2 microM obtained for neutral sugars, to 1.0 microM obtained for sugar alcohols, and 2.0 microM obtained for negatively charged sugar phosphates. We have studied the negative ion collision-induced dissociation (CID) fragmentation behaviour of the non-reducing raffinose family oligosaccharides (RFOs) raffinose, stachyose, and verbascose. Mainly Bi and Ci glycosidic and Ai cross-ring structurally informative cleavages are observed. We have applied this HILIC/ESI-MS method for the analysis of Arabidopsis thaliana wild-type Columbia-0 (Col-0) and its starchless phosphoglucomutase mutant (pgm1) leaf extracts. The method was used to quantify Glc, Suc, raffinose, and Glc6P in A. thaliana extracts. Data obtained using this HILIC/ESI-MS method were compared with those obtained using a comparable porous graphitic carbon-based LC/ESI-MS method.