Students’ conceptual understanding of a function and its derivative in an experimental calculus course

Calculus has been witnessing fundamental changes in its curriculum, with an increased emphasis on visualization. This mode for representing mathematical concepts is gaining more strength due to the advances in computer technology and the development of dynamical mathematical software. This paper focuses on the understanding of the function and its derivative as viewed by students of a reformed Calculus 1 course offered in two experimental sections at the Lebanese American University in Beirut, Lebanon. Results have shown that the general approach adopted in the course proved to be unpopular for a great majority of the students, but rewarding for others. Interviews conducted with some students and a study of their performance on very specific exam questions reveal that for most students, the algebraic representation of a function still dominated their thinking; however, these students showed an almost complete understanding of the derivative, particularly the idea of the instantaneous rate of change and/or the slope of a curve at a given point. Furthermore, very few of these students referred to the mechanical methods for finding derivatives.     

Buckling of a stiff thin film on a compliant substrate in large deformation

A finite-deformation theory is developed to study the mechanics of thin buckled films on compliant substrates. Perturbation analysis is performed for this highly nonlinear system to obtain the analytical solution. The results agree well with experiments and finite element analysis in wavelength and amplitude. In particular, it is found that the wavelength depends on the strain. Based on the accurate wavelength and amplitude, the membrane and peak strains in thin films, and stretchability and compressibility of the system are also obtained analytically.     

Novel fixed‐site–carrier polyvinylamine membrane for carbon dioxide capture

Fixed‐site–carrier membranes were prepared for the facilitated transport of CO₂ by casting polyvinylamine (PVAm) on various supports, such as poly(ether sulfone) (PES), polyacrylonitrile (PAN), cellulose acetate (CA), and polysulfone (PSO). The cast PVAm on the support was crosslinked by various methods with glutaraldehyde, hydrochloric acid, sulfuric acid, and ammonium fluoride. Among the membranes tested, the PVAm cast on polysulfone and crosslinked by ammonium fluoride showed the highest selectivity of CO₂ over CH₄ (>1000). The permeance of CO₂ was then measured to be 0.014 m³ (STP)/(m² bar h) for a 20 μm thick membrane. The effect of the molecular weight of PVAm and feed pressure on the permeance was also investigated. The selectivity increased remarkably with increasing molecular weight and decreased slightly with increased pressure in the range of 1 to 4 bar. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4326–4336, 2004     

Polarity control of GaN epilayers grown on ZnO templates

We report the successful growth of Ga-polar GaN epilayers on O-polar ZnO templates pre-deposited on c-sapphire. Prior to GaN growth, NH₃ is exposed onto the ZnO template. The polarity of the GaN layers is confirmed by etching of the surface and by conversion beam electron diffraction (CBED), while the O-polar ZnO is confirmed by CBED. It is suggested that the NH₃ pre-exposure helps form a Zn₃N₂ layer, which possesses inversion symmetry and inverts the crystal from anion polar to cation polar.     

Effective dielectric constant of a medium with spherical inclusions

The Maxwell-Garnett theory is frequently used to predict the effective, or the average, dielectric constant of a mixture composed of spherical inclusions embedded in a host medium. This effective medium theory assumes that the volume fraction occupied by the spherical inclusions is small and that the size of the inclusions is small compared to the wavelength. Experiments using controlled samples have shown that the Maxwell-Garnett theory is applicable up to an inclusion volume fracton of 0.2. At higher volume fractions, the effective dielectric constant appears to be dependent on the inclusion sizes     

Reactor design considerations for MOCVD growth of thin films

Metal-organic chemical vapor deposition (MOCVD) performance is optimized for growing titanium dioxide (TiO₂) thin films. Different gas flow directions and susceptor rotation, along with reactor geometry and shape variations are considered. Gravity proves to be an important parameter in changing the flow pattern in the reaction chamber. However, since film uniformity is not improved by changing the flow direction, modifying the reactor geometry is also proposed. Among the different geometrical parameters, the susceptor-inlet distance, inlet tube diameter, and susceptor size are considered. To minimize the occurrence of recirculation cells in the reaction chamber, modifications in the reactor shape are also suggested. Acceptable results are achieved by changing the cylindrical reactor to a diamond shape     

Run-to-run failure detection and diagnosis using neural networks and Dempster-Shafer theory: an application to excimer laser ablation

The formation of microvias in multilayer substrates is a critical factor in microelectronic packaging manufacturing. Such microstructures can be produced efficiently by excimer laser ablation. Thus, laser ablation systems are evolving to a level where the need to offset high capital equipment investment and lower equipment downtime are imminent. This paper presents a methodology for inline failure detection and diagnosis of the excimer laser ablation process. The methodology employs response data originating directly from the equipment and characterization of microvias formed by the ablation process. Neural network (NN) models are trained and validated based on this data to generate evidential belief for potential sources of deviations in the responses. Dempster-Shafer (D-S) theory is adopted for evidential reasoning. Successful failure detection is achieved in 100% of 19 possible failure scenarios. Moreover, successful failure diagnosis is also achieved with only a single false alarm occurring in the 19 failure scenarios.     

Observation and analysis ofE mesons in\bar p p annihilation at rest in H2 gas

Antiproton-proton annihilation at rest in a gaseous H₂ target at NTP into the final state π⁺ π^? K ^± π^? (K ⁰) with an undetectedK ⁰ or \(\bar K^0 \) has been investigated. We observe theE(1420) resonance in the invariant mass spectrum (K ⁰)_miss K ^± π^? with massM _E =1413±8 MeV/c² and widthГ ^E =62 ± 16MeV/c² and find evidence for the production of thef ₁(1285). The absolute branching ratio of \(\bar p\) p → π⁺ π^? E ⁰,E ⁰ →K ₀ ^L K ^± π ^? at (61±6)%P wave annihilation is (3.0±0.9)·10^?4 of all annihilations. The observed suppression of theE production fromP wave with respect to theS wave together with some simple selection rules suggest that the quantum numbers of theE(1420) areJ ^pc=0^?+ and not I⁺⁺.