Correlation and volatility in an Indian stock market: A random matrix approach

We examine the volatility of an Indian stock market in terms of correlation of stocks and quantify the volatility using the random matrix approach. First we discuss trends observed in the pattern of stock prices in the Bombay Stock Exchange for the three-year period 2000–2002. Random matrix analysis is then applied to study the relationship between the coupling of stocks and volatility. The study uses daily returns of 70 stocks for successive time windows of length 85 days for the year 2001. We compare the properties of matrix C of correlations between price fluctuations in time regimes characterized by different volatilities. Our analyses reveal that (i) the largest (deviating) eigenvalue of C correlates highly with the volatility of the index, (ii) there is a shift in the distribution of the components of the eigenvector corresponding to the largest eigenvalue across regimes of different volatilities, (iii) the inverse participation ratio for this eigenvector anti-correlates significantly with the market fluctuations and finally, (iv) this eigenvector of C can be used to set up a Correlation Index, CI whose temporal evolution is significantly correlated with the volatility of the overall market index.     

Effect of formal CH/P exchange on tandem Cope rearrangement and [2 + 2] cycloaddition of cis-1,2-diethylnylcyclopropane and its mono-hetero analogues

Abstract

Effect of formal one and two CH/P exchange(s) on tandem Cope rearrangement and [2?+?2] cycloaddition of cis-1,2-diethylnylcyclopropane and its mono-hetero analogues has been investigated theoretically in the gas phase at the DFT (B3LYP/6-31+G(d)) level. The activation free energy for the first step, i.e., Cope rearrangement decreases successively on replacing one and two CH moieties of cis-1,2-diethylnylcyclopropane and its mono-hetero analogues with P atom(s), which could be rationalized on the basis of weaker C?=?P π bond than C?=?C π bond. However, this trend is not maintained in the second step, i.e. [2?+?2] cycloaddition of the initially formed intermediate; instead, the activation free energy for monophospha- and diphospha- analogues is slightly higher, which may be attributed to the lesser stability of monophospha- and diphosphacyclobutene rings than cyclobutene. The CASSCF calculations indicate that except the intermediates generated from the Cope rearrangement of cis-diethynylthiirane and cis-bis(phosphaethynyl)cyclopropane which are expected to follow concerted mechanism for the [2?+?2] cycloaddition, in all other cases, apparently, there is no preference for the concerted or stepwise mechanism. Inclusion of the dispersion correction in the DFT functional does not cause significant changes in energetics.     

Extractive spectrophotometric determination of tungsten(VI) using 3-hydroxy-2-(2'-thienyl)-4-oxo-4H-1-benzopyran

A simple, rapid, highly sensitive and selective spectrophotometric method for the determination of tungsten(VI) in trace amounts is developed using 3-hydroxy-2-(2'-thienyl)-4-oxo-4H-1-benzopyran (HTB) as a reagent for the complexation of metal ion and extracting the 1:2 (metal:ligand) complex into dichloromethane from 0.2 M HCl solution. It obeys Beer's law in the range 0-2.8 microg Wml(-1) with molar absorptivity and Sandell's sensitivity at 415 nm as 6.45 x 10(4) L mol(-1) cm(-1) and 0.0029 microg W(VI) cm(-2), respectively. The method is free from the interference of a large number (39) of elements and handles satisfactorily the analysis of various samples of varying complexity.     

SWKB Approach to Confined Isospectral Potentials

Recently we had formulated the supersymmetric Wentzel–Kramers–Brillouin (SWKB) quantization rule for one-dimensional confined quantum systems and applied the same to two trigonometric potentials, tangentially limited by infinite walls at x=0 and x=L, viz., V(x)=V ₀cot²(x/L) and the Pöschl–Teller potential, V(x)=V ₀₁cosec²({x/(2L))}+V ₀₂sec²(x/(2L)). Both the potentials have received quite a lot of attention by various authors because of their importance in molecular physics. Though these potentials have been studied in the framework of WKB, BS (Bohr–Sommerfeld), mBS (matrix formulation of BS) formalisms, it was observed that the supersymmetric approach not only rendered the calculations simpler and more transparent, it also reproduced the exact analytical energies in both the cases.In this study, we shall generate isospectral Hamiltonians of the above potentials with the help of a modified form of Darboux's theorem. We shall show that though the new potentials look different from the original ones, and have different eigenfunctions, they too, are confined in the same region of space, and share the same energy spectrum as their original counterparts. This may be of substantial importance in determining the energy spectrum of highly non-trivial systems.     

Reactions of coordinated ligands,part II1). Kinetics of iodination of salicylate in bis(ethylenediamine)(salicylato)cobalt(III) cation

Summary The rates of iodination of Salicylate in the bis-(ethylenediamine)(salicylato)cobalt(lII) complex and free Salicylate have been measured in acetate buffer at 40° and I = 0.1 M. The reaction is catalysed by acetate and water. The reactivity order for both acetate- and water-catalysed paths is: [HSal]^– < [(en)₂CoSal]⁺ < [Sal]^2–, where [HSaI]^– and [Sal]^2– stand for the phenol and phenate forms of Salicylate respectively. Chelation of [Sal]^2– to cobalt(III) results in a rate reduction of its iodination by 10⁷.     

