Three types of mathematical representational translations: Comparing empirical and theoretical results

Previous research has investigated the representational translation practices of high school students, high school teachers, and college preservice teachers in various mathematical contexts including linear functions. Findings from qualitative research has frequently led to new notions about participant work and understanding. Many quantitative research has investigated the degree to which some in these populations correctly perform these translations. However, it seems that only infrequently have empirical research investigated findings from qualitative studies and vice versa, and findings regarding one population are rarely compared with findings of another population. This study (a) empirically explores the frequency of success of preservice teachers (N = 80) regarding representational translations in the context of linear functions, (b) quantifies results from previous qualitative, literature‐based research regarding high school students and teachers, and (c) quantitatively compares the results. This study demonstrates that some mathematical representational translations are more difficult than others.     

The effects of temperature and frequency on the magnetization switching mode in circular MI sensors

This paper presents results computed using a meshless method in a point collocation formulation to investigate the effects of temperature and frequency on the magnetization switching mode in the circular amorphous magneto-impedance sensor (element). Specifically, the solutions characterizing the MI effect are solved from a set of coupled nonlinear equations consisting of the Maxwell’s equations, the Landau-Lifshitz-Gilbert equation, and the thermal diffusion equation. This coupled nonlinear space-time model predicts the formation and propagation of dynamic domain walls in switching and it is shown how they contribute to experimentally observed temperature and frequency effects. Computed results (that agree well with reported experimental data) suggest radial domain walls may play a larger role in the MI effect than originally believed even for the realistic conditions considered here at 1 MHz or more.     

Chemical Derivatization and Characterization of Novel Antitrypanosomals for African Trypanosomiasis

The search for novel antitrypanosomals and the investigation into their mode of action remain crucial due to the toxicity and resistance of commercially available antitrypanosomal drugs. In this study, two novel antitrypanosomals, tortodofuordioxamide (compound 2) and tortodofuorpyramide (compound 3), were chemically derived from the natural N-alkylamide tortozanthoxylamide (compound 1) through structural modification. The chemical structures of these compounds were confirmed through spectrometric and spectroscopic analysis, and their in vitro efficacy and possible mechanisms of action were, subsequently, investigated in Trypanosoma brucei (T. brucei), one of the causative species of African trypanosomiasis (AT). The novel compounds 2 and 3 displayed significant antitrypanosomal potencies in terms of half-maximal effective concentrations (EC₅₀) and selectivity indices (SI) (compound 1, EC₅₀ = 7.3 μM, SI = 29.5; compound 2, EC₅₀ = 3.2 μM, SI = 91.3; compound 3, EC₅₀ = 4.5 μM, SI = 69.9). Microscopic analysis indicated that at the EC₅₀ values, the compounds resulted in the coiling and clumping of parasite subpopulations without significantly affecting the normal ratio of nuclei to kinetoplasts. In contrast to the animal antitrypanosomal drug diminazene, compounds 1, 2 and 3 exhibited antioxidant absorbance properties comparable to the standard antioxidant Trolox (Trolox, 0.11 A; diminazene, 0.50 A; compound 1, 0.10 A; compound 2, 0.09 A; compound 3, 0.11 A). The analysis of growth kinetics suggested that the compounds exhibited a relatively gradual but consistent growth inhibition of T. brucei at different concentrations. The results suggest that further pharmacological optimization of compounds 2 and 3 may facilitate their development into novel AT chemotherapy.     

Nanomolar fluorescent detection of c-di-GMP using a modular aptamer strategy

C-di-GMP regulates important processes involved in biofilm formation and virulence factors production in several bacteria. Herein we report a simple fluorescent strategy that allows for the detection of c-di-GMP (as low as 320 nM) using a Vc2 class I riboswitch domain as the sensing region and spinach as the fluorescent reporting module.     

Lost in Translation: Examining Translation Errors Associated With Mathematical Representations

Translation errors and conceptual misunderstandings made by students translating among graphical, tabular, and symbolic representations of linear functions were examined. The study situated student errors in the context of the “Translation‐Verification Model” developed specifically for the purpose of explaining student behavior during the process of translating relationships from one mathematical representation to another. Three distinct error types were identified to explain student performance. An examination of the error types revealed that specific translation errors tend to occur at different stages of the translation process. Translation errors are also related to “attribute density,” the amount of information inherently encoded in a given representation. The findings of the study have implications for teaching linear relationships—student weaknesses and strengths are identified.     

Response Surface Methodology: Photocatalytic Degradation Kinetics of Basic Blue 41 Dye Using Activated Carbon with TiO2

Water decontamination still remains a major challenge to some developing countries not having centralized wastewater systems. Therefore, this study presents the optimization of photocatalytic degradation of Basic Blue 41 dye in an aqueous medium by an activated carbon (AC)-TiO₂ photocatalyst under UV irradiation. The mesoporous AC-TiO₂ synthesized by a sonication method was characterized by X-ray diffraction (XRD) and Fourier-transform infrared (FTIR) spectroscopy for crystal phase identification and molecular bond structures, respectively. The efficiency of the AC-TiO₂ was evaluated as a function of three input variables viz. catalyst load (2–4 g), reaction time (15–45 min) and pH (6–9) by using Box-Behnken design (BBD) adapted from response surface methodology. Using color and turbidity removal as responses, a 17 run experiment matrix was generated by the BBD to investigate the interaction effects of the three aforementioned input factors. From the results, a reduced quadratic model was generated, which showed good predictability of results agreeable to the experimental data. The analysis of variance (ANOVA), signposted the selected models for color and turbidity, was highly significant (p < 0.05) with coefficients of determination (R²) values of 0.972 and 0.988, respectively. The catalyst load was found as the most significant factor with a high antagonistic impact on the process, whereas the interactive effect of reaction time and pH affected the process positively. At optimal conditions of catalyst load (2.6 g), reaction time (45 min), and pH (6); the desirability of 96% was obtained by a numerical optimization approach representing turbidity removal of 93% and color of 96%.     

Comparison of one- and two-dimensional detectors on simulated and spin-stand readback waveforms

Shingled writing (SW) and two-dimensional magnetic recording (TDMR) are two complementary candidate technologies proposed to extend the life of magnetic recording. SW enables the writing of narrow tracks with a wider writer by shingling the tracks; each track partially overlaps the preceding track leaving only a fraction of that track on the medium. TDMR is the companion technology to SW that enables reading of narrower tracks with a wider reader. In this work we compare the performances of 1D and 2D detectors in the shingled writing environment, using both comprehensive channel models and spin-stand readback.