Conceptual metaphors for isomorphism and homomorphism: Instructors’ descriptions for themselves and when teaching

Group isomorphism and homomorphism are topics central to abstract algebra, yet research on instructors’ views of these concepts is limited. Based on interviews from two instructors as well as classroom video from eight class periods, this paper examines the language used to discuss isomorphism and homomorphism. Language used by instructors in interviews and classroom settings are identified and classified into four main categories: formal definition, mapping, sameness, and combinations of sameness and mapping language. How the two instructors drew on language classified into those four categories in the interview and instruction settings are examined for isomorphism and homomorphism. Similarities and differences between the interview and instruction contexts reveal the wide variety of ways of understanding isomorphism and homomorphism as well as a research need to examine mathematicians’ content knowledge in more than one context.     

有机化学实验混合教学模式的设计与实践

通过介绍混合教学模式在有机化学实验课程教学中的设计、实施情况及效果评价与反馈等内容,与大家分享混合教学模式在有机化学实验课程教学中的应用经验与思考。     

HPLC-PDA analysis of ACE-inhibitors,hydrochlorothiazide and indapamide utilizing design of experiments

A simple, rapid, precise, accurate and sensitive high performance liquid chromatographic method has been developed for simultaneous determination of ACE inhibitors with hydrochlorothiazide and indapamide in pharmaceutical formulations. ‘Design of Experiments’ (DoE) using ‘central composite design’ (CCD) was applied to facilitate method development and optimization. Mobile phase was optimized utilizing response surface methodology using Design Expert software. Chromatographic separation was achieved on Hypersil®-Gold C₁₈ (100 × 4.6 mm, 3 μm, Thermo Fisher Scientific, USA), column at 25 °C. The mobile phase was 58% buffer (5 mM KH₂PO₄, containing triethylamine 0.25 ml/L), 25% acetonitrile and 17% methanol (pH adjusted to 2.8 ± 0.1). The analysis was performed at 215 nm. The mobile phase flow rate was 1.0 ml/min and injection volume 10 μl. The method was validated for linearity, limits of quantitation and detection, accuracy, precision, ruggedness and robustness as per the International Conference on Harmonization (ICH) guidelines. Calibration curves (for lisinopril, hydrochlorothiazide, captopril, imidapril, perindopril, indapamide and trandolapril) were linear in the concentration range of 5–35 μg/ml. The limit of detection and limit of quantitation for experimental drugs ranged from 0.03 to 0.61 and 0.08–1.84 μg/ml respectively.     

吡嗪类化合物的合成及其抗血小板凝集活性测试

为提高川芎嗪的抗血小板凝集活性,分别以不同的二胺、2,3-丁二酮和硫辛酸为起始原料,采用溴代、水解、环化、氧化、氢化、取代等反应,通过四条路线合成了7个川芎嗪衍生物,其结构经1H NMR、13C NMR及ESI-MS确证。采用Born比浊法初步测试了化合物的体外抗血小板凝集活性,结果显示,化合物1(IC50=0. 26mmol/L)、2(IC50=0. 27mmol/L)和7(IC50=0. 21mmol/L)对由二磷酸腺苷(ADP)诱导的血小板凝集具有一定的抑制活性,优于先导化合物川芎嗪(IC50=0. 49mmol/L)。因此,在不改变川芎嗪药效团的前提下对其进行不同程度的环化,能明显提高川芎嗪的抗血小板凝集活性,此研究为后期化合物的结构修饰提供了一定的参考价值。     

The impact of a conceptual model-based mathematics computer tutor on multiplicative reasoning and problem-solving of students with learning disabilities

The study explored the impact of Please Go Bring Me-COnceptual Model-based Problem Solving (PGBM-COMPS) computer tutoring system on multiplicative reasoning and problem solving of students with learning disabilities. The PGBM-COMPS program focused on enhancing the multiplicative reasoning and problem solving through nurturing fundamental mathematical ideas and moving students above and beyond the concrete level of operation. This is achieved by taking advantages of the constructivist approach from mathematics education and explicit conceptual model-based problem solving approach from special education. Participants were three elementary students with learning disabilities (LD). A mixed method design was employed to investigate the effect of the PGBM-COMPS program on enhancing students’ multiplicative reasoning and problem solving. It was found that the PGBM-COMPS program significantly improved participating students’ problem solving performance not only on researcher developed criterion tests but also on a norm-referenced standardized test. Qualitative and quantities data from this study indicate that, in addition to nurturing fundamental concept of composite units, it is necessary to help students to understand underlying problem structures and move toward mathematical model-based problem representation and solving for generalized problem solving skills.     

