and Applied Analysis 3 then there exists ε0 > 0 such that for all 0 < ε ≤ ε0 the mapping Θ : Ω ε → R3 is an injective mapping and the three vectors gεi x ε : ∂εiΘ x ε ∂α ∂/∂xα, ∂ ε 3 ∂/∂x ε 3 are linear independent for each x ∈ Ωε. The injectivity of the mapping Θ : Ωε → R3 ensures that the physical problem described below is meaningful. The three vectors gεi x ε form the covariant basis at the...

Mediation analysis is used to review the comparative change in the amount of strength of association of the primary predictor with the outcome after adjustment for the mediator. Mediation models are very widely used in social sciences and biomedical sciences. Before conducting mediation studies, researchers want to know the sample size (i.e. number of subjects) required for achieving the adequa...

There are several parameters that have significant influence in metal forming process. One of the most important of them is friction coefficient. Friction can change the pattern of metal flow and the force needed for deformation. It is necessary to determine the friction coefficient to study the effect of friction on metal forming process. This study is concerned with numerical and experimental...