Modelling truck camper production

This note describes an interdisciplinary project designed to enhance students’ knowledge of the basic techniques taught in a multivariable calculus course. The note discusses the four main requirements of the project and then the solutions for each requirement. Concepts covered include differentials, gradients, Lagrange multipliers, constrained and unconstrained optimization, level curves (isoquants and isocosts), marginal revenue and cost, the law of diminishing returns, marginal productivity, and inventory control.     

The pure rotational spectra of the two lowest energy conformers of the asymmetric ether C4H9OC2H5

An experimental study has been performed shedding light on the conformational energies of the asymmetric ether n-butyl ethyl ether. Rotational spectroscopy between 7.8 GHz and 16.2 GHz has identified two conformers of n-butyl ethyl ether, C₄H₉OC₂H₅. In these experiments spectra were observed as the target compound participated in an argon expansion from high to low pressure causing molecular rotational temperatures to be below 4 K. For one conformer, 95 pure rotational transitions have been recorded, for the second conformer, 20 pure rotational transitions were recorded. Rotational constants and centrifugal distortion constants are presented for both butyl ethyl ether conformers. The structures of both conformers have been identified by exploring the multi-dimensional molecular potential energy surface using ab initio calculations. From the numerous low energy conformers identified using ab initio methods, the three lowest conformers were pursued at increasingly higher levels of theory, i.e. complete basis set extrapolations, coupled cluster methods, and also taking into consideration zero point vibrational energies. The two conformers observed experimentally are only revealed to be the two lowest energy conformers when high levels of quantum chemical methodologies are employed.     

Establishing Validity of the Thai Mathematics Teaching Efficacy Beliefs Instrument

This article presents our work in translating the Mathematics Teaching Efficacy Beliefs Instrument (MTEBI) from English to Thai and our resulting investigation of validity with Thai preservice teachers. The translation process occurred over several meetings between two U.S. mathematics educators and one Thai mathematics educator. To check for reliability the instrument was translated into Thai, back‐translated into English, and then cognitive interviews were conducted with native Thai speakers to check for accuracy, meaning, and readability. We used the newly translated Thai‐Mathematics Teaching Efficacy Beliefs Instrument (T‐MTEBI) to measure teacher efficacy beliefs as they related to Thai preservice mathematics teachers. Eight of the questions measure Mathematics Teaching Outcome Expectancy (MTOE). The mean of the scores on these questions was computed to form a MTOE score for each student. The remaining 13 questions measure Personal Mathematics Teaching Efficacy (PMTE). The mean of these scores was computed to obtain the PMTE score for each student. The mean of all 21 questions was computed to find an overall efficacy score for each student. The results of this study showed that the newly constructed T‐MTEBI produced reliability and validity measures comparable to the original MTEBI (Enochs, Smith, & Huinker, 2000).     

Characterization of Volatile Nylon 6.6 Thermal-Oxidative Degradation Products by Selective Isotopic Labeling and Cryo-GC/MS

Aged materials, such as polymers, can exhibit modifications to their chemical structure and physical properties, which may render the material ineffective for its intended purpose. Isotopic labeling was used to characterize low-molecular weight volatile thermal-oxidative degradation products of nylon 6.6 in an effort to better understand and predict changes in the aged polymer. Headspace gas from aged (up to 243 d at 138?°C) nylon 6.6 monomers (adipic acid and 1,6-hexanediamine) and polymer were preconcentrated, separated, and detected using cryofocusing gas chromatography mass spectrometry (cryo-GC/MS). Observations regarding the relative concentrations observed in each chromatographic peak with respect to aging time were used in conjunction with mass spectra for samples aged under ambient air to determine the presence and identity of 18 degradation products. A comparison of the National Institute of Standards and Technology (NIST) library, unlabeled, and isotopically labeled mass spectra (C-13 or N-15) and expected fragmentation pathways of each degradation product were used to identify the location of isotopically labeled atoms within the product's chemical structure, which can later be used to determine the exact origin of the species. In addition, observations for unlabeled nylon 6.6 aged in an O-18 enriched atmosphere were used to determine if the source of oxygen in the applicable degradation products was from the gaseous environment or the polymer. Approximations for relative isotopic ratios of unlabeled to labeled products are reported, where appropriate.     

Ab initio treatment of the chemical reaction precursor complex Cl(2P)-HF. 1. Three-dimensional diabatic potential energy surfaces

The three adiabatic potential surfaces of the Cl(2P)-HF complex that correlate with the 2P ground state of the Cl atom were calculated with the ab initio RCCSD(T) method (partially spin-restricted coupled cluster theory including single and double excitations and perturbative correction for the triples). With the aid of a geometry-dependent diabatic mixing angle, calculated by the complete active space self-consistent field (CASSCF) and multireference configuration-interaction (MRCI) methods, these adiabatic potential surfaces were converted to a set of four distinct diabatic potential surfaces required to define the full 3 x 3 matrix of diabatic potentials. Each of these diabatic potential surfaces was expanded in terms of the appropriate spherical harmonics in the angle theta between the HF bond axis r and the Cl-HF intermolecular axis R. The dependence of the expansion coefficients on the Cl-HF distance R and the HF bond length r(HF) was fit to an analytic form. The strongest binding occurs for the hydrogen-bonded linear Cl-HF geometry, with D(e) = 676.5 cm(-1) and R(e) = 6.217 a0 when r(HF) = r(e) = 1.7328 a0. This binding energy D(e) depends strongly on r(HF), with larger r(HF) causing stronger binding. An important contribution to the binding energy is provided by the interaction between the quadrupole moment of the Cl(2P) atom and the dipole of HF. In agreement with this electrostatic picture, the ground state of linear Cl-HF is a 2-fold degenerate electronic Pi state. For the linear Cl-FH geometry the states are in opposite order, i.e., the Sigma state is lower in energy than the Pi state. The following paper in this issue describes full three-dimensional computations of the bound states of the Cl-HF complex, based on the ab initio diabatic potentials of this paper.     

Synthesis of novel pyrazoles via [2+3]-dipolar cycloaddition using alkyne surrogates

The syntheses of an important class of hitherto unreported novel pyrazoles are described. The regioselective synthesis of 1,3,4,5-tetrasubstituted pyrazoles was achieved by the Huisgen cyclization of nitrile imines with a trisubstituted bromoalkene. The substituted bromoalkene functions as an alkyne synthon which was used to construct 5,5-disubstituted bromopyrazoline intermediates that undergo aromatization to the analogous pyrazoles through the loss of HBr. The cycloaddition regioselectivity was confirmed through single X-ray crystal data of one of the pyrazoles.     

Continuous precipitation polymerization of vinylidene fluoride in supercritical carbon dioxide: molecular weight distribution

The surfactant-free precipitation polymerization of vinylidene fluoride (VF2) in supercritical carbon dioxide was studied in a continuous stirred autoclave. The polymerization temperature ranged from 65 to 85°C, the average residence time in the reactor varied from 10 to 50 min., and the pressure was between 210 and 305 bar. Diethyl peroxydicarbonate was used as the initiator. The fractional conversion of monomer varied from 7 to 26%, the number-average molecular weight of the polymer was between about 14,000 and 79,000, and the weight-average molecular weight was between about 21,000 and 700,000. In many cases, the polymer exhibited a bimodal molecular-weight distribution, especially at high monomer concentrations.