Secondary Options and Post‐secondary Expectations: Standards‐based Mathematics Programs and Student Achievement on College Mathematics Placement Exams

Research on student achievement within the University of Chicago School Mathematics Project (UCSMP) and Core‐Plus Mathematics Project (CPMP) at the secondary level is beginning to accumulate, however, much less is known about how prepared these students are for post‐secondary education. Therefore this study involving students within one tracked school district used multiple linear regression to examine the role of differential experience within two secondary Standards‐based mathematics programs, gender, and prior mathematics achievement on college algebra and calculus readiness placement test scores. Results show that there are no significant differences between students who had completed three and four years of the CPMP curriculum. UCSMP students with four or five years of experience significantly outperformed CPMP students on both assessments. Prior achievement was a significant predictor of student achievement on both examinations. Male students outperformed female students on the algebra placement exam. Students who had studied from both CPMP and UCSMP significantly outperformed students who had studied from CPMP for four years on the calculus readiness examination.     

Synthesis and characterization of novel aromatic poly(imide–benzoxazole) copolymers

New poly(imide–benzoxazole) copolymers were prepared directly from a dianhydride, a diacid chloride, and a bis(o‐diaminophenol) monomer in a two‐step method. In the first step, poly(amic acid–hydroxyamide) precursors were synthesized by low‐temperature solution polymerization in an organic solvent. Subsequently, the thermal cyclodehydration of the poly(amic acid–hydroxyamide) precursors at 350 °C produced the corresponding poly(imide–benzoxazole) copolymers. The inherent viscosities of the precursor polymers were around 0.19–0.33 dL/g. The cyclized poly(imide–benzoxazole) copolymers had glass‐transition temperatures in the range of 331–377 °C. The 5% weight loss temperatures ranged from 524 to 535 °C in nitrogen and from 500 to 514 °C in air. The poly(imide–benzoxazole) copolymers were amorphous, as evidenced by the wide‐angle X‐ray diffraction measurements. The structures of the precursor copolymers and the fully cyclized copolymers were characterized by Fourier transform infrared, ¹H NMR, and elemental analysis. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 6020–6027, 2005     

Covering theorems of simplexes and systems of linear inequalities

A selection lemma for Ky Fan's coverings is first proved, and then applied together with Ky Fan's generalization of the classical Knaster-Kuratowski Mazurkiewicz theorem to obtain a new covering theorem of simplexes. As applications, results on the consistency for certain systems of linear inequalities are obtained.     

Morphology of microporous poly(vinylidene fluoride) membranes studied by gas permeation and scanning electron microscopy

Microporous poly(vinylidene fluoride) (PVDF) membranes with asymmetric pore structure were prepared by a wet phase inversion process. The polymer was precipitated from a casting solution when immersed in a cold water (gelation) bath. The casting solution was, in most cases, composed of polymer, solvent, and nonsolvent. In this solvent-nonsolvent system, the solvents used were triethylphosphate (TEP) and dimethylsulfoxide (DMSO), and the nonsolvents used were glycerol and ethanol. Mean pore sizes and effective porosity of the microporous membranes were calculated using the gas permeation method. They were studied as a function of evaporation time of wet nascent film, polymer molecular weight, concentration of polymer, and concentration of nonsolvent. The morphology of the membranes was examined by scanning electron microscopy (SEM).     

Some experiments on the effect of isolated protuberances on flow through tubes

At various locations in the arterial system, plaques, or small relatively isolated protuberances, can develop on the inner wall of the vessel and project into the lumen. A number of investigators have suggested that the development and growth of these protuberances is related to the flow in the vicinity of the protuberance. In this study, the conditions under which the flow separates from an isolated protuberance located in a cylindrical tube were investigated. The critical Reynolds number at which separation first takes place for a given protuberance was determined. A series of tests was performed for steady flow of a Newtonian fluid through a rigid tube in which protuberances of various sizes were inserted. The results of the tests show the effect of the protuberance height and shape on the separation characteristics. In general, the results indicate that separation takes place at relatively small values of the Reynolds number; values that commonly occur in the arterial system, so that this phenomenon may be important in the study of the “coupling” between blood flow and arterial lesions.     

Aryne‐Induced Novel Tandem 1,2‐Addition/(3+2) Cycloaddition to Generate Imidazolidines and Pyrrolidines

A new “single‐flask” method was developed for the synthesis of imidazolidines and pyrrolidines with high stereoselectivity. First, a Schiff base was arylated with an aryne. Second, an intramolecular proton transfer took place from the methylene position to the anionic aryne ring. Third, the resultant ylide reacted with a second equivalent of the same Schiff base in situ or an electron‐deficient alkene through a (3+2) cycloaddition. These sequential tandem 1,2‐addition/(3+2) cycloaddition reactions led to the desired heterocycles in 63–88 % yields.     

