How Fast can a Subharmonic Function Decay Along a Ray?

Much is known about the connection between the growth and decayof subharmonic functions. The results indicate that there isa general principle: asubharmonic function cannot decay ‘toofast’ relative to its growth.Three theorems are provedwhich, together with work previously published elsewhere, givea fairly complete account of how this principle works out fora subharmonic function having extremal decay along a ray. 1991Mathematics Subject Classification: 30D20, 31A05.     

Preparation and characterization of cellulose acetate and lithium nitrate for advanced electrochemical devices

Environmental research has the objective of finding solutions to environmental degradation. To this aim, an optimized solid bio-polymer electrolyte (BPE) based on cellulose acetate (CA) with lithium nitrate (LiNO₃) has been developed to achieve the possible energy storage Li-ion batteries. CA is one of the natural polymers with very good film forming capacity. The widespread use of CA is attributed to the availability of renewable resources, non-toxic nature, low cost, and bio-compatible material. Here, we demonstrate an extremely simplest process of solution-casting technique for the development of BPE by incorporating various LiNO₃ compositions (wt.%) with bio-polymer material CA. The crystalline nature of the CA with LiNO₃ has been analyzed by X-ray diffraction (XRD) measurement. The bio-polymer-salt complex formation and the biopolymer-proton interactions have been investigated through Fourier transform infrared (FTIR) spectroscopy. Electrochemical impedance spectroscopy has been used to examine the ionic conductivity of the BPEs at room temperature (303 K). The highest ionic conductivity of 1.93 × 10^?3S/cm has been achieved for 50CA/50LiNO₃ polymer electrolyte. Electrochemical studies show that highest BPE has high electrochemical stability windows. The conducting species is found to be Li⁺ ion, which has been confirmed by transference number measurement (TNM). Primary lithium battery with discharge profile has been constructed for 50CA/50LiNO₃. This research will help to identify a new lithium ion membrane for battery technology and other electrochemical device applications.     

ESR line width and line shape dependence of Overhauser‐enhanced magnetic resonance imaging

Electron spin resonance and Overhauser‐enhanced magnetic resonance imaging studies were carried out for various concentrations of ¹⁴N‐labeled 3‐carbamoyl‐2,2,5,5‐tetramethyl‐pyrrolidine‐1‐oxyl in pure water. Overhauser‐enhancement factor attains maxima in the range of 2.5–3 mm concentration. The leakage factor showed an asymptotic increase with increasing agent concentration. The coupling parameter showed the interaction between the electron and nuclear spins to be mainly dipolar in origin. The electron spin resonance parameters, such as the line width, line shape and g‐factor, were determined. The line width analysis confirms that the line broadening is proportional to the agent concentration, and also the agent concentration is optimized in the range of 2.5–3 mm . The line shape analysis shows that the observed electron spin resonance line shape is a Voigt line shape, in which the Lorentzian component is dominant. The contribution of Lorentzian component was estimated using the winsim package. The Lorentzian component of the resonance line attains maxima in the range of 2.5–3 mm concentration. Therefore, this study reveals that the agent concentration, line width and Lorentzian component are the important factors in determining the Overhauser‐enhancement factor. Hence, the agent concentration was optimized as 2.5–3 mm for in vivo/in vitro electron spin resonance imaging and Overhauser‐enhanced magnetic resonance imaging phantom studies. Copyright © 2016 John Wiley & Sons, Ltd.     

Single crystal EPR of Cu(C5H5NO)6(BF4)2: an example of admixed ground state

Single crystal electron paramagnetic resonance (EPR) of Cu(C5H5NO)6(BF4)2 is studied at 300 K. The spin Hamiltonian parameters obtained at 300 K are A11 = -149.8, A22 = -50.7 and A33 = -37.7 (all in units of 10(-4) cm(-1)), g11 = 2.3452, g22 = 2.0679 and g33 = 2.0695. Angular variation of hyperfine structure lines shows the presence of a single magnetic site. The low magnitude of the A11 value for Cu(C5H5NO)6(BF4)2 is rationalized in terms of a mixed d(x2-y2)/d(z2) ground state.