Reappearance of ferroelectric soft modes in the paraelectric phase of Pb(1-x)Ca(x)TiO3 at high pressures: Raman and x-ray diffraction studies

High pressure Raman spectroscopy and x-ray diffraction measurements have been carried out on Pb(1-x)Ca(x)TiO(3) (x = 0.10 and 0.30). Using high pressure Raman spectroscopic data, it is observed that the phonon instability responsible for the ferroelectric phase reappears in the paraelectric phase after a critical pressure. The observed critical pressures in the Ca(2+) doped PbTiO(3) system are much lower than the unique pressures suggested for PbTiO(3) based materials. A suitable explanation is given to explain this lowering of critical pressure. It is also shown that the ferroelectric phase which stabilizes in the paraelectric phase has a tetragonal symmetry with space group I4cm.     

Statistical convergence of a sequence of random variables and limit theorems

In this paper the ideas of three types of statistical convergence of a sequence of random variables, namely, statistical convergence in probability, statistical convergence in mean of order r and statistical convergence in distribution are introduced and the interrelation among them is investigated. Also their certain basic properties are studied.     

Delocalized nonlinear vibrational modes of triangular lattices

Nonlinear Dynamics - All possible one- and two-component delocalized nonlinear vibrational modes (DNVMs) in triangular lattice are analyzed. DNVMs are obtained considering solely upon the symmetry...     

Reactive chemical dynamics through conical intersections

Reaction dynamics of prototypical, D + H₂ and Cl (²P) + H₂, chemical reactions occurring through the conical intersections of the respective coupled multi-sheeted potential energy surfaces is examined here. In addition to the electronic coupling, nonadiabatic effects due to relativistic spin-orbit coupling are also considered for the latter reaction. A time-dependent wave packet propagation approach is undertaken and the quantum dynamical observables viz., energy resolved reaction probabilities, integral reaction cross-sections and thermal rate constants are reported.     

Synthesis of Hydrophenanthbene Derivatives Related to Diterpenes Involving Reductive Methylation of Aromatic Ketones

The tricyclic ketones 13 and 14, prepared from naphthalene and 2-methoxynaphthalene respectively, were subjected to reductive methylation in anhydrous ammonia to provide the β, γ -unsaturated ketones 16 and 17 in high yield which were stereoselectively converted into the A/B trans-fused compounds 3 and 4 respectively.     

The strong law of large numbers for weighted averages under dependence assumptions

Strong laws of large numbers (SLLN) for weighted averages are proved under various dependence assumptions when the variables are not necessarily independent or identically distributed. The results considerably extend the existing results. Weighted versions of the Marcinkiewicz-Zygmund SLLN are also formulated and proved under a similar set up. It seems that such results are not known even for independent and identically distributed random variables.     

Fly Ash Size Distributions: Use of coulter multisizer and fitting to truncated lognormal distributions

Accurate information on the size distribution of fly ash is needed to determine its role in the radiation transfer process in pulverized coal combustors. The Coulter Multisizer was used to determine the size distribution in the particle diameter range 1–200 μm. To size over such large diameter ranges, data must be obtained using several orifices, and then combined. In order to use the smaller orifices, the larger particles have to be removed from the sample. A wet-sieving apparatus, designed for accurate separation of the particles by size, is described. A scheme for combining data obtained using orifices of different diameters is presented. It appears from this study that the lower limit of size measurement using an orifice is set by sensitivity, rather than by signal/noise. A lognormal distribution function, truncated outside the measurement limits, fits the size distribution data well. This function allows detailed size information to be stored compactly using four parameters. Size parameters for six fly ashes representative of U. S. coals are presented.     

Relativistic Sagnac Effect and Ehrenfest Paradox

There seems to exist a dilemma in the literature as to the correct relativistic formula for the Sagnac phase-shift. The paper addresses this issue in the light of a novel, kinematically equivalent linear Sagnac-type thought experiment, which provides a vantage point from which the effect of rotation in the usual Sagnac effect can be analyzed. The question is shown to be related to the so-called rotating disc problem known as the Ehrenfest paradox. The relativistic formula for the Sagnac phase-shift seems to depend on the way the paradox is resolved. Kinematic resolution of the Ehrenfest paradox proposed by some authors predicts the usually quoted formula for the Sagnac delay but the resolution itself is shown to be based upon some implicit assumptions regarding the behaviour of solid bodies under acceleration. In order to have a greater insight into the problem, a second version of the thought experiment involving linear motion of a special type of a non-rigid frame of reference is discussed. It is shown by analogy that the usually quoted special relativistic formula for the Sagnac delay follows, provided the material of the disc matches the special type.