Central limit theorems for a class of irreducible multicolor urn models

We take a unified approach to central limit theorems for a class of irreducible multicolor urn models with constant replacement matrix. Depending on the eigenvalue, we consider appropriate linear combinations of the number of balls of different colors. Then under appropriate norming the multivariate distribution of the weak limits of these linear combinations is obtained and independence and dependence issues are investigated. Our approach consists of looking at the problem from the viewpoint of recursive equations.     

Investigations on the mechanisms of ionic conductivity in PEO-PU/PAN semi-interpenetrating polymer network-salt complex polymer electrolytes: an impedance spectroscopy study

This paper is a first comprehensive study on the correlated ion transport mechanisms contributing to the overall conductivity behavior in a new class of poly(ethylene oxide)-polyurethane/polyacrylonitrile (PEO-PU/PAN) semi-interpenetrating polymer networks (semi-IPNs)-salt complex polymer electrolytes. A simultaneous investigation of the electrical response on PEO-PU/PAN/LiClO(4) and PEO-PU/PAN/LiCF(3)SO(3) semi-IPNs with varying EO/Li mole ratios (100, 60, 30, 20, 15, 10) has been carried out by impedance spectroscopy. Analysis of the complex plane and spectroscopic plots indicated the presence of two microscopic phases corresponding to the PEO-PU and PAN domains, which leads to space charge polarization in these systems. A suitably modified approach based on the universal power law (UPL) considering the independent contribution from the individual microphases of semi-IPNs facilitates a complete interpretation of the spectroscopic profiles for the real component of conductivity (sigma'(omega)). The sigma'(omega) spectroscopic profiles were fitted with two power law equations, where the frequency region up to approximately 300 kHz is the conductivity profile associated with the PAN phase and beyond this is the superimposed contribution of the PEO-PU phase. Simulated fits using the UPL equation revealed two relaxation times (tau(PEO)(-)(PU), tau(PAN)) related to ionic hopping in the PEO-PU and PAN phases in addition to the conductivity relaxation time (tau(peak)) determined from the Debye peaks. The respective power law exponents (n(PEO)(-)(PU) approximately 0.5-0.8, n(PAN) approximately 1.0-1.6) indicate that though cationic hopping in the softer PEO-PU phase is favored, anionic hopping in the PAN phase contributes significantly to the charge transport processes in these semi-IPNs. Correlation of the experimental results with the simulated fits enable us to distinguish the effects of semi-IPN composition, temperature, morphology, ion-ion, and ion-polymer interactions, which influence the microscopic molecular events, involved in the charge transport in these complex semi-IPN polymer electrolytes.     

theK L-K S mass difference in left-right symmetric models and the right-handed Kobayashi-Maskawa matrix

Zeitschrift für Physik C Particles and Fields - K L-K S mass difference is computed in a left-right symmetric model with three generations of quarks. Under the assumption of...     

On the solution of problems of filtration with a limit gradient

The plane stable filtration of an incompressible liquid with a limit gradient is considered /1/. A special non-linear filtration law is introduced, for which the basic system of equations obtained by transformation of the hodograph /2/ has a general solution which enables the theory of functions of a complex variable to be effectively employed. As a special case the proposed law contains the law considered in /3/. Solutions of the problems of the motion produced by a source in a narrow zone, and the motion from a source-sink pair are presented.     

Development of Flow Cytometric Protocol for Nuclear DNA Content Estimation and Determination of Chromosome Number in Pongamia pinnata L., a Valuable Biodiesel Plant

The potentiality of Pongamia pinnata L. as a sustainable source of feedstock for the biodiesel industry is dependent on an extensive knowledge of the genome structure of the plant. Flow cytometry, with propidium iodide (PI) as the DNA stain, was used to estimate the nuclear DNA content of P. pinnata, with respect to Zea mays ‘CE-777’ as standard. The internal and pseudo-internal standardization was followed on account of the inhibitory effect of secondary compounds on PI intercalation. The antioxidants (PVP-40 and β-mercaptoethanol) were added to the nuclear isolation buffer for the reduction of inhibitory effect of P. pinnata cytosol. Nuclear DNA content estimation was done for P. pinnata leaves from different altitudes (37–117 m height from sea level) of Assam. Flow cytometry analysis indicated that the nuclear DNA content of P. pinnata is 2.66 pg with predicted 1C value of 1,300 Mb using Z. mays as standard. Coefficient of variation in flow cytometric analysis was within the limit of 5 % indicating that the results were reliable. Somatic chromosome numbers were counted from root–tip cells and was found to be 2n?=?22 corresponding to the diploid level (x?=?11). A decreasing trend in the nuclear DNA content was observed for the species of different altitudes.