Block designs signed over groups of order 2n3m

We introduce a new piecewise construction technique for generalised Bhaskar Rao designs and the concepts of generalised Bhaskar Rao block design pieces and holey generalised Bhaskar Rao block designs. We prove composition theorems for these designs. Using this construction technique and the theory of group representations, and the representations of $2$-groups over the field with $3$ elements, we show that the established necessary conditions for the existence of generalised Bhaskar Rao designs of block size $3$ are sufficient for all groups of order $2^n{3}^m$.     

A Tailored Versatile and Efficient NHC-Based NNC-Pincer Manganese Catalyst for Hydrogenation of Polar Unsaturated Compounds

The reactivity of metal-hydride complexes can be harnessed by the modification of ancillary ligands. With the aim of improving the hydride-donor ability of the key Mn−H intermediate and reducing steric hindrance, we herein report the rational design of a versatile and efficient NHC-based NNC-pincer Mn catalyst for hydrogenation reactions. This newly developed catalyst exhibited higher activity than the corresponding NNP-pincer Mn catalyst owing to its reduced steric hindrance and enhanced Mn−H σ-bonding orbital energy level through a π-antibonding interaction. Using this highly active NNC-pincer Mn catalyst, a rich array of polar unsaturated compounds (>80 examples) including esters, N-heteroarenes, amides, carbonates, and urea derivatives, were successfully hydrogenated under relatively mild conditions. This work represents a rare example of a general phosphine-free Mn-catalyzed hydrogenation system.     

Electrocatalytic Synthesis of Nylon-6 Precursor at Almost 100 % Yield

Synthesis of cyclohexanone oxime via the cyclohexanone-hydroxylamine process is widespread in the caprolactam industry, which is an upstream industry for nylon-6 production. However, there are two shortcomings in this process, harsh reaction conditions and the potential danger posed by explosive hydroxylamine. In this study, we presented a direct electrosynthesis of cyclohexanone oxime using nitrogen oxides and cyclohexanone, which eliminated the usage of hydroxylamine and demonstrated a green production of caprolactam. With the Fe electrocatalysts, a production rate of 55.9 g h⁻¹ g_cat⁻¹ can be achieved in a flow cell with almost 100 % yield of cyclohexanone oxime. The high efficiency was attributed to their ability of accumulating adsorbed hydroxylamine and cyclohexanone. This study provides a theoretical basis for electrocatalyst design for C−N coupling reactions and illuminates the tantalizing possibility to upgrade the caprolactam industry towards safety and sustainability.     

Development,stability-indicating assessment,and evaluation of influential method conditions using a full factorial design for the determination of Nintedanib esylate-related impurities

The design of an appropriate analytical method for assessing the quality of pharmaceuticals requires a deep understanding of science, and risk evaluation approaches are appreciated. The current study discusses how a related substance method was developed for Nintedanib esylate. The best possible separation between the critical peak pairs was achieved using an X-Select charged surface hybrid Phenyl Hexyl (150 × 4.6) mm, 3.5 μm column. A mixture of water, acetonitrile, and methanol in mobile phase-A (70:20:10) and mobile phase-B (20:70:10), with 0.1% trifluoroacetic acid and 0.05% formic acid in both eluents. The set flow rate, wavelength, and injection volumes were 1.0 ml/min, 285 nm, and 5 μl, respectively, with gradient elution. The method conditions were validated as per regulatory requirements and United States Pharmacopeia general chapter < 1225 >. The correlation coefficient for all impurities from the linearity experiment was found to be > 0.999. The % relative standard deviation from the precision experiments ranged from 0.4 to 3.6. The mean %recovery from the accuracy study ranged from 92.5 to 106.5. Demonstrated the power of the stability-indicating method through degradation studies; the active drug component is more vulnerable to oxidation than other conditions. Final method conditions were further evaluated using a full-factorial design. The robust method conditions were identified using the graphical optimization from the design space.     

Synthetic Advantages of Defluorinative C−F Bond Functionalization

Much progress has been made in the development of methods to both create compounds that contain C−F bonds and to functionalize C−F bonds. As such, C−F bonds are becoming common and versatile synthetic functional handles. This review summarizes the advantages of defluorinative functionalization reactions for small molecule synthesis. The coverage is organized by the type of carbon framework the fluorine is attached to for mono- and polyfluorinated motifs. The main challenges, opportunities and advances of defluorinative functionalization are discussed for each class of organofluorine. Most of the text focuses on case studies that illustrate how defluorofunctionalization can improve routes to synthetic targets or how the properties of C−F bonds enable unique mechanisms and reactions. The broader goal is to showcase the opportunities for incorporating and exploiting C−F bonds in the design of synthetic routes, improvement of specific reactions and advent of new methods.