Lucas sequences and Fibonacci triads of graphs in PMO calculation on the charge-transfer bands of a series of EDA complexes: Correlation with experimental and AM1 results

The use of Lucas sequences and Fibonacci triads of graphs in a complete PMO calculation on a series of phenols is shown. The results were correlated with charge-transfer absorption maxima of a series of molecular EDA complexes of p-chloranil with these phenols as donors. The correlation brings out the PMO parameters in a straightforward way. The graph theoretical results are also shown to correlate well with the donor ionization potentials calculated by the AM1 method, and this correlation yields a value of the sp²-C Coulomb integral, α, which agrees well with the one obtained from photoelectron spectroscopic results. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 817–825, 1997     

Method for construction of characteristic polynomials via graph linearization

A new method for construction of characteristic polynomials (CP) of complicated graphs having arbitrary edge and vertex weights has been developed. The method first converts the graph into isospectral linear chains with weighted vertices and edges and then builds up the CP coefficients recursively. Two types of graphs have been used for illustration, viz., (i) graphs that can be linearized by symmetry factorization and (ii) graphs without symmetry which are to be linearized by an algorithm involving walks of unit length. Both types have been illustrated, of which type (i) includes the Schlegel of fullerene fragment C₂₀ and another large graph with many fused rings. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65 : 199–204, 1997     

Modelling and system identification of an experimental apparatus for anomaly detection in mechanical systems

This paper presents design, modelling and system identification of a laboratory test apparatus that has been constructed to experimentally validate the concepts of anomaly detection in complex mechanical systems. The test apparatus is designed to be complex in itself due to partially correlated interactions amongst its individual components and functional modules. The experiments are conducted on the test apparatus to represent operations of mechanical systems where both dynamic performance and structural durability are critical.     

A1-homotopy groups,excision, and solvable quotients

We study some properties of ${\mathbb{A}}^1$-homotopy groups: geometric interpretations of connectivity, excision results, and a re-interpretation of quotients by free actions of connected solvable groups in terms of covering spaces in the sense of ${\mathbb{A}}^1$-homotopy theory. These concepts and results are well suited to the study of certain quotients via geometric invariant theory. As a case study in the geometry of solvable group quotients, we investigate ${\mathbb{A}}^1$-homotopy groups of smooth toric varieties. We give simple combinatorial conditions (in terms of fans) guaranteeing vanishing of low degree ${\mathbb{A}}^1$-homotopy groups of smooth (proper) toric varieties. Finally, in certain cases, we can actually compute the “next” non-vanishing ${\mathbb{A}}^1$-homotopy group (beyond ${\pi }_1^{{\mathbb{A}}^1}$) of a smooth toric variety. From this point of view, ${\mathbb{A}}^1$-homotopy theory, even with its exquisite sensitivity to algebro-geometric structure, is almost “as tractable” (in low degrees) as ordinary homotopy for large classes of interesting varieties.     

Vertical ionisation potentials of a number of crown ethers from charge transfer bands of their EDA complexes

Vertical ionisation potentials (I(v)D) of a number of crown ethers, viz. dibenzo-30-crown-10 (Crown 1), benzo-15-crown-5 (Crown 2), dibenzo-24-crown-8 (Crown 3), dicyclohexano-24-crown-8 (Crown 4) and 4'-nitrobenzo-15-crown-5 (Crown 5) are being reported for the first time from a study of EDA interaction of these crown ethers with a number of electron acceptors like C60, C70, o-chloranil, p-chloranil, 2,3-dichloro-5,6-dicyanobenzoquinone (DDQ) and pyromellitic diimide (PMD). The study has been carried out in CCl4 medium by electronic absorption spectroscopy. Charge transfer (CT) absorption bands in the 360-900 nm range have been found in each case (excepting the 60 fullerene-Crown 4 system). The vertical ionisation potentials (I(v)D) of all the crown ethers thus determined show a good correlation with those calculated by the semiempirical AM1 method. Of the six acceptors under study the vertical electron affinity of PMD was not found in the literature. This has also been determined from an analysis of the present h(nu)(CT) data.     

Construction and utilisation of planar graphs of two series of IPR fullerenes through the use of threefold rotational symmetry

Threefold rotational symmetry has been used to develop an algorithm for the construction of planar graphs of IPR fullerenes and to factorize their characteristic polynomials. Two series of fullerenes of the formula C_60+12n and C_60+18n have thus been obtained. The algorithm has been shown to be useful for predicting the nature of variation of the point groups of the fullerenes with increased n, for counting the number of ¹³C nuclear magnetic resonance (NMR) signals (along with their relative intensities), and also for obtaining a large part of their eigenspectra. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Spectroscopic and thermodynamic study of charge transfer interactions of retinol palmitate with [60]- and [70]fullerenes by absorption spectrometric method

Retinol palmitate (1), which is commonly called "Vitamin A palmitate", has been shown to form charge transfer (CT) complexes with a series of electron acceptors including [60]- and [70]fullerenes, and from the trends in CT transition energies the vertical ionization potential of 1 has been estimated to be 7.73eV. Stoichiometries of the fullerene complexes have been shown to be 1(Vitamin 1): 1([70]fullerene) and 1(Vitamin 1): 2([60]fullerene). The enthalpies and entropies of formation of these two complexes have been determined by estimating the formation constants spectrophotometrically at five different temperatures. The complexation phenomenon may be utilised to dissolve the fullerenes in the non-toxic Vitamin A oil and the solution may be used for testing the biological activity of the fullerenes in vivo.     

Shape of the clusters of a percolative system in the presence of tunneling bonds and a finite electric field

We consider a model correlated percolative system on a 2D square lattice with a finite electric field applied accross its two opposite sides. We study the shape of the clusters formed with the addition of a new kind of bond (we call them tunneling bonds) which respond only above a finite threshold voltage. As expected, the clusters do have an overall elongated shape in the-direction of the applied field. Intuitively, one expects the elongation (with the aspect ratio >1) to increased indefinitely with the field. But, in a previous study, we found the model to belong to the same universality clas in the limits of a zero and an infinite electric field. We explain this behavior by studying the change in these elongated shapes as a function of the applied voltage in finite size samples and find that actually the amount of elongation takes on a maximum value at a size (L)-dependent finite voltageV _m (L) and that asV thje overall deviation from isotropy in the field direction tends to zero (i.e., aspect ratio1) again.