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.     

On Riesz spaces with b-property and strongly order bounded operators

A Riesz space E is said to have the b-property if each subset that is order bounded in the bidual remains to be order bounded in E. Properties of a Riesz space with the b-property, the relationship between the b-property and various classes of operators are studied.     

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.     

A remark on CD 0(K)-spaces

A representation of the CD ₀(K)-space is given in [1, 2] for a compact Hausdorff space K without isolated points. We generalize this to an arbitrary countably compact space K without any assumption on isolated points.     

Fonctions rationnelles et problème de Gleason associés à l'opérateur de Dirac

We define developments in terms of homogeneous polynomials for regular functions (that is, in the kernel of the Dirac operator) and obtain new developments for hyperholomorphic functions (that is, in the kernel of the Cauchy–Fueter operator). Rational functions associated to the Dirac operator are also studied. To cite this article: D. Alpay et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

On the Equivalence of Probability Spaces

For a general class of Gaussian processes W, indexed by a sigma-algebra \({\mathscr {F}}\) of a general measure space \((M,{\mathscr {F}}, \sigma )\), we give necessary and sufficient conditions for the validity of a quadratic variation representation for such Gaussian processes, thus recovering \(\sigma (A)\), for \(A\in {\mathscr {F}}\), as a quadratic variation of W over A. We further provide a harmonic analysis representation for this general class of processes. We apply these two results to: (i) a computation of generalized Ito integrals and (ii) a proof of an explicit and measure-theoretic equivalence formula, realizing an equivalence between the two approaches to Gaussian processes, one where the choice of sample space is the traditional path space, and the other where it is Schwartz’ space of tempered distributions.     

A class of Gaussian processes with fractional spectral measures

We study a family of stationary increment Gaussian processes, indexed by time. These processes are determined by certain measures σ (generalized spectral measures), and our focus here is on the case when the measure σ is a singular measure. We characterize the processes arising from σ when σ is in one of the classes of affine selfsimilar measures. Our analysis makes use of Kondratiev white noise spaces. With the use of a priori estimates and the Wick calculus, we extend and sharpen (see Theorem 7.1) earlier computations of Ito stochastic integration developed for the special case of stationary increment processes having absolutely continuous measures. We further obtain an associated Ito formula (see Theorem 8.1).