Identity principles for commuting holomorphic self-maps of the unit disc

Let f,g be two commuting holomorphic self-maps of the unit disc. If f and g agree at the common Wolff point up to a certain order of derivatives (no more than 3 if the Wolff point is on the unit circle), then f≡g.     

Ritt’s theorem and the Heins map in hyperbolic complex manifolds

Let X be a Kobayashi hyperbolic complex manifold, and assume that X does not contain compact complex submanifolds of positive dimension (e.g., X Stein). We shall prove the following generalization of Ritt’s theorem: every holomorphic self-map f:X→X such that f(X) is relatively compact in X has a unique fixed point τ(f) ∈ X, which is attracting. Furthermore, we shall prove that τ(f) depends holomorphically on f in a suitable sense, generalizing results by Heins, Joseph-Kwack and the second author.     

Fixed points of commuting holomorphic mappings other than the Wolff point

Let be the unit disc of and let be such that . For 1$">, let . We study the behavior of on . In particular, we prove that . As a consequence, besides conditions for , we prove a conjecture of C. Cowen in case and are univalent mappings.

     

Correlating natural ageing and Xenon irradiation of Paraloid B72 applied on stone

The ageing of Paraloid^® B72, an acrylic copolymer extensively used in conservation of works of art, has been investigated either under artificial irradiation (Xenon lamp) or in natural environment (external exposure) with the aim to correlate the results of the accelerate test with the real situation. For a better understanding of the involved mechanisms some acrylic homo-polymers were also subjected to the artificial ageing test. Molecular changes induced by ageing were followed by infrared spectroscopy (FT-IR) and size exclusion chromatography (SEC), while the efficiency of the treatment was checked by water capillary absorption test and colour determinations. The results obtained indicate that it is possible to discriminate, easily and within reasonable laboratory time experiment, between polymers that can be used in Conservation, and the macromolecules that should not be employed due to short efficacy life-times.     

Interactions of magnetic monopoles with nuclei and atoms: Formation of bound states and phenomenological consequences

We discuss the binding of magnetic monopoles to nuclear and atomic systems. The energy spectrum is calculated, by assuming an interaction with a hard core. The formation process of monopole-nucleus bound states is analysed and it is shown that monopoles reaching Earth are most likely bound to a proton. We also discuss phenomenological implications of the existence of bound states in connection with the monopole catalysis of proton decay.     

Functionalized azabicycloalkane amino acids by nitrone 1,3-dipolar intramolecular cycloaddition

[reaction: see text] An efficient and operationally simple method for the synthesis of functionalized azaoxobicyclo[X.3.0]alkane amino acids has been devised. The key step is an intramolecular nitrone cycloaddition on 5-allyl- or 5-homoallylproline that was found to be completely regio- and stereoselective.     

Variation of Loewner Chains,Extreme and Support Points in the Class $$S^0$$ in Higher Dimensions

We introduce a family of natural normalized Loewner chains in the unit ball, which we call “geräumig”—spacious—which allow us to construct, by means of suitable variations, other normalized Loewner chains which coincide with the given ones from a certain time on. We apply our construction to the study of support points, extreme points, and time-\(\log M\)-reachable mappings in the class \(S^0\) of mappings admitting parametric representation.     

Contact points and fractional singularities for semigroups of holomorphic self-maps of the unit disc

We study boundary singularities which can appear for infinitesimal generators of one-parameter semigroups of holomorphic self-maps of the unit disc. We introduce “regular” fractional singularities and characterize them in terms of the behavior of the associated semigroups and K?nigs functions. We also provide necessary and sufficient geometric criteria on the shape of the image of the K?nigs function for having such singularities. In order to do this, we study contact points of semigroups and prove that any contact (not fixed) point of a one-parameter semigroup corresponds to a maximal arc on the boundary to which the associated infinitesimal generator extends holomorphically as a vector field tangent to this arc.     

Representations of semigroups of partial isometries

We present a new proof that the irreducible representationsof the von Neumann algebra generated by a strongly continuoussemigroup of partial isometries of index 1 are unique up toequivalence, as well as a proof that when such an algebra isa factor, its representations are completely reducible. As anapplication, we show that the irreducible representations ofa strongly continuous semigroup of isometries {U(), 0} suchthat are equivalent.