The concept of a Lie recurrence was introduced by the first author . It is an infinitesimal transformation with respect to which the Lie derivative of a curvature tensor is proportional to itself. Apart from other results related to a Lie recurrence, it was established that the Weyl projective curvature tensor is Lie recurrent with respect to a Lie recurrence but its converse is not necessarily true. However, an infinitesimal transformation with respect to which the Weyl projective curvature tensor and the Ricci tensor are Lie recurrent, is necessarily a Lie recurrence. Singh  studied an infinitesimal transformation with respect to which the Lie derivative of the curvature tensor is proportional to itself and called such transformation as curvature inheritance. Obviously, a curvature inheritance is nothing but a Lie recurrence. Singh  also considered a curvature inheritance which is a projective motion and called it a projective curvature inheritance. Gatoto and Singh [1,2] studied -curvature inheritance and projective -curvature inheritance. Pandey and Pandey  studied projective Lie recurrence. Mishra and Yadav  studied projective curvature inheritance in an NP-Fn. In the present paper we have established that an infinitesimal transformation in a Finsler space is Lie recurrence if and only if the normal projective curvature tensor is Lie recurrent. A part from this result we have generalized almost all theorems of Mishra and Yadav .
This paper presents the result of thermodynamic studies on Ge1−xSnxSe2.5 (0 ≤ x ≤ 0.5) glasses using differential scanning calorimetry. The obtained experimental results on phase transformations have been
employed to obtain thermodynamic parameters like entropy difference between metastable states in the glassy region, difference
of Gibbs free energy, specific heat, entropy between the glassy and the crystalline phase and the enthalpy released during
phase transformation (glassy to crystalline). The results yield that, Ge0.7Sn0.3Se2.5 sample is least stable among all the samples. The stability increases on addition of Sn beyond 0.3 at. mass% upto 0.5 at.
Results of phase transformations, enthalpy released and specific heat of Ge22Se78–xBix(x=0, 4 and 8) chalcogenide glasses, using differential scanning calorimetry (DSC), under non-isothermal condition have been reported and discussed. The glass transition temperature, Tg, is found to increase with an average coordination number and heating rates. Following Gibbs—Dimarzio equation, the calculated values of Tg (i.e. 462.7, 469.7 and 484.4 K) and the experimental values (i.e. 463.1, 467.3 and 484.5 K) increase with Bi concentration. Both values of Tg, at a heating rate of 5 K min–1, are found to be in good agreement. The glass transition activation energy increases i.e. 102±2, 109±3 and 115±8 kJ mol–1 with Bi concentration. The demand for thermal stability has been ensured through the temperature difference Tc–Tg and the enthalpy released during the crystallization process. Below Tg, specific heat has been observed to be temperature independent but highly compositional dependent. The growth kinetic has been investigated using the Kissinger, Ozawa, Matusita and modified JMA equations. Results indicate that the crystallization ability is enhanced, the activation energy of crystallization increases with increasing the Bi content and the crystal growth of these glasses occur in 3 dimensions.
Authors:D. Patidar, Sonalika Agrawal, and N. S. Saxena
CdS/PMMA nano-composites at different weight percent of CdS (0, 2, 4, 6, and 8) have been prepared using solution casting method. The obtained nano-composites are characterized through the transmission electron microscope (TEM). The differential scanning calorimetry (DSC) measurements have been done on the nano-composites at different heating rates. The peak glass transition temperature is determined using the DSC thermograms. It is found that the glass transition temperature increases with the increase of CdS content up to 6 wt% and then decreases for higher weight percent (8). It is explained on the basis of molecular motion of PMMA, which is restricted when CdS is added into PMMA. An effort is also made to study the activation energy of glass transition in the case of nano-composites of different weight percent of CdS. Variation of activation energy with CdS nano-particle concentration has also been theoretically predicted by using an empirical relation. Thermal stability of these nano-composites has been explained with the help of activation energy in the glassy region.
Se80−xTe20Znx (x = 2, 4, 6, 8, and 10) glasses have been prepared using conventional melt quenching technique. The kinetics of phase transformations (glass transition and crystallization) have been studied using differential scanning calorimetry (DSC) under non-isothermal condition at five different heating rates in these glasses. The activation energy of glass transition (Et), activation energy of crystallization (Ec), Avrami exponent (n), dimensionality of growth (m), and frequency factor (Ko) have been investigated for the better understanding of growth mechanism using different theoretical models. The activation energy is found to be highly dependent on Zn concentration. The rate of crystallization is found to be lowest for Se70Te20Zn10 glassy alloy. The thermal stability of these glasses has been investigated using various stability parameters. The values of these parameters were obtained using characteristic temperatures, such as glass transition temperature Tg, onset crystallization temperature Tc, and peak crystallization temperature Tp. In addition to this, enthalpy-released during crystallization has also been determined. The values of stability parameters show that the thermal stability increases with the increase in Zn concentration in the investigated glassy samples.