Characterising chaos-hyperchaos transition using correlation dimension

Transition to hyperchaos is uaually studied by computing the spectrum of Lyapunov Exponents (LE). But such a procedure can be employed mainly when the equations governing the dynamical system are known. However, if the information available on the system is only through time series, the method becomes difficult to implement. We show that the transition to hyperchaos is followed by a sudden change in the topological structure of the underlying attractor. Our numerical results indicate that the transition to hyperchaos can be characterized accurately through the computation of correlation dimension (D ₂) from time series. We use two standard time delayed hyperchaotic systems as examples since, for such systems, D ₂ varies smoothly as a function of the time delay τ which can be used as the control parameter.     

Crystal and Molecular structure of 3,3-Diethyl–2,4,6–[1 H,3 H,5 H] Pyrimidine Trione

C₈H₁₂O₃N₂, M_r = 184.19, Trigonal, R3 (hexagonal axes) a = b = 26.800(1) Å, c = 6.828(3) Å, α = β = 90°, γ = 120°, V = 4247.11 ų, Z = 18, D_m = 1.297 Mg m⁻³, D_c = 1.296 Mg m⁻³, mu = 0.79 mm⁻¹, F(000) = 1764, T = 293 K, final R = 0.080 for 1205 observed reflections. There are two crystallographically independent molecules in the unit cell of the title compound.     

An efficient one-pot synthesis of novel polysubstituted 4-amino-2,3-dihydropyridines

A convenient and efficient one-pot multi-component synthesis of novel polysubstituted 4-amino-2,3-dihydropyridines from carbonyl compounds, malononitrile and acetonitrile, using indium triflate is reported. Acetonitrile acts both as a solvent as well as a substrate.     

Insights Into How Heme Reduction Potentials Modulate Enzymatic Activities of a Myoglobin-based Functional Oxidase

Heme-copper oxidase (HCO) is a class of respiratory enzymes that use a heme-copper center to catalyze O₂ reduction to H₂O. While heme reduction potential (E°′) of different HCO types has been found to vary >500 mV, its impact on HCO activity remains poorly understood. Here, we use a set of myoglobin-based functional HCO models to investigate the mechanism by which heme E°′ modulates oxidase activity. Rapid stopped-flow kinetic measurements show that increasing heme E°′ by ca. 210 mV results in increases in electron transfer (ET) rates by 30-fold, rate of O₂ binding by 12-fold, O₂ dissociation by 35-fold, while decreasing O₂ affinity by 3-fold. Theoretical calculations reveal that E°′ modulation has significant implications on electronic charge of both heme iron and O₂, resulting in increased O₂ dissociation and reduced O₂ affinity at high E°′ values. Overall, this work suggests that fine-tuning E°′ in HCOs and other heme enzymes can modulate their substrate affinity, ET rate and enzymatic activity.     

Riemann problem in non-ideal gas dynamics

In this paper we consider the Riemann problem for gas dynamic equations governing a one dimensional flow of van der Waals gases. The existence and uniqueness of shocks, contact discontinuities, simple wave solutions are discussed using R-H conditions and Lax conditions. The explicit form of solutions for shocks, contact discontinuities and simple waves are derived. The effects of van der Waals parameter on the shock and simple waves are studied. A condition is derived on the initial data for the existence of a solution to the Riemann problem. Moreover, a necessary and sufficient condition is derived on the initial data which gives the information about the existence of a shock wave or a simple wave for a 1-family and a 3-family of characteristics in the solution of the Riemann problem.     

Group-6 metal carbonyl complexes of pyridylbenzoxazole and pyridylbenzothiazole: Synthesis, structure, electrochemistry, photophysical property and DFT calculations

Cr, Mo and W tetracarbonyl complexes of 2-(2-pyridyl)benzoxazole (PBO) and 2-(2-pyridyl)benzothiazole (PBT) are spectroscopically characterised. The confirmatory structure of [Mo(CO)₄(PBO)] has been determined by X-ray crystallography. The complexes show negative solvatochromic effect, with increasing solvent polarity the MLCT band is shifted to longer wavelength region. Cyclic voltammetry shows M(I)/M(0) redox response and also exhibit fluorescence spectra at room temperature. The electronic structures of the complexes are calculated by density functional theory (DFT) and time dependent-DFT calculated results are used to explain redox property and electronic transitions.     

On interrelations of recurrences and connectivity trends between stock indices

Financial data has been extensively studied for correlations using Pearson’s cross-correlation coefficient ρ$\rho$ as the point of departure. We employ an estimator based on recurrence plots — the correlation of probability of recurrence (CPR$CPR$) — to analyze connections between nine stock indices spread worldwide. We suggest a slight modification of the CPR$CPR$ approach in order to get more robust results. We examine trends in CPR$CPR$ for an approximately 19-month window moved along the time series and compare them to trends in ρ$\rho$. Binning CPR$CPR$ into three levels of connectedness (strong, moderate, and weak), we extract the trends in number of connections in each bin over time. We also look at the behavior of CPR$CPR$ during the dot-com bubble by shifting the time series to align their peaks. CPR$CPR$ mainly uncovers that the markets move in and out of periods of strong connectivity erratically, instead of moving monotonically towards increasing global connectivity. This is in contrast to ρ$\rho$, which gives a picture of ever-increasing correlation. CPR$CPR$ also exhibits that time-shifted markets have high connectivity around the dot-com bubble of 2000. We use significance tests using twin surrogates to interpret all the measures estimated in the study.