NMR spectral analysis of strongly second-order 6-, 8-, 9- and 10- spin-systems (1H─19F, 19F─19F,and 13C─19F) in perfluorotoluyl- and tetrafluoro-pyridyl-aromatics using the lineshape method ANATOLIA

A simple to use nuclear magnetic resonance analysis method has been tested on complex ¹H, ¹⁹F, and ¹³C multiplets. This open-source line-shape analysis method analysis of total lineshape (ANATOLIA)¹ provides some significant advantages over traditional assign-iterate methods of NMR spectral analysis by avoiding false minima and progressing optimisation to the global minimum. The target molecules are 1-perfluorotol-4-yl-2-perfluorotol-4-yl-oxymethyl-1H-benzimidazole (molecule-I) and 1-tetrafluoropyrid-4-yl-2-tetrafluoropyrid-4-yl-thio-1H-benzimidazole (molecule-II) which were produced as part of a family of fluorinated drug scaffolds prepared for anticancer and antiparasitic screening. Spectra display significant second-order effects with ¹H Δδ = 3.68 and 4.67 Hz for the aromatic hydrogen “triplets”, with ¹⁹F ⁴J_AA', ⁴J_BB', ⁴J_XX', and ⁴J_YY' coupling constants range from +4.8 to −14.0 Hz and for ¹³C-isotopomers ¹⁹F Δδ of up to 111.56 Hz. A spin-system of six coupling nuclei (H_aH_bH_cH_d F_YF_Y') was analysed in 12 s, a spin-system of nine coupling fluorine nuclei (AA'BB'CCC-YY') was analysed within 2 min, and 10 coupling nuclei (XX'YY'ZZZ-BB'-H_d) was optimised in 6 min using a laptop computer. ANATOLIA was also robust enough to be able to yield accurate spectral values from inaccurate input values. In both compounds, a fluorine–fluorine coupling constant was identified between the two fluoro-aromatic rings (F_BB' and F_YY') of +4.05 and +4.67 Hz and attributed to a through-space interaction. Ab initio structure optimisations and coupling constant calculations provided useful input data for spectral analysis. A modern ¹⁹F nuclear magnetic resonance spectrum of perfluorotoluene (octafluorotoluene) and analysis from 1975 was used as a test data set to assess ANATOLIA.     

Noncommuting selfmaps and invariant approximations

Common fixed-point results are established for a new class of noncommuting selfmaps. We apply them to obtain several invariant approximation results which unify, extend, and complement well-known results.     

Ab initio Computational Modeling of Glyphosate Analogs: Conformational Perspective

A historical perspective on the application of conformational analysis to structure-based ligand design approach is presented. The application of isodensity molecular electrostatic potential surfaces with the conformational energy surfaces (CES) have allowed us to reach pertinent conclusions for aiding synthetic and biochemical studies. Here we illustrate such an application on the modeling of the potent analogs of an important, environmentally stringent herbicidal compound glyphosate by constructing conformational energy surfaces. The systems were modeled by substituting F, Cl, and NH— OH moiety to the position of pharmacophoric nitrogen center in glyphosate structure. All the calculations were thoroughly performed with ab initio MO theory at Hartree–Fock method using 3-21G(d) basis functions. On the basis of the results, we identified the bioactive conformations for N-fluoro-glyphosate, N-chloro-glyphosate, and N-hydroxyamino-glyphosate as (−38^∘, 77^∘), (−61^∘, 111^∘), and (−167^∘, −169^∘), respectively. Geometry optimization of certain selected conformations of these compounds using hybrid DFT method with 6–31+G(d) basis functions provides nearly equal values of φ and ψ. Moreover, the results indicate that the global minimum structures of N-fluoro and N-chloro analogs of glyphosate show cyclic conformation whereas the N-hydroxyamino-glyphosate global minimum structure shows spyrocyclic and zig-zag conformation. Also, the predicted bioactive conformation of N-hydroxyamino analog optimally overlaps with glyphosate backbone in EPSPS complex with 0.1 Å RMSD value. However, the other two compounds slightly deviate from the backbone of glyphosate with RMSD of 0.92 Å for N-fluoro-glyphosate and 0.83 Å for N-chloro-glyphosate. The linear N-hydroxyamino-glyphosate exhibits relatively more number of intermolecular hydrogen bond interactions as compared to the other two analogs. Further, comparison of CES of previously studied glyphosate analogs such as N-hydroxy-glyphosate (2.2 μM) and N-amino-glyphosate (0.61 μM) with the present systems reveals the order of activity as: N-hydroxyamino-glyphosate > N-fluoro-glyphosate > N-chloro-glyphosate based on CES flexibility. Also, the calculated heats of formation of N-fluoro-glyphosate, N-chloro-glyphosate, and N-hydroxyamino-glyphosate are −288, −209, and −288 kcal/mol, respectively, which clearly indicate that the N-hydroxyamino and N-fluoro analogs of glyphosate are thermodynamically more stable than N-amino-glyphosate (−278 kcal/mol).     

The raised-cosine wavelets in computerized tomography

In Computerized Tomography (CT), an image must be recovered from its sampled projections in the form of values of the Radon transform. In this work a method of recovering the image is based on the properties of the raised-cosine wavelet. This wavelet has a closed form which allows for certain precomputations and avoids convolution. The rate of convergence of the resulting algorithm to the image density function is found under suitable hypotheses. This algorithm is then tested on the standard Shepp–Logan     

Polynomials: a theme which should not be forgotten

There is a definite movement to remove many of the topics concerning polynomials from the school curriculum. The purpose of this paper is to point out why this movement is misguided and should be reversed.     

Double Suzuki cross‐coupling reaction of pyrimidine boronic acid: synthesis of new versatile dielectrophile

The double Suzuki cross‐coupling reaction has successfully been applied for the synthesis of 5,5′‐(5‐butoxy‐1,3‐phenylene)bis(2‐chloropyrimidine) with two reactive chloro groups and an alkoxy side chain starting from 2‐chloropyrimidin‐5‐ylboronic acid and 1,3‐dibromo‐5‐butoxybenzene. The reactivity of this dielectrophile was tested by reaction with aniline and phenol, a nitrogen and oxygen nucleophile, respectively. The new dielectrophile would further provide an ideal platform for the construction of large hetero‐atom bridged macrocycles for desired properties and functions in supramolecular and material chemistry. Copyright © 2012 John Wiley & Sons, Ltd.     

Mathematical attitudes and semantic differentials

The semantic differential—one approach to attitude measurement— basically records a combination of a person's associations with a particular concept with a scaling procedure. This paper considers the implications of such a device for teachers of mathematics.     

Nitrogen dissociation and its excitation/vibrational temperature with hydrogen admixture in 50 Hz DC discharge

Trace rare gas optical emission spectroscopy (TRG-OES) is carried out to determine the excitation temperature, vibrational temperature, dissociation fraction and nitrogen (N) atom density in 50?Hz active screen cage nitrogen plasma, as a function of discharge parameters (current density and fill pressure) and hydrogen concentrations. The excitation temperature is determined from Ar–I emission lines and is found to increase with hydrogen mixing. In a similar fashion, the vibrational temperature of second positive system is determined and found to have increasing trend with hydrogen addition. The dissociation fraction increases with hydrogen concentration up to 40% H₂ in the nitrogen plasma, so as the nitrogen atom density.     

Synthetic approaches toward stilbenes and their related structures

Compounds belonging to the stilbene family have gained remarkable significance in pharmaceutical as well as material chemistry. The current review covers the various synthetic approaches for the syntheses of stilbene scaffold and related structures over last 30 years. In addition, this review also highlights the role of stilbene intermediates used in the synthesis of important molecules with diverse applications in the field of pharmaceutics and material science.