We consider multivalued maps between $\Omega \subset \mathbb{R}^N$ open ($N \ge 2$) and a smooth, compact Riemannian manifold $\mathcal{N}$ locally minimizing the Dirichlet energy. An interior partial H\"older regularity result in the spirit of R. Schoen and K. Uhlenbeck is presented. Consequently a minimizer is H\"older continuous outside a set of Hausdorff dimension at most $N-3$. F. Almgren's original theory includes a global interior H\"older continuity result if the minimizers are valued into some $\mathbb{R}^m$. It cannot hold in general if the target is changed into a Riemannian manifold, since it already fails for "classical" single valued harmonic maps.

Jonas Hirsch

Semiclassical gravity is investigated in a large class of asymptotically flat, static, spherically symmetric spacetimes including those containing static stars, black holes, and wormholes. Specifically the stress-energy tensors of massless free spin 0 and spin 1/2 fields are computed to leading order in the asymptotic regions of these spacetimes. This is done for spin 0 fields in Schwarzschild spacetime using a WKB approximation. It is done numerically for the spin 1/2 field in Schwarzschild, extreme Reissner-Nordstrom, and various wormhole spacetimes. And it is done by finding analytic solutions to the leading order mode equations in a large class of asymptotically flat static spherically symmetric spacetimes. Agreement is shown between these various computational methods. It is found that for all of the spacetimes considered, the energy density and pressure in the asymptotic region are proportional to 1/r^5 to leading order. Furthermore, for the spin 1/2 field and the conformally coupled scalar field, the stress-energy tensor depends only on the leading order geometry in the far field limit. This is also true for the minimally coupled scalar field for spacetimes containing either a static star or a black hole, but not for spacetimes containing a wormhole.

Eric D. Carlson Paul R. Anderson Alessandro Fabbri Serena Fagnocchi William H. Hirsch Sarah A. Klyap

X-ray magnetic circular dichroism spectroscopy using an X-ray free electron laser is demonstrated with spectra over the Fe L$_{3,2}$-edges. This new ultrafast time-resolved capability is then applied to a fluence-dependent study of all-optical magnetic switching dynamics of Fe and Gd magnetic sublattices in a GdFeCo thin film above its magnetization compensation temperature. At the magnetic switching fuence, we corroborate the existence of a transient ferromagnetic-like state. The timescales of the dynamics, however, are longer than previously observed below the magnetization compensation temperature. Above and below the switching fluence range, we observe secondary demagnetization with about 5 ps timescales. This indicates that the spin thermalization takes longer than 5 ps.

Daniel J. Higley Konstantin Hirsch Georgi L. Dakovski Emmanuelle Jal Edwin Yuan Tianmin Liu Alberto A. Lutman James P. MacArthur Elke Arenholz Zhao Chen Giacomo Coslovich Peter Denes Patrick W. Granitzka Philip Hart Matthias C. Hoffmann John Joseph Loïc Le Guyader Ankush Mitra Stefan Moeller Hendrik Ohldag Matthew Seaberg Padraic Shafer Joachim Stöhr Arata Tsukamoto Heinz-Dieter Nuhn Alex H. Reid Hermann A. Dürr William F. Schlotter

We study the h Hirsch index as a local node centrality measure for complex networks in general. The h index is compared with the Degree centrality (a local measure), the Betweenness and Eigenvector centralities (two non-local measures) in the case of a biological network (Yeast interaction protein-protein network) and a linguistic network (Moby Thesaurus II) as test environments. In both networks, the Hirsch index has poor correlation with Betweenness centrality but correlates well with Eigenvector centrality, specially for the more important nodes that are relevant for ranking purposes, say in Search Machine Optimization. In the thesaurus network, the h index seems even to outperform the Eigenvector centrality measure as evaluated by simple linguistic criteria.

Monica G. Campiteli Adriano J. Holanda Paulo R. C. Soles Leonardo H. D. Soares Osame Kinouchi

I propose the index $h$, defined as the number of papers with citation number higher or equal to $h$, as a useful index to characterize the scientific output of a researcher.

J. E. Hirsch

The h-index was introduced by the physicist J.E. Hirsch in 2005 as measure of a researcher's productivity. We consider the "combinatorial Fermi problem" of estimating h given the citation count. Using the Euler-Gauss identity for integer partitions, we compute confidence intervals. An asymptotic theorem about Durfee squares, due to E.R. Canfield-S. Corteel-C.D. Savage from 1998, is reinterpreted as the rule of thumb h=0.54 x (citations)^{1/2}. We compare these intervals and the rule of thumb to empirical data (primarily using mathematicians).

Alexander Yong

A magnetic field H is expelled from the interior of a metal becoming superconducting. Everybody thinks the phenomenon is perfectly well understood, particularly scientists with the highest H-index think that. I don't. I will explain why I believe that without Holes, conceptualized by Heisenberg in 1931 fifty years after Hall had first detected them in some metals, neither magnetic field expulsion nor anything else about superconductivity can be understood. I have been a Heretic in the field of superconductivity for over 30 years, and believe that Hans' little story about the emperor perfectly captures the essence of the situation. Here is (a highly condensed version of) the wHole story.

J. E. Hirsch

We present our survey for subluminous hyper-velocity candidates, which has been successfully initiated at the ESO NTT and the Calar Alto 3.5 m telescope.

A. Tillich U. Heber H. Hirsch

This paper has been withdrawn by the author

F. Natali N. O. V. Plank B. J. Ruck H. J. Trodahl F. Semond S. Sorieul L. Hirsch

We exhibit two relation algebra atom structures such that they are elementarily equivalent but their term algebras are not. This answers Problem 14.19 in the book Hirsch, R. and Hodkinson, I., "Relation Algebras by Games", North-Holland, 2002.

H. Andréka I. Németi