Abstract In this work we consider a problem in the context of the generalized theory of thermoelasticity for a half space. The material of the half space is functionally graded in which Lamé's modulii are functions of the vertical distance from the surface of the medium. The surface is traction free and subjected to a time dependent thermal shock. The problem was solved by using the Laplace transform method together with the perturbation technique. The obtained results are discussed and compared with the solution when Lamé's modulii are constants. Numerical results are computed and represented graphically for the temperature, displacement and stress distributions.

Aspergillus aculeatus tannase was immobilized on several carriers by entrapment and covalent binding with cross - linking. Tannase immobilized on gelatin with cross - linking agent showed the highest activity and immobilization yield. The optimum pH of the immobilized enzyme was shifted to a more acidic range compared with the free enzyme (from pH 5.5 to pH 5.0). The optimum temperature of the reaction was determined to be 50ºC for the free enzyme and 60ºC for the immobilized form. The thermal stability, as well as stability over a wide range of pH, was significantly improved by the immobilization process. The calculated Km of the immobilized tannase (11.8 mg ml-1) is higher than that of the free tannase (6.5 mg ml-1), while Vmax of the immobilized enzyme (0.32 U (µg protein)-1) is lower than that of the free tannase (2.7 U (µg protein)-1). The immobilized enzyme was able to retain 84 % of the initial catalytic activity after 5.0 cycles.