This work is to study an infinite thermoelastic solid that is assumed to be homogeneous and isotropic is subjected to temperature and stress distributions. A cylindrical system of coordinates is used, in which the plane is that of the crack and the z-axis is normal to it at the centre. The corresponding set of the homogeneous thermoelastic equilibrium differential equation is solved by the Hankel transforms method. The mixed boundary conditions reduce the problem to the solution of two pairs of dual integral equations. The both dual integral equations for the thermal and thermoelastic parts are effectively reduced. We deduce, by using the inverse integral transform. These quantities of physical interest are given analytically and represented graphically. A numerical application is considered with some concluding results with discussions. All the definite integrals involved were calculated using Romberg technique of numerical integration with the aid of a Fortran Program compiled with Visual Fortran v.6.1 on a Pentium-IV pc with processor speed 2GHz.

In this paper, a new approach is used for estimation of survival proportions of Coronary Artery Bypass Graft Surgery (CABG) patients by complete population, from its incomplete population. The availability of a complete population may lead to better estimates of the survivor’s proportions. Maximum likelihood method, in-conjunction with Davidon-Fletcher-Powell optimization method and Cubic Interpolation method is used in estimation of survivor’s proportions of some parametric distributions.

The survival rate estimates for the breast cancer censored data have been considered for the 254 patients. The data [10] was treated at the chemotherapy department, Bradford Royal Infirmary for ten years. Here in this paper Gumbel probability distribution (see [3], [4], [5]) model is used to obtain the survival rates of the patients. Maximum likelihood method [9] has been used through unconstrained optimization method [12, 13] (DFP-Davidon-Fletcher-Powell) to find the parameter estimates and variance-covariance matrix for the Gumbel distribution model. Finally the survivor rate estimates for the parametric (Gumbel) probability model has been compared with the non-parametric (Kaplan-Meier) [7] method.