The Finite Element Method on the Sierpinski Gasket

For certain classes of fractal differential equations on the Sierpinski gasket, built using the Kigami Laplacian, we describe how to approximate solutions using the finite element method based on piecewise harmonic or piecewise biharmonic splines. We give theoretical error estimates, and compare these with experimental data obtained using a computer implementation of the method (available at the web site http://mathlab.cit.cornell.edu/\sim gibbons). We also explain some interesting structure concerning the spectrum of the Laplacian that became apparent from the experimental data. March 29, 2000. Date revised: March 6, 2001. Date accepted: March 21, 2001.     

Controlling decoherence via PT-symmetric non-Hermitian open quantum systems

We have studied the effect of a non-Hermitian Bosonic bath on the dynamics of a two-level spin system. The non-Hermitian Hamiltonian of the bath is chosen such that it converges to the harmonic oscillator Hamiltonian when the non-Hermiticity is switched off. We calculate the dynamics of the spin system and found that the non-Hermiticity can have positive as well as negative effects on the coherence of the system. However, the decoherence can be completely eliminated by choosing the non-Hermiticity parameter and the phase of the system bath interaction appropriately. We have also studied the effect of this bath on the entanglement of a two-spin system when the bath is acting only on one spin.     

Electrons, phonons and superconductivity in C16 structured Zr2Fe

Inelastic neutron scattering and low-temperature specific heat measurements are reported for a polycrystalline sample of Zr₂Fe. Lattice dynamical calculation of the phonon spectrum, along with first-principles LMTO electronic structure calculations have been used for deriving the specific heat parameters, the electron–phonon coupling constant and the superconducting transition temperature. The results are in fair agreement with the experimental data.     

LC–UV Assay for Simultaneous Estimation of Aromatic Turmerone, α/β-Turmerone and Curlone: Major Bisabolane Sesquiterpenes of Turmeric Oil in Rabbit Plasma for Application to Pharmacokinetic Studies

The herbal medicament derived from the lipid soluble fraction obtained from Curcuma longa L. (Zingiberaceae) has shown potential neuroprotective activity in disorders like stroke. HM has been standardized with three biomarkers: ar-turmerone, α/β-turmerone and curlone, major bisabolane sesquiterpenes of turmeric oil. Development of a biaonalytical method for these sesquiterpenes was initiated to characterize its preclinical pharmacokinetics in rabbits to accelerate its development as a potential candidate for vascular complications. Since, the compounds are structurally and chemically very similar, gradient elution was utilized on a C-18 reversed phase column with a mobile phase comprising of acetonitrile and deionised water. The UV detector was set at wavelengths 240 and 270 nm. The sample clean-up was performed by protein precipitation with acetonitrile. The method was reasonably sensitive with limits of quantitation (LOQ) of 0.098 μg mL^?1 in plasma for all the analytes. Accuracy and precision were within the acceptable limits, as indicated by relative standard deviation (% RSD) varying from 1.3 to 13.6% and bias values ranging from ?5.5 to 10.3%, respectively. Moreover, the analytes were stable in plasma even after three freeze-thaw cycles. The method was applied to generate preliminary pharmacokinetics of turmeric oil in rabbits after intravenous administration.     

<Emphasis Type="Italic">C</Emphasis>-field Cosmological Models with Variable <Emphasis Type="Italic">G</Emphasis> in FRW Space–Time

C-field cosmological models based on Hoyle-Narlikar theory with variable gravitational constant G in the frame work of FRW (Friedmann-Robertson-Walker) space–time for positive and negative curvatures are investigated. To get the deterministic solutions in terms of cosmic time t, we have assumed G=R ⁿ and discussed for n=−1, −2, R being scalar factor. In both the cases, creation field C increases with time, the gravitational constant G and matter density (ρ) decrease with time in the model (21). In the model (41) G decreases with time and matter density (ρ) is constant. The other physical aspects of the models are also discussed.     

Comprehensive and High-throughput Electrolysis of Water and Urea by 3–5 nm Nickel and Copper Coordination Polymers

Metal-organic coordination polymers (CP) have attracted the scientific attention for electrochemical water oxidation as it has the similar coordination structure like natural photosynthetic coordinated complex. However, the harsh synthesis conditions and bulky nature pose a major challenge in the field of catalysis. Herein, 3–5 nm CP particles synthesized at room temperature using aqueous solutions of Ni²⁺/Cu²⁺ and 2,5-dihydroxyterepthalic acid as precursor were applied for alkaline water and urea electrolysis. The overpotential required is only 300 mV at 10 mA cm⁻² by Nano-Ni CP for water oxidation, with turnover frequency (TOF) of 21.4 s⁻¹ which is around 8 times higher than its bulk-counterpart. Overall water and urea splitting were achieved with Nano-Cu (−) ∥ Nano-Ni (+) couple on Ni foam at 1.69 and 1.52 V to achieve 10 mA cm⁻², respectively. High electrochemical surface area (ECSA), high TOF, and enhanced mass diffusion are found to be the key parameters responsible for the state-of-the-art water and urea splitting performances of nano-CPs as compared to their bulk counterparts.