Rigid systems of second-order linear differential equations

We say that a system of differential equations d^2x(t)/dt^2=Adx(t)/dt+Bx(t)+Cu(t), in which A and B are m-by-m complex matrices and C is an m-by-n complex matrix, is rigid if it can be reduced by substitutions x(t)=Sy(t), u(t)=Udy(t)/dt+Vy(t)+Pv(t) with nonsingular S and P to each system obtained from it by a small enough perturbation of its matrices A,B,C. We prove that there exists a rigid system if and only if m<n(1+square_root{5})/2, and describe all rigid systems.Comment: 22 page

Exploiting growing stock volume maps for large scale forest resource assessment: Cross-comparisons of ASAR- and PALSAR-based GSV estimates with forest inventory in Central Siberia

Growing stock volume is an important biophysical parameter describing the state and dynamics of the Boreal zone. Validation of growing stock volume (GSV) maps based on satellite remote sensing is challenging due to the lack of consistent ground reference data. The monitoring and assessment of the remote Russian forest resources of Siberia can only be done by integrating remote sensing techniques and interdisciplinary collaboration. In this paper, we assess the information content of GSV estimates in Central Siberian forests obtained at 25m from ALOS-PALSAR and 1km from ENVISAT-ASAR backscatter data. The estimates have been cross-compared with respect to forest inventory data showing 34% relative RMSE for the ASAR-based GSV retrievals and 39.4% for the PALSAR-based estimates of GSV. Fragmentation analyses using a MODIS-based land cover dataset revealed an increase of retrieval error with increasing fragmentation of the landscape. Cross-comparisons of multiple SAR-based GSV estimates helped to detect inconsistencies in the forest inventory data and can support an update of outdated forest inventory stands

Nuclear dependence of the transverse single-spin asymmetry in the production of charged hadrons at forward rapidity in polarized p+pp+p, p+p+Al, and p+p+Au collisions at sNN=200\sqrt{s_{_{NN}}}=200 GeV

We report on the nuclear dependence of transverse single-spin asymmetries (TSSAs) in the production of positively-charged hadrons in polarized $p^{\uparrow}+p$, $p^{\uparrow}+$Al and $p^{\uparrow}+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV. The measurements have been performed at forward rapidity ($1.4<\eta<2.4$) over the range of $1.8<p_{T}<7.0$ GeV$/c$ and $0.1<x_{F}<0.2$. We observed a positive asymmetry $A_{N}$ for positively-charged hadrons in \polpp collisions, and a significantly reduced asymmetry in $p^{\uparrow}$+$A$ collisions. These results reveal a nuclear dependence of charged hadron $A_N$ in a regime where perturbative techniques are relevant. These results provide new opportunities to use \polpA collisions as a tool to investigate the rich phenomena behind TSSAs in hadronic collisions and to use TSSA as a new handle in studying small-system collisions.Comment: 303 authors from 66 institutions, 9 pages, 2 figures, 1 table. v1 is version accepted for publication in Physical Review Letters. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.htm