Application of LFER to pKas and Dipole Moments of 1H and 2H Tautomers of Tetrazole: Mimicking Structure-Function Relation as a Chemical Education Perspective

Structure-function relation is a 155 year old concept to explain the dependence of biological activity of a drug molecule on its structure put forward by Crum-Brown and Fraser*. Similar line of interest is followed in the present work, and it stimulates the understanding of structure-activity relation (SAR) among the graduate students. An attempt is made for the first time from our laboratory to apply the Hammett and Taft equations to a five membered ring system with four nitrogens as heteroatoms viz. tetrazole to identify the aqueous medium 1H and 2H Tautomers. For this purpose experimentally determined aqueous medium pKa values of NH-acidities of a total of fifteen 5-X-1,2,3,4-tetrazoles and DFT/B3LYP method at the 6-31G* level calculated dipole moments of seven 1H and 2H tautomers of 5-X-1,2,3,4-tetrazoles are used to correlate with Hammett para and meta, and Taft _ortho^* values. Good correlations are obtained. The promising response of more abundant and more polar 1H tautomer with less susceptibility (* = -1.38 in pKa correlations and * = -0.55 in dipole moments correlation) to Taft equation and less abundant and less polar 2H tautomer with more susceptibility (para = 6.56, meta = 7.79 in pKa correlations, and para = 2.69, meta = 3.26 in dipole moments correlation) to Hammett equation of the tetrazole is well distinguished. Thus it mimics a principle of structure-function study on a chemical property like the ionization of NH proton of tetrazole and on a physical property like dipole moment for the first time. Therefore finding a way is achieved to get the equilibrium identification of 1H and 2H tautomers without using any expensive and time consuming experimental techniques.

Fuzzy Least Squares Approximation Using Fuzzy Polynomial

In this paper, the fuzzy polynomial is introduced and applied to investigate the least squares approximation problem based on LR fuzzy numbers. A new and simple approach to solve the original problem is constructed by using approximate fuzzy polynomial. Two numerical examples are given to illustrate the proposed method. Since a large number of data exist as an uncertain property and need a function relation to reflect the laws between different variables, our results enrich fuzzy numerical approximation theory.

The challenge of relational referents in early word extensions: Evidence from noun-noun compounds

Young children struggle more with mapping novel words onto relational referents (e.g., verbs) compared to non-relational referents (e.g., nouns). We present further evidence for this notion by investigating children's extensions of noun-noun compounds, which map onto combinations of non-relational referents, i.e., objects (e.g., baby and bottle for baby bottle), and relations (e.g., a bottle FOR babies). We tested two- to five-year-olds’ and adults’ generalisations of novel compounds composed of novel (e.g., kig donka) or familiar (e.g., star hat) nouns that were combined by one of two relations (e.g., donka that has a kig attached (=attachment relation) versus donka that stores a kig (=function relation)). Participants chose between a relational (shared relation) and a non-relational (same colour) match. Results showed a developmental shift from encoding non-relational aspects (colour) towards relations of compound referents, supporting the challenge of relational word referents. Also, attachment relations were more frequently encoded than function relations.