Factors affecting the electro-optical and structural characteristics of nano crystalline Cu doped (Cd–Zn)S films

This work investigates the effects of the temperature, deposition time and annealing ambient on the electro-optical and structural properties of nano crystalline (Cd–Zn)S films prepared by chemical bath deposition (CBD). The deposited films being uniform and adherent to the glass substrates are amorphous in nature and the crystallinity as well as the grain size is found to increase on post-deposition annealing. The obtained specimens are thoroughly characterized before and after annealing paying particular attention to their structure, composition and morphology. Annealing in air reduces the extent of disorder in grain boundaries and energy band-gap. A correlation between the structural and optical properties is investigated in detail. The surface morphology and structural properties of the as-deposited and annealed (Cd–Zn)S thin films are studied using X-ray diffraction (XRD), scanning electron microscope (SEM) and optical transmission spectra. The optical transmission spectra are recorded within the range of 300–800 nm and 300–900 nm. The electroluminescent (EL) intensity is found to be maximum at a particular temperature, which decreases with further increase in temperature and peaks of photoluminescent (PL) and EL spectra are centered at 546 nm and 592 nm. The emission intensity also increases with increasing thickness of the film.     

On isomorphisms between deformation rings and Hecke rings

Inventiones mathematicae -     

Ionic noise measurement in polymer electrolytes

Electrical noise associated with ion transport (termed as “ionic noise”) has been measured at different temperatures, using a lock-in amplifier and dynamic signal analyzer for a polymer electrolyte PEO:NH₄I and its CdS dispersed composite. The ionic noise suddenly increases as the polymer passes through its phase transition at T _g and T _m. The T _g-peak in the noise measurement appears more clearly than what it does in DTA/DSC or conductivity measurements. Therefore, we suggest the noise technique as a good probe for studying phase transitions in ion conducting solid electrolytes. Further, the present noise measurements also confirm the known results of DTA/DSC studies that both T _g and T _m of polymer electrolytes shift on the formation of composites.     

Inner-shell ionization of atoms by electron,positron and photon impacts

Plane wave Born approximation with Coulomb, relativistic and exchange corrections is employed to obtain L1-, L2- and L3-subshell ionization cross sections of several atoms due to electron and positron impacts for projectile energy varying from the threshold of ionization to 60 times the threshold energy. Photoionization cross sections for all the three L-subshells of the atoms are also calculated using the hydrogenic approximation for the atomic wave functions. For L3-subshell the present cross sections due to electron impact are in good agreement with a number of experimental data for different atoms over the entire energy range investigated. For L1- and L2-subshells the present calculations yield qualitative agreement with the experimental data. The agreement between the present results and the limited experimental data for positron impact is also satisfactory. The hydrogenic approximation for the L-subshell photoionization is found to be good at small photon energies but it underestimates the cross sections at large photon energies.     

The phase of the Riemann zeta function

We, offer an alternative interpretation of the Riemann zeta functionζ(s) as a scattering amplitude and its nontrivial zeros as the resonances in the scattering amplitude. We also look at several different facets of the phase of theζ function. For example, we show that the smooth part of theζ function along the line of the zeros is related to the quantum density of states of an inverted oscillator. On the other hand, for ℜs>1/2, we show that the memory of the zeros fades only gradually through a Lorentzian smoothing of the delta functions. The corresponding trace formula for ℜs≫1 is shown to be of the same form as generated by a one-dimensional harmonic oscillator in one direction along with an inverted oscillator in the transverse direction. Quite remarkably for this simple model, the Gutzwiller trace formula can be obtained analytically and is found to agree with the quantum result.     

Connecting Jacobi elliptic functions with different modulus parameters

The simplest formulas connecting Jacobi elliptic functions with different modulus parameters were first obtained over two hundred years ago by John Landen. His approach was to change integration variables in elliptic integrals. We show that Landen’s formulas and their subsequent generalizations can also be obtained from a different approach, using which we also obtain several new Landen transformations. Our new method is based on recently obtained periodic solutions of physically interesting non-linear differential equations and remarkable new cyclic identities involving Jacobi elliptic functions.