Organocatalyzed Asymmetric Conjugate Addition of Heteroaryl and Aryl Trifluoroborates: a Synthetic Strategy for Discoipyrrole D

Bis‐heteroaryl or bis‐aryl stereocenters were formed by an organocatalytic enantioselective conjugate addition using the respective trifluoroborate salts as nucleophiles. Control studies suggested that fluoride dissociation is necessary in the anhydrous conditions. This strategy is applicable to the synthesis of discoipyrrole D, an inhibitor of BR5 fibroblast migration.     

Electronic quantum trajectories in a quantum dot

This article gives a quantum‐trajectory demonstration of the observed electric, magnetic, and thermal effects on a quantum dot with circular or elliptic shape. By applying quantum trajectory method to a quantum dot, we reveal the quantum‐mechanical meanings of the classical concepts of backscattering and commensurability, which were used in the literature to explain the peak locations of the magnetoresistance curve. Under the quantum commensurability condition, electronic quantum trajectories in a circular quantum dot are shown to be stationary like a standing wave, whose presence increases the electrical resistance. A hidden quantum effect called magnetic stagnation is discovered and shown to be the main cause of the observed jumps of the magnetoresistance curve. Quantum trajectories in an elliptic quantum dot are found to be chaotic and an index of chaos called Lyapunov exponent is proposed to measure the irregularity of the various quantum trajectories. It is shown that the response of the Lyapunov exponent to the applied magnetic field captures the main features of the experimental magnetoresistance curve. © 2014 Wiley Periodicals, Inc.     

Mesomorphism and luminescence properties of platinum(II) complexes with tris(alkoxy)phenyl-functionalized pyridyl pyrazolate chelates

A series of new mesomorphic platinum(II) complexes 1 – 4 bearing pyridyl pyrazolate chelates are reported herein. In this approach, pyridyl azolate ligands have been strategically functionalized with tris(alkoxy)phenyl groups with various alkyl chain lengths. As a result, they are ascribed to a class of luminescent metallomesogens that possess distinctive morphological properties, such as their intermolecular packing arrangement and their associated photophysical behavior. In CH₂Cl₂, independent of the applied concentration in the range 10^?6–10^?3 M , all Pt^II complexes exhibit bright phosphorescence centered at around 520 nm, which is characteristic for monomeric Pt^II complexes. In stark contrast, the single‐crystal X‐ray structure determination of [Pt(C4pz)₂] ( 1 ) shows the formation of a dimeric aggregate with a notable Pt???Pt contact of 3.258 Å. Upon heating, all Pt^II complexes 1 – 4 melted to form columnar suprastructures, for which similar intracolumnar Pt???Pt distances of approx. 3.4–3.5 Å are observed within an exceptionally wide temperature range (>250 °C), according to the powder XRD data. Upon casting into a neat thin film at RT, the luminescence of 1 – 4 is dominated by a red emission that spans 630–660 nm, which originates from the one‐dimensional, chainlike structure with Pt–Pt interaction in the ground state. Taking complex 4 as a representative, the emission intensity and wavelength were significantly decreased and blueshifted, respectively, on heating from RT to 250 °C. Further heating to liquefy the sample alters the red emission back to the green phosphorescence of the monomer. The results highlight the pivotal role of tris(alkoxy)phenyl groups in the structural versus luminescence behavior of these Pt^II complexes.     

Sensitive and simple flow injection analysis of formaldehyde using an activated barrel plating nickel electrode

A flow injection analysis coupled with electrochemical detection at an activated barrel plating nickel electrode (Ni-BPE) was developed as a sensitive, simple, and low-cost formaldehyde sensor. The mechanism of Ni-BPE toward the electrocatalytic oxidation of formaldehyde in alkaline medium at ambient temperature was proposed to be based on the electrocatalytic oxidation of formaldehyde by Ni(III)O(OH) species. Under the optimized conditions (flow rate = 1.2 mL/min; detection potential = +0.5 V versus Ag/AgCl), a good linearity in the window of 0.037 to 10 microg/mL formaldehyde was observed, and the LOD of 0.23 microg/L was calculated. The RSDs of intraday (n = 10) and interday (n = 6) replicate measurements of 0.185-5 microg/mL formaldehyde ranged from 1.45 to 3.60%, indicating good reproducibility of the proposed method. The proposed method was successfully applied to the determination of formaldehyde in commercial nail polish samples and a drinking water sample.