Quadratically parametrized smooth maps from one complex projective space to another are constructed as projections of the Segre map of the complexification. A classification theorem relates equivalence classes of projections to congruence classes of matrix pencils. Maps from the 2-sphere to the complex projective plane, which generalize stereographic projection, and immersions of the complex pr...

This article tests Diessel’s ‘integration’ path of development of adverbial clauses (cf. Diessel, 2004), with special focus on the acquisition of ‘causal’ adverbial clauses, in the context of the overall development of grammatical/semantic complexification in a French child’s longitudinal corpus of spontaneous speech (Madeleine, Paris Corpus) from 10 months to 4;01 years old. Three main pattern...

We study the realization of conformal symmetry in the QHE as part of the W∞ algebra. Conformal symmetry can be realized already at the classical level and implies the complexification of coordinate space. Its quantum version is not unitary. Nevertheless, it can be rendered unitary by a suitable modification of its definition which amounts to taking proper care of the quantum measure. The conseq...

We show that a twistor space of a self-dual metric on 4CP with U(1)-isometry is not Moishezon iff there is a C∗-orbit biholomorphic to a smooth elliptic curve, where the C∗-action is the complexification of the U(1)action on the twistor space. It follows that the U(1)-isometry has a two-sphere whose isotropy group is Z2. We also prove the existence of such twistor spaces in a strong form to sho...

We prove two general theorems, which appear to be very useful in investigation of the Hyers-Ulam stability of a higher order linear functional equation in single variable, with constant coefficients. We give several examples of their applications. In particular we show that we obtain in this way several fixed point results for a particular operator. The main tool in the proofs is a complexifica...

In this paper, we use the KK-theory of Kasparov to prove exactness of sequences relating the K-theory of a real C∗ -algebra and of its complexification (generalizing results of Boersema). We use this to relate the real version of the Baum-Connes conjecture for a discrete group to its complex counterpart. In particular, the complex Baum-Connes assembly map is an isomorphism if and only if the re...

An Hamiltonian formulation with complex fluxes and currents is proposed. This formulation is derived from a recent Lagrangian formulation with complex electrical quantities. The complexification process avoids the usual separation into real and imaginary parts and notably simplifies modeling issues. Simple modifications of the magnetic energy underlying standard (α, β) models yield new (α, β) m...

Using a cohomological characterization of the consistent and the covariant Lorentz and gauge anomalies, derived from the complexification of the relevant algebras, we study in d = 2 the definition of the Weyl determinant for a non-abelian theory with Riemannian background. We obtain two second order operators that produce, by means of ζ-function regularization, respectively the consistent and t...