A comparison of European systems of direct access to constitutional judges: exploring advantages for the Italian Constitutional Court

As protection of fundamental rights increasingly becomes a defining feature of modern constitutionalism, some countries debate over the opportunity to introduce systems of direct individual access to constitutional judges to increase protection of constitutional rights. Part I of the article provides a comparative overview of the systems of individual constitutional complaint adopted in Europe, focusing on their functioning, structure and admissibility requirements. Part II addresses possible benefits of the introduction of such a system in Italy. After describing the main features of the Italian system of judicial review, the article details proposals that, since 1947, have been presented to introduce a system of direct individual access to the Italian Constitutional Court. Finally, Part III offers reflections on the potential advantages that adoption of such complaint would bring to the Italian legal system, compared to the currently existing avenues of access to the Court

Regular Moebius transformations of the space of quaternions

Let H be the real algebra of quaternions. The notion of regular function of a quaternionic variable recently presented by G. Gentili and D. C. Struppa developed into a quite rich theory. Several properties of regular quaternionic functions are analogous to those of holomorphic functions of one complex variable, although the diversity of the quaternionic setting introduces new phenomena. This paper studies regular quaternionic transformations. We first find a quaternionic analog to the Casorati-Weierstrass theorem and prove that all regular injective functions from H to itself are affine. In particular, the group Aut(H) of biregular functions on H coincides with the group of regular affine transformations. Inspired by the classical quaternionic linear fractional transformations, we define the regular fractional transformations. We then show that each regular injective function from the Alexandroff compactification of H to itself is a regular fractional transformation. Finally, we study regular Moebius transformations, which map the unit ball B onto itself. All regular bijections from B to itself prove to be regular Moebius transformations.Comment: 12 page

Some notions of subharmonicity over the quaternions

This works introduces several notions of subharmonicity for real-valued functions of one quaternionic variable. These notions are related to the theory of slice regular quaternionic functions introduced by Gentili and Struppa in 2006. The interesting properties of these new classes of functions are studied and applied to construct the analogs of Green's functions.Comment: 16 page

Extending Human Perception of Electromagnetic Radiation to the UV Region through Biologically Inspired Photochromic Fuzzy Logic (BIPFUL) Systems.

Photochromic Fuzzy Logic Systems have been designed that extend human visual perception into the UV region. The systems are founded on a detailed knowledge of the activation wavelengths and quantum yields of a series of thermally reversible photochromic compounds. By appropriate matching of the photochromic behaviour unique colour signatures are generated in response differing UV activation frequencies

Landau-Toeplitz theorems for slice regular functions over quaternions

The theory of slice regular functions of a quaternionic variable extends the notion of holomorphic function to the quaternionic setting. This theory, already rich of results, is sometimes surprisingly different from the theory of holomorphic functions of a complex variable. However, several fundamental results in the two environments are similar, even if their proofs for the case of quaternions need new technical tools. In this paper we prove the Landau-Toeplitz Theorem for slice regular functions, in a formulation that involves an appropriate notion of regular $2$-diameter. We then show that the Landau-Toeplitz inequalities hold in the case of the regular $n$-diameter, for all $n\geq 2$. Finally, a $3$-diameter version of the Landau-Toeplitz Theorem is proved using the notion of slice $3$-diameter.Comment: 20 page

The Mittag-Leffler Theorem for regular functions of a quaternionic variable

We prove a version of the classical Mittag-Leffler Theorem for regular functions over quaternions. Our result relies upon an appropriate notion of principal part, that is inspired by the recent definition of spherical analyticity.Comment: 10 page

A local representation formula for quaternionic slice regular functions

After their introduction in 2006, quaternionic slice regular functions have mostly been studied over domains that are symmetric with respect to the real axis. This choice was motivated by some foundational results published in 2009, such as the Representation Formula for axially symmetric domains. The present work studies slice regular functions over domains that are not axially symmetric, partly correcting the hypotheses of some previously published results. In particular, this work includes a Local Representation Formula valid without the symmetry hypothesis. Moreover, it determines a class of domains, called simple, having the following property: every slice regular function on a simple domain can be uniquely extended to the symmetric completion of its domain.Comment: 10 pages, to appear in Proc. Amer. Math. So