to evaluate the earth seismic response due to earthquake effects, ground response analyses are used to predict ground surface motions for development of design response spectra, to compute dynamic stresses and strains for evaluation of liquefaction hazards, and to determine the earthquake induced forces that can lead to instability of earth and earth-retaining structures. most of the analytical...

We propose a general framework for approximating the potential of mean force (PMF) along a reaction coordinate in conformational space. This framework, based on the method of weighted residuals, can be viewed as a generalization of thermodynamic integration and direct histogram methods. Using weighted residuals allows for higher-order approximations to the PMF in the form of a global spectral m...

where φ(x) is the dependent variable and is unknown and f (x) is a known function. L denotes the differential operator involving spatial derivative of φ , which specifies the actual form of the differential equation. Weighted residual method involves two major steps. In the first step, an approximate solution based on the general behavior of the dependent variable is assumed. The assumed soluti...

In this paper, we introduce the concept of quantile-based generalized cumulative residual entropy of order $(alpha,beta)$ for residual and past lifetimes and study their properties. Further we study the proposed information measure for series and parallel system when random variable are untruncated or truncated in nature and some characterization results are presented. At the end, we study gene...