Natural extensions of holomorphic motions

We consider an arbitrary real analytic family X_z, , over the closed unit disc , of real analytic plane Jordan curves X_z. Ifj _e ^iθ ,e ^iθ ∋ ∂D, is an arbitrary real-analytic family of orientation-reversing homeomorphisms of fixingX _e ^iθ pointwise, we show that there is a unique holomorphic motion of extending the given motion of Jordan curves and consistent with the given family of involutions. If these generalized reflections are defined using the barycentric extension construction of Douady-Earle-Nag, then the resulting extension method for holomorphic motions of X is natural, that is Moebius-invariant and continuous with respect to variation of the given motion of X₀.     

New computer program for three-dimensional relativistic hydrodynamical model

An effective computer program for three-dimensional relativistic hydrodynamical model has been developed. It implements a new approach to the early hot phase of relativistic heavy-ion collisions. The computer program simulates time-space evolution of nuclear matter in terms of ideal-fluid dynamics. Equations of motions of hydrodynamics are solved making use of finite difference methods. Commonly-used algorithms of numerical relativistic hydrodynamics RHLLE and MUSTA-FORCE have been applied in simulations. To speed-up calculations, parallel processing has been made available for solving hydrodynamical equations. The test results of simulations for 3D, 2D and Bjorken expansion are reported in this paper. As a next step we plan to implement the hadronization algorithm by implementing the continuous particle emission for freeze-out and comparing it with Cooper-Frye formula.     

Semigroups of Operators on Hardy Spaces and Cocycles of Holomorphic Flows

In this paper the strongly continuous semigroups of bounded cocycle-weighted composition operators for holomorphic flows on Hardy spaces are characterized. In the process, an easy-to-check criterion for an operator to be a weighted composition operator is established.     

Minimal kernels of weakly complete spaces

Let X be a weakly complete space i.e. X a complex space endowed with a C^k-smooth, k?0, plurisubharmonic exhaustion function. We give the notion of minimal kernelΣ¹=Σ¹(X) of X by the following property: x∈Σ¹ if no continuous plurisubharmonic exhaustion function is strictly plurisubharmonic near x. The study of the geometric properties of the minimal kernels is the aim of present paper. After stating that the minimal kernel Σ¹ of a weakly complete space can be defined by a single plurisubharmonic exhaustion function ?, called minimal, using the characterization in terms of Bremermann envelopes, we prove the following, crucial, result: if X is a weakly complete manifold and ? a minimal function for X, the nonempty level sets Σ_c¹=Σ¹∩{?=c} have the local maximum property. In the last section we discuss the special case of weakly complete surfaces. We prove that if dim_cX=2 and c is a regular value of a minimal function ? then the nonempty level sets Σ_c¹=Σ¹∩{?=c} are compact spaces foliated by holomorphic curves.     

Interferometric testing of the spacing error of a plane diffraction grating

Two measuring methods of the plane diffraction grating spacing error are presented in this work. The first one resembles real- time holographic interferometry. The hologram is exposed when an object beam is the nth diffraction order, and is then illuminated by the -nth diffraction order wave. The second method makes use of double-exposure holographic interferometry. The first exposure is performed when the nth diffraction order is an object beam. During the second exposure the -nth diffraction order is an object beam. Both methods allow to measure the spacing error separately, not only from the grating surface error but also from the aberrations introduced by the other optical elements of the set-up.     

Canonical models for a class of polynomially convex hulls

We use holomorphic motions and Beltrami equation to study a class of polynomially convex hulls in ℂ ² with Jordan fibers over the disc D. It is shown that every such hull is biholomorphically equivalent to a unique (up to suitable normalisation) canonical model. These models are the hulls whose complements in D×ℂmacr; are biholomorphic to a bidisc and are further characterized in terms of capacity of the fibers, Green’s function, pseudoconcavity and approximability by (very) special analytic polyhedra. Received: 11 September 1995 / Revised version: 11 March 1996