Density conditions for interpolation inA −∞

We give a necessary and sufficient density condition for a sequence {a _k} _k in the unit disk ofC to be interpolating for the classA ^−∞ of holomorphic functions with polynomial growth. The condition goes along the lines of those found by Seip for the analogous problem in Bergman spaces of the disk and by Berenstein and Li for some weighted spaces of entire functions. The result complements an earlier characterization given by Bruna and Pascuas. Partially supported by DGICYT grant PB95-0956-C02-02 and CIRIT grant 1998 SGR 00052. Also supported by a program of the Comunitat de Treball dels Pirineus.     

Zero sets of holomorphic functions in the unit ball with slow growth

We study the zero-varieties of holomorphic functions in the unit ball satisfying the growth condition log |f(z)|≤c _fλ(|z|), where λ:(0,1)→ℝ⁺ is a positive increasing function. We obtain some sufficient conditions on an analytic variety to be defined by such a function. Some results for the particular case λ(r)=log(e/(1−r)), corresponding to the classA ^−∞, generalize those of B. Korenblum in one variable. Both authors supported by DGICYT grant PB92-0804-C02-02.     

Fast topological imaging

Mathematical optimization methods based on the topological sensitivity analysis have been used to develop innovative ultrasonic imaging methods. With a single illumination of the medium, they have proved experimentally to yield a lateral resolution comparable to classical multiple-illumination techniques. As these methods are based on the numerical simulations of two wave fields, they require extensive computation. A time-domain finite-difference scheme is usually used for that purpose. This paper presents the development of an experimental imaging method based on the topological sensitivity. The numerical cost is reduced by replacing the numerical simulations by simple mathematical operations between the radiation patterns of the array’s transducers and the frequency-domain signals to be emitted. These radiation patterns are preliminary computed once and for all. They were obtained with a finite element model for the anisotropic elastodynamic case and with semi-analytical integrations for the acoustic case. Experimental results are presented for a composite material sample and for a prefractal network immersed in water. A lateral resolution below 2.5 times the wavelength is obtained with a single plane wave illumination. The method is also applied with multiple illuminations, so that objects hidden in complex media can be investigated.     

A Shack–Hartmann measuring head for the two‐dimensional characterization of X‐ray mirrors

The recent development of short‐wavelength optics (X/EUV, synchrotrons) requires improved metrology techniques in terms of accuracy and curvature dynamic range. In this article a stitching Shack–Hartmann head dedicated to be mounted on translation stages for the characterization of X‐ray mirrors is presented. The principle of the instrument is described and experimental results for an X‐ray toroidal mirror are presented. Submicroradian performances can be achieved and systematic comparison with a classical long‐trace profiler is presented. The accuracy and wide dynamic range of the Shack–Hartmann long‐trace‐profiler head allow two‐dimensional characterizations of surface figure and curvature with a submillimeter spatial resolution.     

Very first tests on SOLEIL regarding the Zn environment in pathological calcifications made of apatite determined by X‐ray absorption spectroscopy

This very first report of an X‐ray absorption spectroscopy experiment at Synchrotron SOLEIL is part of a long‐term study dedicated to pathological calcifications. Such biological entities composed of various inorganic and/or organic compounds also contain trace elements. In the case of urinary calculi, different papers already published have pointed out that these oligo‐elements may promote or inhibit crystal nucleation as well as growth of mineral. Use of this analytical tool specific to synchrotron radiation, allowing the determination of the local environment of oligo‐elements and thus their occupation site, contributes to the understanding of the role of trace elements in pathological calcifications.