In [3] we described a technique for solving certain linear operator equations by studying the operator power series de…ned by the system. Essential for obtaining explicit solutions is a Lagrange inversion formula for power series with coe¢ cients in an integral domain K. Such a formula can be found in “Recursive Matrices and Umbral Calculus”by Barnabei, Brini and Nicoletti [1]. J. F. Freeman’s ...

Moebius syndrome is a rare congenital disorder that is characterized by lifetime paralysis, involving a group of cranial nerves. It involves the abducent, facial, oculomotor and hypoglossal nerve. In literature, the definition and diagnostic criteria vary among different authors. Here we report 2 interesting cases of Moebius syndrome in a 12 1⁄4 year and a 5-year old female patients with peculi...

In this work, we define a parabolic equation on digital spaces and study its properties. The equation can be used in investigation of mechanical, aerodynamic, structural and technological properties of a Moebius strip, which is used as a basic element of a new configuration of an airplane wing. Condition for existence of exact solutions by a matrix method and a method of separation of variables...

We derive a (/-analogue of the classical formula for the number of derangements of an n element set. Our derivation is entirely analogous to the classical derivation, but relies on a descent set preserving bijection between the set of permutations with a given derangement part and the set of shuffles of two permutations. A classical application of binomial inversion (more generally the principl...

This talk first introduces the m-arithmetic triangle — a generalization of Pascal’s triangle, and then presents an explicit formula for the numbers of the m-arithmetic triangle; we have found some asymptotic expansions for these numbers. With a new formula for inversion of analytic functions, which we introduced recently, we get inversion formulas, in which new special numbers An appear. We pre...

INTRODUCTION Moebius syndrome is a rare congenital disorder characterized by unilateral or bilateral involvement of the sixth and seventh cranial nerves, resulting in a lack of facial expression and eye movements. These patients suffer a series of oral manifestations that may complicate their dental treatment, such as facial and tongue muscle weakness, uncontrolled salivation secondary to defic...

We study Hopf algebras over projection functions of the complex vector C appropriate for computing inversion formulas from discrete mathematics. Using calculus of projection functions introduced in this way, we derived various inversion formulas, including Gould’s inversion formula and its generalizations.

The European MOEBIUS project (Mobile Extranet Based Integrated User Services) is developing a platform for remote access to intranet services using mobile access technology and investigating its performance characteristics to demonstrate the advantages for health care, business and residential applications. This paper focuses on the studies that are being done in MOEBIUS on two particular items...

Micron-sized black holes do not necessarily have a constant horizon temperature distribution. The black hole remote-sensing problem means to find out the ‘surface’ temperature distribution of a small black hole from the spectral measurement of its (Hawking) grey pulse. This problem has been previously considered by Rosu, who used Chen’s modified Moebius inverse transform. Here, we hint on a Ram...

This focus group study explored the social interaction experiences and strategies of 12 adults with Moebius Syndrome, a rare congenital condition characterized by facial paralysis. Content analysis revealed five themes of social functioning: social engagement/disengagement; resilience/sensitivity; social support/stigma; being understood/misunderstood; and public awareness/lack of awareness of M...