We study different types of aggregation operators. We focus on the generalized OWA (GOWA) operator developed by Yager which represents a generalization to a wide range of aggregation operators. We distinguish between aggregations with a descending or with an ascending order. We introduce the induced generalized OWA (IGOWA) operator which represents an extension to the GOWA operator. It generali...

Using the free-space translation representation (modified Radon transform) of Lax and Phillips in odd dimensions, it is shown that the generalized backscattering transform (so outgoing angle ω = Sθ in terms of the incoming angle with S orthogonal and Id−S invertible) may be further restricted to give an entire, globally Fredholm, operator on appropriate Sobolev spaces of potentials with compact...

In this paper, we study the existence and uniqueness theorem for solving the generalized operator equation of the form F(x) + G(x) + T(x) ∋ 0, where F is a Fréchet differentiable operator, G is a maximal monotone operator and T is a Lipschitzian operator defined on an open convex subset of a Hilbert space. Our results are improvements upon corresponding results of Uko [Generalized equations and...

In this paper, we define a border operator for generalized maps, a data structure for representing cellular quasi-manifolds. The interest of this work lies in the optimization of homology computation, by using a model with less cells than models in which cells are regular ones as tetrahedra and cubes. For instance, generalized maps have been used for representing segmented images. We first defi...

The problem of nding adapted solutions to systems of coupled linear forward-backward stochastic dierential equations (FBSDEs, for short) is investigated. A necessary condition of solvability leads to a reduction of general linear FBSDEs to a special one. By some ideas from controllability in control theory, using some functional analysis, we obtain a necessary and sucient condition for the solv...

We analyze different types of aggregation operators. We focus on the generalized OWA (GOWA) operator and the Quasi-OWA operator which generalize a wide range of aggregation operators. We also analyze a recent approach that unifies the weighted average and the OWA operator in the same formulation called ordered weighted averaging – weighted averaging (OWAWA) operator. We introduce the fuzzy gene...

We present gauge invariant, self adjoint Einstein operators for mixed symmetry higher spin theories. The result applies to multi-forms, multi-symmetric forms and mixed antisymmetric and symmetric multiforms. It also yields explicit action principles for these theories in terms of their minimal covariant field content. For known cases, these actions imply the mixed symmetry equations of motion o...

We consider maps of the family of convex bodies in Euclidean ddimensional space into itself that are compatible with certain structures on this family: A Minkowski-endomorphism is a continuous, Minkowski-additive map that commutes with rotations. For d ≥ 3, a representation theorem for such maps is given, showing that they are mixtures of certain prototypes. These prototypes are obtained by app...