Multi-adjoint logic programming represents a very recent, extremely flexible attempt for introducing fuzzy logic into logic programming. In this setting, the execution of a goal w.r.t. a given program is done in two separate phases. During the operational one, admissible steps are systematically applied in a similar way to classical resolution steps in pure logic programming, thus returning a c...

The objective of the present work is to extend the adjoint-based error estimate and the adaptive mesh refinement algorithm of the high-order CPR method to the 3D NavierStokes equations. A dual-consistent high-order correction procedure via reconstruction method is utilized to obtain the adjoint solution and derive the output-based local error indicator. Several inviscid and viscous flow cases a...

A mathematical model is presented in the present study to control‎ ‎the light propagation in an inhomogeneous media‎. ‎The method is ‎based on the identification of the optimal materials distribution‎ ‎in the media such that the trajectories of light rays follow the‎ ‎desired path‎. ‎The problem is formulated as a distributed parameter ‎identification problem and it is solved by a numerical met...

‎this paper considers a non-local initial-boundary value problem containing a first order partial differential equation with variable coefficients‎. ‎at first‎, ‎the non-self-adjoint spectral problem is derived‎. ‎then its adjoint problem is calculated‎. ‎after that‎, ‎for the adjoint problem the associated eigenvalues and the subsequent eigenfunctions are determined‎. ‎finally the convergence ...

In aerodynamics, Optimal Shape Design (OSD) aims to find the minimum of an objective function describing an aerodynamic property, by controlling the Partial Differential Equation (PDE) modeling the dynamics of the flow that surrounds an aircraft. The objective function minimization is usually achieved by means of an iterative process which requires the computation of the gradients of the cost f...

Traditional transmission travel-time tomography hinges on ray tracing techniques. We propose a PDE-based Eulerian approach to travel-time tomography so that we can avoid the cumbersome ray-tracing. We start from the eikonal equation, define a mismatching functional and derive the gradient of the nonlinear functional by an adjoint state method. The resulting forward and adjoint problems can be e...

In this paper we propose a new method based on adjoint systems for parametric sensitivity analysis of DAE’s. This method is employed in a series of experiments, and the results are compared with the estimation of sensitivity by a finite differences method, widely used because of the simplicity of its implementation. In addition, we propose a method extension based on the use of estimation funct...

This paper develops an adaptive finite element method for shape optimization in stationary incompressible flow with damping. The continuous shape gradient of an objective functional with respect to the boundary shape is derived by using the adjoint equation method and a function space parametrization technique. A projection a-posteriori error estimator is proposed, which can be computed easily ...

Let $A=U|A|$ be the polar decomposition of an operator $A$ on a Hilbert space $mathscr{H}$ and $lambdain(0,1)$. The $lambda$-Aluthge transform of $A$ is defined by $tilde{A}_lambda:=|A|^lambda U|A|^{1-lambda}$. In this paper we show that emph{i}) when $mathscr{N}(|A|)=0$, $A$ is self-adjoint if and only if so is $tilde{A}_lambda$ for some $lambdaneq{1over2}$. Also $A$ is self adjoint if and onl...

In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions...