We show that the complicated ⋆-structure characterizing for positive q the Uqso(N)-covariant differential calculus on R N q boils down to similarity transformations involving the ribbon element of a central extension of Uqso(N) and its formal square root ṽ. Subspaces of the spaces of functions and of p-forms on Rq are made into Hilbert spaces by introducing nonconventional “weights” in the inte...

Robust Lipschitzian properties of set-valued mappings and marginal functions play a crucial role in many aspects of variati01~al analysis and its applications, especially for issues related to variational stability and optimizatiou. \Ve develop an approach to variational stability based on generalized differentiation. The principal achievements of this paper include new results on coderivative ...

and Applied Analysis 3 We denote by ∧l ∧l R the space of l-covectors in R and the direct sum ∧ R n ⊕ l 0 ∧l R 2.1 is a graded algebra with respect to the wedge product ∧. We will make use of the exterior derivative: d : C∞ ( Ω,∧l ) −→ C∞ ( Ω,∧l 1 ) 2.2 and its formal adjoint operator d∗ −1 nl 1 ∗ d∗ : C∞ ( Ω,∧l 1 ) −→ C∞ ( Ω,∧l ) , 2.3 known as the Hodge codifferential, where the symbol ∗ denot...

Documents are co-derivative if they share content: for two documents to be co-derived, some portion of one must be derived from the other or some portion of both must be derived from a third document. The current technique for concurrently detecting all co-derivatives in a collection is document fingerprinting, which matches documents based on the hash values of selected document subsequences, ...

The paper concerns the computation of the graphical derivative and the regular (Fréchet) coderivative of the solution map to a class of generalized equations, where the multi-valued term amounts to the regular normal cone to a (possibly nonconvex) set given by C2 inequalities. Instead of the Linear Independence qualification condition, standardly used in this context, one assumes a combination ...

The paper concerns a new method to obtain a direct proof of the openness at linear rate/metric regularity of composite set-valued maps on metric spaces by the uni…cation and re…nement of several methods developed somehow separately in several works of the authors. In fact, this work is a synthesis and a precise specialization to a general situation of some techniques explored in the last years ...

GLq(N)and SOq(N)-covariant deformations of the completely symmetric/antisymmetric projectors with an arbitrary number of indices are explicitly constructed as polynomials in the braid matrices. The precise relation between the completely antisymmetric projectors and the completely antisymmetric tensor is determined. Adopting the GLq(N)and SOq(N)-covariant differential calculi on the correspondi...

GLq(N)and SOq(N)-covariant deformations of the completely symmetric/antisymmetric projectors with an arbitrary number of indices are explicitly constructed as polynomials in the braid matrices. The precise relation between the completely antisymmetric projectors and the completely antisymmetric tensor is determined. Adopting the GLq(N)and SOq(N)-covariant differential calculi on the correspondi...

The original motivation for this paper was to provide an efficient . quantitative analysis of convex infinite.(or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional) Banach spaces and that are indexed by an arbitrary fixed set J. Parameter perturbations on the right-hand side of the inequalities are required to be merely bo...

Fundamental insights into the properties of a function come from the study of its Moreau envelopes and Proximal point mappings. In this paper we examine the stability of these two objects under several types of perturbations. In the simplest case, we consider tilt-perturbations, i.e. perturbations which correspond to adding a linear term to the objective function. We show that for functions tha...