in this paper, simultaneous control of source terms is considered in a vibrational string problem.in the considered problem, the terms to be controlled are the force and the initial velocity functions. we statethe generalized (weak) solution about the considered problem. the existence and uniqueness of the solutionfor optimal control problem is investigated. the frechet derivative of the functi...

Computing the gradient of a function provides fundamental information about its behavior. This is essential for several applications and algorithms across various fields. One common application that require gradients are optimization techniques such as stochastic descent, Newton's method trust region methods. However, these methods usually requires numerical computation at every iteration which...

in classical mechanics, considering hook’s law stress is a linear function of strain. while in strain gradient theory stress is a function of strain and strain differentials. in this paper, novel formulation relating stress and strain and also new boundary conditions are derived based on minimum potential energy principle. in strain gradient theory a length coefficient parameter is defined. thi...

abstract rockfill dams are a type of hydraulic control structures used to protect river bed in cases where a considerable reservoir volume is available behind these structures; it could mitigate the floods and provide a gradual depletion of incoming volume of water so that the discharge passing downstream is decreased. one of the main issues on utilizing rockfill dams is to keep its permeabilit...