Quasi-analyticity in Carleman ultraholomorphic classes

We give a characterization for two different concepts of quasi-analyticity in Carleman ultraholomorphic classes of functions of several variables in polysectors. Also, working with strongly regular sequences, we establish generalizations of Watson's Lemma under an additional condition related to the growth index of the sequence.Comment: To appear in Ann. Inst. Fourier, Grenobl

On q-asymptotics for linear q-difference-differential equations with Fuchsian and irregular singularities

We consider a Cauchy problem for some family of q-difference-differential equations with Fuchsian and irregular singularities, that admit a unique formal power series solution in two variables t and z for given formal power series initial conditions. Under suitable conditions and by the application of certain q-Borel and Laplace transforms (introduced by J.-P. Ramis and C. Zhang), we are able to deal with the small divisors phenomenon caused by the Fuchsian singularity, and to construct actual holomorphic solutions of the Cauchy problem whose q-asymptotic expansion in t, uniformly for z in the compact sets of the complex plane, is the formal solution. The small divisors's effect is an increase in the order of q-exponential growth and the appearance of a power of the factorial in the corresponding q-Gevrey bounds in the asymptotics.Comment: 31 pages. Proofs of Propositions 1 and 3 improved. Some references added, typos correcte

Torres Blancas, a Vertical Garden City

Torres Blancas, the building designed by Francisco Javier Sáenz de Oíza for the Huarte company, was built between 1964 and 1972. Its powerful sculptural form, the expressive use of bare concrete and its experimental nature make it an iconic example of Madrid’s architecture. Proposed as a vertical city with an organic emphasis, Torres Blancas is not the usual stack of flats, but a residential complex of independent housing units with garden terraces and the amenities of a small community. This building thus combines Le Corbusier’s unités d’habitation and Frank Lloyd Wright’s towers