A Positive Doubly Power Bounded Operator with a Nonpositive Inverse Exists on any Infinite-dimensional AL-Space

In this paper we construct a positive doubly power bounded operator with a nonpositive inverse on an AL-space.     

Un théorème de type Beurling–Lax dans la boule unitéA Beurling–Lax type theorem in the unit ball

We prove a Beurling–Lax theorem for a family of reproducing kernel Hilbert spaces of functions analytic in an open subset of the unit ball containing the origin. The spaces under consideration are characterized by functions called Schur multipliers. Using the theory of linear relations in Pontryagin spaces we also give coisometric realizations of Schur multipliers. To cite this article: D. Alpay et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 349–354.     

Pure uterine lipoma

Lipomatous tumors of the uterus are unusual, benign neoplasms seen in postmenopausal women. Although many of the mixed-type cases such as lipoleiomyoma and fibrolipoma have been reported, pure uterine lipomas are extremely rare. In the literature, a few cases with pure uterine lipoma have been reported. We first present the advanced magnetic resonance findings of pure uterine lipoma, followed by those of ultrasonography (US) and computed tomography (CT). We markedly detected lipid peaks on the magnetic resonance spectroscopy (MRS) and the apparent diffusion coefficient value to be 0.00 due to chemical-shift effects with diffusion-weighted imaging (DWI). Although pelvic lipomatous tumors can be diagnosed with US and CT, in some cases, further workup may be required to localize the lesion. MRI may yield more valuable data for differential diagnosis. MRS and DWI findings provide additional clues on the nature of the lesion.     

Occupational prolonged organic solvent exposure in shoemakers: brain MR spectroscopy findings

Our purpose was to investigate, by magnetic resonance (MR) spectroscopy, the metabolite changes in the brains of subjects in the shoemaking industry who had been chronically exposed to organic solvents. A total of 49 male subjects and 30 age-matched healthy volunteers underwent detailed neurological and psychiatric examinations. All subjects had long-echo [repetition time (TR) 2000 ms, echo time (TE) 136 ms] single-voxel MR spectroscopy. Voxels (15 x 15 x 15 mm(3)) were placed in the parietal white matter, thalamus, and basal ganglia. N-acetylaspartate (NAA)/creatine (Cr) and choline (Cho)/Cr ratios were calculated. There was no significant difference between the study subjects and the control group in NAA/Cr ratios obtained from thalamus, basal ganglia, and parietal white matter. Cho/Cr ratios in thalamus, basal ganglia, and parietal white matter were found to be significantly increased compared to controls. There was a positive correlation between basal ganglia Cho/Cr ratio and duration of exposure (r = 0.63). MR spectroscopy should be performed to reveal metabolite changes and determine the degree of brain involvement in solvent-related industry workers.     

Boundary interpolation in the ball

We solve a boundary interpolation problem in the reproducing kernel Hilbert space of functions analytic in the unit ball of with reproducing kernel 1/(1−∑₁^Nz_kw_k^*). We introduce the notion of Brune factor (or Blaschke–Potapov factor of the third kind) in this setting.     

On the Loewner problem in the class

Loewner's theorem on boundary interpolation of functions is proved under rather general conditions. In particular, the hypothesis of Alpay and Rovnyak (1999) that the function , which is to be extended to an function, is defined and continuously differentiable on a nonempty open subset of the real line, is replaced by the hypothesis that the set on which is defined contains an accumulation point at which satisfies some kind of differentiability condition. The proof of the theorem in this note uses the representation of functions in terms of selfadjoint relations in Pontryagin spaces and the extension theory of symmetric relations in Pontryagin spaces.

     

On the intersection of null spaces for matrix substitutions in a non-commutative rational formal power series

For a rational formal power series in N non-commuting indeterminates, with matrix coefficients, we establish the formula which relates the intersection of the null spaces of coefficients to the intersection of the null spaces of values of this series at N-tuples of $n\times n$ matrices, for n large enough. As an application, we formulate the criteria of observability, controllability, and minimality for a recognizable formal power series representation in terms of matrix substitutions. To cite this article: D. Alpay, D.S. Kalyuzhny??-Verbovetzki??, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

An unusual case of acute disseminated encephalomyelitis confined to brainstem

Acute disseminated encephalomyelitis (ADEM) is an immune-mediated demyelinating disorder usually encountered in children or adolescents and characterized by multifocal neurological deficits of rapid onset. Typical target areas of demyelination include the corona radiata, centrum semiovale, periventricular white matter, cerebellar peduncles and brainstem. Involvement of deep gray matter nuclei is also frequent. We report a 6-year-old boy with ADEM who had only brainstem involvement. Serial magnetic resonance images representing the stage of disease and response to steroid treatment are presented.     

Realizations for Schur upper triangular operators centered at an arbitrary point

Reproducing kernel spaces introduced by L. de Branges and J. Rovnyak provide isometric, coisometric and unitary realizations for Schur functions, i.e. for matrix-valued functions analytic and contractive in the open unit disk. In our previous paper [12] we showed that similar realizations exist in the nonstationary setting, i.e. when one considers upper triangular contractions (which appear in time-variant system theory as transfer functions of dissipative systems) rather than Schur functions and diagonal operators rather than complex numbers. We considered in [12] realizations centered at the origin. In the present paper we study realizations of a more general kind, centered at an arbitrary diagonal operator. Analogous realizations (centered at a point of the open unit disk) for Schur functions were introduced and studied in [3] and [4].     

Measurement of internal stresses via the polarization in epitaxial ferroelectric films

The relations between electrical and mechanical properties of constrained ferroelectric films are analyzed. It is shown that the internal stresses and the elastic constants can be determined through the measurement of the electrical response. The change in the polarization is proportional to internal stresses due to film-substrate misfit, whereas the linear electrical and electromechanical responses to external field do not depend on the misfit and are determined by the film constraint. The theoretical results are successfully applied to PbZr 0.2Ti 0.8O (3) films on (001) LaAlO (3) substrate which exhibit a considerable increase in the saturation polarization due to epitaxial stresses. Significant recovery in the piezoelectric constant and susceptibility is theoretically predicted and experimentally verified for specific film configurations which reduce the degree of constraint. The concept presented in this Letter can be expanded to constrained ferromagnetic and superconductor films.