Majorization in de Branges spaces I. Representability of subspaces

In this series of papers we study subspaces of de Branges spaces of entire functions which are generated by majorization on subsets D of the closed upper half-plane. The present, first, part is addressed to the question which subspaces of a given de Branges space can be represented by means of majorization. Results depend on the set D where majorization is permitted. Significantly different situations are encountered when D is close to the real axis or accumulates to i∞.     

Recurrence of Ancestral Lines and Offspring Trees in Time Stationary Branching Populations

For time stationary Galton- Watson-branching populations on a general type space, the structure of the “individually positive recurrent part” of the system is described: its building blocks consist of finitely many “clans” with positive recurrent trunks. Conditions are given when this nubsystem is void, and when it equals the full system. In addition, positive recurrence on the clan level is characterized. Whereas individual positive recurrence turns out to be a symmetric concept with respect to forward and backward time direction (i. e., with respect to anceatral lines and offspring trees), with individual null recurrence this symmetry can fail even in the absence of branching, i.e., for independently migrating particle systems (Example 13.1). For discrete type spaces a classification of types as to the various individual recurrence concepts (positive, null, forward and backward in time) is proposed and illustrated by a couple of results and examples. For finite type spaces conditiom on the branching dynamics and its mean matrix for the existence of nontrivial equilibria are given.     

Photoproduction of positive pions from hydrogen with PHOENICS at ELSA

The differential cross section of the reaction γp→π⁺n has been measured with the PHOENICS detector at ELSA in Bonn. For the first time this cross section has been determined simultaneously over a large range of photon energies (E_γ = 220−900 MeV) and pion angles (Θ^c.m._pi = 35°−135°) with a tagged photon facility. The experimental set-up allowed a considerable kinematic overdetermination of the investigated reaction. Accordingly, the background contributions have been suppressed to below 1%. The measured differential cross section is in good agreement with existing data. The comparison with different model calculations is presented.     

Recent results from the TCV tokamak

During the first two years of operation, the TCV tokamak has produced a large variety of plasma shapes and magnetic configurations, with 1.0B _tor1.46T,I _p800kA,k2.05, –0.71. A new shape control algorithm, based on a finite element reconstruction of the plasma current in real time, has been implemented. Vertical growth rates up to 1000s^–1 have been stabilized using the external coil system. Ohmic H-modes with Troyon factors ( _tor aB/I _p) up to two and densities up to 2.25×10²⁰m^–3, corresponding to the Greenwald limit, have been obtained in diverted discharges. Limiter H-modes with line averaged electron densities up to 1.7×10²⁰m^–3 have been obtained in elongated D-shaped plasmas with 360 kAI _P600 kA.Presented at 17^th Symposium Plasma Physics and Technology, Prague, June 13–16, 1995.This work was partly supported by the Fonds National Suisse de la Recherche Scientifique.     

Convergence to equilibrium of critical branching particle systems and superprocesses,and related nonlinear partial differential equations

We consider a class of multitype particle systems in ^d undergoing spatial diffusion and critical stable multitype branching, and their limits known as critical stable multitype Dawson-Watanabe processes, or superprocesses. We show that for large classes of initial states, the particle process and the superprocess converge in distribution towards known equilibrium states as time tends to infinity. As an application we obtain the asymptotic behavior of a system of nonlinear partial differential equations whose solution is related to the distribution of both the particle process and the superprocess.Research partially supported by CONACyT (Mexico), CNRS (France) and BMfWuF (Austria).     

Experimental realization of linear-optical partial swap gates

We present a linear-optical implementation of a class of two-qubit partial SWAP gates for polarization states of photons. Different gate operations, including the SWAP and entangling sqrt[SWAP], can be obtained by changing a classical control parameter, namely, the path difference in the interferometer. Reconstruction of output states, full quantum process tomography, and an evaluation of entanglement of formation prove very good performance of the gates.     

Superbase‐catalyzed domino 3H‐pyrroles synthesis from ketoximes and acetylene: DFT study vs experiment

Elimination of vinyl alcohol from 5‐vinyloxypyrrolines in the presence of superbases (final step of domino 3H‐pyrroles synthesis from ketoximes and acetylene) is studied computationally at different levels of theory in DMSO solution (PCM). The sequences of transformations starting from nucleophilic addition of hydroxide ion to carbon‐carbon or carbon‐nitrogen double bonds are proposed as possible mechanisms. Unusual reactivity of 2,5‐dimethylphenyl substituted 5‐vinyloxypyrroline is explained within these mechanisms.     

Purcell Effect and Nonlinear Behavior of the Emission in a Periodic Structure Composed of InAs Monolayers Embedded in a GaAs Matrix

Enhancement of spontaneous emission in a resonant Bragg quantum well (QW) structure with 60 periods of triple InAs monolayers embedded in a GaAs matrix is studied experimentally and theoretically. From measurements of the time‐resolved photoluminescence, besides the QW exciton at 1.47 eV, a specific super‐radiant (SR) emission demonstrating nonlinear properties is found. The SR mode shows a near‐quadratic dependence of intensity on excitation power, while its energy position follows the Bragg condition. It is revealed that the SR mode shows a peculiar non‐monotonic dependence of intensity on direction, with a maximum observed at approximately 40°. The enhancement in the SR emission at a specific direction is correlated well with suggested theoretical consideration of the modal Purcell factor for periodic quantum well structures.     

Size‐Dependence of the Melting Temperature of Individual Au Nanoparticles

Nanoparticles have an immense importance in various fields, such as medicine, catalysis, and various technological applications. Nanoparticles exhibit a significant depression in melting point as their size goes below ≈10 nm. However, nanoparticles are frequently used in high temperature applications such as catalysis where temperatures often exceed several 100 degrees which makes it interesting to study not only the melting temperature depression, but also how the melting progresses through the particle. Using high‐resolution transmission electron microscopy, the melting process of gold nanoparticles in the size range of 2–20 nm Au nanoparticles combined with molecular dynamics studies is investigated. A linear dependence of the melting temperature on the inverse particle size is confirmed; electron microscopy imaging reveals that the particles start melting at the surface and the liquid shell formed then rapidly expands to the particle core.