Exact bound states for the potentialV(r)=r 2+βr −4+λr −6 using partial algebraization technique

For the potential considered new sets of ground state and first few excited states are obtained. Also the defect of the wave function suggested by Kaushal and Parashar [Phys. Lett. A170 (1992) 335] and Gaurdiala and Ros [J. Phys. A25 (1992) 1351] has been shown.     

Multifractal properties of the Indian financial market

We investigate the multifractal properties of the logarithmic returns of the Indian financial indices (BSE & NSE) by applying the multifractal detrended fluctuation analysis. The results are compared with that of the US S&P 500 index. Numerically we find that qth-order generalized Hurst exponents h(q) and τ(q) change with the moments q. The nonlinear dependence of these scaling exponents and the singularity spectrum f(α) show that the returns possess multifractality. By comparing the MF-DFA results of the original series to those for the shuffled series, we find that the multifractality is due to the contributions of long-range correlations as well as the broad probability density function. The financial markets studied here are compared with the Binomial Multifractal Model (BMFM) and have a smaller multifractal strength than the BMFM.     

β-Trioxopyrrocorphins: pyrrocorphins of graded aromaticity

Octaethyltrioxopyrrocorphins unexpectedly show macrocycle-aromatic properties, even though they contain the macrocyclic π-system of the non-aromatic pyrrocorphins (hexahydroporphyrins). Two of the four possible triketone regioisomers were first reported in 1969 by one-pot oxidation of octaethylporphyrin but remained essentially unexplored since. We detail here the targeted preparation of the remaining two triketone isomers and the optical and NMR spectroscopic properties of all isomers. All four regioisomers possess unique electronic properties, including broadly varying degrees of diatropicity that were experimentally determined using ¹H NMR spectroscopy and computationally verified. Structural patterns modulating the aromaticity were recognized. These differences highlight the regioisomerically differentiated influences of the three β-oxo-functionalities. We also present the solid state structure of the two most common isomers (in their free base form or as zinc complexes), allowing further conclusions to be made about the resonance structures present in these triketones. Remarkably, also, the halochromic properties of the triketones differ sharply from those of regular (hydro)porphyrins, providing further support for the proposed 16-membered, 18 π-electron aromatic ring-current. The work conceptually expands the understanding of tris-modified hydroporphyrinoid analogues and the factors that enable and control porphyrinoid aromaticity.

The four possible pyrrocorphin isomers were prepared. Remarkably, they show regiochemically dependent aromaticity attributed to the presence of a 16-membered, 18 π-electron aromatic ring-current.     

Vesicular assembly and thermo-responsive vesicle-to-micelle transition from an amphiphilic random copolymer

Vesicular assembly from a thermo-responsive amphiphilic random copolymer is reported. Vesicle-to-micelle transition above a critical morphology transition temperature (CMTT) resulted in selective triggered release of encapsulated hydrophilic guests over hydrophobic ones. The aggregation pattern of a control polymer indicated a defined role of the methacrylamide groups in the polymer backbone for such unprecedented self-assembly from a simple polymer.     

Aromatic interaction profile to understand the molecular basis of raltegravir resistance

Integrase (IN) is the enzyme of human immunodeficiency virus (HIV) which inserts the viral DNA (vDNA) into the host genome for successful viral replication leading to the infection. However, the chemical basis of HIV IN catalysis is speculative due to lack of complete co-crystal structure. Using the recently published prototype foamy virus IN crystal structure, we developed a model structure of HIV IN showing interaction of vDNA, the metal (Mg²⁺) cofactor, and raltegravir (RLT) in the active site. Molecular docking and dynamics simulations studies showed that RLT uses it core central ring with diketo motif for Mg²⁺ chelation and bridge interaction with DDE motif. The triple arene interactions mediated by RLT with neighboring molecular motifs (Y143, cytosine, and adenine) is maintained during long simulation in wild type (WT). The fluorobenzyl and oxadiazole moieties of RLT forms aromatic stacking with cytosine base (head stacking) aromatic side chain of Y143 (tail stacking), respectively, while central ring further establishes aromatic stacking with distorted adenine base of vDNA (central stacking). The novel triple stacking systems were further explored to understand the molecular basis of drug resistance by molecular simulation. The in silico mutation (N155H, Q148H, and Q148H + G140S) and simulation studies elucidated the structural mechanism of resistance to RLT. The simulation studies provided the molecular basis for interdependency observed for the primary and secondary (Q148H and G140S) mutations and also explained the mechanism of viral fitness regain. Our study reveals that triple stacking and its consequence in terms of VdW energetic profile acts as a critical point to understand the drug-resistance. Here, we demonstrate that the root mean square deviation of centroid system (aromatic stacking) can be used as a major determinant of RLT binding toward the fold resistance. This is first kind of report, which discloses a strategy to explore the molecular level of drug resistance profile using aromatic interactions.