Reductants are a special kind of fuzzy rules which constitute an essential theoretical tool for proving correctness properties. A multi-adjoint logic program, when interpreted on an arbitrary lattice, has to include all its reductants in order to preserve the approximate completeness property. In this work, after revisiting the different notions of reductant arisen in the framework of multi-adj...

The adjoint method is an elegant approach for the computation of the gradient of a cost function to identify a set of parameters. An additional set of differential equations has to be solved to compute the adjoint variables, which are further used for the gradient computation. However, the accuracy of the numerical solution of the adjoint differential equation has a great impact on the gradient...

In this investigation we address the problem of adjoint–based optimization of PDE systems in moving domains. As an example we consider the one–dimensional heat equation with prescribed boundary temperatures and heat fluxes. We discuss two methods of deriving an adjoint system necessary to obtain a gradient of a cost functional. In the first approach we derive the adjoint system after mapping th...

An adjoint preprocess for an adjoint-based turbomachinery design process is described. The resulting process is compared to a previously established adjoint process based on three-dimensional adjoint solutions and deformed meshes. Within the new process, the calculation of sensitivities is performed using shape sensitivities and surface displacements, where the design parameters are computer-ai...

This paper compares the continuous and discrete viscous adjoint-based automatic aerodynamic optimization. The objective is to study the complexity of the discretization of the adjoint equation for both the continuous and discrete approach, the accuracy of the resulting estimate of the gradient, and its impact on the computational cost to approach an optimum solution. First, this paper presents ...

The uniformity, for the family of exceptional Lie algebras g, of the decompositions of the powers of their adjoint representations is well-known now for powers up to the fourth. The paper describes an extension of this uniformity for the totally antisymmetrised n-th powers up to n = 9, identifying (see Tables 3 and 6) families of representations with integer eigenvalues 5, . . . , 9 for the qua...

I have four long-term goals. My first goal is to finalize the large body of work already carried out by the PI on the predictability of tropical cyclone (TC) forecast tracks out to 72 hours ahead. My second goal is to apply similar, as well as new, ideas to the predictability of forecast intensity out to 72 hours ahead. My third goal is to carry out observing system simulation experiments (OSSE...

Optimal control of fractional linear systems on a finite horizon can be classically formulated using the adjoint system. But the adjoint of a causal fractional integral or derivative operator happens to be an anti-causal operator: hence, the adjoint equations are not easy to solve in the first place. Using an equivalent diffusive realization helps transform the original problem into a coupled s...

We present a discrete adjoint version of OpenFOAM obtained by operator overloading which yields, in comparison to continuous adjoint versions, a greater flexibility and robustness. We discuss our implementation and how the discrete adjoint version of OpenFOAM differs from existing continuous implementations. To reduce the inherent memory requirement of discrete adjoint code we introduce a check...

The local equivalence problem for sub-Riemannian structures on threemanifolds is solved. In the course of the solution, it is shown how to attach a canonical Riemannian metric and connection to the given sub-Riemannian metric and it is shown how all of the differential invariants of the sub-Riemannian structure can be calculated. The relation between the completeness of the sub-Riemannian metri...