Designing the Molybdopterin Core through Regioselective Coupling of Building Blocks

Molybdopterin is an essential cofactor for all forms of life. The cofactor is composed of a pterin moiety appended to a dithiolene‐functionalized pyran ring, and through the dithiolene moiety it binds metal ions. Different synthetic strategies for dithiolene‐functionalized pyran precursors that have been designed and synthesized are discussed. These precursors also harbor 1,2‐diketone or osone functionality that has been condensed with 1,2‐diaminobenzene or other heterocycles resulting in several quinoxaline or pterin derivatives. Use of additives improves the regioselectivity of the complexes. The molecules have been characterized by ¹H and ¹³C NMR and IR spectroscopies, as well as by mass spectrometry. In addition, several compounds have been crystallographically characterized. The geometries of the synthesized molecules are more planar than the geometry of the cofactor found in proteins.     

Indium-mediated propargylation of imines and imine oxides in aqueous media: propargylation of CN- centres

The indium-catalysed coupling of propargyl bromide with a variety of imines and imine oxides afforded the corresponding propargylated products in high yields under mild conditions.     

Geodesic flows, bi-Hamiltonian structure and coupled KdV type systems

We show that all the Antonowicz-Fordy type coupled KdV equations have the same symmetry group and similar bi-Hamiltonian structures. It turns out that their configuration space is , where is the Bott-Virasoro group of orientation preserving diffeomorphisms of the circle, and all these systems can be interpreted as equations of a geodesic flow with respect to L² metric on the semidirect product space .     

Sugar-thioacetamide backbone in oligodeoxyribonucleosides for specific recognition of nucleic acids

The amide linkage being shorter than the natural phosphate linkage, an additional atom is introduced into oligodeoxyribonucleosides (ODNs) with sugar-thioacetamide backbone that show very good RNA recognition properties.     

Heat flow and a faster algorithm to compute the surface area of a convex body

We draw on the observation that the amount of heat diffusing outside of a heated body in a short period of time is proportional to its surface area, to design a simple algorithm for approximating the surface area of a convex body given by a membership oracle. Our method has a complexity of O^*(n⁴), where n is the dimension, compared to O^*(n⁸) for the previous best algorithm. We show that our complexity cannot be improved given the current state‐of‐the‐art in volume estimation. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 43, 407–428, 2013     

Singular Lagrangian, Hamiltonization and Jacobi last multiplier for certain biological systems

We study the construction of singular Lagrangians using Jacobi’s last multiplier (JLM). We also demonstrate the significance of the last multiplier in Hamiltonian theory by explicitly constructing the Hamiltonian of the Host-Parasite model and a Lotka-Volterra mutualistic system, both of which are well known first-order systems of differential equations arising in biology.     

Inverse analysis of an internal reforming solid oxide fuel cell system using simplex search method

An inverse problem is solved for estimating fuel cell operating parameters such as current density, pressure and fuel flow rate (FFR) separately and then simultaneously two parameters in an internal reforming solid oxide fuel cell (IRSOFC). Initially, a mathematical model for the forward problem is developed to simulate the IRSOFC steady state operation and its performance in terms of power output and then an inverse problem is solved for recovering the above parameters using a simplex search minimization algorithm. The objective function (IRSOFC power) and the estimation accuracy are studied for the effects of initial guess values of the operating parameters and the number of iterations required for retrieval of these parameters. The objective function is represented by the sum of square of the error between a given IRSOFC power and the power evaluated based on some arbitrary guessed values of the unknowns which is then regularized in an iterative manner for solution of the inverse fuel cell problem. The study reveals that a multiple combinations of parameters (current density, operating pressure and FFR) exist which provides guidelines for selecting feasible combinations of these parameters required for meeting a given power requirement. The results show relatively good agreement between the inverse and exact solutions.     

Self‐Assembled Discrete Molecules for Sensing Nitroaromatics

Efficient sensing of trace amount nitroaromatic (NAC) explosives has become a major research focus in recent time due to concerns over national security as well as their role as environment pollutants. NO₂‐containing electron‐deficient aromatic compounds, such as picric acid (PA), trinitrotoluene (TNT), and dinitrotoluene (DNT), are the common constituents of many commercially available chemical explosives. In this article, we have summarized our recent developments on the rational design of electron‐rich self‐assembled discrete molecular sensors and their efficacy in sensing nitroaromatics both in solution as well as in vapor phase. Several π‐electron‐rich fluorescent metallacycles (squares, rectangles, and tweezers/pincers) and metallacages (trigonal and tetragonal prisms) have been synthesized by means of metal–ligand coordination‐bonding interactions, with enough internal space to accommodate electron‐deficient nitroaromatics at the molecular level by multiple supramolecular interactions. Such interactions subsequently result in the detectable fluorescence quenching of sensors even in the presence of trace quantities of nitroaromatics. The fascinating sensing characteristics of molecular architectures discussed in this article may enable future development of improved sensors for nitroaromatic explosives.     

Temperature-dependent vibrational spectroscopic studies of pure and gold nanoparticles dispersed 4-n-Hexyloxy-4’-cyanobiphenyls

Raman spectra of pure and 2 wt.% gold nanoparticles (GNPs) dispersed liquid crystalline compound 4-n-Hexyloxy-4?- cyanobiphenyls (6OCB) has been recorded as a function of temperature from room temperature (solid crystal) to 80°C (isotropic liquid) in the spectral region of 500–2500 cm^?1. The variation of Raman spectral parameters (peak positions and line width) with temperature is used to explain the changes in molecular alignment and its effect on inter-/intra-molecular interactions at crystal-Nematic (K-N) transition. To understand the change in molecular structure during phase transition and on account of dispersion of gold nanoparticles in pure liquid crystal more precisely, two spectral regions 1000–1500 cm^?1 and 1500–2400 cm^?1 have been selected separately. From the detailed study, it is concluded that increased orientational/vibrational freedom of the molecules as well as delocalisation of electron clouds results in the spectral anomalies at K-N transition. The geometrical structure of 6OCB was optimised using density functional theory (DFT) and theoretical Raman spectra have been obtained for comparison with experimental spectra. The tentative assignment of vibrational modes observed in our region of study was calculated based on potential energy distribution (PED) using vibrational energy distribution analysis (VEDA) calculation.