I show that the general implicit-function problem (or parametrized fixedpoint problem) in one complex variable has an explicit series solution given by a trivial generalization of the Lagrange inversion formula. I give versions of this formula for both analytic functions and formal power series.

The integral image approach allows the optimal computation of Haar-based features for realtime recognition of objects in image sequences. This short note gives a direction to generalize the approach to high-dimensional images. We o er a formula for optimal computation of sums on high-dimensional rectangles. Integral Image Haar-Based Features High-Dimensional Image Möbius Inversion Formula

The phase-noise spectrum determines the Allan variance by a well-known integral formula. It is shown here that unique inversion of this formula is not possible in general because the mapping from spectrum to Allan variance is not one-to-one. A necessary and sufficient condition for two distinct phase spectra to have the same Allan variance is given.

The Krĕın-Langer integral representation of a matrix-valued generalized Nevanlinna function arises in problems of spectral theory and interpolation. A version of this formula which is suitable for such problems, and a corresponding Stieltjes inversion formula, are derived. Some classes of generalized Nevanlinna functions which are defined in terms of behavior at infinity are characterized in te...

We report a case showing the association of Moebius syndrome, the use of misoprostol during pregnancy and the development of central congenital alveolar hypoventilation. Pathophysiological aspects of these three diseases are discussed and also the unfavorable prognosis of this association.

We explore the ‘Moebius disjointness property’ in the special context of rank-one transformations and verify this phenomenon for many of the ‘classical’ models. (0). Introduction and Preliminaries This note is a follow up on [B-S-Z]. Recall that the general problem considered is the orthogonality of the Moebius sequence {μ(n);n ∈ Z+} with orbits of dynamical systems of zero (topological) entrop...

Moebius syndrome, also called congenital facial paralysis is a rare neurological disease, whose etiology is not fully elucidated. It affects especially facial and oculomotor cranial nerves and its clinical feature is peripheral facial paralysis. The objective of the study is to highlight the anatomical and functional changes in the Moebius syndrome and establish certain criteria that should be ...